Answer:
345.6
Or 345 full cubes
Step-by-step explanation:
To answer this question we first need to find the volume of the cuboid!
To find volume we use the equation...
area of cross-section × heightor l × w × hFor the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...
60 × 24 × 30 = 43200We now need to the the volume of the cube which we can just do by cubing the value given
5³ = 125We now need to divide the two results together to find out how many cubes would fit...
43200 ÷ 125 = 345.6Or 345 full cubesHope this helps, have a lovely day!
you wish to compute the 90% confidence interval for the population proportion. how large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05? no prior estimate for the population proportion is available.
To compute the 90% confidence interval for the population proportion, large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05, 271 is the minimum sample
How do we find the minimum sample size?A confidence interval is a range of values where an unknown population parameter lies. The level of confidence is the likelihood of the interval containing the parameter.
The formula to calculate the sample size required to produce a specific margin of error with a known level of confidence for the estimation of a population proportion is given below: 95% confidence interval for population proportion using a sample size formula
[tex]\[n=\frac{z^{2}p(1-p)}{E^{2}}\][/tex]
Where
[tex]\[E\][/tex]is the margin of error[tex]\[p\][/tex] is the sample proportion.[tex]\[z\][/tex] is the z-score The formula is modified to calculate the sample size required to produce a specific margin of error with a known level of confidence as follows:
[tex]\[n=\frac{z^{2}}{4E^{2}}\][/tex]
Note: For this problem, the sample size needs to be large enough to ensure that the sample proportion does not deviate from the population proportion by more than 0.05.
Using a Z-score Table, the z-value that corresponds to 90% confidence interval is 1.645.
[tex]n=\frac{z^{2}}{4E^{2}}\ = \frac{1.645^{2}}{4(0.05)^{2}} = \frac{2.706225}{0.0100} = 270.6[/tex]
(rounded up to the next highest integer)Therefore, 271 is the minimum sample size required to compute a 90% confidence interval for the population proportion.
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Let n be a positive integer. If a == (3^{2n}+4)^-1 mod(9), what is the remainder when a is divided by 9?
Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.
We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.
Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.
32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.
Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.
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The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
source: trust me bro
Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.06 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.
(a) For first-time college students, what is the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places)?
(b) For transfer students, what is the ratio in favor of having graduated in the top 25 percent of their high school class?
Odds and Probability:
Odds in favor of an event is expressed as a ratio:
O
(
f
)
=
favorable cases
:
unfavourable cases
Similarly odds against are expressed as:
O
(
a
)
=
unfavorable cases
:
favourable cases
.
Odds and probability are closely related, as the probability in favor of an even is computed as:
P
=
favorable cases
favorable cases+unfavorable cases
The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.
(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
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which part of this graph shows a non-linear relationship
Answer:
A.
Step-by-step explanation:
in how many ways can a class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer and a secretary g
The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040
A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.
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The coordinates of the endpoints of PQ are P( – 12,7) and Q( – 4, – 9). Point R is on PQ and divides it such that PR:QR is 3:5
The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.
Using the distance formula, we have:
d(P,Q) = √((x2-x1)² + (y2-y1)²)
= √((-4-(-12))² + (-9-7)²)
= √(8² + (-16)²)
= √(320)
= 8 √(5)
Since PR:QR is 3:5, we can set up the following equation:
d(P,R)/d(R,Q) = 3/5
Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.
Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)
Using the distance formula again, we can find the distance between P and R:
d(P,R) = (3/8) d(P,Q)
= (3/8) (8 √(5))
= 3 √(5)
Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:
d(R,Q) = (5/3) d(P,R)
= (5/3) (3 √(5))
= 5 √(5)
Finally, we can use the midpoint formula to find the coordinates of R:
x = (-12 + (3/8) (8))/2 = -8
y = (7 + (-1))/2 = 3
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Complete Question:
The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?
Suppose that the insurance companies did do a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.a.i. x = __________ii. n = __________iii. p′ = __________b. Define the random variables X and P′, in words.c. Which distribution should you use for this problem? Explain your choice.d. Construct a 95% confidence interval for the population proportion who claim they always buckle up.i. State the confidence interval.ii. Sketch the graph.iii. Calculate the error bound.e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.
We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8
b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.
c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.
d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).
ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].
iii. The error bound is 0.0291.
e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:
Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.
Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.
Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.
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Can anyone please help with this math problem? Thanks!
Answer: Yes Sofia will have enough money
=======================================================
Explanation:
Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.
The area of the rectangle is 16*7 = 112 square meters.
The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be
sum of the exterior sides = perimeter
6+7+16+7+6+x = 54
42+x = 54
x = 54-42
x = 12
The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.
area of the trapezoid = 0.5*height*(base1+base2)
area = 0.5*5.66*(16+12)
area = 79.24 square meters
----------------
Recap so far
area of the rectangle at the bottom = 112 square metersarea of the trapezoid up top = 79.24 square metersThe total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.
Let's convert that to square decimeters.
Recall that 1 decimeter = 10 centimeters
Multiply both sides by 10
1 decimeter = 10 centimeters
10*(1 decimeter) = 10*(10 centimeters)
10 decimeters = 100 centimeters
10 decimeters = 1 meter
Then,
[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]
The entire lawn is 19124 square decimeters.
----------------
We have one final block of calculations to determine the total price.
x = number of rolls
1 roll covers 90 square decimeters
x rolls cover 90x square decimeters
90x = 19124
x = 19124/90
x = 212.489 approximately
Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).
In short, Sofia needs 213 rolls.
1 roll costs $4.50
213 rolls will cost 213*4.50 = 958.50 dollars.
This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).
Sofia will have enough money to pay for all of the grass.
a parachutist rate during a free fall reaches 132 feet per second. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 10 seconds of free fall. in your computations, assume that 1 meter is equal to 3.3 feet. (do not round your answer)
Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.
How to convert feet to meters?First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:
[tex]$\frac{3meter}{3.3 feet}[/tex]
To convert feet per second to meters per second, we can multiply by the conversion factor:
[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]
Therefore, the parachutist's rate during free fall is 40 meters per second.
Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:
distance =[tex]\frac{1}{2}[/tex] * acceleration * time²
where acceleration due to gravity is approximately 9.8 meters/second^2.
Substituting the given values, we get:
distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²
distance = 490 meters
Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.
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One little cat can eat a bag of treats in 15 minutes while another cat can eat the same bag of treats in 10 minutes. What part of the bag can they eat together in the given time? 1 minute. 2 minute, and 3 min
Answer:
1 minute = 1/6
2 minutes = 1/3
3 minutes =1/2
Step-by-step explanation:
one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag
the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag
to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3
calculate the expected value, the variance, and the standard deviation of the given random variable x. (round all answers to two decimal places.) x is the number of red marbles that suzan has in her hand after she selects three marbles from a bag containing three red marbles and two green ones. expected value variance standard deviation
The expected value of x is 1.80, the variance is 0.72, and the standard deviation is 0.85.
Calculate the expected value, variance, and standard deviation of the random variable x as follows. Round all answers to two decimal places, and keep in mind that x is the number of red marbles that Suzan has in her hand after selecting three marbles from a bag containing three red marbles and two green ones.
Expected Value: Since there are 3 red marbles and 2 green marbles in the bag, the probability of drawing a red marble is: P(R) = 3/5The probability of drawing a green marble is P(G) = 2/5Therefore, the expected value of the random variable X is: E(X) = μ = np = 3/5 * 3 = 1.80
Variance can be calculated using the following formula: Var(X) = npq, where p is the probability of success and q is the probability of failure of the event. In this scenario, the probability of drawing a red marble is P(R) = 3/5, and the probability of drawing a green marble is P(G) = 2/5.
Therefore, Var(X) = npq Var(X) = (3/5)*(2/5)*3Var(X) = 1.80 * 0.4Var(X) = 0.72Standard Deviation: The square root of the variance is equal to the standard deviation. Hence, the formula for standard deviation is: S.D. = √Var(X)S.D. = √0.72S.D. = 0.85
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Audrey and Harper are selling fruit for a band fundraiser. Customers can buy small crates of apples and large containers of peaches. Audrey sold 3 small crates of apples and 10 large containers of peaches for a total of $116. Harper sold 11 small crates of apples and 20 large containers of peaches for a total of $292. Find the cost each of one small crate of apples and one large container of peaches. A) Define your variables. Write a system of equations to represent the situation. Solve using any method. Show all of your work. Andrew decides he wants to help the band as well. He sells 7 small crates of apples and 5 larges containers of peaches. How much money does he raise for the band?
The cost of one small crate of apples is $12 and the cost of one large crate of peaches is $8. The cost of 7 small cates of apples and 5 large containers of peach is $126.
What is the cost of 7 small crates and 5 large containers?The system of equations that describe the question is:
3s + 10l = 116 equation 1
11s + 20l = 292 equation 2
Where:
s = cost of one small crate of apples
l = cost of one large crate of peaches
The elimination method would be used to determine the values of s and l.
