Answer:
12
Step-by-step explanation:
Just substitute 60 for a and divide it by 5
Ta Da!!
The scores on one portion of a standardized test are approximately Normally distributed, N(572, 51). a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores. b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Answer:
a) The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b) The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Step-by-step explanation:
68-95-99.7 rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Z-score:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu = 572[/tex], standard deviation [tex]\sigma = 51[/tex]
a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores.
By the 68-95-99.7 rule, within 2 standard deviations of the mean.
572 - 2*51 = 470
572 + 2*51 = 674
The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Using the z-score formula.
Between these following percentiles:
50 - (90/2) = 5th percentile
50 + (90/2) = 95th percentile.
5th percentile.
X when Z has a pvalue of 0.05. So when X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = -1.645*51[/tex]
[tex]X = 488.1[/tex]
95th percentile.
X when Z has a pvalue of 0.95. So when X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = 1.645*51[/tex]
[tex]X = 655.9[/tex]
The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
The object below is a cubical lunch box having each edge as 10 cm.
Find its surface area.
A
600 cm2
B
360 cm2
C
300 cm2
D
36 cm2
Answer:
B
Step-by-step explanation:
The total surface area of a cubical lunch box having each edge as 10 cm is 600 square centimeter. Therefore, option A is the correct answer.
What is surface area of a cube?The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.
Given that, the cubical lunch box having each edge as 10 cm.
Here, surface area = 6×10²
= 600 square centimeter
Therefore, option A is the correct answer.
Learn more about the surface area of a cube here:
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plzz help i hav a test after i need the answer quick plzz.
Answer:Oop
Step-by-step explanation:
The average cost of tuition plus room and board at small private liberal arts colleges is reported to be less than $18,500 per term. A financial administrator at one of the colleges believes that the average cost is higher. The administrator conducted a study using 150 small liberal arts colleges. It showed that the average cost per term is $18,200. The population standard deviation is known to be $1,400. Let α= 0.05. What are the null and alternative hypothesis for this study?
Answer:
The null and alternative hypothesis for this study are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The null hypothesis is rejected (P-value=0.004).
There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The significance level is 0.05.
The sample has a size n=150.
The sample mean is M=18200.
The standard deviation of the population is known and has a value of σ=1400.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-2.624)=0.004[/tex]
As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
The probability of event A is 0.5 and probability of event B is 0.2. Given that A and B are independent, then the probability of A and B (A intersection B) is:
A) 2.5%
B)7 %
C)10%
D) 14%
Select the correct answer.
The surface areas of two cubes are in a ratio of 1 : 9. What is the ratio of their volumes?
A 1:3
B. 1:9
C. 1:27
D. 1:81
Answer:
C. 1:27
Step-by-step explanation:
a²/b²=1/9 => a=1 and b=3
a³/b³=1³/3³=1/27
C. 1:27
I agree with the other answer. Here's another way to see why the answer is 1:27
The surface areas are in ratio 1:9. This means we could have one square that has area 1 and the larger square is area 9.
The smaller square has sides of 1 and the larger square has sides of 3 (square root both area values).
Now if we had a cube that has dimensions of 1 unit, then the volume is 1*1*1 = 1 cubic unit. If we had a larger cube with dimensions of 3 units, then the volume is 3^3 = 3*3*3 = 27 cubic units. We can fit 27 smaller 1x1x1 cubes into the larger 3x3x3 cube.
A fair coin is flipped 10 times and lands on heads 8 times. Provide a reason to justify the difference between the experimental and theoretical
probabilities. Use the drop-down menus to explain your answer.
There should be a
Choose...
number of trials. With Choose...
flips of the coin, the experimental probability will likely
approach the theoretical probability of Choose...
Answer:
THere will be 8 heads and 2 tails
Step-by-step explanation:
I don't know
You walk in a room and on the bed there are 2 dogs, 4 cats, one giraffe, 5 cows and a duck, 3 chickens flying above; how many legs are on the floor?
