X+5 is either
x,y,f(y)
.
Y+5 is either
x,y,f(x)
.
Y is either
x-5,x+5,y-5
.
X-5 is either
x,g(x),g(y)

Answer:

lower 95% Cl is 0.292

Step-by-step explanation:

p^ = 0.4783

n = 23

for 95% Cl,

z = 1.9600

Inputting all the available data into P as attached below

LCL = 0.292

UCL = 0.670

therefore, lower 95% Cl = 0.292

Answer:

One ounce of almonds is $0.78

One ounce of cashews is $0.63

Step-by-step explanation:

Set up a system of equations where a is the price of one ounce of almonds and c is the price of one ounce of cashews:

20a + 12c = 23.16

18a + 14c = 22.86

Solve by elimination by multiplying the top equation by 7 and the bottom equation by -6:

140a + 84c = 162.12

-108a - 84c = -137.16

Add them together and solve:

32a = 24.96

a = 0.78

Now, plug in 0.78 for a and solve for c:

20a + 12c = 23.16

20(0.78) + 12c = 23.16

15.6 + 12c = 23.16

12c = 7.56

c = 0.63

Answer:

B

D

A

Step-by-step explanation:

Given:

A. [tex]2x^3-x^{2} -6x[/tex]

B. [tex]2x^3+8x+4[/tex]

C. [tex]3x^4+x^{2} +x-7[/tex]

D. [tex]3x^4-3x^{2} +5x-7[/tex]

Now, let us evaluate the given expressions one by one.

[tex](4x^3-4+ 7x)-(2x^3-x-8)\\\Rightarrow 4x^3-4+ 7x-2x^3+x+8\\\Rightarrow 2x^3+8x+ 4[/tex]

It is equation B.

So, [tex](4x^3-4+ 7x)-(2x^3-x-8)[/tex] is equivalent to B.

[tex](-3x^2+x^4+x)+(2x^4-7+4x)\\\Rightarrow -3x^2+x^4+x+2x^4-7+4x\\\Rightarrow3x^4-3x^{2} +5x-7[/tex]

It is equation D.

So, [tex](-3x^2+x^4+x)+(2x^4-7+4x)[/tex]  is equivalent to D.

[tex](x^{2} -2x)(2x+3)\\\Rightarrow 2x^3-4x^{2} +3x^{2} -6x\\\Rightarrow 2x^3-x^{2} -6x[/tex]

It is equation A.

So, [tex](x^{2} -2x)(2x+3)[/tex] is equivalent to A.

So, answer is:

B

D

A

Answer:

B D A

Step-by-step explanation:

Hope I Helped

Answer:

B / px= k

Step-by-step explanation:

B = kpx

Divide each side by px

B / px= kpx/px

B / px= k

Answer:

First option

Step-by-step explanation:

B=kpx

B=k*(px)

Then,

[tex]k = \frac{b}{px} [/tex]

Answer:

Polly can choose 33264 schedules.

Step-by-step explanation:

None of these sections interfere with each other, so:

For each statistics choice, there are 12 composition choices.

For each composition choice, there are 11 section of Ethics choices.

For each section of Ethics choice, there are 18 Physics choises.

There are 14 statistics choices.

From how many possible schedules can Polly choose?

14*12*11*18 = 33264

Polly can choose 33264 schedules.

Answer:

See steps

Step-by-step explanation:

Volume of cubes is proportional to the cube of the side length.

Using proportions,

Volume of smaller cube / 1728 = (3/4)^3

Cross multiply,

Volume of smaller cube

= 1728 * (3/4)^3

= 1728 * (27/64)

= 729 cubic metres.

Note: all cubes are similar and each has 6 congruent faces.

Answer:

Step-by-step explanation:

To find the common ratio of the geometric sequence divide the previous term by the next term

That's

0.9 / 0.45 = 2

1.8 / 0.9 = 2

Therefore the common ratio is 2

Hope this helps you

Answer:

0.01386 or 1.386%

Step-by-step explanation:

Each question has a binomial distribution with probability of success p =0.25 (1 correct answer out of four alternatives).