Multiply equation 1 by 2
6s + 20l = 232 equation 3
Subtract equation 3 from equation 2:
5s = 60
Divide both sides of the equation by 5
s = 60 / 5
s = $12
Substitute for s in equation 1:
3(12) + 10l = 116
36 + 10l = 116
10l = 116 - 36
10l = 80
l = 80 / 10
l = 8
Cost of 7 small crates of apples and 5 large containers of peaches = (7 x 12) + (8 x 5) = $124
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The sum of the base and the height of a triangle is 22 cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of_____cm and a base of cm_____.
The dimensions of the triangle with maximum area are a base of 11 cm and a height of 11 cm.
We are given that the sum of the base and height of a triangle is 22 cm. Let's call the base of the triangle "b" and the height "h". Then we have the equation:
b + h = 22
We want to find the dimensions of the triangle that will give us the maximum area.
The formula for the area of a triangle is A = (1/2)bh.
We can use the equation b + h = 22 to solve for one of the variables in terms of the other.
we can solve for h:
h = 22 - b
Substituting this into the formula for the area, we get:
A = (1/2)b(22 - b)
The equation 0 = 11b - (1/2)b² can be rearranged to:
(1/2)b² - 11b = 0
We can then use the quadratic formula to solve for "b"
b = 11 ± 11
So the value of b that gives us the maximum area is b = 11 cm. Substituting this back into the equation h = 22 - b, we get:
h = 22 - 11 = 11 cm
Triangle has a base of 11 cm and a height of 11 cm.
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1 0 6
0 1 1
0 0 0
Find the solution(s) to the system, if it exists. State the solution as a point (be sure to use parentheses), use parameter(s) s and t if needed. If the system is inconsistent, then state no solution.
The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
To solve the system of equations:
1x + 0y + 60z = 1
1x + 10y + 0z = 0
0x + 0y + 0z = 0
The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:
From the first equation, we get x = 1 - 60z
From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z
Therefore, the solution to the system can be written as a point in terms of z as:
(x, y, z) = (1 - 60z, -10 + 600z, z)
Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:
(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
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6. 4 The point Q (3, -1) has been translated from P by the vector (3) What are the coordinates of the point P?
The coordinates of the point P is (-1,2) .
What is translation?
In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.
Finding the coordinates of the point P :
The coordinates of point P can be found by subtracting the vector from point Q.
To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).
Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:
3 - 4 = -1
Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:
-1 - (-3) = 2
Therefore, the coordinates of point P are (-1, 2).
So, the correct answer is (C) (-1, 2).
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Helppppp will give brainlyest
Answer: 4
Step-by-step explanation:
4. shift the boundary line up 1
8. A department store
buys 300 shirts for
a total cost of $7,200 and sells them for
$30 each. Find the percent markup.
The percent markup is 25%.
What is percent markup?Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus it's cost to make or purchase for resale) by the cost of that unit.
Given that, A department store buys 300 shirts for a total cost of $7,200 and sells them for $30 each.
Cost of one shirt [tex]= 7200 \div 300 = \$24[/tex]
And they sold at $30 each,
Percent markup [tex]= 30-24 \div 24 \times 100[/tex]
[tex]= 25\%[/tex]
Hence, the percent markup is 25%.
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If Jacob spent 45$ on dinner and wanted to top the waitress 15%, which of the following would be a good estimate for the tip?
Answer: 6.75
Step-by-step explanation:
45 x 0.15= 6.75
A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.
Find the probability that a 0 is received. (Enter the value of the probability in decimal format and round the final answer to one decimal place.)
P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).
0.5333
A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly
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Weight: 20kg Order: 10 mg q6 hours Therapeutic range : 2-3 mg/kg/day. What is daily dose? Is it safe? Is it therapeutic?
The daily dose is 40mg, this dose per kilogram per day is within the therapeutic range of 2-3mg/kg/day, which means that the medication is within the safe and effective range for this patient's weight.
The weight of the patient is 20kg, and the prescribed dosage is 10mg every 6 hours. To calculate the daily dose, we need to multiply the prescribed dosage by the number of doses per day. Since the medication is prescribed every 6 hours, this means that the patient will take it 4 times a day.
=> (10mg x 4 doses) = 40 mg
The therapeutic range is the range of doses at which the medication is most effective and safe. In this case, the therapeutic range is 2-3mg/kg/day. To determine if the daily dose is within the therapeutic range, we need to divide the daily dose (40mg) by the patient's weight (20kg) to get the dose per kilogram per day, which is 2mg/kg/day.