Answer:
0
Step-by-step explanation:
they are on the bed
The total legs on the floor excluding chicken is 50 legs
Word problemsFrom the given question, the following animals have 4 legs
dogs, cats, girraffe and cows
Duck and chickens both have 2 legs
The total number of legs on the floor = 4(2) + 4(4) + 1(4) + 5(4) + 1(2)
Total number. = 8 + 20 + 22
Total number = 50legs
Hence the total legs on the floor excluding chicken is 50 legs
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How many sundaes did the shop make if they used 32 spoonfuls of sprinkles?
Answer:
32?
Step-by-step explanation:
Answer:
Depends on how many spoonfuls of sprinkles per sundae. Is there more details to this question?
A theater can seat 160 people . If the theater is 60%full, how many more can fit in the theater
Answer:
64 people can fit in the theater.
Step-by-step explanation:
If 60% is full then calculate how many people is it
[tex] \frac{60}{100} \times 160 = 96 \\ 160 - 96 = 64[/tex]
64 is 40% of 160
So this many people can be accommodated in the theater
Answer:
64 more people can fit in the theater
Step-by-step explanation:
You need to find 60% of 160
10%=16 (divided by 10)
16×6=96
160 (total people)-96(60%)=64
A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the
function has a negative leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (-0, 5).
The graph of the function is negative on (-5, 3)
The graph of the function is positive on (-0, 1).
The graph of the function is negative on (3,co)
Mark this and return
Save and Exit
Sabem
Answer:
The graph of the function is negative on (3, ∞)
Step-by-step explanation:
The function starts negative at the left side of the graph, crosses the x-axis at x = -5, touches the x-axis at x = 1, again crosses into negative values at x = 3.
The function is positive on the open intervals (-5, 1) and (1, 3). It is negative on the open intervals (-∞, -5) and (3, ∞). The latter description matches the last answer choice:
the graph of the function is negative on (3, ∞).
How would you describe the translation from f(x)=x2 to f(x)=x2+5 ?
Answer:
5 units up
Step-by-step explanation:
Adding 5 to the y-value of an (x, y) coordinate moves it up 5 units.
f(x) = x^2 +5 is translated 5 units upward from f(x) = x^2.
................................................
Answer:
V =108 ft^3
Step-by-step explanation:
The volume is found by
V = Bh where B is the area of the base
B = the area of the trapezoid
B = 1/2 (b1+b2)*h of the trapezoid
B = 1/2(4+6)*4 = 1/2(10)*4 = 20
Now we can find the volume
V = 20* 9
V =108 ft^3
The function fff is given in three equivalent forms. Which form most quickly reveals the zeros (or "roots") of the function? Choose 1 answer: Choose 1 answer: (Choice A) A f(x)=-3(x-2)^2+27f(x)=−3(x−2) 2 +27f, (, x, ), equals, minus, 3, (, x, minus, 2, ), squared, plus, 27 (Choice B) B f(x)=-3(x+1)(x-5)f(x)=−3(x+1)(x−5)f, (, x, ), equals, minus, 3, (, x, plus, 1, ), (, x, minus, 5, )(Choice C) C f(x)=-3x^2+12x+15f(x)=−3x 2 +12x+15f, (, x, ), equals, minus, 3, x, squared, plus, 12, x, plus, 15 Write one of the zeros. xxx =
Answer:
(B) [tex]f(x)=-3(x+1)(x-5)[/tex]
x=5
Step-by-step explanation:
Given the three equivalent forms of f(x):
[tex]f(x)=-3(x-2)^2+27\\f(x)=-3(x+1)(x-5)\\f(x)=-3x^2+12x+15[/tex]
The form which most quickly reveals the zeros (or "roots") of f(x) is
(B) [tex]f(x)=-3(x+1)(x-5)[/tex]
This is as a result of the fact that on equating to zero, the roots becomes immediately evident.
