Find the first term and the common ratio of the following geometric
sequence: 8, 16, 32, ...
a = 8, r = 2
a = 8, r = 8
a = 8, r = 4
a = 32, r= 1

Answer:

[tex]p \± ME[/tex] [tex]\to[/tex] [tex]71.2\% \± 7.9\%[/tex]

Step-by-step explanation:

Given

[tex](63.3\%,79.1\%)[/tex]

Required

Express in form of: [tex]p \± ME[/tex]

First, calculate the midpiont (p)

[tex]p = \frac{63.3\% + 79.1\%}{2}[/tex]

[tex]p = \frac{142.4\%}{2}[/tex]

[tex]p = 71.2\%[/tex]

The margin of error (ME) is:

[tex]ME =79.1\% - 71.2\%[/tex]

[tex]ME =7.9\%[/tex]

So, we have:

[tex]p \± ME[/tex] [tex]\to[/tex] [tex]71.2\% \± 7.9\%[/tex]

Answers:

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Explanations:

Problem 14

There are n = 10 toppings to choose from.

If you order r = 0 toppings, then there is nCr = 13C0 = 1 way to do this.

Use the combination formula nCr = (n!)/(r!*(n-r)!)

If you order r = 1 topping, then there are 13C1 = 13 ways to do this.

If r = 2, then we have 13C2 = 78 different combos

If r = 3, then 13C3 = 286

If r = 4, then 13C4 = 715

Add up those subtotals: 1+13+78+286+715 = 1093

Note the use of nCr instead of nPr. The order of toppings doesn't matter.

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Problem 15

Again order doesn't matter. We have n = 10 books to pick from and r = 3 selections to make.

nCr = (n!)/(r!*(n-r)!)

10C3 = (10!)/(3!*(10-3)!)

10C3 = (10*9*8*7!)/(3!*7!)

10C3 = (10*9*8)/(3!)

10C3 = (10*9*8)/(3*2*1)

10C3 = (720)/(6)

10C3 = 120

There are 120 different ways to pick the three books (from a pool of ten).

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Problem 16

Follow the same steps as problem 15. This time you'll have n = 15 and r = 4. The answer you should get is 1365

Or you could follow these steps below:

We have 15*14*13*12 = 32,760 permutations and 4! = 24 different ways to arrange any group of 4, so we have (32,760)/(24) = 1365 combinations.

nCr = (nPr)/(r!)

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Problem 17

There are 7C1 = 7 ways to pick the color and 10C2 = 45 ways to pick the two options. Therefore, there are 7*45 = 315 different cars possible.

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Problem 18

"At least 15" means "15 or more".

Add up the subtotals to get

15504+4845+1140+190+20+1 = 21,700

Answer:

(17/12)π radians

Step-by-step explanation:

π radians = 180º

255 * (π/180) = (17/12)π

Answer:

A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is reflected over the y axis, the new point is at A'(-x, y).

From the document attached, the vertices of the quadrilateral is at A(-6, 2), B(-6, 5), C(-3, 6) and D(-2, 1). Hence if quadrilateral ABCD is reflected over the y axis, the new point is at A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1).

Answer:

emm who exactly is chipo bcause i literally have no idea

Answer:

4 miles.

Step by step explanation

Answer:

The area of the rectangle is 12

6x2=12

Answer:

x = 58

Step-by-step explanation:

Hope this helps

enjoy

Answer:

the answer is d because that is how much degrees it is

Step-by-step explanation:

Answer:

Step-by-step explanation:

Log25 1000

Answer:

log5 (1000)

Step-by-step explanation:

logb (x) + logb (y) = logb (xy)

log5 (4) + log5 (250) = log5 (4 * 250) = log5 (1000)

Answer:

56

Step-by-step explanation:

g(2) = 3(2) + 2

      = 6 + 2

      = 8

f(8) = 8^2 - 8

     = 64 - 8

     = 56

Answer:

9.8 sq. in.

Step-by-step explanation:

A = πr²

Diameter: 10 inches

Radius: 5 inches

A = π · 5²

A = π · 25

A = 78.54

Section 4 is about one eighth of the circle.

78.54 ÷ 8

9.8175

9.8175 ≈ 9.8

Answer:

a) The model for the sales of Garmin is represented by [tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112[/tex].

b) The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

Step-by-step explanation:

a) The model for the sales of Garmin is obtained by integration:

[tex]S(t) = -0.0972\int {t^{2}} \, dt + 2.136\int {t}\,dt -11.9 \int\,dt[/tex]

[tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + C[/tex] (1)

Where [tex]C[/tex] is the integration constant.

If we know that [tex]t = 9[/tex] and [tex]S(t) = 2.9[/tex], then the model for the sales of Garmin is:

[tex]-\frac{81}{2500} \cdot 9^{3} + \frac{267}{250}\cdot 9^{2}-11.9\cdot (9) + C = 2.9[/tex]

[tex]C = 47.112[/tex]

The model for the sales of Garmin is represented by [tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112[/tex].

b) The average sales of the Garmin from 2008 through 2013 ([tex]\bar{S}[/tex]) is determined by the integral form of the definition of average, this is:

[tex]\bar{S} = \frac{1}{13 - 8} \cdot \int\limits^{13}_{8} {S(t)} \, dt[/tex] (2)

[tex]\bar S = \frac{1}{5}\cdot \int\limits^{13}_{8} {\left[-\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2}-11.9\cdot t + 47.112 \right]} \, dt[/tex]

[tex]\bar S = \frac{1}{5}\cdot \left[-\frac{81}{10000}\cdot (13^{4}-8^{4}) +\frac{89}{250}\cdot (13^{3}-8^{3}) -\frac{119}{20}\cdot (13^{2}-8^{2}) +47.112\cdot (13-8) \right][/tex][tex]\bar{S} = \frac{1}{5}\cdot (-198.167+599.86-624.75+235.56)[/tex]

[tex]\bar{S} = 2.5[/tex]

The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

Answer:

B

Step-by-step explanation:

that's how exponential functions are shaped

Answer:

red: 12/35

yellow: 18/35

blue: 1/7

Step-by-step explanation:

The experimental probability is the total number of each outcome over the total outcomes. The total outcomes would be the sum, 12 + 18 + 5, or 35.

If we are looking for the experimental probability of red, we divide the spins on red by the total:

red - [tex]\frac{12}{35}[/tex]

If we are looking for the experimental probability of yellow, we divide the spins on yellow by the total:

yellow - [tex]\frac{18}{35}[/tex]

If we are looking for the experimental probability of blue, we divide the spins on blue by the total:

blue - [tex]\frac{5}{35}[/tex] = [tex]\frac{1}{7}[/tex]

Answer:

[tex](\frac{3\sqrt{3} }{2}(14)^2)*16[/tex]

[tex]=509.22+16[/tex]

[tex]8147.52m^3[/tex]

[tex]ANSWER:8147.50~m^3[/tex]

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

hope it helps..

have a great day!!

Answer:

[tex]x=19.67[/tex]cm

Step-by-step explanation:

Por Pitágoras,

[tex]x^{2} = 26^{2} - 17^{2} \\\\x^{2} = 676 - 289\\\\x^{2} =387\\\\x=\sqrt{387} \\\\x=19.67[/tex]

Answer:

[tex]x=73[/tex]

Answer:

0, - 1.732 , 1.732

Step-by-step explanation:

The slope of the line is the angle of the tangent from the positive X axis in counter clock wise direction.

The slope of line AB is

tan 180 = 0

The slope of line BC is

tan 300 = - 1.732

The sloe of line AC is

tan 240 = 1.732

Answer:

Yeah its B or 99

Step-by-step explanation:

This problem is easy to solve even without a calculator. Simply 10 times 10 would be 100 (since its asking for square root) and the closest number to 100 would be 99 and the square root of 99 is around 9.94.

Answer:

2

Step-by-step explanation add 1+1

Answer:

[tex]P(81)=56.16[/tex]

Step-by-step explanation:

From the question we are told that:

Mean [tex]\mu=50[/tex]

Standard Deviation [tex]\sigma=7[/tex]

Percentile 81st

Generally Probability of 81st Percentile

 [tex]P(Z<x)=81\%[/tex]

Using Standard normal Table

 [tex]P(Z<0.88)=81\%[/tex]

Therefore the 81st percentile is given as

 [tex]P(81)=z*\sigma *\mu[/tex]

 [tex]P(81)=0.88*7*50[/tex]

 [tex]P(81)=56.16[/tex]

Answer:

21

Step-by-step explanation:

We have to create an identity

3x + 21 = 3x + k

if we substitute k with 21 we have

3x + 21 = 3x + 21

that is an identity so it’s true for every value of x

Answer:

hello there! I am mizuki, and I'll be helping you with this problem.

Mean is the average in numbers by the way!

Anyways, the answer is about 14.3

or...

14 1/3

Step-by-step explanation:

14 + 12 + 17 = 43

43 ÷ 3 = 14.333333...

Answer:

147 sq meters

Step-by-step explanation:

To find the area of a trapezoid, use the formula ( (a+b)/2 ) x h, where a is base value 1 and b is base value 2. Plugging it all in : ( (4+17)/2 ) = 10.5 x 14 = 147 sq meters.

Answer: the answer is 147 square meters.

Step-by-step explanation:

formula: (a+b)/2 * h

bases are a and b: 4 and 17 meters.

h =14 meters

Plug numbers in (4+7)/2*14

solve and you get 147 square  meters as answer

Answer:

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

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

The margin of error is of:

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

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that [tex]n = 2161, \pi = \frac{1214}{2161} = 0.5618[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Margin of error:

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

[tex]M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}[/tex]

[tex]M = 0.0209[/tex]

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Given:

The length of the ladder  = 12 ft

The angle of ladder with ground = 60 degrees

To find:

How far up the building the ladder will reach.

Solution:

Using the given information draw a figure as shown below.

We need to find the vertical distance between the top of ladder and the ground.

Let x be the required distance.

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the below triangle ABC,

[tex]\sin A=\dfrac{BC}{AC}[/tex]

[tex]\sin 60^\circ=\dfrac{x}{12}[/tex]

[tex]\dfrac{\sqrt{3}}{2}=\dfrac{x}{12}[/tex]

Multiply both sides by 12.

[tex]\dfrac{\sqrt{3}}{2}\times 12=x[/tex]

[tex]6\sqrt{3}=x[/tex]

Therefore, the ladder will reach [tex]6\sqrt{3}[/tex] ft far up the building.

Answer:

I don’t know if this is correct

Step-by-step explanation:

Answer:

4(3+x)

4x+12

Step-by-step explanation:

Hi there! I am Mizuki, and I'm just answering lol

Anyways, the answer for the first problem is 12 + 4x = 44

The answer for the second problem is 8

Work:

12 + 4x = 44

4x = 32

x = 8