Operations and scientific notation math project need to know how to find the scientific notation

Answer:

a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Answer:

Step-by-step explanation:

I assume the sequence is 0, 2, 4, 6

nth term = 2(n-1)

Answer:

3.5 inches

Step-by-step explanation:

Sample mean basically means that we need to find the average of the samples.

So the formula for finding average is

Number of observations/ Number of Occurrences

So when we add the values together we get

42.

So there are 12 numbers

So, 42/12 =

3.5 inches

The sample mean of the heights of the plants in Susan's garden is

3.5 inches.

Here,

Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.

She measured the heights (in inches) of 12 randomly selected plants and recorded the data:

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

We have to find the sample mean of the heights of the plants in Susan's garden.

What is Average?

Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.

Now,

The recorded data is;

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.

Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]

Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]

Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.

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Answer:

a) The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.

b) Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.

c) 37 cars would have to be sampled.

Step-by-step explanation:

Question a:

We have the sample standard deviation, and thus, the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{6.2}{\sqrt{15}} = 3.4[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 26.7 - 3.4 = 23.3 mpg.

The upper end of the interval is the sample mean added to M. So it is 26.7 + 3.4 = 30.1 mpg.

The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.

b. What would happen to the interval if you increased the confidence level from 95% to 99%? Explain

Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.

c. The lead engineer is not happy with the interval you constructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?

Width is twice the margin of error, so a margin of error of 2 would be need. To solve this, we have to consider the population standard deviation as [tex]\sigma = 6.2[/tex], and then use the z-distribution.

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 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

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.

How many cars would you have to sample to create the interval the engineer is requesting?

This is n for which M = 2. So

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

[tex]2 = 1.96\frac{6.2}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 1.96*6.2[/tex]

[tex]\sqrt{n} = \frac{1.96*6.2}{2}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*6.2}{2})^2[/tex]

[tex]n = 36.9[/tex]

Rounding up:

37 cars would have to be sampled.

===============================================

Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

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

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.

Answer:

-52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

Answer: -52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

Answer:

x = -3

Step-by-step explanation:

12 -4x-5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from each side

12-9x-12 = 39-12

-9x = 27

Divide by -9

-9x/-9 = 27/-9

x = -3

Answer:

x = -3

Step-by-step explanation:

12 - 4x - 5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from both sides

12 - 12 - 9x = 39 - 12

-9x = 27

Divide both sides by -9

-9x/-9 = 27/-9

x = -3

Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.

To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81

The formula for calculating the z-score is expressed as;

[tex]z=\frac{x-\overline x}{s}[/tex] where:

[tex]\overline x[/tex] is the mean

s is the standard deviation

z is the z-scores

Given the following

[tex]\overline x[/tex]=2.7 in

s = 0.25

if z = -2.81

[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]

Similarly:

[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]

Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.

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A well formatted table of the distribution is attached below :

Answer:

0.124

0.733

0.408

Step-by-step explanation:

Using the table Given :

1.) P(AP Statistics) = 90 / 725 = 0.124

2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733

3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408

Observe that the x coords of the roots of a polynomial are,

[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]

Which can be put into form,

[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]

with data

[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]

Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,

[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]

and a will be "lost" in the process.

If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.

Hope this helps :)

The system of inequalities that is graphed is:

y ≤ - (2/3)*x

y < x - 3

So the correct option is B.

First, we can see that for both of the inequalities the shaded part is below the lines.

You also can see that the solid line (correspondent to the symbol ≤) is the one with a negative slope, and the dashed line (correspondent with the line <) is the one with a positive slope.

Only with that, we conclude that the correct option is B.

y ≤ - (2/3)*x

y < x - 3

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Answer:

4/27

Step-by-step explanation:

total number of marbles=9

probability of red=4/9

since you returned the first marble, the total number of marbles remains the same

prob(Blue)=(3/9)=1/3

P(red then blue)=(4/9)*(1/3)

=4/27

Answer:

I believe its  EG and NE but i might be wrong

Step-by-step explanation:

Answer:

answer is 10

explanation

when u add 7 with 10 u get 17 then double of 17 is 34

I hope It helps

It is found that the unknown number was 10.

An equation is an expression that shows the relationship between two or more numbers and variables. The addition is one of the mathematical operations. then the addition of two numbers results in the total amount of the combined value.

Given that "I add 7 to a certain number. I double the result. My final answer is 34".

Let consider the number be 10.

When we add 7 with 10 we get;

7 + 10 =  17

then double the result of 17 = 34

Hence, the unknown number was 10.

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Answer:

The volume of the resulting solid is π/2 cubic units.

Step-by-step explanation:

Please refer to the diagram below.

The shell method is given by:

[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]

Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.

From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:

[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]

The volume of the resulting solid is π/2 cubic units.

Answer:

pi/2

Step-by-step explanation:

I always like to draw an illustration for these problems.

For shells method think volume of cylinder=2pi×r×h

Integrate(2pi(2-x)(x-x^2) ,x=0...1)

Multiply

Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)

Combine like terms

Integrate(2pi(2x-3x^2+x^3) ,x=0...1)

Begin to evaluate

2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1

2pi(x^2-x^3+x^4/4), x=0...1

2pi(1-1+1/4)

2pi/4

pi/2

9514 1404 393

Answer:

  -8,257,536·u^5·v^10

Step-by-step explanation:

The expansion of (a +b)^n is ...

  (c0)a^nb^0 +(c1)a^(n-1)b^1 +(c2)a^(n-2)b^2 +... +(ck)a^(n-k)b^k +... +(cn)a^0b^n

Then the k-th term is (ck)a^(n-k)b^k, where k is counted from 0 to n.

The value of ck can be found using Pascal's triangle, or by the formula ...

  ck = n!/(k!(n-k)!) . . . . where x! is the factorial of x, the product of all positive integers less than or equal to x.

This expansion has 11 terms, so the middle one is the one for k=5. That term will be ...

  5th term = (10!/(5!(10-5)!)(2u)^(10-5)(-4v^2)^5

  = (252)(32u^5)(-1024v^10) = -8,257,536·u^5·v^10

Answer:

answer is (4x^4+3y)(16x^8-12x^4y+9y^2)

Step-by-step explanation:

Answer:

soory i dont know just report me if you angry

Answer:

605 boys.

Step-by-step explanation:

5:7 means 5 parts consists of boys and 7 parts consist of girls.

Since 7 parts = 847, 1 part = 121 and 5 parts = 605

Hence there are 605 boys.

Hope you have a nice day :)

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

Answer:

582-600

1,234-1,200

640-600

770-800

1,104-1,100

a) the cost of a bunch of grapes compared with its weight

GRAAAAAAAAAAAAAAAAAAAAAAAAAAAAPES!!!!!

Answer:

(-2,0)

Step-by-step explanation:

The x intercept is the value when it crosses the x axis ( the y value is zero)

x = -2 and y =0

(-2,0)

Answer:

82.8

Step-by-step explanation:

mean = sum of all points, over the total given number of points

84 * 26 = 2184

2184 + 69 + 66 = 2319

Now the total number of tests is 26 + 2 or 28

So divide 2319 by 28

2319/28 = 82.82142

rounded to the nearest tenth is 82.8

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

4y

They would have the same value if a number was substituted for y

Step-by-step explanation:

y+y+2y =

Combine like terms

4y

These are all like terms

They would have the same value if a number was substituted for y

Let y = 5

5+5+2(5) = 5+5+10 = 20

4(5) =20

Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]

Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]

                       = 2.145

Substitute the values

[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]

(26.17, 21.83)

When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]

b). The formula to calculate 95% prediction interval is given by :

    [tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]

   [tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]

   (31.13, 16.87)

Answer:

n=39/5

Step-by-step explanation:

24=5(n-3)

24=5n-15

-5n= -15-24

-5n=39

n= 39/5