However, it's important to note that the therapeutic range is a general guideline and may vary depending on the patient's individual circumstances and medical history.
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Consider a square whose side-length is one unit. Select any five points from inside this square. Prove that at least two of these points are within squareroot 2/2 units of each other.
The given square with a side length of one unit is known to contain five points. One must prove that at least two of these points are within square root 2/2 units of each other.
According to the Pigeonhole principle, "if n items are put into m containers, with n > m, then at least one container must contain more than one item."In this context, the square is the container, and the points inside it are the objects. If more than four points are picked, the theorem is true, and two points are nearer to each other than the square root of 2/2 units.
Let's place four points on the square's four corners. The distance between any two of these points is the square root of two units since the square's side length is 1.
Let's add another point to the mix. That point is either inside the square or outside it. Without loss of generality, let us assume that the point is inside the square. It must then be within the perimeter outlined by joining the square's corners to the point that was not a corner already.
The perimeter of the square described above is a square with a side length of square root 2 units.
Since we have five points in the square, at least two of them must be in the same smaller square, due to the pigeonhole principle. Without loss of generality, let's assume that two of the points are in the upper-left square. As a result, any points within this square are within the square root 2 units of any of the other four points. Hence, at least two points of the five selected are within the square root of 2/2 units of each other.
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I need help asap I just need atleast one of these explained and I can do the rest
The factοred fοrm οf a pοlynοmial is
1. 30b³- 54b² = 6b²(5b−9)
2. 3y⁵ - 48y³ = 3y³(y −4)(y + 4)
3. x³ + 8 = (x + 2) (x² – 2x + 2²)
4. y³ - 64 = (y - 4) (y² – 4y + 4²)
5. 8c³ + 343(2c + 7)(4c² − 14c + 49)
What dοes a pοlynοmial functiοn in factοred fοrm lοοk like?The factοred fοrm οf a pοlynοmial is represented as a³ + b³ = (a + b) (a² – ab + b²). All equatiοns are cοmpοsed οf pοlynοmials. Earlier we've οnly shοwn yοu hοw tο sοlve equatiοns cοntaining pοlynοmials οf the first degree, but it is οf cοurse pοssible tο sοlve equatiοns οf a higher degree.
One way tο sοlve a pοlynοmial equatiοn is tο use the zerο-prοduct prοperty. If yοu remember frοm earlier chapters the prοperty οf zerο tells us that the prοduct οf any real number and zerο is zerο.
We will use the formula
a³ + b³ = (a + b) (a² – ab + b²)
And
a³ - b³ = (a - b) (a² – ab + b²)
1. [tex]30b^3-\ 54b^2[/tex]
⇒ 6b²(5b−9)
2. 3y⁵ - 48y³
⇒ 3y³( y² - 16y)
⇒ 3y³( y² - 4 + 4 - 16y)
⇒ 3y³(y −4)(y + 4)
3. x³ + 8
⇒ x³ + 2³
Using a³ + b³ = (a + b) (a² – ab + b²)
⇒ x³ + 2³
⇒ (x + 2) (x² – 2x + 2²)
4. y³ - 64
⇒ y³ - 4³
Using a³ - b³ = (a - b) (a² – ab + b²)
⇒ y³ - 4³
⇒ (y - 4) (y² – 4y + 4²)
5. 8c³ + 343
Using a³ + b³ = (a + b) (a² – ab + b²)
2c + 7
(2c + 7)(4c² − 14c + 49)
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how to calculate the product of two random variable that follows normal distribution with mean 0 and variance 1
The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.
To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:
Since the mean of the normal distribution is 0 and the variance is 1, we can assume that the standard deviation is also 1.Thus, we can write the probability density function of the normal distribution as:
f(x) = (1/√2π) * e^(-x^2/2)
Using the definition of expected value, we can write the expected value of a random variable X as:E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.
Similarly, we can write the expected value of a random variable Y as:E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.
Since the two random variables are independent, the expected value of their product is the product of their expected values. Thus, we can write:E[XY] = E[X] * E[Y]
Substituting the probability density function of the normal distribution into the expected value formula, we can write:E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0
E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0
Thus, the expected value of the product of two random variables that follow a normal distribution with mean 0 and variance 1 is:E[XY] = E[X] * E[Y]
= 0 * 0 ⇒ 0
Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.
