4. As part of your retirement planning, you purchase an annuity that pays 4 % annual
interest compounded quarterly
a. If you make quarterly payments of $900 how much will you have saved in 5
years?
b. Instead, if you make quarterly payments of $450, how much will you have saved
in 10 years?

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

Work Shown:

sin(angle) = opposite/hypotenuse

sin(29) = x/24

24*sin(29) = x

x = 24*sin(29) ..... exact value

x = 11.635430885912 .... approximate value

x = 11.6

To get the approximate value, you'll need a calculator. Make sure the calculator is in degree mode.

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:

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:

it simple as look

Step-by-step explanation:

He y I a m r a v I t ha n k S

Wowowowowowowowowk

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:

135.7 yd²

Step-by-step explanation:

Surface area of the cone,

πr²+πrl

= π×3²+π×11.4×3

= 43.2π

= 135.7 yd² (rounded to the nearest tenth)

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

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

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

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

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.

9514 1404 393

Answer:

  (d) 6√3

Step-by-step explanation:

There are several ways to work multiple-choice problems. One of the simplest is to choose the only answer that makes any sense. Here, that is 6√3.

y is the hypotenuse of the medium-sized right triangle, so will be longer than that triangle's longest leg. y > 9

The only answer choice that meets this requirement is ...

  y = 6√3

__

In this geometry, all of the right triangles are similar. This means corresponding sides have the same ratio. For y, we're interested in the ratio of long leg to hypotenuse.

  long leg/hypotenuse = y/(9+3) = 9/y

  y² = 9(9+3) = 9·4·3

  y = 3·2·√3 . . . . . . take the square root

  y = 6√3

__

Additional comments

You may notice that y is the root of the product of the longer hypotenuse segment (9) and the whole hypotenuse (9+3 = 12). We can say that y is the "geometric mean" of these segment lengths. Similarly (pun only partially intended), x will be the root of the product of the short segment (3) and the whole hypotenuse (12)

  x = √(3·12) = 6

This is another "geometric mean" relation.

Further, the altitude will be the geometric mean of the two segments of the hypotenuse:

  h = √(9·3) = 3√3

A way to summarize all of these relations is to say that the legs of the right triangle that are not the hypotenuse are equal to the geometric mean of the segments of the hypotenuse that the leg intercepts.

  x = √(3·12)

  y = √(9·12)

  h = √(3·9)

Answer:

Scheme a 45000 is the 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.

9514 1404 393

Answer:

corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)4)

Step-by-step explanation:

In this geometry, "corresponding" angles are in the same direction from the point of intersection of the transversal with the parallel line.

"Alternate" refers to angles on opposite sides of the transversal. "Interior" and "exterior" refer to angles between and outside of the parallel lines, respectively.

Here, we list all angle pairs in each classification, so you can answer questions 1-12 based on this list.

alternate interior: (2, 4), (3, 5)

alternate exterior: (1, 7), (43°, 6)

corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)

__

Additional classifications are also used:

consecutive (same-side) interior: (2, 5), (3, 4)

consecutive (same-side) exterior: (1, 6), (43°, 7)

vertical: (1, 3), (2, 43°), (4, 6), (5, 7)

linear pairs: (1, 2), (1, 43°), (2, 3), (3, 43°), (4, 5), (4, 7), (5, 6), (6, 7)

Answer:

582-600

1,234-1,200

640-600

770-800

1,104-1,100

Answer:

13

Step-by-step explanation:

f(x) = 4x + 1

Let x= 3

f(3) = 4*3+1

    = 12+1

   = 13

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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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:

Step-by-step explanation:

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

nth term = 2(n-1)

Perimeter = Sum of all sides

Perimeter = 14cm + 8cm + 10cm + 5cm

Perimeter = 22cm + 15cm

Perimeter = 37cm

Step-by-step explanation:

hope it helps you

...

........

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:

I believe its  EG and NE but i might be wrong

Step-by-step explanation:

[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto m\approx0.5[/tex]

Answer:

[tex]m=\frac{1}{2}[/tex]

Step-by-step explanation:

The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-4}{10-4}[/tex]

[tex]m=\frac{3}{6}[/tex]

[tex]m=\frac{1}{2}[/tex]

[tex]m=0.5[/tex]

Answer:

soory i dont know just report me if you angry

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

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:

628 mi^3

Step-by-step explanation:

the volume of a cylinder is given by:

V = base area x height

thus,

V = (3.14)(5)^2(8)

V = (3.14)(25)(8)

V = 628 mi^3

the volume of the cylinder is 628 cubic miles

The volume of the cylinder is 628 cubic miles.

We have a cylinder of radius 5 mi and height 8 mi.

We have to find the volume of the figure and round it to nearest tenth.

The volume of cylinder is given by the formula -

Volume [tex]=\pi r^{2} h[/tex]

We can use the above formula to calculate the volume of cylinder. In our case -

r = 5 mi

h = 8 mi

Substituting the values in the formula -

Volume [tex]=\pi\times5^{2}\times 8\\\\[/tex] = 628 cubic miles.

Hence, the volume of the cylinder is 628 cubic miles.

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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.