The probability of 'k' successes in n trials is given by:

[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]

Pat will pass the exam if x ≥ 10. The probability that Pat will pass is:

[tex]P(pass)=P(x=10)+P(x=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)+P(x=17)+P(x=18)+P(x=19)+P(x=20)[/tex]

The probability for each number of success is:

[tex]P(x=10)=\frac{20!}{(20-10)!10!}*0.25^{10}*0.75^{10}=0.0099\\\\P(x=11)= \frac{20!}{(20-11)!11!}*0.25^{11}*0.75^{9}=0.0030\\\\P(x=12)=\frac{20!}{(20-12)!12!}*0.25^{12}*0.75^{8}=0.00075\\\\P(x=13)=\frac{20!}{(20-13)!13!}*0.25^{13}*0.75^{7}=0.00015\\\\P(x=14)=\frac{20!}{(20-14)!14!}*0.25^{14}*0.75^{6}=0.0000257\\\\P(x=15)=\frac{20!}{(20-15)!15!}*0.25^{15}*0.75^{5}=3.426*10^{-6}\\\\[/tex]

[tex]P(x=16)=\frac{20!}{(20-16)!16!}*0.25^{16}*0.75^{4}=3.569*10^{-7}\\\\P(x=17)=\frac{20!}{(20-17)!17!}*0.25^{17}*0.75^{3}=2.799*10^{-8}\\\\P(x=18)=\frac{20!}{(20-18)!18!}*0.25^{18}*0.75^{2}=1.555*10^{-9}\\\\P(x=19)=\frac{20!}{(20-19)!19!}*0.25^{19}*0.75^{1}=5.457*10^{-11}\\\\P(x=20)=\frac{20!}{(20-20)!20!}*0.25^{20}*0.75^{0}=9.095*10^{-13}\\\\[/tex]

The probability that Pat will pass his exam is:

[tex]P(pass)=0.01386[/tex]

Answer:

The formula is 10 - 3n

Step-by-step explanation:

For an nth term in an arithmetic sequence

U( n ) = a + ( n - 1)d

Where n is the number of terms

a is the first term

d is the common difference

From the sequence above

a = 7

d = 4 - 7 = - 3

The formula for an nth term is

U(n) = 7 + (n - 1)-3

= 7 - 3n + 3

The final answer is

= 10 - 3n

Hope this helps you.

Answer:

100

Step-by-step explanation:

So this equation would look something like this -->

8(9.75 - 3.25) + 12 x 4 => Since we have decimals then we should subtract in the parenthasees.

9.75 - 3.25 = 6.5

--> 8(6.5) + 12 x 4 --> 8(6.5) + 48 =>

8(6.5) = 52 --> 52 + 48 = 50 + 50 = 100

Thus, we have our answer of 100

Hope this helps!

Answer:

The answer is 100

Step-by-step explanation:

The equation that we are solving is 8(9.75 - 3.25) + 12 x 4

The order of operations are:

These are my steps that I did to solve the problem:

The final answer is 100.

Answer:14/3 ×2/7Step-by-step explanation:14/3÷7/2

take reciprocal

=14/3×2/7

Hope this may help you

If the answer is correct please mark me the brainlest

Answer:

Option 2

Step-by-step explanation:

=> [tex]4\frac{2}{3} / 3\frac{1}{2}[/tex]

Changing them into improper fractions

=> [tex]\frac{14}{3} / \frac{7}{2}[/tex]

Changing division sign into multiplication and inverting the term after it

=> [tex]\frac{14}{3} * \frac{2}{7}[/tex]

Answer:

0

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

    = (4-4)/(3-4)

     = 0/-1

   = 0

Answer:

EF ≈ 3.8

Step-by-step explanation:

Using the Sine rule in Δ DEF

[tex]\frac{EF}{sin75}[/tex] = [tex]\frac{DE}{sin50}[/tex] , that is

[tex]\frac{EF}{sin75}[/tex] = [tex]\frac{3}{sin50}[/tex] ( cross- multiply )

EF × sin50° = 3 × sin75° ( divide both sides by sin50° )

EF = [tex]\frac{3sin75}{sin50}[/tex] ≈ 3.8

Answer:

the second one

Step-by-step explanation:

We can see that the fence is made by a rectangle and a trapezoid

A1 is the area of the rectangle and A2 is the area of the trapezoid

Answer:

(a)[tex]R(x)=-0.02x^2+610x[/tex]

(b)[tex]R'(x)=-0.04x+610[/tex]

(c)R'(5400)=$394

Step-by-step explanation:

Given that x is the quantity demanded and the speaker's unit price (in dollars) is p where:

p = −0.02x + 610 (0 ≤ x ≤ 20,000)

(a)Revenue function R.

