How large a sample should be selected to provide a 95 confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.

Answer:

Area = 64 cm²

Step-by-step explanation:

To find the area, we have to follow some steps:

=> Step 1: Make the bases similar:

Since we have 2 bases given 6 and 10 we have to come up with a third base by finding their average:

(6 + 10) / 2

(16) / 2

8

So now that we know our base,

=> Our second step is to multiply the base we found by the height of the trapezoid:

Area = common base * height

Area = 8 * 8

Area = 64 cm²

Hope this helps!

Answer:

2e = c

Step-by-step explanation:

Let :

Egg = e

Cookies = c

2 eggs for every 1 dozen of cookies

This gives the Mathematical expression :

2 eggs = 1 c

2e = c

Answer:

50% or 1/2

Step-by-step explanation:

A coin has 2 sides so 100/2 equals 50 so either 50% or 1/2. There is your answer

Answer:

[tex]f(x) = x^3 +5x^2-4x-20[/tex]

Step-by-step explanation:

Given

[tex]Zeros: -5,-2,2[/tex]

Required

The polynomial function

If a function has a, b and c as its zeros, the function is:

[tex]f(x) = (x - a)(x - b)(x - c)[/tex]

So, we have:

[tex]Zeros: -5,-2,2[/tex]

[tex]f(x) = (x - (-5))(x - (-2))(x - 2)[/tex]

Open the inner brackets

[tex]f(x) = (x +5)(x +2)(x - 2)[/tex]

Expand the difference of two squares

[tex]f(x) = (x +5)(x^2 - 4)[/tex]

Expand

[tex]f(x) = x^3 +5x^2-4x-20[/tex]

Answer:

5. m<A = 25.3°; m<B = 64.7°

6. m<A = 40.2°; m<B = 49.8°

Step-by-step explanation:

Recall: SOHCAHTOA

5. Reference angle = <A

Opposite = 9

Adjacent = 19

Apply TOA:

Tan A = Opp/Adj

Tan A = 9/19

A = Tan^{-1}(9/19)

A = 25.3461759° ≈ 25.3° (nearest tenth)

Reference angle = <B

Opposite = 19

Adjacent = 9

Apply TOA:

Tan B = Opp/Adj

Tan B = 19/9

B = Tan^{-1}(19/9)

B = 64.6538241° ≈ 64.7° (nearest tenth)

6. Reference angle = A

Opposite = 20

Hypotenuse = 31

Apply SOH:

Sin A = Opp/Hyp

Sin A = 20/31

A = sin^{-1}(20/31)

A = 40.2° (nearest tenth)

Reference angle = B

Adjacent = 20

Hypotenuse = 31

Apply CAH:

Cos B = Adj/Hyp

Cos B = 20/31

B = cos^{-1}(20/31)

B = 49.8° (nearest tenth)

Answer:

n > 4 I think is the answer, I'm not 100% sure

Answer:

n<1/4

Step-by-step explanation:

4<n Sub n on both sides

4n<0 Divide by 4 on both sides

n<1/4

Answer:

The solution is [tex]x = -\frac{5}{6}[/tex]

Step-by-step explanation:

We solve this question using exponential properties.

We have that:

[tex](\frac{25}{4})^{3x} = \frac{32}{3125}[/tex]

Simplifying:

[tex](\frac{5^2}{2^2})^{3x} = \frac{2^5}{5^5}[/tex]

[tex]([\frac{5}{2}]^{2})^{3x} = (\frac{2}{5})^{5}[/tex]

[tex](\frac{5}{2})^{6x} = (\frac{2}{5})^{5}[/tex]

Changing the numerator and denominator in the right side:

[tex](\frac{5}{2})^{6x} = (\frac{5}{2})^{-5}[/tex]

Since both bases are equal:

[tex]6x = -5[/tex]

[tex]x = -\frac{5}{6}[/tex]

The solution is [tex]x = -\frac{5}{6}[/tex]

Answer: y>-2 (The symbol has a underline)

Step-by-step explanation:

Since you want to move -4 to the -6 spot, do the opposite of the negative which is positive. So add +4 to each side. And the -4 will disappear and you will be left with y>-6+4. Solve -6+4= -2 And so the answer is y>-2.

Hope this helps

Answer:

x^2(x-5)

Step-by-step explanation:

f(x)=x-5

g(x)=x^2

g(f(x)=?

x^2(f(x)=?

x^2(x-5)

If this helps please mark as brainliest

9514 1404 393

Answer:

  D.  (x -5)²

Step-by-step explanation:

Replace the variable with the function argument.

  G(F(x)) = G(x -5) = (x -5)² . . . . . matches choice D

9514 1404 393

Answer:

  160°

Step-by-step explanation:

The path is a triangle with side lengths 796, 1054, and 411 meters. The turn is opposite the short side. The interior angle of the triangle at that point can be computed using the law of cosines. If we label the sides a, b, c, respectively, then ...

  c² = a² + b² - 2ab·cos(C)

  C = arccos((a² +b² -c²)/(2ab)) = arccos(1575611/1677968) ≈ 20.116°

The external angle at the buoy is 180° -20° = 160°.

The jet skier's turn was about 160°.

Answer:

A

Step-by-step explanation:

where the graph

WHERE THE GRAPH???

Answer:

0

Step-by-step explanation:

Coolin

Answer:

73 Papers

Step-by-step explanation:

Let's start by finding out how many papers Mrs. Thiel has already graded.

56 + 49 = 105

Now, let's subtract how many papers she has already graded from how many she has to grade in total.

178 - 105 = 73

So, Mrs. Thiel has to grade 73 papers this evening.

Answer:

[tex]B. ~(f+g)(x)=6x^3+4x-2[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2+4x-5[/tex]

[tex]g(x)=6x^3-2x^2+3[/tex]

[tex]Find~(f+g)(x)[/tex]

[tex]=2x^2+4x-5+6x^3[/tex]

[tex]-2x^2+3[/tex]

[tex](f+g)(x)=6x^3+4x-2[/tex]

--------------------------------

hope it helps....

have a great day!!

Answer:

sin49= 0.7

Step-by-step explanation:

Answer:

a) 0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.

b) 369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.

c) Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

A result is considered significantly high if it is more than 2.5 standard deviations above the mean.

Normal probability distribution

Problems of normally distributed distributions can be 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Assume that 24.5% of people have sleepwalked.

This means that [tex]p = 0.245[/tex]

Sample of 1478 adults:

This means that [tex]n = 1478[/tex]

Mean and standard deviation:

[tex]\mu = 1478*0.245 = 362.11[/tex]

[tex]\sigma = \sqrt{1478*0.245*0.755} = 16.5346[/tex]

a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.

Using continuity correction, this is [tex]P(X \geq 369 - 0.5) = P(X \geq 368.5)[/tex], which is 1 subtracted by the p-value of Z when X = 368.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{368.5 - 362.11}{16.5346}[/tex]

[tex]Z = 0.39[/tex]

[tex]Z = 0.39[/tex] has a p-value of 0.6517

1 - 0.6517 = 0.3483

0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.

b. Is that result of 369 or more significantly high?

362.11 + 2.5*16.5346 = 403.4

369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.

c. What does the result suggest about the rate of 24.5%?

Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.

Answer: 6x+6

Step-by-step explanation:

3*2x=6x

3*2=6

Therefore 3(2x+2) = 6x+6

Step-by-step explanation:

-4y+5>-15

-4y>-15-5

-4y>-20

divide both (-)

4y>20

divide through by 4

y>20/4

y>5

Answer:

I got 6.

Step-by-step explanation:

I picked my number to be 3. I took away 1 to make it 2. I then multiplied 2 by 3, to get 6.

Answer:

We reject H₀.  We support that the new average credit card debt is bigger than the previous average

Step-by-step explanation:

Five years earlier

μ   = 8189

σ  =  690

Sample size   n  = 32

Recent year debt

x  =  8776

Sample size   n  = 32

a) Hypothesis Test:

Null Hypothesis                        H₀            x  =  μ   = 8189

Alternative Hypothesis           Hₐ             x >  μ

b) z(c)  Alternative Hypothesis establishes that the test is a one tail-test to the right.

z(c)   for significance level  α = 0.05    is  from z-table      z(c) = 1,64

c) z(s)  =  (  x  -   μ ) / σ /√n

z(s)  =  ( 8776  - 8189 ) / 690 /√32

z(s)  =  587 *5,66/ 690

z(s) = 4,81

d) Comparing   z(c)    and z(s)

z(s)  >  z(c)   Then z(c) is in the rejection region and we reject H₀

e) We have evidence that at 95 % of confidence the new value for the debt in credit card is now bigger than the average

Answer:

you need to post a pic with it.

Step-by-step explanation:

115

Answer:

Hello, it appears you did not provide an image that was supposed to be included in order to help answer your question, so I'm afraid I cannot assist you without seeing it. If you supply the necessary photo, I would be more than happy to help you.

Answer:

0.01

Step-by-step explanation:

The probability of making a Type I error is equal to  \alphaα = 0.01, the significance level of the test

The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

An orange juice manufacturer advertises a new orange juice product that contains 50% less sugar.

An inspector wants to investigate whether the actual percentage of water in the product is within 5% of the intended 50%.

He plans to conduct a significance test at a = 0.01 level to see if there is convincing evidence that the proportion of water added is different from 0.50.

Type I error is referred to as false positives and it means that when a statistically significant difference is validated by the researcher even though the results aren't statistically significant.

Type I error is when one rejects the null hypothesis even though it's true. In this case, the inspector rejects the hypothesis that the proportion of water that is contained in the product is 0.5.

The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.

Learn more about probability here;

https://brainly.com/question/11234923

#SPJ2

Answer:

= 15x^9/10

Step-by-step explanation:

Multiply the numbers: 3 . 5 = 15

= 15x^1/2x2/5

Apply exponent rule: a^b . A^c = a^b + c

= 15x^1/2+2/5

1/2 + 2/5 = 9/10

= 15x^9/10

Answer:

(5, 8)

Step-by-step explanation:

(5. – 5) down 3 units => (5, -8)

reflect x-axis => (5 , 8)

Answer:

15.46

Step-by-step explanation:

Answer:

15.46

Step-by-step explanation: if this isnt it im sory

Answer:

Hello!

16

Step-by-step explanation:

Because

-5+16=11

Answer:

If y - 4 = 5 then:

y = 5 + 4

y = 9