Using the normal distribution and the central limit theorem, it is found that the power of the test is of 0.9992 = 99.92%.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is [tex]\mu = 8.5[/tex].The standard deviation is [tex]\sigma = 0.87[/tex].A sample of 30 is taken, hence [tex]n = 30, s = \frac{0.87}{\sqrt{30}} = 0.1588[/tex].The power of the test is given by the probability of a sample mean above 8, which is 1 subtracted by the p-value of Z when X = 8, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8 - 8.5}{0.1588}[/tex]
[tex]Z = -3.15[/tex]
[tex]Z = -3.15[/tex] has a p-value of 0.0008.
1 - 0.0008 = 0.9992.
The power of the test is of 0.9992 = 99.92%.
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Ms. James bought 3 world maps for her classroom. The total cost of the 3 maps was $73.77. The clerk told Ms. James that each map cost $2.45. Do you agree with the clerks calculations? Explain your reasoning.
please help ASAP please will give branlyist if i can figure it out
Answer:
The clerk is wrong because the total cost per map is $24.59
Step-by-step explanation:
since you know that you spent $73.77 for 3 maps you can set up the equation 73.77 = 3X (where x = cost per map)
once you divide 73.77 by 3 you get 24.59 and that equals the price per map
if it was like the clerk said and each map was 2.45 then the total cost shoud have been 7.35.
find the value of x ?
Answer:
Step-by-step explanation:
∠E = ∠G
∠D= ∠F because it’s a parallelogram ==> D=F=2x+12 and E=G=5x
5x+2x+12=180
7x=168
X=24
Solution 2:
2*5x+2*(2x+12)=360
10x+4x+24=360
14x=360-24=336
X=336/14
X=24
Answer:
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A/Q
5x+2x+12=180(Sum of adjacent angles is 180)
=>7x+12=180
=>7x=180-12
=>x=168/7
Hence,x=24....
The least common denominator for 3/9 and 3/6
Answer:
The least common denominator is 18:)
In the expression 12r what values of r makes the expression equal a number less than 12
answer:
any value below 1
r<1
examples:
12×0=1
12×0.99= 0.0825
12×-12=-144 (which is less than 12)
etc.
Identify whether each variable is categorical or continuous.
Hand length (cm) ?
Kneeling height (cm) ?
Hours studied for exam ?
Exam score?
Perfect attendance (100=perfect; 0 = not perfect)?
Answer:
u33u3373737
Step-by-step explanation:
hheeheheheheheheheheheehehehehebeheheheheheheheheehehe
D=1/3fk, solve for f
Answer:
f=3d/k
Step-by-step explanation:
electrician cuts a 21 ft piece of wire into two pieces. One piece is 4 ft longer than the other. How long are the pieces?
21=a+(a+4)
one piece is 8.5 ft
the other is 12.5 ft
PLEASE HELP WILL GIVE BRAINLIEST!!!!
Answer:
C E A F B D
Step-by-step explanation:
A function is translated to the right by h units when x is replaced by (x-h) in the function. So, the larger h is, the farther right the vertex of the quadratic is.
The vertices will be arranged left to right by the ordering ...
[tex]\boxed{y=f(x+3)}\rightarrow\boxed{y=f(x+2)}\rightarrow\boxed{y=f(x)}\rightarrow\boxed{y=f\left(x-\dfrac{1}{2}\right)}\\\\\rightarrow\boxed{y=f(x-4)}\rightarrow\boxed{y=f(x-7)}[/tex]
52. What are the given facts?plssss?help this is
HELPPP PLEASE!!!!
Write an equation for the nth term of the
arithmetic sequence below.
-12, -3, 6, ...
A. f(n) = -9n - 21
B. f(n) = 9n - 21
C. f(n) = 9n + 21
D. f(n) = -9n + 21
Activate
Answer: B.f(n)9n-12
Step-by-step explanation:
Choose the expression that is equal to 28.3
There are no other expressions intered. Please write them too.
Answer:
It CAN be 28.30
What is the y-intercept for the equation y=-4(x – 3)2 +1?
Answer:
(0,25)
Step-by-step explanation:
Answer:
I believe the y intercept is (0,25)
What’s the value of x?
Answer:
x=15°
Step-by-step explanation:
165°+x=180°(sum of the adjacent angles on a straight line is 180)
x=180-165
x=15°
What is the solution to the system of equations?
(4, 7)
(7, 4)
(12, 5)
(5, 12)
What is the solution to the system of equations?
3x+2y = 39
5x-y = 13
Answer ↷(5,12)
Solution ↷Given that,
3x + 2y = 39......(1)
5x - y = 13.......(2)
multiplying equation 1 by 5 & 2nd by 3 ,we get,
15x + 10y = 195.......(3)
15x - 3y = 39........(4)
Subtracting equation 4th by equation 3rd,
we get,
15x + 10y = 195
-15x - 3y = 39
_____________
ㅤ ㅤ13y = 156
ㅤㅤㅤ y = 12
_____________
so , y = 12 & x = 5
⤿5x-12 = 13⤿5x = 25⤿x = 5_____________
hence, option 4th ⇢ (5,12) is correct ✓
Graph Attached
Solution is (5,12)Option D
10 yd
10 yd
Find the area of each?
Answer:
20 yards
Step-by-step explanation:
i got 100 0n the quiz
2x+3≤x−5 solve for x
Answer:
x≤−8
Step-by-step explanation:
2x+3≤x−5
Step 1: Subtract x from both sides.
2x+3−x≤x−5−x
x+3≤−5
Step 2: Subtract 3 from both sides.
x+3−3≤−5−3
Answer is
x≤−8
the midpoint of (1,4) and (-7,10)
Answer:
i’m pretty sure the answer is y=3/4x-13/4
Step-by-step explanation:
solve for x ~
[tex]\bold{2(x + 1) - 4x = 3x + 5} [/tex]
spammers stay away .-.
thankyou ~
Answer:
x = -0.6
solving steps:
[tex]\sf \rightarrow 2\left(x+1\right)-4x=3x+5[/tex]
remove the parenthesis
[tex]\sf \rightarrow 2x+2\right)-4x=3x+5[/tex]
group the variables
[tex]\sf \rightarrow 2x-4x-3x\right)=5-2[/tex]
simplify
[tex]\sf \rightarrow -5x\right)=3[/tex]
change sides
[tex]\sf \rightarrow x\right)=\dfrac{3}{-5}[/tex]
answer in fraction
[tex]\sf \rightarrow x\right)=-\dfrac{3}{5}[/tex]
answer in decimals
[tex]\sf \rightarrow x\right)=-0.6[/tex]
Answer:
[tex]x=-0.6[/tex]
Step-by-step explanation:
[tex]2\left(x+1\right)-4x=3x+5\quad :\quad x=-\frac{3}{5}\quad \left(\mathrm{Decimal}:\quad x=-0.6\right)[/tex]
[tex]2\left(x+1\right)-4x=3x+5[/tex]
[tex]2(x+1)-4:-2x+2[/tex]
[tex]-2x+2=3x+5[/tex]
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x+2-2=3x+5-2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-2x=3x+3[/tex]
[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x-3x=3x+3-3x[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-5x=3[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-5[/tex]
[tex]\frac{-5x}{-5}=\frac{3}{-5}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=-\frac{3}{5}[/tex]
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Mill river middle school has 320 families with students at the school. For the open house, 240 families were present. What percentage of families came to open house?
Answer:
75%
Step-by-step explanation:
in order to find the percentage of something like this, all you need to do is divide the part by the whole, thus 240/320 to make 75%
Refer to the following information on full-term births in the United States over a given period of time.Type of Birth Number of BirthsSingle birth 47,200,000Twins 600,000Triplets 3000Quadruplets 200Use this information to estimate the probabilities of the following events.(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures.)
Answer:
Refer to the following information on full-term births in the United States over a given period of time.
Type of Birth Number of Births
Single birth 47,200,000
Twins 600,000
Triplets 3000
Quadruplets 200
Use this information to estimate the probabilities of the following events.
(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)
(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)
(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures
The radii of two similar cones are 1 and 2.5. What is the ratio of their volumes?
Answer:
Assuming the cones are the same height, then
V1 = pi * r^2 * h/3 = 3.14159*1^2*h/3
V2 = 3.14159*2.5^2*h/3 = 3.14159*6.25*h/3
V1/V2=(3.14159*h/3)/(3.14159*6.25)*h/3
V1/V2 = 1/6.25 = .16
V2/V1=(3.14159*6.25)*h/3/(3.14159*h/3)
V2/V1=6.25/1 = 6.25
$55 for 20 people............
Answer:
total amount of money: $1100
Step-by-step explanation:
multiply the number of people by the money for each of them
so $55 x 20 = $1100
Answer:
55 divied by 20..witch mean 50 divied between 20 ppl witch is
11/4 and as a decimal 2.75 hope this helped
What is the property name of 3 (6 + 2 ) = ( 3 x 6 ) + ( 3 x 2) ?
Answer:
The distributive property
Step-by-step explanation:
It says
[tex]a(b+c)=a(b)+a(c)[/tex]
I hope you understand the generalization of the property.
A researcher collected data from car shoppers about their favorite car color. He asked 250 people about their favorite vehicle color. How many more people said their favorite color is white compared to those who said black. Your answer should be written as a number not a percentage. And then the percents for the circle graph are 20% red 24% white 32% blue 18% black 4% silver and 2% other
Answer:
35 more preferred white
Step-by-step explanation:
Black 18% * 250 = 18/100 * 250 = 45
White 32%*250 = 32/100 * 250 = 80
The difference is 80 - 45 = 35
This table shows the ratio of daisies to roses.
Complete the statement about the equivalent ratios in
this table.
Daisies
Roses
To find the values in each row,
the values
in the previous row by
256
192
64
48
16
12
Answer:
Its divide and 4
Step-by-step explanation:
To find the values in each row divide the values in previous row by 4.
What is the Ratio?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Clearly, from observation,
Each column represent geometric progression with common ratio r = 1/4. So when moving downward, the element in the rows decreases as multiple of 1/4.
Here,
R(1, 1) = 256
R (2 ,1) = 64
R(2,1)/R(1,1)=1/4
Thus, To find the values in each row divide the values in previous row by 4.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each circle equation to its corresponding center and radius.
center = (3,-5)
radius = 2 units
center = (-3,-5)
radius = 4 units
center = (3,5)
radius = 2 units
center = (-3,5)
radius = 2 units
center = (3,-5)
radius = 4 units
center = (3,5)
radius = 4 units
(x + 3)2 + (1 + 5)2
= 16
(x + 3)2 + (1 – 5)2 = 4
+
=
(x – 3)2 + (x – 5)2
= 4
|(1 – 3)2 + (1 + 5)2 = 16
-
=
By using the general equation for a circle, we will see that the correct options are:
1) This is a circle centered at (-3, - 5) with a radius of 4 units.2) The center is (-3, 5) and the radius is 2 units.3) The center is (3, 5) and the radius is 2 units.4) This is a circle centered at (3, - 5) with a radius of 4 units.How to write a circle equation?
For a circle of radius R and center (a, b), the equation is given by:
(x - a)^2 + (y - b)^2 = R^2
With that in mind, if we look at the first equation:
(x + 3)^2 + (y + 5)^2 = 16 = 4^2
This is a circle centered at (-3, - 5) with a radius of 4 units.
For the second equation:
(x + 3)^2 + (y - 5)^2 = 4 = 2^2
The center is (-3, 5) and the radius is 2 units.
The third equation is:
(x - 3)^2 + (y - 5)^2 = 4 = 2^2
The center is (3, 5) and the radius is 2 units.
The fourth equation is:
(x - 3)^2 + (y + 5)^2 = 16 = 4^2
This is a circle centered at (3, - 5) with a radius of 4 units.
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If the salinity of ocean water at the entrance to an estuary is 35 and 63 percent of the volume of water in the estuary is ocean water, what is the average salinity of the estuary
The correct answer for the average salinity of the estuary would be 22.235.
Given in the question,
Salinity of ocean water at the entrance to the estuary: 35.
Volume of ocean water in the estuary: 63% (or 0.63).
Volume of freshwater in the estuary: 37% (or 0.37).
Consider, salinity of freshwater as 0.5.
To calculate the average salinity of the estuary, the formula know is:
Average Salinity = (Salinity of Ocean Water * Volume of Ocean Water + Salinity of Freshwater * Volume of Freshwater) / Total Volume of Estuary
[tex]= \dfrac{35*0.63 + 0.5 * 0.37}{1}\\\\= 22.05 + 0.185\\\\= 22.235[/tex]
Therefore, Average salinity of the estuary would be approximately 22.235.
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Angelo’s score in a video game was changed by -75 points because he missed some targets. He got -15 points for each missed target. How many targets did he miss?
Answer:
the answer is 5 targets
I love my chocolate company makes dark chocolate and light chocolate
Answer:
this is great to hear I personally like light
7500 in account paying 1.5 compound interest, how much after 8 years
Answer:
The amount of money after 8 years is $8448.69
Step-by-step explanation:
The rule of the compound interest is
[tex]A=p(1+r)^{t}[/tex] , where
A is the new valueP is the original valuer is the rate in decimalt is the time in years∵ There is $7500 in an account
∴ P = 7500
∵ The account paying 1.5% compound interest
∴ r = 1.5% = 1.5/100 = 0.015
∵ The money will invest for 8 years
∴ t = 8
→ Substitute all of these values in the rule above to find A
∵ [tex]A=7500(1+0.015)^{8}[/tex]
→ Use your calculator to find the answer
∴ A = 8448.69
∴ The amount of money after 8 years is $8448.69