Answer:
(a) A score of 450 on Test A corresponds to a score of 146 on Test B.
(b) A score of 625 on Test A corresponds to a score of 88.75 on Test C.
Step-by-step explanation:
We are given the means and standard deviations of some well-known standardized tests referred to as Test A, Test B, and Test C. All three yield normal distributions.
Test Mean Standard deviation
Test A 500 100
Test B 150 8
Test C 70 15
So, [tex]\mu_A[/tex] = 500 and [tex]\sigma_A[/tex] = 100
[tex]\mu_B[/tex] = 150 and [tex]\sigma_B[/tex] = 8
[tex]\mu_C[/tex] = 70 and [tex]\sigma_C[/tex] = 15
(a) We have to find a score of 450 on Test A corresponds to what score on Test B.
For this, firstly we will find the z-score for a score on Test A and then equate with that of Test B.
z-score of 450 on test A = [tex]\frac{X_A-\mu_A}{\sigma_A}[/tex]
= [tex]\frac{450-500}{100}[/tex] = -0.5
So, this z-score corresponds to the score on test B, i.e;
z-score on test B = [tex]\frac{X_B-\mu_B}{\sigma_B}[/tex]
-0.5 = [tex]\frac{X_B-150}{8}[/tex]
[tex]X_B= 150-(0.5 \times 8)[/tex]
= 150 - 4 = 146
Hence, a score of 450 on Test A corresponds to a score of 146 on Test B.
(b) We have to find a score of 625 on Test A corresponds to what score on Test C.
For this, firstly we will find the z-score for a score on Test A and then equate with that of Test C.
z-score of 625 on test A = [tex]\frac{X_A-\mu_A}{\sigma_A}[/tex]
= [tex]\frac{625-500}{100}[/tex] = 1.25
So, this z-score corresponds to the score on test C, i.e;
z-score on test C = [tex]\frac{X_C-\mu_C}{\sigma_C}[/tex]
1.25 = [tex]\frac{X_C-70}{15}[/tex]
[tex]X_C= 70+(1.25 \times 15)[/tex]
= 70 + 18.75 = 88.75
Hence, a score of 625 on Test A corresponds to a score of 88.75 on Test C.
The area of a rectangular wall of a barn is 90 square feet. It’s length is 8 feet longer than twice it’s width. Find the length and width of the wall of the barn
Answer: The answer is that the length is square ft, and the width is .
Step-by-step explanation:
The length and width of the wall of the barn are 18, 9
What is the area of rectangle?The area of rectangle is product of length and width
Given area of rectangle is 90 ft²
given length = 8 ft + 2ₓ width
l = 8 +2 w
area = l × w
90 = (8 +2 w) × w
90= 8w +2w²
2w²+ 8w -90 =0 or w²+4w - 45 =0
On solving w= 9, -5
as width cannot be negative so w= 9
l= 8+2×9
l=26
Thus the length and width of the wall of the barn are 18, 9
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Perimeter of square = 12 1/2 in
Side length of square=
Given h(x) = -2x + 5, solve for a when h(x) = 3.
Answer:
Step-by-step explanation:
-2x + 5 = 3
-2x = -2
x = 1
You are descending from the top of a 32-foot tall rock climbing wall at an average rate of -2.3 feet per minute. How many feet off the floor are you in 5 minutes? How many feet off the floor are you in 10 minutes? Approximately when will you reach the ground?
Answer:
You are 11.5 feet off the floor are you in 5 minutes
You are 23 feet off the floor are you in 10 minutes
it will take 13.91 minutes to reach the ground
Step-by-step explanation:
If you are top , height will keep decreasing as you move downward.
Given
top height 32 feet
Descending speed = -2.3 feet /minute
Here negative sign implies that height is decreasing.
concept used
distance = speed * time
How many feet off the floor are you in 5 minutes?
time = 5 minutes
distance descended = -2.3 feet /minute*5 minutes = - 11.5 feet
Hence ,
I would have moved 11.5 feet from the top.
Distance from ground will be = Top height - distance descended
Distance from ground will be = 32 - 11.5 = 20.5 feet
____________________________________________
How many feet off the floor are you in 10 minutes
distance descended = -2.3 feet /minute*10 minutes = - 23 feet
Hence ,
I would have moved 23 feet from the top.
Distance from ground will be = Top height - distance descended
Distance from ground will be = 32 - 23= 9 feet
______________________________________________
When you reach the ground distance descended will be 32 feet.
Since its a descend distance off the floor has to be taken as negative value
Thus, distance descend in this case will be -32 feet
-32 feet= -2.3 feet /minute*Time
Time = -32/-2.3 = 13. 91 minutes.
Thus, it will take 13.91 minutes to reach the ground.
Find the value of x in the triangle shown below.
Answer:
55
Step-by-step explanation:
98+27+x=180
Answer:
Step-by-step explanation:
x + 98° + 27° = 180
x + 125° = 180°
x = 55°
4x+5x=63
Solving linear equations
Answer:
x = 7
Step-by-step explanation:
4x+5x=63
Combine like terms
9x = 63
Divide by 9
9x/9 =63/9
x = 7
A ver si responden correctamente! Yo tenía $50 Mi mamá me dio $100 Mi papá me dio $500 Mi tío y mi tía me dieron $100 Yo tenía otros $75 ¿Cuánto tenía?
Tu tenías $825.
Dado que tu tenías $50, tu mamá te dio $100, tu papá te dio $500, tus tíos te dieron $100 y tu tenías otros $75, para determinar cuanto dinero tenías en total se debe realizar la siguiente operación matemática, consistente en una suma:
50 + 100 + 500 + 100 + 75 = X150 + 600 + 75 = X750 + 75 = X825 = XPor lo tanto, en total tu tenías $825.
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Which equation has a solution of x = 1.5
3 + root 3 *2 +root 2
Answer:
6 + 3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
(3 + [tex]\sqrt{3}[/tex] )(2 + [tex]\sqrt{2}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
3(2 + [tex]\sqrt{2}[/tex] ) + [tex]\sqrt{3}[/tex] (2 + [tex]\sqrt{2}[/tex] ) ← distribute both parenthesis
= 6 + 3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex]
expand and simplify
2a + 3(a + 5)
Answer:
5a + 15
Step-by-step explanation:
2a + 3(a + 5)
open brackets
2a + 3a + 15
5a + 15
The table below shows the birth weight and the weight for the first three weeks of a baby whale. Determine the slope and y-intercept of the linear equation that models this data, write the equation and predict the baby whale’s weight at 4 weeks.
Week
Weight (lbs)
0
5000
1
6400
2
7800
3
9200
Student’s Work
Student’s Answer
A. y= 9200x+1400; 10,600 lbs
B. y= 5000x+1400; 21,400 lbs
C. y= 1400x+ 5000; 10,600 lbs
D. y= 5000 +41400; 21,400 lbs
Answer:
C
Step-by-step explanation:
The slope is 1400. And the y intercept is 5000 because when x=0 y=5000. And if you multiply 1400 by 4 and then add 5000 you get 10,600 lbs for the weight at 4 weeks.
The slope is 1400 and the y-intercept is 5000 of the linear equation which is the correct answer would be option (C) y = 1400x + 5000; 10,600 lbs.
What is the slope of the line?The slope of the line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We have to determine the slope and y-intercept of the linear equation that models this data,
Week Weight (lbs)
0 5000
1 6400
2 7800
3 9200
Slope = (7800 - 6400)/(2 - 1) = 1400
There is a 1400 slope.
And since y=5000 for x=0, the y-intercept is 5000.
So the equation of a baby whale’s weight at 4 weeks is y = 1400x + 5000
Hence, the correct answer would be option (C)
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Determine the input value for which the statement f(x) = g(x) is true.
Answer:
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Step-by-step explanation:
1. Mr. Jones's class collected tissue boxes. The
class brought in a total of 30 boxes. If the tissue
box dimensions are listed below, then how much
space will Mr. Jones need?
4 in
С
3 in
7 in
Answer:
420 inches of space in all equal length width and height
Step-by-step explanation:
Because 4+3+7 = 14 x 30
it all equals up to 420
Mr. Jones will need 420 inches of space in all equal length, width, and height.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations.
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
We have been given that the tissue box dimensions are 4, 3, and 7
If the class brought in a total of 30 boxes.
So the required space would be : (4+3+7)×30 = 14 × 30
it all equals up to 420.
Hence, he will need 420 inches of space in all equal length, width, and height.
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How many times does 12 go into 110
Answer:
it goes into 110 about 9 times
Step-by-step explanation:
Answer:
9 times
Step-by-step explanation:
12 * 9 = 108
Which of the following dot plots shows data that is symmetrical?
Hey there! I'm happy to help!
If something is symmetrical you can cut a line through it and it will be the same on both sides. If you have a perfect circle you can cut it in half and it will be the same on both sides, so it is symmetrical.
We see that W looks the same on both sides if you cut it in half at the 3. It is the same on both sides, so the answer is W.
Have a wonderful day! :D
Answer:
Y
Step-by-step explanation:
S=(n-2).180
(Solve for n)
Answer:
[tex]n = \frac{S}{180} + 2[/tex]Step-by-step explanation:
S = 180 × ( n - 2)
To solve for n divide both sides by 180°
That's
[tex]n - 2 = \frac{S}{180} [/tex]Add 2 to both sides in order to isolate n
That's
[tex]n + 2 - 2 = \frac{S}{180} + 2[/tex]We have the final answer as
[tex]n = \frac{S}{180} + 2[/tex]Hope this helps you
Please help this would mean a lot to me
Answer: D. m∠x+m∠y=180°
Step-by-step explanation:
m∠x and m∠y creates a linear pair (two angles formed one line)
a line is 180°, this means:
m∠x+m∠y=linear pair
m∠x+m∠y=180°
Hope this helps!! :)
Please let me know if you have any question
Solve for b:
3(b - 4) = -3
Answer:
b=3
Step-by-step explanation:
it is in the picture
Answer:
b = 3Step-by-step explanation:
=> 3(b - 4) = -3
=> 3b - 12 = -3
=> 3b = -3 + 12
=> 3b = 9
=> b = 9/3
=> b = 3
Admission price to Universal Studios park is Php 2600 per person. The average patron attending spends about Php 1500 on food, drinks, games, and souvenirs. Find the function notation that accurately describes this situation.
