Answer: The required sample size = 97
Step-by-step explanation:
If prior population standard deviation is known, then the minimum sample size can be computed as:
[tex]n=(\frac{z^*\times\sigma}{E})^2[/tex]
,where z* = critical z-value
[tex]\sigma[/tex] = population standard deviation
E = Margin of error
As per given,
[tex]\sigma=20,\ E= 4[/tex]
Critical value for 95% confidence = 1.96
[tex]n=(\frac{1.96\times20}{4})^2\\= (1.96\times 5)^2\\= (9.8)^2\\=96.04\approx97[/tex]
Hence, the required sample size = 97
15 POINTS. Ronna is estimating the amount of a 15% tip for a $20.36 bill. Her friend Suri said that $2 is a good estimate. Do you agree? Explain.
Hi
It's not a good estimation. 2 is 10% of 20, so 5% is 1 dollar.
As the bill is above 20, and 15 = 10+5 , so 15% is at least more than 3.
So 3 would be a better estimation.
In fact, 15% of 20.36 is : 20.36 *0.15 = 3.054
In a math class with 20 students, a test was given the same day that an assignment was due. There were 11 students who passed the test and 15 students who completed the assignment. There were 9 students who passed the test and also completed the assignment. What is the probability that a student chosen randomly from the class failed the test and did not complete the homework?
Answer: 3/20 or .15
Step-by-step explanation:
For the function f(x) = 7/2x-16, what is the difference quotient for all nonzero values of h?
Answer:
[tex]\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{7}{2}x - 16[/tex]
Required
The difference quotient for h
The difference quotient is calculated as:
[tex]\frac{f(x + h) - f(x)}{ h}[/tex]
Calculate f(x + h)
[tex]f(x) = \frac{7}{2}x - 16[/tex]
[tex]f(x+h) = \frac{7}{2}(x+h) - 16[/tex]
[tex]f(x+h) = \frac{7}{2}x+ \frac{7}{2}h- 16[/tex]
The numerator of [tex]\frac{f(x + h) - f(x)}{ h}[/tex] is:
[tex]f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -(\frac{7}{2}x - 16)[/tex]
[tex]f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -\frac{7}{2}x + 16[/tex]
Collect like terms
[tex]f(x + h) - f(x) = \frac{7}{2}x -\frac{7}{2}x + \frac{7}{2}h- 16 + 16[/tex]
[tex]f(x + h) - f(x) = \frac{7}{2}h[/tex]
So, we have:
[tex]\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h \div h[/tex]
Rewrite as:
[tex]\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h * \frac{1}{h}[/tex]
[tex]\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}[/tex]
Answer:
It is A.
Step-by-step explanation:
Just took the test
Find the simple interest on an investment of $3500 for 2.5 years at
5.5% per annum.
$428.52
$482.52
$418.25
$481.25
Answer:
$481.25
Step-by-step explanation:
The formula for simple interest is i = p*r*t, in which p is the principal, r is the interest rate as a decimal fraction, and t is the time in years.
Here p = $3500, r = 0.055 and t =2.5 yrs, and so the simple interest is
i = ($3500.00)(0.055)(2.5 yr), or
i = $481.25
can anyone help me with this?
Answer:
120 degrees is x
Step-by-step explanation:
because both are equal angles
btw nice Pikachu meme
Brody deposited $500 into an account that earns 4.2% interest compounded annually. He makes no additional deposits and no withdrawals. How much interest will the account have earned after 7 years?
A $167
B $420
C $542
D $665
Explain correctly. No nonsense, please.
Thank you
Which numbers are irrational? Select all that apply.
Answer:
I believe Option 1, 2 and 4 are all irrational numbers Hope this helps
Step-by-step explanation:
If anyone could help it would be great
Answer:
See the pictureStep-by-step explanation:
Solved, green filled arrows in the picturethere are 420 students in a school 1/3 if the population is made up of girl
Round 893.38 to the nearest tenth
PLEASEEEEEE IM BEGGING SOMEONE PLEASEEEE HELPPPP PLEASEEEEE PLEASEEEEE SOEMONE HELPPPP PLEASEEEEEEEEEEEEEEEEEEEE
Answer:
8 nachos and 5 hot dogs
Step-by-step explanation:
Let x equal number of nachos
let y equal number of how dogs
1.5x + 2y = 22
x + y = 13
y = 13 - x
1.5x + 2(13 - x) = 22
1.5x + 26 - 2x = 22
1.5x - 2x = 22 - 26
-0.5x = - 4
x = -4/-0.5
x = 8
y = 13 - x
y = 13 - 8
y = 5
Please help meeeeeeee
Answer:
5040
Step-by-step explanation:
This is a problem of permutation where one has to arrange all the letters of the word taken all at a time. Since in N lettered word if all the letters are different then it can be arranged in N! ways i.e factorial N ways.
In the problem mentioned given
Word : Musical
number of words = 7 (all the words are different)
Number of ways to arrange it = 7!
7*6*5*4*3*2*1 = 5040
Hence 5040 is the answer!
II. Write whether each number is an EXPRESSION or an EQUATION.
11.
2 + 5
12.
2 + 5 = 7
Ć XLN13.
4x = 12
14.
X + 25
15.
16-6 = 10
Answer:
11. Expression
12. Equation
13. Equation
14. Expression
15. Equation
Step-by-step explanation:
Expression:
Has no equal sign.
Equation:
Has equal sign.
11. 2 + 5
14. X + 25
Those which do not have the equal sign are expressions.
12. 2 + 5 = 7
13. 4x = 12
15. 16 - 6 = 10
Those with the equal sign are equations.
y is directly proportional ( x+2)²
when x = 8 y= 250
find y when x = 4
Answer:
y=90 when x=4
Step-by-step explanation:
We are given that
[tex]y\propto (x+2)^2[/tex]
When x=8 and y=250
We have to find the value of y when x=4
[tex]y=k(x+2)^2[/tex]
Where k= Proportionality constant
Substitute the values
[tex]250=k(8+2)^2[/tex]
[tex]250=100k[/tex]
[tex]k=\frac{250}{100}[/tex]
[tex]k=5/2[/tex]
Now, substitute x=4 and k=5/2
Then, we get
[tex]y=\frac{5}{2}(4+2)^2[/tex]
[tex]y=\frac{5}{2}\times 36[/tex]
[tex]y=90[/tex]
If you know how to solve this, Please answer it. Thank You
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
y = ( x + 9 )^2 - 2
................................
................................
evaluate -5/z for z=5
Answer:-5/z ; z=5 solution -1
Step-by-step explanation:
-5/5
Problem Solving
Find the exact solution of each equation for 0 and greater than or equal to q and less than 2pi.
4 cos^2q=3
Of the men in the survey, what percent of them prefer movies? Write your answer as a percent and round to one decimal place.
Answer:
40%Step-by-step explanation:
There are 20 men and 8 of them prefer movies.
P = 8/20 = 0.4 = 40%
The distance from Kevin's home to his school is 2 kilometers. Adrian lives 750
meters from the same school. How much closer does Adrian live to school than
Kevin?
1>) 250 meters
1>) 550 meters
» 1,250 meters
2,750 meters
Answer:
see my explanation!!
Step-by-step explanation:
2000-750=1250m
A boy collects a total of 316 stamps, sticker and coins altogether. He collects 4 times as many stamps as stickers. There are 46 coins. How many stamps are there?
Answer:
216 stamps
Step-by-step explanation:
Stamps =4x
stickers=x
coins=46
4x+x+46=316 (stamps, stickers and coins)
5x=270
x=54 (stickers)
4x=stamps
4(54)=stamps
216=stamps
check answer
54 (stickers)+216(stamps)+46 (coins)=316
316=316
PLEASE HELP (failing this class and this is a 100 point assignment) (i mark brainlist)
Help me on this question please. Thx
Need help with this math question 15 points
A desktop is shaped like a semicircle with a diameter of 28 what is the area of the desktop?
Answer:
307.72
Step-by-step explanation:
if the diameter is 28 then the radius is 14 (half of the diameter)
Questions
The distances covered by each of two runners during the first 21 minutes of a race are
shown in the graph below. The time at which one runner passes the other is between
(A 2 minutes and 3 minutes
(B 6 minutes and 9 minutes
(C 9 minutes and 12 minutes
(D 18 minutes and 21 minutes
Answer: 9 minutes and 12 minutes
Step-by-step explanation:
The weight of laboratory grasshoppers follows a Normal distribution, with a mean of 90 grams and a standard deviation of 2 grams. What percentage of the grasshoppers weigh between 86 grams and 94 grams
Answer:
95.44% of the grasshoppers weigh between 86 grams and 94 grams.
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.
Mean of 90 grams and a standard deviation of 2 grams.
This means that [tex]\mu = 90, \sigma = 2[/tex]
What percentage of the grasshoppers weigh between 86 grams and 94 grams?
The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 86. So
X = 94
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{94 - 90}{2}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
X = 86
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{86 - 90}{2}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544*100% = 95.44%
95.44% of the grasshoppers weigh between 86 grams and 94 grams.
QUICK!! GIVING BRAINLIEST TO CORRECT ANSWER QUICK!!
Answer:
Im fairly sure it is 45ft^3
Answer:
[tex]45ft^{2}[/tex]
Step-by-step explanation:
V=L*W*H
Can someone please help and explain how to use the Pythagorean Theorem to prove a triangle is a right triangle.
Hi there!
For the Pythagorean Theorem, basically you just need to apply this formula: a^2 + b^2 = c^2
And then find the root of the hypotenuse.
For example,
15^2 + 8^2 = the hypotenuse^2
Which equals, 225 + 64 = 289
Square root of 289 = 17
Please mark me brainliest if this helps!
Have a wonderful day!
pls help!! Need the answer asap!!
Step-by-step explanation:
19+k=90°
k=90-17
k=71°
stay safe healthy and happy .Which factorization is equivalent to this expression?
−20x − 5y
Answer:
[tex] - 20x - 5y \\ - (20x + 5y) \\ = - 5(4x + y)[/tex]