Answer:
Keenan's z-score was of 0.61.
Rachel's z-score was of 0.81.
Step-by-step explanation:
Z-score:
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.
Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4.9 points.
This means that [tex]X = 80, \mu = 77, \sigma = 4.9[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 77}{4.9}[/tex]
[tex]Z = 0.61[/tex]
Keenan's z-score was of 0.61.
Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3.7 points.
This means that [tex]X = 78, \mu = 75, \sigma = 3.7[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 78}{3.7}[/tex]
[tex]Z = 0.81[/tex]
Rachel's z-score was of 0.81.
for each of the figures write an absolute value equation to satisfy the given solution set
5 and 17
Answer:
|x-11|=6
hope this helps
Step-by-step explanation:
PLEASE HELP ME SOLVE THIS.
STEP-BY STEP
THANK YOU !!!
I really don't know how to calculate this question.
(3 tan 45°)(4 sin 60°)-(2 cos 30°)(3 sin 30°)
Answer:
[tex]9\,\sin(60^\circ)[/tex], which is equal to [tex]\displaystyle \frac{9\sqrt{3}}{2}[/tex].
Step-by-step explanation:
An angle of [tex]45^\circ[/tex] corresponds to an isosceles right triangle: the length of the two legs (adjacent and opposite) would be equal. Accordingly:
[tex]\displaystyle \tan(45^\circ) = \frac{\text{Opposite Leg}}{\text{Adjacent Leg}} = 1[/tex].
Let [tex]A[/tex] denote the measure of an angle. Double-angle identity for sine:
[tex]2\, \sin(A) \cdot \cos(A) = \sin(2\, A)[/tex].
By this identity:
[tex]\begin{aligned}& (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \\ &= 3\, (2\, \cos(30^\circ) \cdot \sin(30^\circ)) \\ &= 3\, \sin(2 \times 30^\circ) \\ &= 3\, \sin(60^\circ)\end{aligned}[/tex].
([tex]A = 30^\circ[/tex] in this instance.)
Hence:
[tex]\begin{aligned}&(3\, \tan(45^\circ)) \cdot (4\, \sin(60^\circ)) - (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \\ &= 12\, \sin(60^\circ) - 3\, \sin(60^\circ) \\ &= 9\, \sin(60^\circ)\end{aligned}[/tex].
[tex]\displaystyle \sin(60^\circ) = \frac{\sqrt{3}}{2}[/tex]. Therefore, [tex]\displaystyle 9\, \sin(60^\circ) = \frac{9 \sqrt{3}}{2}[/tex].
NEED ANSWER ASAP,BRAINLIEST FOR CORRECT ANSWER. IM FAILING SCHOOL
Answer:
Step-by-step explanation:
D and F are alternate exterior angles
A , D , F , G are exterior angles. In this that are on the opposite sides are alternate exterior angles.
Alternate exterior angles:
1) D and F
2) A and G
The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited.
Answer:
Hello your question is incomplete attached below is the complete question
answer : 1596 ± 2.861 [tex]\sqrt{\frac{1580^2 }{20 } +\frac{2350^2 }{20 } }[/tex] ------ ( A )
Step-by-step explanation:
I will use excel function to resolve this question
Determine the 99% confidence of interval for the difference in mean number of steps by all people
∝ = 0.01
critical value ( t ) = 2.861 ( = TINV ( 0.01, 19 )
Given that :
S1 = 1580
S2 = 2350
n1 = 20
n2 = 20
Difference in mean = x1 - x2 = 1596
Margin of Error = t * [tex]\sqrt{\frac{S^2_{1} }{n_{1} } +\frac{s^2_{2} }{n_{2} } }[/tex]
∴ 99% confidence of interval
= 1596 ± 2.861 [tex]\sqrt{\frac{1580^2 }{20 } +\frac{2350^2 }{20 } }[/tex] ------
To investigate the relationship between the selling price of a house, y , in dollars, and the size of the house x, in square feet, a local builder collected data on a random sample of 120 houses from a certain region. Assume that the conditions for inference for the slope of a regression line are met. The resulting 95 percent confidence interval for the population slope of the regression line relating price and size is given by (62,99). The local builder claims that the selling price of houses from the region increases by $104 for every extra square foot of space in the house. Which of the following best describes the conclusion that can be reached about this claim based on the confidence interval?
a. The claim is supported by the interval, since the interval does not contain the value 0.
b. The claim is supported by the interval, since all values in the interval are positive.
Ñ. The claim is supported by the interval, since the interval does not contain the value 104.
d. The claim is not supported by the interval, since the interval does not contain the value 0.
e. The claim is not supported by the interval, E since the interval does not contain the value 104.
Answer:
E) The claim is not supported by the interval, since the interval does not contain the value 104.
Step-by-step explanation:
A claim that the selling price increases by $104 for each square foot increase in space is not supported by the interval. The interval represents plausible values for the slope of the regression line, and the interval does not include the value 104.
A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results SampleService Life (hours) 1495500505500 2525515505515 3470480460470 If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control
Answer:
Sample number 3
Step-by-step explanation:
From the given information:
Sample Service life(hours) Total Mean(X)
1 2 3 4
1 495 500 505 500 2000 500
2 525 515 505 515 2060 515
3 470 480 460 470 1880 470
Total = [tex]\text{addition \ of \ numbers \ of \ observations}[/tex]
Mean = [tex]\dfrac{\text{addition \ of \ numbers \ of \ observations}}{4}[/tex]
Thus;
[tex]UCL = \mu+x = 500 + 20 = 520\\ \\ LCL= \mu -x = 500 -20 =480[/tex]
To plot on an X_Bar chart, we have:
Sample Mean (X) UCL LCL
1 500 520 480
5 515 520 480
6 470 520 480
The x-Bar chart is shown in the image attached below. From the image, we realize that the average service life for sample number 3 occurs to be out of the statistical control.
According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of 1550 children, 214 were found to be living with at least one grandparent. At a 2% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%
Answer:
The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.
Step-by-step explanation:
Proportion of all children in the United States who currently live with at least one grandparent is higher than 11%
This means that the null hypothesis is:
[tex]H_0: p = 0.11[/tex]
And the alternate hypothesis is:
[tex]H_a: p > 0.11[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.11 is tested at the null hypothesis:
This means that [tex]\mu = 0.11, \sigma = \sqrt{0.11*0.89}[/tex]
Suppose that in a recent sample of 1550 children, 214 were found to be living with at least one grandparent.
This means that:
[tex]n = 1550, X = \frac{214}{1550} = 0.1381[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.1381 - 0.11}{\frac{\sqrt{0.11*0.89}}{\sqrt{1550}}}[/tex]
[tex]z = 3.54[/tex]
Pvalue of the test and decision:
This is the probability of finding a sample proportion above 0.1381, which is 1 subtracted by the pvalue of Z = 3.54.
[tex]z = 3.54[/tex] has a pvalue of 0.9999
1 - 0.9999 = 0.0001
The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.
A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at
random. How many possible outcomes are there?
0 3
O 5
0 6
O 14
Answer:
14
Step-by-step explanation:
hope it helps!
What is the absolute value of 2 1/2
Write your answer as a mixed number.
Answer:
it is 2 1/2
Step-by-step explanation:
I hope this helps
Find the amount of tax and the tax rate. Round to nearest hundredth of a percent.
Cost of item: $52
Selling price: $71.97
Answer:
Amount of Tax = $19.97
Tax Rate = 28%
Step-by-step explanation:
Amount of Tax = $71.97 - $52 = $19.97
Tax Rate = 19.97/71.97 × 100
= 0.28 × 100 = 28%
Please help!
If f(x) is an exponential function where f(- 2.5) = 9 and f(2.5) = 45 , then find the value of f(3.5) , to the nearest hundredth
The value of g(3.5) is 41.49 to the nearest hundredth
Exponential functionThe standard exponential function is given as g(x) = ab^x
If g(-2.5) = 9 and g(2.5) = 45, hence;
9 = ab^-2.5 .............. 1
45 = ab^2.5 .............2
Divide both equations:
9/45 = b^{-2.5-2.5}
1.5 = b^-5
1.5= 1/b^5
b^5 = 0.6666
b = 0.922
Also since 45 = ab^2.5 .
45 = a(0.922)^2.5
45 = 0.81625a
a = 55.13
g(3.5) = 55.13(0.922)^3.5
g(3.5) = 41.49
Hence the value of g(3.5) is 41.49 to the nearest hundredth
Learn more on exponential function here: https://brainly.com/question/12940982
Find the lateral surface area of the prism below in square yards.
Answer:
Step-by-step explanation:
Answer: 14*2 * 3
=> 6 * 14
=> 84Please mark as brainliest for further answers :)PLEASE HELP
A town has a population of 40,000 persons.
There are 6000 school-age children in the
town. What is the ratio of the school children
to the total population?
And please add the formula or how you did it
Answer:
3:20
Step-by-step explanation:
6000:40,000
find HCF (2000)
divide both sides by 2000
3:20
What can you tell about the mean of each distribution
1) There is a LARGE DIFFERENCE in the mean number of stray cats placed in homes by a New Leash on Life Animal Clinic each week and the mean number of stray cats placed in homes by No Ruff Stuff Animal Hospital each week.
2) There is a SMALL DIFFERENCE in the mean number of stray cats placed in homes by A New Leash on Life Animal Clinic each week and the mean number of stray cats placed in homes by No Ruff Stuff Animal Hospital each week
3) A New Leash on Life Animal Clinic placed more stray cats in homes than No Ruff Stuff Animal Hospital each week
4) No Ruff Stuff Animal Hospital placed more stray cats in homes than A New Leash on Life Animal Clinic each week
Answer: there is a small difference in the main number of stray cats placed in homes buy a new lease on life animal clinic each week and they’re mean number of stray cats place in homes by no raft staff animal hospital each week
Step-by-step explanation:
Answer:
There is a small difference in the mean number of stray cats placed in homes by A New Leash on Life Animal Clinic each week and ... each week.
Step-by-step explanation:
I got it right.
(two graphs: almost overlapped)
What is the complementary angle
of 65 degrees
The angle of 25° is the complement of the angle of 65° and the angle of 65° is the complement of the angle of 25°.
Answer:
25°
Step-by-step explanation:
Two angles are complementary if the sum of the angle measures add up to (90) degrees. To find the complementary angle of a given angle, subtract the given angle from (90) degrees, the result will be the complementary angle.
(90) - (65) = (25)
Write the equation of the line in SLOPE- INTERCEPT form:
1. (4, 2); slope 3
2. (3, -1); slope 4
3. (-4,-2), (4,0)
Answer:
Step-by-step explanation:
1) slope = m = 3
(4 , 2) ; x₁ = 4 ; y₁ = 2
y - y₁ = m(x - x₁)
y - 2 = 3(x - 4)
y - 2 = 3x - 4*3
y - 2 = 3x - 12
y = 3x - 12 + 2
y = 3x - 10 {Slope -intercept form: y = mx + b}
3) (-4 , -2) , (4 , 0)
We have to find the slope
[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \frac{0-[-2]}{4-[-4]}\\\\=\frac{0+2}{4+4}\\\\=\frac{2}{8}\\\\=\frac{1}{4}\\[/tex]
m = 1/4 ; (4 , 0)
y - y₁ = m(x - x₁)
[tex]y - 0 = \frac{1}{2}(x - 4)\\\\y =\frac{1}{2}x - 4 *\frac{1}{2}\\\\y =\frac{1}{2}x - 2[/tex]
HELP PLEASE 40 Points both questions please
6. It's B. x2+y2=25
9. (x + 3)² + (y – 2)² = 25
Hope this helps since this is solved by a 10-year old girl, me.
Write an expression to represent the perimeter of the figure below. Simplify. pls helpp
Step-by-step explanation:
perimeter of a rectangle is 2(length + width)
p= 2[ (2x -3) + (x+2 )]
combines like terms
p = 2 ( 3x -1 )
p = 6x -2
1. What number will make this expression a perfect square trinomial? Show your work. x2 - 6x +
Answer:
.......
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Take half of b (6/2=3)
Square it (3^2=9)
What is the volume, in cubic centimeters, of a cube with an edge length of 15 centimeters?
Answer:
3375cm
Step-by-step explanation:
because it is asking for volume it is cubed
wich 15 x 15 x 15 3 times equals volume of cube hope that makes sense
A shipment of sugar fills 8 containers. If each container holds 2 1/6 tons of sugar, what is the amount of sugar in the entire shipment?
Answer:
17 1/3 tons of suger
Step-by-step explanation:
2 1/6 * 8 = 17 2/6 or 17 1/3
A competitive cliff diver jumps into
water 81 feet below. The distance d that the diver falls
in t seconds is given by the equation d = 16t^2. How
long does it take the diver to hit the water?
Answer:
2.25 seconds
Step-by-step explanation
[tex]d=16t^{2}[/tex]
[tex]d=81 feet\\t=?[/tex]
Because you know what distance equals you can plug it into the equation
[tex]81=16t^{2}[/tex]
From there you can solve by dividing the 16 over and then square rooting.
[tex]\frac{81}{16}=t^{2}[/tex]
[tex]5.0625=t^{2}[/tex]
You take the square-root to get rid of [tex]t^{2}[/tex]
[tex]\sqrt{5.0625} =\sqrt{t}^{2}[/tex]
[tex]t=2.25[/tex]
Find the surface area of the regular pyramid.
help TvT
If you invested $2000 in an account that paid 8% annual interest compounded quarterly, how much would the account be worth in 10 years?
Answer:
4,317.85
Step-by-step explanation:
Answer:
$1600
Step-by-step explanation:
8 = 0.08% Turn the percent to a decimal
2000 / 0.08 = 160 Divide it by 2000
160 * 10 = 1600 Mutiply by 10
Have a good day
The midpoint of AB is M(1,-2). If the coordinates of A are (-3, -8), what are the coordinates of B?
9514 1404 393
Answer:
B(5, 4)
Step-by-step explanation:
The midpoint formula is ...
M = (A +B)/2
Solving for B gives ...
B = 2M -A
B = 2(1, -2) -(-3, -8) = (2+3, -4+8) = (5, 4)
The coordinates of B are (5, 4).
Expand 68*104.........
Answer:
7072
Step-by-step explanation:
I’ll mark you if you get the right answer and I have another problem so if you can find it pls help!
Answer:
D
Step-by-step explanation:
1/2 * 3/4 equals 0.375 which is less than .5
.5= 1/2
so therefore, im right i guess.
The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 33 who smoke. Step 1 of 2: Suppose a sample of 1267 Americans over 33 is drawn. Of these people, 913 don't smoke. Using the data, estimate the proportion of Americans over 33 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The estimate for the proportion of Americans over 33 who smoke is 0.28.
Step-by-step explanation:
Proportion of Americans over 33 who smoke.
Number who smoke divided by the size of the sample.
In this question:
Sample of 1267.
913 don't smoke, so 1267 - 913 = 354 smoke. Then
[tex]p = \frac{354}{1267} = 0.28[/tex]
The estimate for the proportion of Americans over 33 who smoke is 0.28.
answer this please thanks
Answer:
4. c
6. e, a
Step-by-step explanation:
Hopefully, it correct
Need help plzzzzzzzzzzxx
9514 1404 393
Answer:
(a) 15/17
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the cosine relation:
Cos = Adjacent/Hypotenuse
cos(P) = PQ/PR
cos(P) = 15/17