A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 10% margin of error at a 95% confidence level, what size of sample is needed

Answer:

x = 6

Step-by-step explanation:

In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.

The final value of x will be 6.

[tex] PQ^2 + QO^2 = PO^2 \\

x^2 + 8^2 = (4+x)^2 \\

x^2 + 64 = 16 + 8x + x^2 \\

64 = 16 + 8x \\

64 - 16 = 8x \\

48 = 8x \\

6 = x\\[/tex]

Answer:

=6 units squared

Step-by-step explanation:

area=1/2h(a+b)

        =1/2×2(4+2)

        =6

Answer:

1 +3i

Step-by-step explanation:

(4 - 2i) - (3 - 5i)

Subtract the reals

4 - 3 =1

Subtract the imaginary

-2i - -5i

-2i + 5i = 3i

1 +3i

Answer:

A

Step-by-step explanation:

Subtract all real numbers

4 - 3 = 1

Subtract all imaginary numbers

-2i - (-5i) = 3i

Put back together

1 + 3i

Best of Luck!

Answer:

252

Step-by-step explanation:

Divide 7812 by 31 and we get the average daily answer... Hope this helps!!

Answer:

Step-by-step explanation:

f(x) = (x+1)³ + 4

To find f-¹(x) equate f(x) to y

That's

y = (x+1)³ + 4

Next interchange the terms x becomes y and y becomes x

That's

x = ( y+1)³ + 4

Make y the subject

(y+1)³ = x - 4

Find the cube root of both sides

That's

[tex]y + 1 = \sqrt[3]{x - 4} [/tex]

Send 1 to the right side of the equation

That's

[tex]y = \sqrt[3]{x - 4} - 1[/tex]

So we have the final answer as

[tex]f ^{ - 1} (x) = \sqrt[3]{x - 4} - 1[/tex]

Hope this helps you

Answer:

option 1

Step-by-step explanation:

f(x)=(x+1)³+4

to find the inverse interchange the variable and solve for y

inverse f(x)=(y+1)³+4

x=(y+1)³+4

x-4=(y+1)³

y+1=∛x-4

y=∛x-4 -1

Answer:

Step-by-step explanation:

No, it is an ancient problem which has been proved to be impossible (in 1837), at least not for an arbitray angle.

However, we can trisect certain angles, such as 90 degrees, but rather than trisection, we are just constructing 30 degree angles.

For further reading, google "angle trisection"

Answer:

−  1049

Step-by-step explanation:

-13.62-(27.9)

primero haremos los paréntesis y después las demás multiplicaciones de izquierda a derecha.

-13.62-243

-806-243

Finalmente tenemos −  1049

Espero te ayude :)

Answer:

-41.52

Step-by-step explanation:

When you subtract from a negative, the answer will be smaller than the starting number:

Therefore, the answer is -41.52.

Answer:

Attachment 1 : Option A,

Attachment 2 : Option C

Step-by-step explanation:

( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.

6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals

( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...

The answer here will be option c, but let's prove it,

cos(5π / 3) = 1 / 2,

sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]

Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "

[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]

= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]

Hence proved that your solution is option c.

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.

Let the total surface of the rectangular box be expressed as:

S = 2xy + 2yz + 2xz

where,

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz .................(1)

Given:

Volume V = xyz = 8000 .............(2)

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since, Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20*20*20.

Find more information about Surface area here:

brainly.com/question/1090412

Answer:

[tex] - 24 + 16i + 45i + 15 = 9 + 61i[/tex]

Answer:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14

Step-by-step explanation:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT

Answer: 0.9844

Step-by-step explanation:

given data:

sample size n = 6

It’s assumed that half the population are male and the remaining half are females

F = 1/2

M = 1/2

the probability that the investigator would draw altleats one male

P ( x ≥ 1 ) =

= 1 - ( 0.5 ) ^ 6

= ( 0.5 )^6

= 0.9844

Answer:

(x,y) -> (x+6, y-3)

Step-by-step explanation:

I followed c and it translated like the  last ans choice.

Answer:

Ok, the first step is to count all the possible selections that we have and the number of options in each selection:

1) Sandwich: 2 options, ham or turkey.

2) Soup, 2 options, tomato or vegetable.

3) Drink, 2 options, coffee or milk.

(i assume that the sandwich and the soup are separated selections)

Now, if the customer chooses at random, the probability that in one given selection he selects a given outcome is equal to the number of options that match the outcome divided by the total number of options for that selection.

Then in the soup selection we have: options that match the outcome (one, is the vegetable soup). Total number of options = 2.

Then the probability is:

P = 1/2 = 0.5

or 0.5*100% = 50% in percentage form.

Answer:

1/2

Step-by-step explanation:

Step-by-step explanation:

Ellen - 115/23

Classmates and Ellen got = 5 each

Answer:

The dimensions or Area of the rectangle is 1200cm².

Answer:

157

Step-by-step explanation:

135+144+116+132=527

527+136.8=762.8

762.8÷5= 157

Answer:

[tex]\frac{19351}{11220}[/tex]

Step-by-step explanation:

[tex]\frac{2640+3366+5049+3060+5236}{11220} = \frac{19251}{11220}[/tex]

Answer:

a)

H₀ : µd = 0  

H₁ : µd < 0  

b)

The test statistic is

tₙ₋₁ = α / s√n

c)

at 0.10 level of significance,

tₙ₋₁ , ₐ

t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311

d)

given that  T(critical) = 1.62

∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311

at 10% level of significance,

REJECT H₀

Since 1.62 > 1.311, we can reject the null hypothesis.

Answer:

1) a) 0.8

b) 0.6

2) a) 0.08

b) 0.14

Step-by-step explanation:

1) Given

[tex]P(A) = 0.3[/tex] and [tex]P(B) = 0.5[/tex]

Let us learn about a formula:

[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)[/tex]

(a) If A and B are mutually exclusive i.e. no common thing in the two events.

In other words:

[tex]P(A\ and\ B)[/tex] = [tex]P(A \cap B)[/tex] = 0

Using above formula:

[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}[/tex]

(b)  P(A and B) = 0.2

Using above formula:

[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}[/tex]

*************************************

1) Given

[tex]P(A) = 0.4[/tex] and [tex]P(B) = 0.2[/tex]

Let us learn about a formula:

[tex]P(A\ and\ B) = P(B) \times P(A/B)[/tex]  for dependent events

[tex]P(A\ and\ B) = P(A) \times P(B)[/tex] for independent events.

(a) If A and B are independent events :

Using the above formula for independent events:

[tex]P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}[/tex]

(b)  [tex]P(A / B) = 0.7[/tex]

Using above formula:

[tex]P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}[/tex]

Answer:

The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Step-by-step explanation:

Call X is the number of hours that the author uses on monthly basis.

Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.

Total bill value if the author uses TalkLots service is $20 + $4X

The total fees between 2 providers equal as:

$80 + $1 X = $20 + $4X => 3X = $60 => X = 20

Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Answer:

a. 7k - 7

Step-by-step explanation:

Step 1: Write out expression

-k - (-8k + 7)

Step 2: Distribute negative

-k + 8k - 7

Step 3: Combine like terms

7k - 7

And we have our answer!

Complete Question

A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26

Answer:

The mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is [tex]\mu_{\= x } = 77[/tex]

The standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is  

    [tex]\sigma _{\= x} = 2.746[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 77[/tex]

     The  standard deviation is  [tex]\sigma = 14[/tex]

     The sample size is  [tex]n = 26[/tex]

Generally the standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is  mathematically represented as

           [tex]\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }[/tex]

substituting values  

          [tex]\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }[/tex]

          [tex]\sigma _{\= x} = 2.746[/tex]

Generally the mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is  equivalent to the population mean i.e  

      [tex]\mu_{\= x } = \mu[/tex]

      [tex]\mu_{\= x } = 77[/tex]

Answer:

  C.  As x → –∞, y → +∞, and as x → +∞, y → +∞

Step-by-step explanation:

The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.

_____

When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.

When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.

Answer:

  log(1/10) = -1

Step-by-step explanation:

Use the law of exponents and the meaning of logarithm.

  1/10 = 10^-1

  log(10^x) = x

So, you have ...

  log(1/10) = log(10^-1)

  log(1/10) = -1

Answer:

15.7% of students made above an 89.

Step-by-step explanation:

If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                         P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%

           n = sample of American adults = 331

           p = population proportion of Americans who decide to not go to

                 college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                        of significance are -1.645 & 1.645}  

P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90

P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]

 = [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

              [tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]

              [tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]

              [tex]\sqrt{n}[/tex] = 54.79

               n = [tex]54.79^{2}[/tex]

               n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Answer:

2.8

Step-by-step explanation:

11.1-8.3=2.8

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                            PEACE!

Answer:

its multiple choice

A. 26inches (1inch/25.4mm)

B. 26inches (25.4mm/1inch)

C. 25.4inches (1mm/26inch)

D. 26inches (1mm/25.4inch)

and its b