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Use the following function to find d(0)
d(x)=-x+-3
d(0)=
When the function d(x) = -x +(-3), then the value of d(0) is -3
In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.
In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.
To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:
d(0) = -(0) - 3
The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as
d(0) = -3
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The Turners have purchased a house for $170,000. They made an initial down payment of $34,000 and secured a mortgage with interest charged at a rate of 3.5%/year on the unpaid balance. (Interest computations are made at the end of each month.) Assume that the loan is amortized over 15 years. (Round all answers to the nearest cent.)
(a) What monthly payment will the Turners be required to make?
$
(b) What will be their total interest payment?
$
(c) What will be their equity (disregard depreciation and inflation) after 10 years?
$
(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).
What monthly payment will the Turners be required to make?Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).
Applying the values provided, we obtain:
(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.
Amount paid: $1,054.63
Hence, the installment will be $1,054.63 per month.
What will be their total interest payment?(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:
Total interest equals PV minus (Payment x n)
Applying the values provided, we obtain:
$1,054.63 multiplied by 180 equals $136,000 in interest.
Interest totaled $88,833.40.
The total interest payment will therefore be $88,833.40.
What will be their equity (disregard depreciation and inflation) after 10 years?(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:
The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i
Where n denotes how many payments are still due (180 - 120 = 60).
Applying the values provided, we obtain:
The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917
Balance remaining: $71,587.90
As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.
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Ñamandu es un genio dibujó un cuadrado de x cm cada lado en la parte superior del cuadrado partió en tres partes iguales quedando el corte expresado de esta manera x bajo 3 unió el primer punto de corte con el vértice del lado paralelo trazando un segmento a lo que llamó y Descubre que figuras se forman y entra el perímetro de cada figura formado
The figures created are a square and a right triangle, and the perimeter of the entire figure is (13x/3) + x × sqrt(10).
When Namandu divides the top side of the square into three equal parts, he creates two segments of length x/3 each. By connecting the first point of division with the vertex of the parallel side, he creates a right triangle with legs of length x/3 and x, and hypotenuse of length y.
Using the Pythagorean theorem, we can solve for y:
y^2 = (x/3)^2 + x^2
y^2 = x^2/9 + x^2
y^2 = (10x^2)/9
y = x×sqrt(10)/3
Now we can find the perimeter of each figure that is created
Perimeter of the original square = 4x
Perimeter of the right triangle = x + x/3 + y = x + x/3 + xsqrt(10)/3
Perimeter of the entire figure = 4x + x + x/3 + xsqrt(10)/3 = (13x/3) + x×sqrt(10)
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find the area and circumference of the circle below.round your answers to the nearest hundredth
Answer:
Step-by-step explanation:
The area of given circle is 28.27 sq.m. The circumference of given circle is 18.85 m (rounded to the nearest hundredth).
Give a short note on Circumference?The circumference of a circle is the distance around the edge or boundary of the circle. It is also the perimeter of the circle. The circumference is calculated using the formula:
C = 2πr
where "C" is the circumference, "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle.
The circumference of a circle is proportional to its diameter, which is the distance across the circle passing through its center. Specifically, the circumference is equal to the diameter multiplied by π, or:
C = πd
where "d" is the diameter of the circle.
Given that the diameter of the circle is 6m.
We know that the radius (r) of the circle is half of the diameter (d), so:
r = d/2 = 6/2 = 3m
The area (A) of the circle is given by the formula:
A = πr²
Substituting the value of r, we get:
A = π(3)² = 9π ≈ 28.27 sq.m (rounded to the nearest hundredth)
The circumference (C) of the circle is given by the formula:
C = 2πr
Substituting the value of r, we get:
C = 2π(3) = 6π ≈ 18.85 m (rounded to the nearest hundredth)
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The complete question is:
It is well documented that a typical washing machine can last anywhere between 5 to 20 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 14 years and 2 years, respectively. [You may find it useful to reference the z table.] a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) b. What proportion of the washing machines will last for more than 15 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) c. What proportion of the washing machines will last for less than 10 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) d. Compute the 90th percentile of the life of the washing machines. (Round your intermediate calculations to at least 4 decimal places, "z" value to 3 decimal places, and final answer to the nearest whole number.)
a. The mean of X is 1.7549 and the standard deviation is 0.3536.
b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.
c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.
d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.
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evaluate the diagram below, and find the measures of the missing angles
Answer:
A=100
B= 80
C=80
D=100
E=80
F=80
G=100
Step-by-step explanation:
