Answer:
B = 55°
b = 17.1 (rounded to the nearest tenth)
c = 20.9 (rounded to the nearest tenth)
Find the slope of the line passing through the points (9, 1) and (9,-4).
Answer:
slope is undefined
Step-by-step explanation:
(9, 1 ) and (9, - 4 )
Since the x- coordinates of the 2 points are 9, then the line is vertical and parallel to the y- axis with slope being undefined.
Slope is the change in y over the change in x.
Slope = (-4 - 1) / (9 -9) = -5/0 you cannot divide by 0,so the slope is undefined. This means it is a vertical line
a certain number plus two is five find the number
x=3
Step-by-step explanation:
x+2=5
x=5-2
x=3
3. Find the least common denominator for the group of denominators using the method of prime numbers. 45, 75, 63
We have to find LCM
3 | 45,75,63
3 | 15,25,21
5 | 5,25,7
5 | 1,5,7
7 | 1,1,7
LCM=3×3×5×5×7=1575
The least common denominator for the group of denominators using the method of prime numbers is 1575.
What is least common multiple?LCM stands for Least Common Multiple. It is a method to find the smallest common multiple between any two or more numbers. A factor is one of the numbers that multiplies by a whole number to get that number.
For the given situation,
The numbers are 45, 75, 63
Prime factors of 45 = [tex]3,3,5[/tex]
Prime factors of 75 = [tex]3,5,5[/tex]
Prime factors of 63 = [tex]3,3,7[/tex]
Then the LCM can be found by, first take the common factors then multiple the remaining factors as,
⇒ [tex](3)(3)(5)(5)(7)[/tex]
⇒ [tex]1575[/tex]
Hence we can conclude that the least common denominator for the group of denominators using the method of prime numbers is 1575.
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Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-12x^2+2160x-59000 To maximize the monthly rental profit, how many units should be rented out? units What is the maximum monthly profit realizable?
Answer:
To maximize the monthly rental profit, 90 units should be rented out.
The maximum monthly profit realizable is $38,200.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]
To maximize the monthly rental profit, how many units should be rented out?
This is the x-value of the vertex, so:
[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]
To maximize the monthly rental profit, 90 units should be rented out.
What is the maximum monthly profit realizable?
This is p(90). So
[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]
The maximum monthly profit realizable is $38,200.
An urn contains 12 balls, five of which are red. Selection of a red ball is desired and is therefore considered to be a success. If three balls are selected, what is the expected value of the distribution of the number of selected red balls
The expected value of the distribution of the number of selected red balls is 0.795.
What is the expected value?The expected value of the distribution is the mean or average of the possible outcomes.
There are 12 balls in an urn, five of which are crimson. The selection of a red ball is desired and hence considered a success.
In this case, the possible outcomes are 0, 1, 2, or 3 red balls.
To calculate the expected value, we need to find the probability of each outcome and multiply it by the value of the outcome.
The probability of selecting 0 red balls is :
[tex]$\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$[/tex].
The probability of selecting 1 red ball is :
[tex]$3 \cdot \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{315}{660}$[/tex].
The probability of selecting 2 red balls is
[tex]:$\dfrac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$.[/tex]
The probability of selecting 3 red balls is
[tex]$\dfrac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10} = \frac{15}{660}$[/tex]
The expected value is then :
[tex]$0 \cdot \frac{105}{660} + 1 \cdot \frac{315}{660} + 2 \cdot \frac{105}{660} + 3 \cdot \frac{15}{660} = \frac{525}{660} = \frac{175}{220} \approx \boxed{0.795}$[/tex]
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Please help !!! Plzzzz
Explanation:
Because we have a midsegment, this means that it is half as long as the side it's parallel to. You can think of "mid" as "middle" and that could lead to "halfway" to remember to take half.
So z = 14/2 = 7
If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?
Answer:
$80
Step-by-step explanation:
To find the largest price, assume that all 20 copies of the workbook will have 400 pages.
Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.
Find the total cost by multiplying this by 20:
20(4)
= 80
So, the largest price to print 20 copies is $80
Given the parent graph h(x) = x, what happens when it is changed to h(x + 9)?
Answer:
If the parent graph is h(x) = x, then h(x+9) would actually be shifting the graph 9 units to the LEFT.
Let me know if this helps!
Can someone please help me solve the equation?
Answer:
(0,0) is the x and y intercept of the function
Step-by-step explanation:
The parabola touches the x and y axis at 0
The x intercept is (0,0) and the y intercept is (0,0)
Answer:
(0, 0) is the x and y intercepts
Step-by-step explanation:
intercepts are where the curve of the equation contacts an axis
The equation is y = x²
fernando charges a flat fee of 4.50 plus 2.00 per mile for his taxi service, when he got to the airport the cab fare was 12.50 how many miles was the trip to the airport
the trip to the airport was 6.25 miles.
Please Help me! I will mark brainliest for correct answer!!!
Answer:
y=2/3x+1
Step-by-step explanation:
Identify the terminal point for a 45° angle in a unit circle.
O A (231)
O B.
O c.
V2 72
Answer:
D
Step-by-step explanation:
x- coordinate = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
y- coordinate = sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
That is ( [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{\sqrt{2} }{2}[/tex] ) → D
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 2525 hours and the mean lifetime of a bulb is 590590 hours. Find the probability of a bulb lasting for at most 622622 hours. Round your answer to four decimal places.
Answer:
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 590 hours, standard deviation of 25 hours.
This means that [tex]\mu = 590, \sigma = 25[/tex]
Find the probability of a bulb lasting for at most 622 hours.
This is the p-value of Z when X = 622.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{622 - 590}{25}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997.
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
A 5 ounce bottle of juice cost $1.35 and an 8 ounce bottle of juice cost $2.16 a what is the unit cost per ounce of juice and b what is the better buy
Answers:
First bottle's unit cost = 27 cents per oz
Second bottle's unit cost = 27 cents per oz
Both have the same unit cost.
----------------------------------------
Work Shown:
unit cost = price/(number of ounces)
1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz
2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz
Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.
A zookeeper published the following stem-and-leaf plot showing the number of lizards at each major zoo in the country:
∣
0
1
2
3
4
5
6
∣
0
6
8
8
8
0
2
6
6
7
8
1
2
6
6
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
00
10
20
30
40
50
60
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
0
0
0
0
1
0
0
6
2
2
8
6
6
8
6
6
8
7
0
0
8
0
Key:
2
∣
0
=
20
2∣0=202, vertical bar, 0, equals, 20 lizards
How many zoos have more than 26 lizards
The surface area of a cylinder?
Answer:
18. 84 ft² or 18.85 ft² when rounded to the nearest tenth
Step-by-step explanation:
2πrh+2πr²
2× 3.14 × 1 × 2= 12.56
2 × 3.14 × 1² = 6.28
12.56 + 6.28 = 18.84
Have a great day :)
Answer:
18.85 [tex]ft^2\\[/tex]
*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*
Step-by-step explanation:
Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]
Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.
I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.
Radius: 1 Height: 2
Plug numbers into equation:
[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]
I hope that helps!
i would like some help please i am stuck
Answer: -2(d) is the answer.
Step-by-step explanation:
x1 = 3
y1 = -5
x2 = -2
y2 = 5
slope (m) = rise/run = (y2 - y1)/(x2-x1)
=(5-(-5))/(-2-3)
= 10/-5
= -2
Ilang litro ng tubig ang kailangang isalin sa timba na naglalaman ng 10 000 mililitro
Answer
nghiệmTrảingu từng bước:
If x+y=8 and xy =15 find the value of x³+y³.
Answer:
152Step-by-step explanation:
let x= 5 and y= 3x + y = 85 + 3 = 8xy = 155 × 3 = 15x³ + y³ = ?5³ + 3³ = ?125 + 27 = 152[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
give ABCD is a trapizod , Ab = 13, CD= 14, BC = 15, and AD = 20 what is the area
Step-by-step explanation:
A=140sq. units
Step-by-step explanation:
ABCD
A=13
B=15
C=14
D=20
C=14×14
=196sqr.units
Assume that x and y are both differentiable functions of t. Find dx/dt when x=11 and dy/dt=-4 for the equation xy=99 .
Differentiating both sides of
xy = 99
with respect to t yields
x dy/dt + y dx/dt = 0
When x = 11, we have
11y = 99 ==> y = 9
and we're given that dy/dt = -4 at this point, which means
11 (-4) + 9 dx/dt = 0 ==> dx/dt = 44/9
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 83 months with a variance of 81. If the claim is true, what is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors? Round your answer to four decimal places.
Answer:
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The production manager claims they have a mean life of 83 months with a variance of 81.
This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]
Sample of 146:
This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]
What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?
This is 1 subtracted by the p-value of Z when X = 81.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
1 - 0.0078 = 0.9922.
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
A rational expression is _______ for those values of the variable(s) that make the denominator zero.