Answer:
f(x)=2600x+1500 at least I think because it's 2600 per person
Suppose a social networking site has roughly 1,000,000 users, and as each
member signs up for an account, he or she is assigned a number. Which of these would result in the largest sample size using systematic sampling?
A. Surveying every 25,000th number
B. Surveying every 25th number
C. Surveying every 250th number
D. Surveying every 2,500th number.
The option that results in the largest sample size using systematic sampling is; Surveying every 25,000th number
How to find the Sample Size?
If the numbers of people are assigned in order of 1 to 1,000,000 then the smallest sample would be obtained by conducting surveys every 25 000th numbers.
The calculation of the sample size would be made by dividing 1, 000,000 by 25000.
1,000,000/25000 = 40
Therefore, the smallest sample selected would be 40 people.
If the surveys were made every 25th numbers, then the sample size would be:
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find the angle made by the line joining 5,3 and -1,-3 with the positive direction of x-axis
Answer:
45°
Step-by-step explanation:
gradient of the line:
Let A (-1,-3) and B (5,3)
tan a = (yB - yA) / (xB - xA) = (3 - -3) / (5 - -1) = 6/6 = 1
--> the angle made by the line and positive direction of x-axis is:
[tex]a = { \tan}^{ - 1} (1) = 45[/tex]
What are the 2-dimensional components of a cylinder
Answer: 2 circles and a rectangle
Step-by-step explanation:
please answer this I need it asap
Answer: i believe the answer would be the 3rd option
Step-by-step explanation:
1.) A boy has $12 saved. He decides to start saving on a regular basis. He figures out that he
can
save $1.50 per day. What is the total amount he will have saved after 1 day? 2 days? 3 days?
17days? X days?
Answer:
12 + (1.50 multiplied by x)
Step-by-step explanation:
You have 12 dollars as the base. For every x days (x is the amount of how many days) he'd save $1.50. For one day, he'd save 1.50 plus his 12 dollars. Two days, he'd save 12 + (1.50 x x). Three, it'll be 12 + (1.50 x x) and so on.
I hope this helped. :)
I dont understand what this mean or how to solve it.
-(8 - 2)
Answer:
-6
Step-by-step explanation:
1. Always do the parentheses first. solve 8-2 to get 6.
-(8-2) = -(6) = -6
1. simplify inside parentheses
a) 8 - 2 = 6
2. multiply by whatever is outside the parentheses
a) (-1)(6) = -6
Let me know if you need me to clarify on something!
Chicken eggs can be categorized as large if they weigh at least 2 ounces. Clare weighs 48 large eggs and finds that they have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces. Interpret 0.08 ounces in this situation.
Answer: The average difference of weights of all 48 eggs from mean eight is 0.08.
Step-by-step explanation:
The mean absolute deviation of a data interprets the mean distance between each data point and the mean.
When this distance goes larger it means data has greater variability
Given, 48 large eggs have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces.
It means that the average difference of weights of all 48 eggs from mean eight is 0.08.
Given the formula C= 1/2t(c1-c2), solve for t.
Answer:
[tex]t=\frac{2C}{c1-c2}[/tex]
Step-by-step explanation:
[tex]C=\frac{1}{2}t(c1-c2)\\2(C)=2(\frac{1}{2}t(c1-c2))\\2C=t(c1-c2)\\\frac{2C}{c1-c2}=\frac{t(c1-c2)}{c1-c2}\\t=\frac{2C}{c1-c2}[/tex]
Answer:
[tex]t=\frac{2C}{c_{1}-c_{2}}[/tex]
Step-by-step explanation:
[tex]C=\frac{1}{2}*t(c_{1}-C_{2})\\\\[/tex]
Multiply both sides by 2,
[tex]2*C=2*\frac{1}{2}*t*(c_{1}-c_{2})\\\\2C=t*(c_{1}-c_{2})\\\\\frac{2C}{(c_{1}-c_{2})}=t\\\\\\t=\frac{2C}{c_{1}-c_{2}}[/tex]
Mrs. Brown bought 42 juice boxes. One-sixth of the juice boxes are cherry. How many cherry juice boxes did Mrs. Brown buy?
Answer:
the answer 1s 7
Step-by-step explanation:
1 sixth of 42
1/6 × 42
6
Answer as a decimal with four decimal places.
Answer:
Answer as a fraction. Do not include spaces in your answer.
1st question
-31/15
2nd question
19/40
3rd = Answer as a decimal with four decimal places
0.8333…
4th = fraction
5th =rational
6th =rational
Step-by-step explanation:
edge 2021
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression can be reduced to 0.8333.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be written as shown below,
[tex]2.5 \times 0.\bar3[/tex]
= (25/10) × (1/3)
= 25/30
= 5/6
= 0.8333....
Hence, the given expression can be reduced to 0.8333.
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a trapezium with equal non parallel sides is called
Answer:
It is called an isosceles trapezoid/ trapezium
Step-by-step explanation: