Answer:
The critical value is [tex]T = 4.604[/tex].
The 99% confidence interval for the average net change in a student's score after completing the course is (6.236, 22.164).
Step-by-step explanation:
The first step to solve this question is finding the sample mean and sample standard deviation:
14,11,18,9,19
Sample mean is sum of all values divided by the number of values. Thus:
[tex]\overline{x} = \frac{14+11+18+9+19}{5} = 14.2[/tex]
The sample standard deviation is the square root of the division of the sum of the subtractions squared of each value and the mean, and the number of values. Thus:
[tex]s = \sqrt{\frac{(14-14.2)^2+(11-14.2)^2+(18-14.2)^2+(9-14.2)^2+(19-14.2)^2}{5}} = 3.868[/tex]
Confidence interval:
We have the standard deviation for the sample, and so we use the t-distribution to build the confidence interval.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 5 - 1 = 4
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 4.604.
The critical value is [tex]T = 4.604[/tex].
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 4.604\frac{3.868}{\sqrt{5}} = 7.964[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 14.2 - 7.964 = 6.236.
The upper end of the interval is the sample mean added to M. So it is 14.2 + 7.964 = 22.164.
The 99% confidence interval for the average net change in a student's score after completing the course is (6.236, 22.164).
James drove 29 hours at a rate of 65 mph. How many miles did he drive?
what time is seven to eight
A consumer group claims that the average annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds. You believe it is higher. You take a simple random sample of 35 people in the U.S. and find an average of 53.8 pounds with a standard deviation of 4.4 pounds. Test at 1% significance. Round to the fourth
Answer:
[tex]6.7159[/tex]
Step-by-step explanation:
[tex]\mu=48.8\\n=35\\\bar{x}=53.8\\\sigma=4.4\\\alpha=1\%=0.01[/tex]
Null and alternative hypothesis :
[tex]H_0:\mu=48.8\\H_a:\mu>48.8[/tex]
Test statistic,
[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]\Rightarrow t=\frac{53.8-48.8}{\frac{4.4}{\sqrt{35}}}[/tex]
[tex]\Rightarrow t=\frac{5\times 5.91}{4.4}[/tex]
[tex]\Rightarrow t=6.715[/tex]
Test statistic [tex]t=6.715[/tex]
[tex]P-[/tex]value [tex]=P(t>6.715)[/tex]
[tex]P-[/tex] value [tex]=0.0001[/tex] by the p- table
Significance level [tex]0.01[/tex]
[tex]p-[/tex]value [tex]<0.01[/tex]
We reject [tex]H_0[/tex]
guys help me
can u give me the answer
Answer:
A factor, in mathematics, a number or algebraic expression that divides another number or expression evenly, with no remainder. A multiple of a number is any integer multiplied by the number. Try it yourself, now you know the how it works.
Find the diameter of the object 3/5
Answer:
6/5 cm
Step-by-step explanation:
Double the radius
2*3/5=6/5
Answer:
1 1/5 or 6/5
Step-by-step explanation:
3/5 (2) = 6/5 or 1 1/5
Give reasons why teachers use measures of variability i
n examination analysis
Answer:
The range is the simplest measure of variability to compute. The standard deviation can be an effective tool for teachers. The standarddeviation can be useful in analyzing class room test results. A large standarddeviation might tell a teacher the class grades were spead a great distance from the mean.Step-by-step explanation:
PLEASE MARK ME BRAINLIEST AND FOLLOW ME LOTS OF LOVE FROM MY HEART'AND SOUL DARLING TEJASVINI SINHA HERE ❤️17x+15= 66 then what is the value of x
Milan fills an aquarium to a depth of 3/8 meters in 6 minutes.
What is the unit rate in minutes per meter?
Answer:
1/16m per minute
Step-by-step explanation:
If Milan fills the aquarium to a depth of 3/8 in 6 minutes then just divide 3/8 by 6 to find how much she fills in 1 minute
What two numbers have a product of -36 and sum of -9
Answer:-12 and -25
Step-by-step explanation:
Answer: 3 and -12
Step-by-step explanation:
I used this
www.calculatorsoup.com/calculators/math/diamond-problem-solver.php
Phone bills from the residents of the city have a mean of $64 and a standard deviation of $9. Random samples of 100 phone bills are drawn from this
population. Find the mean and standard error of the sampling distribution.
O mean is 6.4: standard error is 9
O mean is 64; standard error is 9
O mean is 6.4: standard error is.9
O mean is 64: standard error is.9
Answer:
Mean of 64 and standard error of 0.9.
Step-by-step explanation:
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.
Phone bills from the residents of the city have a mean of $64 and a standard deviation of $9. Sample of 10.