9514 1404 393
Answer:
undefined
Step-by-step explanation:
A rational expression is undefined when its denominator is zero.
Translate and solve: five less than z is 4
z -5 =4
neutralize the left -5 by adding 5 on both sides
z -5 (+5) = 4 (+5)
z = 9
Determine the remaining sides and angles of the triangle ABC.
c=6 mi, B = 38.71°, C = 32.51°
Find the measure of angle A.
A=°
(Type an integer or a decimal.)
Find the length of side a.
а:
mi
(Round to the nearest mile as needed.)
Find the length of side b.
b=mi
(Round to the nearest mile as needed.)
9514 1404 393
Answer:
A = 108.78°
a = 11 mi
b = 7 mi
Step-by-step explanation:
The sum of angles in a triangle is 180°, so the third angle is ...
A = 180° -38.71° -32.51°
A = 108.78°
__
The remaining sides can be found from the law of sines.
a/sin(A) = c/sin(C)
a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896
a ≈ 11 mi
b = sin(B)·11.163896 ≈ 0.625379 × 11.163896
b ≈ 7 mi
A cash register contains $10 bills and $50 bills with a total value of $1080.If there are 28 bills total, then how many of each does the register contain?
Answer:
8 ten dollar bills
20 fifty dollar bills
Step-by-step explanation:
x = number of 10 dollar bills
y = number of 50 dollar bills
x+y = 28
10x+50y = 1080
Multiply the first equation by -10
-10x -10y = -280
Add this to the second equation
-10x -10y = -280
10x+50y = 1080
-----------------------
40y = 800
Divide by 40
40y/40 = 800/40
y = 20
Now find x
x+y =28
x+20 = 28
x = 28-20
x= 8
URGENT! 15 PNTS
Points T, R, and P, define _____
A. plane B
B. line e
C. line segment PR⎯⎯⎯⎯⎯⎯⎯
D. plane M
Answer:
Since points T, R, and P are all present on plane B, the answer is A.
Points T, R, and P define plane B
We have given that,
A. plane B
B. line e
C. line segment PR⎯⎯⎯⎯⎯⎯⎯
D. plane M
We have to determine the Points T, R, and P, define
What is the plane?A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.
Since points T, R, and P are all present on plane B, the answer is A
Points T, R, and P define plane B.
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PLEASE HELP NOW
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
2y-3x=10
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Answer:
Step-by-step explanation:
Solve for y:
[tex]2y-3x=10\\2y=3x+10\\y=\frac{3}{2} x+5[/tex]
Therefore:
y = 3/2x + 5
m = 3/2
b = 5
Graph below courtesy of Desmos.
8
6
4
2
6
8
-8 -6 -4 -2 0-3
21
.
-6
-8
O A. y -[x]-2
OB. y -[x]+3
O C. y = (x) - 3
O D. y = [x]+2
The required equation of the line is y = [x]+2
From the graph shown, we can see that the line dotted points forms a straight line. We are to find the required equation of the line formed.
The formula for calculating the equation of a straight line is expressed as
y = mx+b where
m is the slope b is the y-intercept
Get the slope 'm'
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the coordinate points (2, 0) and (4, 2)
[tex]m=\frac{2-0}{4-2}\\m=\frac{2}{2}\\m=1[/tex]
Get the y-intercept 'b'
Substitute m = 1 and (2, 0) into y = mx+b as shown;
[tex]2=1(0)+b\\2=0+b\\b=2[/tex]
Get the required equation. Recall that y = mx+b, hence;
[tex]y = 1x + 2\\y=x+2[/tex]
Hence the required equation of the line is y = [x]+2
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Find m∠F.
Find the answer to m∠F
Answer:
m∠F = 45°
Step-by-step explanation:
Notice the lengths of the given sides and the right angle. This is enough information to prove that this is a 45-45-90 triangle, or just basically a square cut diagonally.
Regardless if even just one side is given for a 45-45-90 triangle, all 45-45-90 triangles have one thing in common. The sides that form the right angle are equivalent and the hypotenuse is equal to one of the sides that form the right angle times the square root of two. I'm aware that it sounded confusing, as I'm awful at explaining, so just look at the picture I've attached instead of trying to understand my explanation that seemed like trying to learn a second language.
Look at the picture. See that FD = x times that square root of 2 and that DE = x. Now look back at your picture. It's connecting, now isn't it?
Now that we know that this is indeed a 45-45-90 triangle, we can confirm that m∠F = 45°