Revenue = Price X Quantity Demanded

Therefore:

R(x)=xp

[tex]=x(-0.02x + 610)\\R(x)=-0.02x^2+610x[/tex]

(b)Marginal revenue function R'(x)

If [tex]R(x)=-0.02x^2+610x[/tex]

Then, the marginal revenue function

[tex]R'(x)=-0.04x+610[/tex]

(c)We want to compute R'(5,400)

[tex]R'(5400)=-0.04(5400)+610\\R'(5400)=394[/tex]

From the above, we can infer that the revenue that will be generated on the sales of the 5401st item is $394.

Answer:

5

Step-by-step explanation:

=> 2x+3

For x = 1

=> 2(1) + 3

=> 2+3

=> 5

Answer:

5

Step-by-step explanation:

2x + 3

Put x as 1 and evaluate.

2(1) + 3

2 + 3

= 5

Answer:

Richard will have $60,000 in his account in 20 years.

Step-by-step explanation:

(1) Multiply $250 x 12

(2) Multiply the answer of $250 x 12 which is 3000 by 20

(3) Final answer would be $60,000

Answer:

S = 2π/9 [³/₂√10 − ½ ln(-3 + √10)]

S ≈ 3.946

Step-by-step explanation:

For a curve rotated about the x-axis, the surface area is:

S = ∫ₐᵇ 2πy ds,

where ds = √(1 + (dy/dx)²) dx.

y = e⁻³ˣ

dy/dx = -3e⁻³ˣ

ds = √(1 + (-3e⁻³ˣ)²) dx

S = ∫₀°° 2πe⁻³ˣ √(1 + (-3e⁻³ˣ)²) dx

If u = -3e⁻³ˣ, then du = 9e⁻³ˣ dx, or du/9 = e⁻³ˣ dx.

When x = 0, u = -3.  When x = ∞, u = 0.

S = ∫₋₃⁰ 2π √(1 + u²) (du/9)

S = 2π/9 ∫₋₃⁰ √(1 + u²) du

S = 2π/9 [ ½ u √(1 + u²) + ½ ln|u + √(1 + u²)| ] |₋₃⁰

S = 2π/9 {[0] − [ -³/₂√10 + ½ ln(-3 + √10) ]}

S = 2π/9 [³/₂√10 − ½ ln(-3 + √10)]

S ≈ 3.946

The area of a surface is the amount of space it occupies.

The area of the resulting surface is [tex]3.947[/tex] square units

The infinite curve is given as:

[tex]y =e^{-3x},\ \ x \ge 0[/tex]

Integrate y, with respect to x

[tex]\frac{dy}{dx} = -3e^{-3x}[/tex]

The area of the curve about the x-axis is:

[tex]S = \int\limits^a_b {2\pi y} \, ds[/tex]

[tex]ds = \sqrt{(1 + (\frac{dy}{dx})^2)}\ dx[/tex]

Substitute [tex]\frac{dy}{dx} = -3e^{-3x}[/tex] in [tex]ds = \sqrt{(1 + (\frac{dy}{dx})^2)}\ dx[/tex]

[tex]ds = \sqrt{(1 + (-3e^{-3x})^2)}\ dx[/tex]

Let

[tex]u = -3e^{-3x}[/tex]

So:

[tex]\frac{du}{dx} = 9e^{-3x}[/tex]

Make [tex]e^{-3x}\ dx[/tex] the subject

[tex]e^{-3x}\ dx = \frac{du}9[/tex]

[tex]x \ge 0[/tex] means that, the value of x is: [tex][0,\infty][/tex]

When [tex]x = 0[/tex]

[tex]u = -3e^{-3x}[/tex]

[tex]u = -3 \times e^{-3 \times 0} = -3[/tex]

When [tex]x = \infty[/tex]

[tex]u = -3 \times e^{-3 \times \infty} = 0[/tex]

Recall that:

[tex]S = \int\limits^a_b {2\pi y} \, ds[/tex]

Substitute [tex]ds = \sqrt{(1 + (-3e^{-3x})^2)}\ dx[/tex] and [tex]y =e^{-3x}[/tex]

This gives

[tex]S = \int\limits^0_{-3} {2\pi (e^{-3x}) \sqrt{(1 + (-3e^{-3x})^2)}\ dx}[/tex]

Rewrite as:

[tex]S = \int\limits^0_{-3} {2\pi \sqrt{(1 + (-3e^{-3x})^2)}\ (e^{-3x})\ dx}[/tex]

Substitute [tex]u = -3e^{-3x}[/tex] and [tex]e^{-3x}\ dx = \frac{du}9[/tex]

[tex]S = \int\limits^0_{-3} {2\pi \sqrt{(1 + u^2)}\ \frac{du}9}[/tex]

This gives

[tex]S = \frac{2\pi}{9} \int\limits^0_{-3} {\sqrt{(1 + u^2)}\ du}[/tex]

Integrate with respect to u

[tex]S = \frac{2\pi}{9}[\frac 12 u\sqrt{(1 + u^2)} + \frac 12\ln|u + \sqrt{1 + u^2}|\ ]|\limits^0_{-3}[/tex]

Substitute 0 and -3 for u

[tex]S = \frac{2\pi}{9}([\frac 12\times 0 \times \sqrt{(1 + 0^2)} + \frac 12\ln|0 + \sqrt{1 + 0^2} ] - [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}([0] - [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}(- [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}(- [\frac{-3}2 \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}( [\frac{3}2 \times \sqrt{10} - \frac 12\ln(-3 + \sqrt{10}\ )] )[/tex]

[tex]S = \frac{2\pi}{9}( [4.743 + 0.909] )[/tex]

[tex]S = \frac{2\pi}{9}( 5.652 )[/tex]

[tex]S = 3.947[/tex]

Hence, the area of the resulting surface is [tex]3.947[/tex] square units

Read more about areas at:

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The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

We have,

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = X ± (Z * (σ/√n))

where:

CI is the confidence interval

X is the sample mean

Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)

σ is the population standard deviation

n is the sample size

Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:

CI = 2.7 ± (1.645 * (17.8/√47))

Calculating the standard error (SE):

SE = σ/√n = 17.8/√47 ≈ 2.587

Substituting the values into the confidence interval formula:

CI = 2.7 ± (1.645 * 2.587)

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199

Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799

Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.

Interpreting the confidence interval:

Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).

However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.

Thus,

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

Learn more about confidence intervals here:

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The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = mean ± (Z * (standard deviation / √n))

Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.

Plugging in the values:

CI = 2.7 ± (1.645 * (17.8 / √47))

CI = 2.7 ± (1.645 * (17.8 / 6.856))

CI = 2.7 ± (1.645 * (2.596))

CI = 2.7 ± 4.270

CI = 2.7 + 4.270  ;  CI = 2.7 - 4.270

CI = 6.97             ;  CI = -1.57

Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).

The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.

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Answer:

a. Test statistic t = -0.14

b. P-value = 0.443

c. D. Fail to reject H0. There is insufficient evidence to support the claim that those given a sham treatment have pain reductions that vary more than those treated with magnets.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0[/tex]

The significance level is α=0.05.

The sample 1 (sham), of size n1=20 has a mean of 0.44 and a standard deviation of 1.24.

The sample 2 (magnet), of size n2=20 has a mean of 0.49 and a standard deviation of 0.95.

The difference between sample means is Md=-0.05.

[tex]M_d=M_1-M_2=0.44-0.49=-0.05[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1.24^2+0.95^2}{20}}\\\\\\s_{M_d}=\sqrt{\dfrac{2.4401}{20}}=\sqrt{0.122}=0.3493[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-0.05-0}{0.3493}=\dfrac{-0.05}{0.3493}=-0.14[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=20+20-2=38[/tex]

This test is a left-tailed test, with 38 degrees of freedom and t=-0.14, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t<-0.14)=0.443[/tex]

As the P-value (0.443) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.