[tex]f(x)=-3(x+1)(x-5)=0\\-3\neq 0\\Therefore:\\x+1=0$ or x-5=0\\The zeros are x=-1 or x=5[/tex]
Therefore, one of the zeros, x=5
Answer:
i dont think the one above is correct. here is the correct answer
Step-by-step explanation:
The fair spinner shown in the diagram above is spun.
Work out the probability of getting a factor of 10.
Give your answer in its simplest form.
Answer:
The answer is "0.2"
Step-by-step explanation:
Given value:
factor = 10
The amount of two divided by the number of options. When both fours and eight gaps are available, that probability can be defined as follows:
[tex]\Rightarrow \frac{2}{10}\\\\\Rightarrow \frac{1}{5}\\\\\Rightarrow 0.2\\[/tex]
Can somebody please solve this? I'm confused
Answer:
9
Step-by-step explanation:
Not sure if it is right, don't at me :)
Find an equation for the nth term of the arithmetic sequence.
a16 = 21, a17 = -1
Answer:nth term=a1 - 27n + 27
Step-by-step explanation:
first term =a1
common difference=d=-1-21
d=-27
Using the formula
Tn=a1 + d x (n-1)
nth term=a1 + (-27)(n-1)
nth term=a1 - 27n + 27
if f(x)=-x^2 and g(x) = -x^2+4x+5 what is the product
Answer:
[tex]x^{4}[/tex] - 4x³ - 5x²
Step-by-step explanation:
-x²(-x² + 4x + 5) Distribute
[tex]x^{4}[/tex] - 4x³ - 5x²
If this answer is correct, please make me Brainliest!
Johanna wrote the system of equations.
4x-3y=1, 5x+4y=9
If the second equation is multiplied by 4, what should the first equation be multiplied by to eliminate the x-variable by addition?
Answer:
-5
Step-by-step explanation:
If the second equation is multiplied by 4, the coefficient of the x-variable will be 5·4 = 20. To eliminate the x-variable by addition, the first equation needs to be multiplied by a value that will result in an x-coefficient of -20. If that value is k, then we have ...
4k = -20
k = -20/4 = -5
The first equation should be multiplied by -5 to eliminate the x-variable by addition.
_____
Comment on general case
In general, if you have ...
ax +by = c
dx +ey = f
to eliminate the x-variable by addition, you can multiply the second equation by "a" and the first equation by "-d". In the problem above, those numbers are 4 and -5.
Answer:
-5
Step-by-step explanation:
WILL MARK BRAINLIEST!
I thought of a three-digit number. If I add all the possible two-digit numbers made by using only the digits of this number, then one third of this sum is equal to the number I thought of. What is the number I thought of?
Answer:
198
Step-by-step explanation:
If you add 11,18, 19, 81, 88, 89, 91, 98, 99 then the sum would be 594 then dividing by 3 would be 198.
PLZ MARK BRAINLIEST!!!
whats the answer for 45 meters every 5 seconds = meters per second
Answer:
9 meters every second
Step-by-step explanation:
45/5=9
5/5=1
9:1
What is the value of 5x+3 when x = 4?
Answer:
Step-by-step explanation:
5(4)+ 3
20+3
23
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 18, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
One-half of the dogs in each shelter are between which weights?
between 8 and 30 pounds in shelter A; between 10 and 28 pounds in shelter B
between 8 and 17 pounds in shelter A; between 10 and 16 pounds in shelter B
between 21 and 30 pounds in shelter A; between 18 and 28 pounds in shelter B
between 28 and 30 pounds in shelter A; between 20 and 28 pounds in shelter B
Answer:
the 2nd one
i am pretty sure
Step-by-step explanation:
Find the compound interest on GHS 50,200 invested at 13% p.a. compounded annually for 3 years ( to the nearest
GHS).
Select one:
A. GHS 19,578
B. GHS 69,778
O
C. GHS 72,433
D. GHS 22.233
Answer:
D
Step-by-step explanation:
First found amount yielded
A = P(1+r)^nt
P is amount deposited 50,200
r is interest rate 13% = 13/100 = 0.13
t = 3
A = 50,200(1+0.13)^3
A = 50,200(1,13)^3
A = 72,433.42939999998
A is approximately 72,433.43
interest = A - P = 72,433.43-50,200 = 22,233.43= 22,233 to the nearest GHS
The difference of two supplementary angles is 70 degrees. Find the measures of the angles.
Answer:
DUEDY A. 32 degrees
Step-by-step explanation:
PATROLLING WEE WOOO
Xd
Answer:
55 125
Step-by-step explanation:
Let the smaller angle = x
Let the larger angle = x + 70
They are supplementary so the total of the two angles, by definition must be 180 degrees. Note that you should understand that any number of angles can but supplementary as long as they all add up to 180 degrees.
x + x + 70 = 180
2x + 70 = 180
2x + 70 - 70 = 180 - 70
2x = 110
2x/2 = 110/2
x = 55
the smaller angle = 55 degrees
The larger angle = 55 + 70 = 125
help timed help plss!!
Answer:
V1 = Base x Height = 43 x 15 = 645 (mm3)
V2 = Base x Height = 12 x 7 = 84 (mm3)
Hope this helps!
:)
Answer:
1) 645 mm³
2) 84 cm³
Step-by-step explanation:
Volume of prism:
Base area × height
1) 43 × 15 = 645 mm³
2) 12 × 7 = 84 cm³
There is one missing number in the “Which One Doesn’t Belong” game.
• Select a number that does not belong with any of the numbers. Explain your reasoning.
• Select a number that has a characteristic similar to the other two numbers. Explain your reasoning.
Answer:
I am not I understand the game but
1. 17 doesn't belong cause it a prime number and doesn't dived with any of the other numbers and double digit
2. 4 divides with 216 and 8 and single digit similar to 8
Step-by-step explanation:
Find the first five terms of the geometric sequence defined by a (n)=10
(.1)^n
Answer:
Step-by-step explanation:
a(1) = 10(.1)^1 = 1
a(2) = 10(.1)^2 = 10(0.01) = 0.1
a(3) = 10(.1)^3 = 10(0.001) = 0.01
a(4) = 0.001
a(5) = 0.0001
Problem 1.) A researcher claims that 96% of college graduates say their college degree has
been a good investment. In a random sample of 2000 graduates, 1500 say their college degree has
been a good investment. At a = 0.05 is there enough evidence to reject the researcher's claim?
Answer:
|Z| = |-52.5| = 52.5 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
We rejected the researcher's claim
A researcher do not claims that 96% of college graduates say their college degree has been a good investment.
Step-by-step explanation:
Explanation:-
Given data A researcher claims that 96% of college graduates say their college degree has been a good investment.
Population proportion 'P' = 0.96
Q = 1-P = 1- 0.96 = 0.04
In a random sample of 2000 graduates, 1500 say their college degree has
been a good investment.
Sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{1500}{2000} = 0.75[/tex]
Level of significance ∝ = 0.05
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
Test statistic
[tex]Z = \frac{p^{-} - P }{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.75 - 0.96 }{\sqrt{\frac{0.96 X 0.04}{2000} } }[/tex]
[tex]Z = \frac{-0.21}{0.00435} = -52.5[/tex]
|Z| = |-52.5| = 52.5 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
We rejected the researcher's claim
Conclusion:-
A researcher do not claims that 96% of college graduates say their college degree has been a good investment.
Which equation represents the line that passes through points (1, –5) and (3, –17)?
A. y = -6x + 1
B. y = 6x + 1
C. y = -6x - 1
D. y = 6x - 1
Answer:
C
Step-by-step explanation:
I’m rusty with my math, so I’m not 100% sure this is correct. My best attempt.
(1,-5) & (3,-17)
1=1x, -5=1y, 3=2x, -17=2y
Formula is y2-y1/x2-x1
-17 - -5 = -12
3 - 1 =2
So -12/2 = -6
Formula for the line is
y-y1 = m (x-x1)
In this equation m=-6
Y - -5 = -6 ( x - 1 )
Answer:C
Step-by-step explanation:
