Andrea and Helen participated in a donut eating contest. Andrea ate six more than four times the number of donuts that Helen ate. Let d represents the number of donuts Helen ate. Write the expression that gives the number of donuts that Andrea ate.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

How large of a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to be within $2,000? The population standard deviation is assumed to be $10,500. z-value for 98% confidence level is 2.326.

Answer:

Sample size = n = 150

Step-by-step explanation:

Recall that the margin of error is given by

[tex]$ MoE = z \cdot (\frac{\sigma}{\sqrt{n} } ) $\\\\[/tex]

Re-arranging for the sample size (n)

[tex]$ n = (\frac{z \cdot \sigma }{MoE})^{2} $[/tex]

Where z is the value of z-score corresponding to the 98% confidence level.

Since we want mean salary to be within $2,000, therefore, the margin of error is 2,000.

The z-score for a 98% confidence level is 2.326

So the required sample size is

[tex]n = (\frac{2.326 \cdot 10,500 }{2,000})^{2}\\\\n = (12.212)^{2}\\\\n = 149.13\\\\n = 150[/tex]

Therefore, we need to take a sample size of at least 150 state employees to estimate with 98% confidence the mean salary to be within $2,000.

Answer:

a) 26.33 kg/d and 29.67 kg/d

b) 94.5%

Step-by-step explanation:

a. Find a 99% confidence interval for the true mean milk production.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d

The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d

The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d

b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?

We need to find z initially, when M = 1.25.

[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]2.25z = 1.25\sqrt{12}[/tex]

[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]

[tex]z = 1.92[/tex]

When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.

1 - 2*(1 - 0.9725) = 0.945

So we should use a confidence level of 94.5%.

Answer:

[tex]x = 9\ or\ x = 1[/tex]

Step-by-step explanation:

Given

[tex]x = 5 + \sqrt{16}[/tex]

Required

Find the value of x

[tex]x = 5 + \sqrt{16}[/tex]

We start by taking the square root of 16; Square root of 16 is +4 or -4; So, we have:-

[tex]x = 5 \±4[/tex]

The expression above can be split into two; This is as follows

[tex]x = 5 + 4\ or\ x = 5 - 4[/tex]

[tex]x = 9\ or\ x = 1[/tex]

Hence, the solution to [tex]x = 5 + \sqrt{16}[/tex] is B. 1 and C. 9

Answer:

its b and c

Step-by-step explanation:

the guy who answered first said so

also i just did it

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

Answer:  x = -10

Step-by-step explanation:

see image

A) congruent sides implies congruent angles A = 64°

B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°

C) B and C are complimentary angles: 52° + C = 90°  --> C = 38°

D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180°  --> D = 71°

∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180°  --> ∠2 = 109°

Solve for x:

109° = x + 119

 -10  = x

Answer:

x = -10

Step-by-step explanation:

Find the measure of angle m∠2

The triangles are isosceles triangles, the base angles are equal.

The other base angle is also 64°.

Using Triangle Sum Theorem.

64 + 64 + y = 180

y = 52

The top angle is 52°.

The whole angle is 90°.

90 - 52 = 38

The second triangle has base angles equal.

Using Triangle Sum Theorem.

38 + z + z = 180

z = 71

The two base angles are 71°.

Angles on a straight line add up to 180°.

71 + m∠2 = 180

m∠2 = 109

The measure of m∠2 is 109°

Find the value of x

m∠2 = x + 119

109 = x + 119

x = 109 - 119

x = -10

Answer:

It's written as

[tex]89.7 \times {10}^{9} [/tex]

Or

[tex]8.97 \times {10}^{10} [/tex]

Hope this helps you

Answer:

8.97 * 10 ^10

Step-by-step explanation:

We want one nonzero digit to the left of the decimal

8.97

We moved the decimal 10 places to the left

The exponent is positive 10 since we moved 10 places to the left

8.97 * 10 ^10

Answer:

No

Step-by-step explanation:

If they were opposite, they would be equal.

But they are not, (on one of the spaces in between them is smaller and one is larger.)

Hope I have helped you, since it seems I haven't helped "other people" the last time :/

Answer:

No

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

Learn more about BODMAS rule here:

https://brainly.com/question/16738857

#SPJ4

Answer:

2317.44

Step-by-step explanation:

Solution for What is 408 percent of 568:

408 percent *568 =

(408:100)*568 =

(408*568):100 =

231744:100 = 2317.44

Answer:

2317.44

Step-by-step explanation:

Answer:

Answer C

Step-by-step explanation:

You are balancing this equation out by subtracting 7x from both sides. This means you are using the subtraction property of equality.

Answer:

3.025

Step-by-step explanation:

3.4-1/2(0.75)

3.4-0.375

3.025

The 4 angles need to add to 360.

2 of them are 70

The other two need to equal 360-140 = 220

They are both the same so one angle needs to equal 220/2 = 110

Now find x:

X + 60 = 110

Subtract 60 from both sides:

X = 50. The answer is D

Answer:

-3+(-5)

Checking our answer:

Adding this does indeed give -8

Answer:

3

Step-by-step explanation:

To begin with notice that  

        [tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]

From that equation you get that

10 tan(x)  +  30tan(x) cot(x) = 30

therefore

tan(x) + 3 tan(x) cot(x) = 3

Answer:

Step-by-step explanation:

y + 8 = 0(x - 0)

y + 8 = 0

y = -8

Answer:

48.3 cm²

Step-by-step explanation:

Let A be the area of the yellow region

A= the area of the square - the area of the quarter square

A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²

Answer:

20% jumped the turnstile

80% paid

Step-by-step explanation:

We can calculate the percent of people that jumped it by dividing the number that did by the total:

12/60 = 0.2, which is 20%

If 20% jumped it, then this means 80% paid.

Answer:

jumped= 20%

paid= 80%

Step-by-step explanation:

[tex]\frac{12}{60}[/tex]×100 = 20%

[tex]\frac{48}{60}[/tex]×100 = 80%

Answer:

12x/2 or 52/2

Step-by-step explanation:

Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.

u/4 - 4 = -20

Add 4 to both sides:

u/4 = -16

Multiply both sides by 4:

u = -64

Answer:

u=-64

Step-by-step explanation:

u/4 -4 = -20

First add 4 to both sides.

u/4=-16

Now multiply both sides by 4

u=-64

Answer:

2.26 repeating

Step-by-step explanation:

Convert the fraction to a decimal by dividing the numerator by the denominator.

hope this helpes

be sure to give brainliest

Answer:

segment I'm and segment ad

Answer:

The answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x(x + 3) + 6(x + 3)

The final answer is

( 5x + 6 ) ( x + 3 )

Hope this helps you

Answer:

d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle

Step-by-step explanation:

13 − 01 + 1 = 13

34 − 14 + 1 = 21

56 − 35 + 1 = 22

99 − 57 + 1 + 1 = 44

Answer:

(CX3)+10

Step-by-step explanation:

Answer:

c×3+10= j

Step-by-step explanation:

Answer:

Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]

Step-by-step explanation:

Ratio of the areas of the given circles are 1 : 4 : 16

Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]

                                                                             = 1 : 2 : 4

If the radius of the smallest circle = x units

Then the radius of the middle circle = 2x units

and the radius of the largest circle = 4x units

Area of the smallest circle = πx²

Area of the middle circle = π(2x)² = 4πx²

Area of the largest circle = π(4x)²= 16πx²

Area of the region which is not shaded in the middle circle = πx²(4 - 1)

                                                                                                  = 3πx²

Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded

= 16πx² - 3πx²

= 13πx²

Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]

= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]

= [tex]\frac{13}{16}[/tex]

Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  [tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]

Using the Pythagorean theorem

Hypotenuse = sqrt( 11^2 + 7^2)

= sqrt( 121 + 39)

= sqrt( 160)

= 12.694

Answer: [tex]2\sqrt{1+tant}+C[/tex]

Step-by-step explanation:

To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.

[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]

Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.

[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]

[tex]u=\sqrt{1+tant}[/tex]

[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]

Now that we have u and du, we can plug them back in.

[tex]\int\limits {2} \, du[/tex]

[tex]\int\limits{2} \, du=2u[/tex]

Since we know u, we can plug that in.

[tex]2\sqrt{1+tant}[/tex]

This may seem like the correct answer, but we forgot to add the constant.

[tex]2\sqrt{1+tant}+C[/tex]

Answer:

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 28.983051

Chi-square value = χ² = 2.154239

Degree of freedom = 1

Critical value = 3.841

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Step-by-step explanation:

He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.

So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Data collected by Dr. Pagels:

                                              meadow voles     common voles      Row Total

apple slices                                     26                          32                      58

peanut butter-oatmeal                   35                          25                     60

Column Total                                   61                          57                     118

Where 118 is the grand total.

The expected number is given by

Expected = (row total)×(column total)/grand total

Expected meadow vole/apple slices = 58×61/118

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 58×57/118

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 60×61/118

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 60×57/118

Expected common vole/peanut butter-oatmeal = 28.983051

The chi-square statistic value is given by

χ² = Σ(Observed - Expected)²/Expected

χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051

χ² = 2.154239

The degrees of freedom is given by

DoF = (row - 1)×(col - 1)

For the given case, we have 2 rows and 2 columns

DoF = (2 - 1)×(2 - 1)

DoF = 1

The given level of significance = 0.05

The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be

Critical value = 3.841

Conclusion:

Reject H₀ If χ² > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

For the given case,

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Answer:

Yup P is the right one having 62.26%

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

We can set it up as

P = 33/53

Q = 20/48

R = 54/90

S = 44/83

This is because we are calculating the percent of yellow birds in the total amt. of birds in a specified park.

Now we calculate =>

P = 33/53 = around 0.62

Q = 20/48 = around 0.416

R = 54/90 = 0.6

S = 44/83 = around 0.53

We find that Park P has the greatest percentage and -->

Thus, Park P is our answer and yes, you are correct.