Answer:

A

Step-by-step explanation:

Answer:

A True, law of detachment.

Answer:

mean score of class B = 1778/25 = 71.12

Step-by-step explanation:

This was your question : Class A has 12 pupils and class B has 25 pupils. Both classes sit the same maths test. The mean score for class A is 80. The mean score for both classes is 74. What is the mean score (rounded to 2 DP) in the maths test for class B?

mean of class A = Σfx/Σf

mean of class A =  80

Σfx = 80 × 12 = 960

Mean score for both classes = 74

where

b = Σfx  of class B

960 + b/37 = 74

cross multiply

960 + b = 2738

b = 2738 - 960

b = 1778

mean score of class B = Σfx/Σf

Σfx = 1778

Σf = 25

Therefore,

1778/25 = 71.12

Step-by-step explanation:

-2× [A1] + [A2]

-2* [A1]+[A2]: 12x -4y-7x+5y = -12 -9 ⇒ 5x+y = -21

this gives us system B

-2*[B2]+[B1] :

Answer:

-2 * A2 + A 1 = B2

-2 *B2   + B1 = C1

Step-by-step explanation:

-6x +2y = 6

-7x +5y = -9

We want to end up with 5x+ y = -21

Multiply the A2 by -2

-2 (-6x +2y) = 6*-2

12x -4y = -12

And add this to the A2

12x -4y = -12

-7x +5y = -9

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

5x + y = -21

Take this equation and multiply by -2

-2(5x + y) = -21*-2

-10x -2y = 42

Add this to equation B1

-10x -2y = 42

-6x +2y = 6

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

-16x + 0y = 48  This is equation C1

B2 * -2  + B1 = C1

Answer:

1/20

Step-by-step explanation:

5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles

P( brown) = brown / total = 5/20 = 1/4

Replace

5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles

P( red) = red / total = 4/20 = 1/5

P( brown, replace, red) = 1/4 * 1/5 = 1/20

Answer:

y=3

Step-by-step explanation:

y + 3 = –y + 9

Add y to each side

y+y + 3 = –y+y + 9

2y+3 = 9

Subtract 3 from each side

2y+3-3 = 9-3

2y = 6

Divide by 2

2y/2 = 6/3

y =3

Answer:

Hello!

_______________________

Your answer would be (B) y = 3

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you!

Answer:

[tex]\boxed{CD = 7.1}[/tex]

Step-by-step explanation:

The coordinates are (6,-5) and (-1,-4)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

CD = [tex]\sqrt{(-1-6)^2+(-4+5)^2}[/tex]

CD = [tex]\sqrt{(-7)^2+(1)^2}[/tex]

CD = [tex]\sqrt{49+1}[/tex]

CD = [tex]\sqrt{50}[/tex]

CD = 7.1 units (nearest tenth)

Answer: CD = 7.1

Step-by-step explanation:

Plug in each x coordinate and y coordinate into the distance formula.

d = √(-1 - 6)² + (-4 + 5)²

d = √(-7)² + (1)²

d = √49 + 1

d = √50

√50 = 7.1

d = 7.1

Answer:

[tex]6\frac{1}{3}[/tex]

Step-by-step explanation:

You can divide 19 by 3 a total of 6 times with a remainder of 1.  

Answer:

56 ft

Step-by-step explanation:

Because the bedroom is similar to the bed we can write that

7 : 15 = 6 : x

x = 15*6/7 ≈ 12.86 ft

Perimeter of the bedroom is

15*2 + 12.86 *2 ≈ 56 ft

Answer:

The margin of error is of 0.038 = 3.8%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 320, \pi = \frac{70}{320} = 0.21875[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.645\sqrt{\frac{0.21875(1-0.21875)}{320}}[/tex]

[tex]M = 0.038[/tex]

The margin of error is of 0.038 = 3.8%.

Answer:

The answer is "1.555"

Step-by-step explanation:

In the given question choices were not defined som the correct answer to this question can be defined as follows:

Given:

The value of  z* for 88% confidence interval are:

[tex]\to \frac{Z_{\alpha}}{2} \\\\\to Z_{0.06}\\\\\to \boxed{1.555}[/tex]