By the Central Limit Theorem, the mean is 64 and the standard error is [tex]s = \frac{9}{\sqrt{100}} = \frac{9}{10} = 0.9[/tex]
So mean of 64 and standard error of 0.9.
Find a polynomial equation that has roots of -2 and double root 3
Answer:
x³ + 2x² -3x +6
Step-by-step explanation:
We need to find the polynomial whose roots are ,
-2 , √3 and √3.Say of we have zeroes as , α , β and γ , then the polynomial is ,
=> p(x) = k[ (x - α ) ( x - β) ( x - γ) ]
where k is constant. Substituting the respective values , we have ,=> p(x) = k [ ( x - (-2)) ( x - √3) ( x -√3)]
=> p(x) = k[ (x+2)(x² - 3)]
=> p(x) = k[ x(x² - 3) + 2(x² - 3) ]
=> p(x) = k[ x³ - 3x + 2x² - 6 ]
=> p(x) = k[ x³ + 2x² - 3x - 6 ]
Hence the cubic polynomial is x³ + 2x² - 3x + 6 .HELP JIMTHOMPSON5910
I'll do the first three problems (numbers 15 through 17) to get you started.
===================================================
Problem 15
Answer: 21.98--------------------
Explanation:
We cut the diameter in half to get the radius. We can think of cutting the 14 in half to get 7, ignoring the pi while we cut in half. Then after we do that, we tack the pi back on.
In short, 14pi cuts in half to 7pi.
Then we could see that 7*pi = 7*3.14 = 21.98
The radius is about 21.98 inches.
===================================================
Problem 16
Answer: 78.5--------------------
Explanation:
We'll plug r = 5 into the area of a circle formula.
A = pi*r^2
A = 3.14*5^2
A = 78.5 square yards approximately
===================================================
Problem 17
Answer: 6--------------------
Explanation:
We'll use the formula
C = pi*d
which is the formula that ties together the circumference C with the diameter d.
Plug in the given circumference C = 12pi and isolate d
C = pi*d
12pi = pi*d
12 = d .... divided both sides by pi, which cancels out
d = 12
The diameter is 12. Your step by step picture doesn't have to be this wordy, but I'm doing this to help show that the circumference like 12pi simply has the "pi" part erased to get the diameter. This allows a reader to quickly spot the diameter if given the circumference in this form. And it also allows to go from the diameter to the exact circumference without any calculator involved.
Once you get the diameter, you cut it in half to get the radius. Half of 12 is 6, so the radius is 6 cm.
------------
You could also have this as your steps
C = 2*pi*r
12pi = 2*pi*r
12 = 2r
2r = 12
r = 12/2
r = 6
which is an alternative way to see that the radius is 6 cm.
3. The function c(d) = 50 – 2.5d represents
how much money have in my cafeteria
account, c, after d days of eating lunch in
the cafeteria. Evaluate c(10) and interpret
its meaning
Answer:
c(10) is 25 which means there is a balance of $25 in cafe account after 10 days
Step-by-step explanation:
c(10) = 50 - 2.5(10)
c(10) = 50 - 25 which is 25
Two boys work to earn money
Brendon earns $72 in 6 hours mowing lawns.
Casey earns $80 in 8 hours pet sitting
One week the boys worked the same number of hours. the difference in their earnings that week was $24
how many hours did the boys work that week?
A boy is flying a kite. The length of the string is 20 meters and the horizontal distance between the boy and the kite is 15 meters. Assuming there is no slack in the string, find the height of the kite from the ground.
A.
B.
C.
D.
Answer:
5√(7)m or 13.23m
Step-by-step explanation:
use pythagorean theorem
a²+b²=c²
c=20
b=15
a²+225=400
a²=175
√(175) = 5√(7) = 13.23
The height of the kite is 13.23 meters.
What is Pythagoras' theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
A boy is flying a kite.
The length of the string is 20 meters and the horizontal distance between the boy and the kite is 15 meters.
Assuming there is no slack in the string,
then the height of the kite is,
= √(20)² - (15)²
= 13.23 feet.
Therefore, the height is 13.23 meters.
To learn more about the Pythagoras theorem;
https://brainly.com/question/343682
#SPJ2
(3 marks) A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year. The battery lives are assumed normally distributed. (a) What is the probability that a given battery will last between 2.3 and 3.6 years
Answer:
0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years
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.
A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year
This means that [tex]\mu = 3, \sigma = 0.5[/tex]
What is the probability that a given battery will last between 2.3 and 3.6 years?
This is the p-value of Z when X = 3.6 subtracted by the p-value of Z when X = 2.3. So
X = 3.6
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.6 - 3}{0.5}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a p-value of 0.8849
X = 2.3
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.3 - 3}{0.5}[/tex]
[tex]Z = -1.4[/tex]
[tex]Z = -1.4[/tex] has a p-value of 0.0808
0.8849 - 0.0808 = 0.8041
0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years
Please help fast........
Answer:
b
Step-by-step explanation:
It’s my final and I haven’t paid attention
Answer:
f(x)= (1/2)x-3
Step-by-step explanation:
Plz help ASAP plz help ASAP
Answer:
4 is f and 5 is t
Step-by-step explanation:
Answer:
number 4 is true
number 5 is false
hope it helps :)
A square has an area of 196 square centimeters. What is the length of each side?
Answer:
The answer is simply 49.
Step-by-step explanation:
196 ÷ 4 is why because their are 4 sides on a square if you divide it by 4 you get the answer 49. You're probably in like 3rd grade or smth this is so easy.
A Labrador retriever club has 130 members: 65 black Labs, 44 golden Labs, and 21 chocolate Labs. Pablo is going to perform a chi-square goodness-of-fit test to see if the distribution of Labrador retrievers in the club is the same as the distribution nationally. Pablo is going to test his sample against the following null hypothesis, which reflects the national distribution.If the distribution of Labrador retrievers in the club were to match that of the national average, how many of each type of Labrador retriever would Pablo expect to see in his club?
Answer:
Step-by-step explanation:
Ap classroom
Mahad and Eren made 17 ounces of pizza dough. They used 5/8 of the dough to make a pizza and used the rest to make calzones.
What is the difference between the amount of dough they used to make pizza and the amount of dough they used to make calzones?
A) 6 3/8 ounces
B) 4 2/8 ounces
C) 10 5/8 ounces
D) 17 5/8 ounces
Explain how you know.
9514 1404 393
Answer:
B) 4 2/8 ounces
Step-by-step explanation:
After 5/8 of the dough was used for pizza, the remaining amount is ...
1 -5/8 = 3/8
The difference between the amounts is then ...
(5/8×17 oz) - (3/8×17 oz) = (5/8 -3/8)×17 oz = 2/8×17 oz = 34/8 oz
= 4 2/8 oz
HELP ME PLEASEEEEEEEEEEEEEEEEEEE
daniel’s print shop purchased a new printer for 35,000 each year it depreciates at a rate of 5% how much will the printer be worth in 8 years
Answer:
$23,219.72
Step-by-step explanation:
ab^x
a: initial value
b: value remaining after depreciation per year (in percentage)
x: number of years that have passed
35000(0.95)^8= 23219.7151
Round to the nearest hundredth value:
About $23219.72
Prove <4 and <1 are supplementary.
Answer:
the = 180
Step-by-step explanation:
Answer:
proof:
Triangle is isosceles, so angle 4 and 5 are equal
Angle 5 + Angle 1 = 180°
Angle 4+ Angle 1 = 180°
Step-by-step explanation:
<4 ≅ <5. <5 + <1 = 180° <4 + <1 are supplementary
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Add.
(-8y2 + 7y? - 4y - 6) + (3y + 5y3)
us.
Answer:
3y²+4y²-4y-6
Step-by-step explanation:
If 2^2x = 2^3, what is the value of x?
Answer:
x = 3/2
Step-by-step explanation:
2^2x = 2^3
2x = 3
x = 3/2
PLZ ANSWER WORTH 20 POINTS!! URGENT!
A set of equations is given below: Equation C: y = 3x + 7 Equation D: y = 3x + 2 Which of the following best describes the number of solutions to the given set of equations? (1 point) A. One solution B. Two solutions C. Many solutions D. No solution
Answer:
D. No solution
Step-by-step explanation:
Given
[tex]y = 3x + 7[/tex]
[tex]y = 3x + 2[/tex]
Required
The number of solutions
We have:
[tex]y = 3x + 7[/tex] and [tex]y = 3x + 2[/tex]
Equate both i.e.
[tex]y = y[/tex]
So, we have:
[tex]3x + 7 = 3x + 2[/tex]
Subtract 3x from both sides
[tex]3x -3x + 7 = 3x -3x + 2[/tex]
[tex]7 = 2[/tex]
The above is false
i.e. [tex]7 \ne 2[/tex]
Hence, the system has no solution
Amy and Ebony are shopping. Amy has $93. Together, Amy and Ebony have less than $191. If x represents the amount of money Ebony has, which of the following inequalities represents this information?
A.
$191 + x < $93
B.
$93 + x < $191
C.
x - $93 < $191
D.
$93 + x > $191
Answer:
d
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Since their sum is less the sign will be: sum < $191
This eliminates A and D
It's not C because their money is additive, not subtractive
So it's B, $93+x < $191
For the polyhedron, use Euler's Formula to find the missing number.
faces:
edges: 11
vertices: 6
The number of faces is