The probability of getting an ace and a three is (4/52) × (3/51) = 12/2652 which simplifies to 1/221.
There are 4 aces and 4 threes in a deck of 52 standard cards.
The probability of getting an ace on your first draw is 4/52.
Once you have the ace, there are 51 cards left in the deck, 3 of which are threes.
Therefore, the probability of drawing a three is 3/51.
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[Pre-calculus honors, grade 11] The light from a lighthouse can be seen from an 18-mile radius. A boat is anchored so that it can just see the light from the lighthouse. A second boat is located 25 miles from the lighthouse and is headed straight toward it, making a 44° angle with the lighthouse and the first boat. Find the distance between the two boats when the second boat enters the radius of the lighthouse light.
Using trigonometry, the distance between the two vessels when the second boat enters the lighthouse's radius is 13.46 miles.
Trigonometry: What Is It?The relationships between angles and length ratios are investigated in the branch of mathematics known as trigonometry. The use of geometry in astronomical study led to the establishment of the field during the Hellenistic era in the third century BC.
The distance between the two boats when the second boat enters the radius of the lighthouse light is 13.46 miles using trigonometry.
Triangle - what is it?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the vertices A, B, and C is represented by the Δ ABC.
Any three points that are not collinear create a singular triangle and a singular plane in Euclidean geometry. (i.e. a two-dimensional Euclidean space). In other words, every triangle is a part of a plane, and that triangle is a part of only one plane. In the Euclidean plane, all triangles are contained within a single plane, but in higher-dimensional Euclidean spaces, this is no longer the case. This page covers triangles in Euclidean geometry, especially the Euclidean plane, unless otherwise specified.
In this question,
The side of the isosceles triangle is given by,
l=2a sin(θ/2)
where a= 18 miles
θ= 44°
l= 2*18*sin 22°
= 36*0.374
= 13.46 miles
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7,600 dollars is placed in a savings account with an annual interest rate of 6%. If no money is added or removed from the account, which equation represents how much will be in the account after 7 years?
Answers:
M=7,600(1+0.06)(1+0.06)
M=7,600(1-0.06)^7
M=7,600(1+0.06)^7
M=7,600(0.06)^7
Step-by-step explanation:
The equation that represents how much will be in the account after 7 years is:
M = 7,600(1+0.06)^7
Here's the explanation:
The formula for calculating the future value (M) of a present value (P) invested at an annual interest rate (r) for a certain number of years (t) is M = P(1+r)^t.
In this case, the present value (P) is 7,600 dollars, the annual interest rate (r) is 6% or 0.06, and the number of years (t) is 7.
Substituting these values into the formula, we get M = 7,600(1+0.06)^7. This represents how much will be in the account after 7 years if no money is added or removed from the account.
Find the volume and surface area of soda if the radius is 6cm and the height is 11cm
The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.
To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:
Volume of cylinder = πr²h
Surface area of cylinder = 2πrh + 2πr²
Substituting the given values, we get:
Volume = π × 6² × 11
Volume = 1,026.72 cubic centimeters (rounded to two decimal places)
Surface area = 2π × 6 × 11 + 2π × 6²
Surface area = 452.39 square centimeters (rounded to two decimal places)
Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.
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you walk 1 1.5 miles to the gym and then another 1 1/10 miles to a basketball court. How many yards did you walk in all?
You walked a total of 4576 yards to get to the basketball court.
What is unit conversion?In order to represent amounts in a more practical or acceptable unit of measurement, unit conversions are crucial for addressing mathematical issues. In this task, for instance, we were given distances in miles but had to translate them into yards to get the overall distance travelled. We wouldn't be able to compare or combine values that are stated in various units without unit conversions. When working with formulae or equations that contain physical quantities with multiple units, unit conversions are also crucial.
Given that, the distance walked is 1.5 miles and 1 1/10 miles.
Coverting into yards we have:
1.5 miles is equal to 1.5 x 1760 = 2640 yards
1 1/10 miles is equal to (1 + 1/10) x 1760 = 1936 yards
Total distance is:
2640 + 1936 = 4576 yards
Hence, you walked a total of 4576 yards to get to the basketball court.
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In Exercise 5.12 , we were given the following joint probability density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide: f(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhere
Are Y1 and Y2 independent?
The conclude that the Y1 and Y2 are not independent.
The joint probability density function for the random variables Y1 and Y2 for a mixture of insecticide isf(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhereTo verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Therefore, we need to find the marginal density functions of Y1 and Y2.Probability Density Function:We know that for a given joint probability density function, the probability density function of Y1 is given by integrating over all possible values of Y2, and vice versa.Mathematically,P(Y1)=∫0∫1f(y1,y2)dy2... (1)P(Y2)=∫0∫1f(y1,y2)dy1... (2)Using equation (1) to calculate P(Y1), we get, P(Y1)=∫0∫1f(y1,y2)dy2=∫0∫1(2)dy2=2... (3)Similarly, we can use equation (2) to calculate P(Y2) as follows:P(Y2)=∫0∫1f(y1,y2)dy1=∫0∫1(2)dy1=2... (4)Product of marginal density functions:Now we can find the product of marginal density functions as follows:P(Y1)P(Y2)=2×2=4... (5)Thus, to verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Since 2 ≠ 4, Y1 and Y2 are not independent. Hence, we can conclude that the Y1 and Y2 are not independent.
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Which of the following statements are true?(Choose all correct answers)Methods cannot be written with parameters.Parameter values can never be used within the method code block.Methods can be written with any number of parameters.Methods can never be written with more than four parameters.Parameter values can be used within the method code block
The true statement is, Parameter values can be used within the method code block. (option e).
In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.
Parameter values can be used within the method code block.
This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.
In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.
Hence the option (e) is correct.
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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
Find the Laplace transform Y(s) of the solution of the given initial value problem. Then invert to find y(t) . Write uc for the Heaviside function that turns on at c , not uc(t) .y'' + 16y = e^(?2t)u2y(0) = 0 y'(0) = 0Y(s) =y(t) =
The Laplace transform is a mathematical technique used to solve differential equations and analyze signals and systems in engineering, physics, and other fields. It is named after the French mathematician Pierre-Simon Laplace.
The Laplace transform of the given initial value problem is given by:
Y(s) = (2s^2 + 16) / (s^2(s^2+16))
Inverting the Laplace transform to find y(t) gives us:
y(t) = e^(-8t) * (1-cos(4t)) + 2sin(4t) + u2(t)
Where u2(t) is the Heaviside function that turns on at t = 2.
To find the Laplace transform of y(t), we first take the Laplace transform of both sides of the differential equation:
L(y''(t)) + 16L(y(t)) = L(e^(-2t)u_2(t))
Using the property L(y''(t)) = s^2Y(s) - sy(0) - y'(0) and noting that y(0) = 0 and y'(0) = 0, we can simplify to get:
s^2Y(s) + 16Y(s) = L(e^(-2t)u_2(t))
Using the property L(e^(-at)u_c(t)) = 1/(s + a) * e^(-cs), we can substitute to get:
s^2Y(s) + 16Y(s) = 1/(s + 2)^2
Now we can solve for Y(s):
Y(s) = 1/(s^2 + 16) * 1/(s + 2)^2
To find y(t), we need to take the inverse Laplace transform of Y(s). We can use partial fraction decomposition to simplify the expression:
Y(s) = A/(s^2 + 16) + B/(s + 2) + C/(s + 2)^2
Multiplying both sides by the denominator and solving for A, B, and C, we get:
A = 1/8
B = -1/4
C = 1/8
Substituting these values, we get:
Y(s) = 1/8 * 1/(s^2 + 16) - 1/4 * 1/(s + 2) + 1/8 * 1/(s + 2)^2
Taking the inverse Laplace transform of each term, we get:
y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t)
Therefore, the solution to the initial value problem y'' + 16y = e^(-2t)u_2(t), y(0) = 0, y'(0) = 0 is y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t).
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What is the next number in the sequence 3, 4, 7, 12, 19
Answer:28
Step-by-step explanation:
Answer: 28
Explanation: Look for a pattern or reason for the following number in the sequence. In this case 3+1=4, 4+3=7, 7+5=12, 12+7=19, so the probable answer is to add the following odd number to the last one in the line to get the next. (19+9=28)
Help me solve it I need to show my work please help
Step-by-step explanation:
5x - 30 = 3x
2x = 30
x = 15
that's the answer
Let X >0 denote a random variable with p.d.f. fx(2) and c.d.f. Fx (I). Assume Fx() is monotone increasing, and let Y = FX(X). That is, Y is a random variable that takes the value Fx (1) when X = r. Find fy(y). Mark the correct answer (a) fy(y) = 1,0
The probability density function (PDF) of Y can be determined by the transformation of the PDF of X. Using the transformation rule, we can calculate that fy(y) = fx(x) |dx/dy|, where x is a function of y, since y = Fx(x).
We can use the Chain Rule to determine the derivative of x with respect to y. Since Fx is a monotone increasing function, dx/dy = 1/F'x(x). Substituting this into the transformation rule, fy(y) = fx(x) / F'x(x).
Therefore, to find fy(y), we need to calculate F'x(x). Fx is the cumulative distribution function, which means that its derivative F'x(x) is the probability density function of X, or fx(x). Substituting this into the transformation rule, fy(y) = fx(x) / fx(x). Since fx(x) = fx(2) and fx(2) is a constant, fy(y) = 1/fx(2).
To summarize, the probability density function of Y is given by fy(y) = 1/fx(2).
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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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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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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
Helppppp will give brainlyest
Answer: 4
Step-by-step explanation:
4. shift the boundary line up 1
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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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:
The _________ method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.- Non probability sampling- Systematic sampling- Simple random sampling - Stratified sampling
The Simple random sampling method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.
What is Simple random sampling?
The Simple random sampling is a sampling technique in which every member of the population has an equal chance of being chosen as a sample. The samples are chosen randomly, without any specific criterion. In this method, the selection of individuals for the sample is done without any specific pattern. This means that each member of the population is equally likely to be selected as a sample.In Simple random sampling, each member of the population is assigned a number, and the samples are selected using a random number generator or drawing names out of a hat. The selected samples are then analyzed to make predictions about the entire population.For example, if a researcher wanted to know the average age of students in a school, they might use Simple random sampling to choose a sample of 50 students. The researcher would assign each student a number and then use a random number generator to select the samples.There are some advantages and disadvantages of Simple random sampling, which are listed below:Advantages of Simple random sampling It is easy to understand and conduct the process.Each member of the population has an equal chance of being selected as a sample.It ensures that the sample is representative of the entire population.Disadvantages of Simple random sampling It can be time-consuming to select the samples.There may be a chance of human error when selecting samples.The sample size may not be large enough to draw meaningful conclusions.
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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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Complete the table. In the row with X as the input write the rule as an algebraic expression for the output then complete the last row of the table using the rule. Express the values in your answers as decimals
The last two rows of the table should be completed as follows:
Input Output
8 22.80
10 28.50
What is algebraic expression?An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It is used to represent a single quantity or value, and can be written in terms of one or more variables.
The rule given is an algebraic expression, x, which is the input, multiplied by 2.85, which is the output. Using this information, we can determine the cost of 10 muffins.
To find the cost of 10 muffins, we can use the algebraic expression given. First, we will multiply 10, the number of muffins, by 2.85, the cost of one muffin. This gives us a total of 28.50. Therefore, the cost of 10 muffins is 28.50.
Using this same rule and process, we can also determine the cost of any number of muffins. For example, if we want to know the cost of 15 muffins, we can simply multiply 15 by 2.85, giving us a total of 42.75.
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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:
Michaela holds her state high school record for the 500-meter freestyle swimming event. She can swim the event in 4 minutes and 50 seconds. At this same rate, how far will she swim in 10 minutes?
Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.
1 minute = 60 seconds
4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds
So, Michaela's rate is:
distance / time = x / 290 seconds
where x is the distance she can swim in 290 seconds.
Simplifying the equation:
x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance
We know that Michaela can swim 500 meters in 290 seconds:
500 meters / 290 seconds = 1.724 meters per second
Therefore, in 10 minutes (600 seconds), she will swim:
distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters
So, Michaela will swim 1034.4 meters in 10 minutes.
Step-by-step explanation:
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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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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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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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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Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching
jim
rate, in
of the cupric chloride.
min
After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so
he used the data to calculate the following least squares regression equation for predicting the etching rate from
the room temperature:
= 2 + 5
1
-2
What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5
min
The residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min is equals to the -2 μm/min.
The residual for each observation in statistics is the difference between predicted values of y (dependent variable) and observed values of y. That is Residual= observed y value − predicted y.
Here, cupric chloride is used to etch circuit boards. The linear regression equation is, y = 2 + (1/5)x
where, x = temperature in °C
y = etching rate in μm/min
Observed value of etching rate of cupric chloride = 5 μm/min for 25°C
To determine the estimated or predicted value of etching rate of cupric chloride, we substite x = 25, in the above linear equation, y = 2 + (1/5)x
=> y = 2 + (1/5)× 25
=> y = 7
So, Predicted Value = 7 μm/min
Observed Value = 5 μm/min.
Residual = Observed Value - Predicted
= 5 - 7 = -2
Hence, required value is -2 μm/min.
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Complete question:
Calculating and interpreting residuals You might need: Calculator Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching rate, in μm/min of the cupric chloride. After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature: y = 2 + 5/x, What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min. ? Show Calculator
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.
which part of this graph shows a non-linear relationship
Answer:
A.
Step-by-step explanation:
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 ?
