Can someone help me solve question number 14? I've tried to solve it and got 3426 while the answers in the book say it's 2,6. Can someone pls explain why it's wrong?

The geometric mean is used to determine the average annual percent increase, as it accurately accounts for compounding growth over multiple periods. The correct option is E.

The measure of central tendency that is typically used to determine the average annual percent increase is the arithmetic mean. This measure takes the sum of all the values and divides it by the total number of values.

It is important to note that other measures, such as the geometric mean, can also be used in certain situations. But for most cases, the arithmetic mean is the go-to measure for determining the average annual percent increase.

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Step-by-step explanation:

'y - intercept'  is shorthand for ' y-axis intercept' ....or the value of the graph where it crosses the y - axis

this one is     point (0,3)  or  y-intercept  = 3

To calculate the height of the tree that would leave a 35 cm space from a 250 cm tall ceiling, subtract the desired space from the total height. Hence, the tree should be 215 centimeters tall.

The calculation involves understanding and using the concepts of height and ceiling space. When you want a tree to leave a certain amount of space from the ceiling, you have to subtract that desired space from the total height of the room. So, if your ceiling is 250 centimeters high and you desire a space of 35 centimeters to be left, the tree's height should be calculated as follows:

So, in this scenario, the tree must be 215 centimeters tall to fit perfectly under your ceiling with 35 centimeters of space left.

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Step-by-step explanation:

green is 6 out of  a total of ( 8+6+6 = 20 ) beads

   so  6/20 ths of the time it should be a green bead

              6/20  * 150 = 45 times should be green

The term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.

To find the limit of the given sequence, we can use the ratio test:

StartFraction
(9(n+1)+1)! / (9(n+1))!
Over
(9n+1)! / (9n)!
EndFraction

Simplifying the expression, we get:

StartFraction
(9n+10)(9n+9)(9n+8)...(9n+2)(9n+1)
Over
(9n+1)(9n)(9n-1)...(2)(1)
EndFraction

The terms cancel out and we are left with:

StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction

Taking the limit as n approaches infinity, we get:

lim (n → ∞) StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction

= lim (n → ∞) StartFraction
81n² + 81n + 90
Over
81n² + 9n
EndFraction

= lim (n → ∞) StartFraction
n² + n + 10 / n² + n / 9
EndFraction

As n approaches infinity, the higher order terms dominate, so we can ignore the constants and simplify the expression to:

lim (n → ∞) StartFraction
n² / n²
EndFraction

= 1

Since the limit exists and is finite, the sequence converges. Therefore, the limit of the sequence is 1.

To find the limit of the given sequence or determine if it diverges, consider the sequence:

a_n = (9n+1)! / (9n)!

We can rewrite the sequence using the properties of factorials:

a_n = [(9n+1)(9n)(9n-1)...(9n-(9n-1))] / (9n)!

a_n = (9n+1)

Now, we'll examine the limit as n approaches infinity:

lim (n -> ∞) a_n = lim (n -> ∞) (9n+1)

Since the term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.

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Answer:

RS = 15 units

Step-by-step explanation:

Given:
RT = 9
TS = 12

To find: Length of RS

Proof:

In right triangle RTS,

[tex]RT^{2} + TS^{2} = RS^{2}[/tex]
[tex]9^{2} + 12^{2} = RS^{2}[/tex]
[tex]81 + 144 = RS^{2}[/tex]
[tex]225 = RS^{2}[/tex]
[tex]\sqrt{225} = RS[/tex]
15 = RS
∴ The length of RS is 15 units.

There are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.

To determine the number of possible configurations, we multiply the number of choices available for each component of the system. Since the customer can choose one of two amplifiers, one of four CD players, and one of eight speaker models, the total number of possible configurations is given by:

2 (amplifiers) × 4 (CD players) × 8 (speakers) = 64

Therefore, there are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.

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Answer:

The answer is 460m²

Step-by-step explanation:

Area of rectangle =Length × Width

A=20×23

A=460m²

Answer:460

Step-by-step explanation: 20

                                          x 23

                                          _____

                                               60

                                             +400

Answer:

x - 2 > 7

Step-by-step explanation:

Substitute the value 5 for x.

x = 5

-2x ≤ 12

-2(5) ≤ 12

-10 ≤ 12  True

-10 is less than or equal to 12

x - 2 > 7

5 - 2 > 7

3 > 7       Not true

3 is greater than 7

2x < 12

2(5) < 12

10 < 12   True

10 is less than 12

x - 7 < 2

5 - 7 < 2

-2 < 2   True

-2 is less than 2

The sketch of the graph of the logarithm function is added s an attachment

From the question, we have the following parameters that can be used in our computation:

y = 3log₂(-x) - 9

The above equations is an illustration of a logarithm function that has been transformed using the following

Next, we plot the graph using a graphing tool

The graph of the logarithm function is added as an attachment

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Answer:

18.8

Step-by-step explanation:

To find the range of a data set, you subtract the smallest value from the largest value.

In this case, the smallest value is 2.8 and the largest value is 21.6.

Range = largest value - smallest value = 21.6 - 2.8 = 18.8

Therefore, the range of the data set is 18.8.

The linear regression equation that best fits the data set is y = 126x + 462.

To find the linear regression equation, we can use the following steps:

Calculate the slope and the y-intercept..

In this case, we have the following values:

y₂ = 4,920

y₁ = 650

x₂= 20

x₁ = 2

Substituting these values into the formula, we get the following:

m = (4,920 - 650)/(20 - 2) = 2,270/18 = 126.11

The y-intercept is calculated using the following formula:

b = y - mx

In this case, we can use the point (2, 650) because it is the first point in the table. Substituting these values into the formula, we get the following:

b = 650 - 126.11(2) = 461.89

The linear regression equation that best fits the data set is y = 126.11x + 461.89. Round each parameter to the nearest whole number, we get y = 126x + 462.

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The number of views of a video on the internet is shown in the table below as a function of the time since the video was posted (in hours).

Number of hours, x

Number of views, y

2

650

5

1,280

8 12

2,140

3,120

17

4,050

20

4,920

Find a linear regression equation, in the form y=ax+b, that best fits this data set. Round each parameter to the nearest whole number.

Answer: 7, 6 ,7

Step-by-step explanation:

We can use the formula for the confidence interval for a population mean with a known standard deviation. Plugging in the values, we get the interval  (6817.22, 7182.78).

To find the 99% confidence interval for the scholarship averages of thirty students, we need to use the following formula:

CI = X ± zα/2 * (σ/√n)

Where

X = sample mean ($7,000 in this case)

zα/2 = the z-score corresponding to the desired confidence level (99% in this case), which is 2.576

σ = population standard deviation ($500 in this case)

n = sample size (30 in this case)

Substituting these values into the formula, we get:

CI = 7000 ± 2.576 * (500/√30)

Simplifying this expression, we get:

CI = 7000 ± 182.78

Therefore, the 99% confidence interval for the scholarship averages of thirty students is

(7000 - 182.78, 7000 + 182.78)

= (6817.22, 7182.78)

So we can say with 99% confidence that the true population mean scholarship amount lies within this interval.

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Answer:

To work out 3.4 cos 13 degrees, you can use a calculator or a table of trigonometric functions that includes cosine values.

Using a calculator, you can simply enter "3.4 * cos(13)" and get the answer. Rounding to 2 decimal places gives:

3.4 * cos(13) ≈ 3.298

Therefore, 3.4 cos 13 degrees, rounded to 2 decimal places, is approximately equal to 3.30.

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A ratio is a relationship in which for every x units of one quantity there are y units of another quantity. Ratios are considered to be equivalent if they express the same x/y. A ratio compares 2 like or unlike quantities by division. Ratios can be shown visually using a graph or a ratio table.

Given the pattern:

In words, this pattern represents:

The numbers are obtained by squaring the integers 3, 4, 5, 6, and 7, respectively.

Algebraically, we can represent the pattern using the formula:

The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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Tom does have enough fertilizer to cover the triangular area, as the triangular area is of 179.6 m², and he has 300 m² of fertilizer.

We are given the three sides of the triangle, hence the first step in obtaining the area is obtaining the semi-perimeter, which is half the perimeter, hence:

s = (26 + 20 + 18)/2

s = 32 m.

The area of the triangle is then obtained as follows:

[tex]A = \sqrt{s(s - a)(s - b)(s - c)}[/tex]

[tex]A = \sqrt{32(32 - 26)(32 - 20)(32 - 18)}[/tex]

A = 179.6 m².

Hence Tom does have enough fertilizer to cover the triangular area, as the triangular area is of 179.6 m², and he has 300 m² of fertilizer.

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If the points  D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG then the area  is 40 square units.

The length of the rectangle can be found by finding the distance between D and E (or F and G), which is:

√(5 - (-3))² + (0 - (-4))²] = √8² + 4²

= √80

= 4√5

The width of the rectangle can be found by finding the distance between D and G (or E and F), which is:

√-5 - (-3))² + (0 - (-4))²

= √(-2)²+ 4²

= √20

= 2√5

Therefore, the area of the rectangle is:

length x width = 4√5 x 2√5

= 8 x 5

= 40

Hence,  40 square units is area of the given rectangle DEFG.

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The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53 when polynomial is p(x) = 2x³ - 5x² + 7x - 3 with one variable.

Given that,

The polynomial is p(x) = 2x³ - 5x² + 7x - 3

We have to find the value of p(2), p(0), p(-1) and p(-2).

We know that,

Take polynomial,

p(x) = 2x³ - 5x² + 7x - 3

Now, to find p(2) take x = 2 in polynomial

By substituting,

p(2) = 2(2)³ - 5(2)² + 7(2) - 3

p(2) = 16 - 20 + 14 - 3

p(2) = 30 - 23

p(2) = 7

Now, to find p(0) take x = 0 in polynomial

p(0) = 2(0)³ - 5(0)² + 7(0) - 3     [multiplication]

p(0) = 0 - 0 + 0 - 3

p(0) = -3

Now, to find p(-1) take x = -1 in polynomial

p(-1) = 2(-1)³ - 5(-1)² + 7(-1) - 3

p(-1) = -2 - 5 - 7 - 3                  [subtraction]

p(-1) = -17

Now, to find p(-2) take x = -2 in polynomial

p(-2) = 2(-2)³ - 5(-2)² + 7(-2) - 3

p(-2) = -16 - 20 - 14 - 3

p(-2) = -53

Therefore, The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53.

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As a bank officer, Elena's claims would not be enough to encourage me to approve the loan. It's important to look at the details of her business plan, her financial history and her credit score before making a decision. Even if Elena believes that her business idea cannot fail, there is always a risk involved in lending money. It's important to assess the risk and make a decision based on the facts, rather than on promises or guarantees.

Answer:

Step-by-step explanation:

Her claims encourage you.

The appropriate inference method to test for a difference between the average IQ scores of identical twins raised by birth parents and in a foster home is paired t-test.

A paired t-test is used when comparing two sets of observations that are paired or matched in some way, such as in the case of identical twins. In this scenario, the twins are matched based on their genetic makeup, and their IQ scores are compared based on their different upbringing environments (birth parents vs. foster home). The paired t-test allows us to analyze the difference between the paired observations (IQ scores) and determine if there is a statistically significant difference between the two groups.

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Therefore, the reliability of the results may be questioned due to the small sample size and the fact that the observed and expected counts in some cells are too small.

The fact that two of the six observed counts are 5 or less should make you the most worried about the reliability of the results of the test in this case. This is because when the observed counts in a cell are too small, it is difficult to draw reliable conclusions from them. In such cases, the chi-squared statistic may not accurately reflect the true relationship between the variables being studied. This is because the chi-squared statistic is based on the difference between the observed counts and the expected counts, and if the observed counts are too small, the chi-squared statistic may be biased and not accurately reflect the true relationship between the variables.
Moreover, the fact that two of the six expected counts are less than 5 also raises concerns about the reliability of the results. This is because when the expected counts in a cell are too small, it may indicate that the sample size is too small or that the sample is not representative of the population being studied. In this case, the sample size was only 300 black women, which may not be representative of all black women.

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Answer:

-5 and 5

Step-by-step explanation:

[tex]-5*5=-25\\\\-5+5=0[/tex]

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill PQ=\sqrt{(~~ 3- 1~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill PQ=\sqrt{( 2 )^2 + ( -2)^2} \implies \boxed{PQ=\sqrt{ 8}}[/tex]

[tex]Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill QR=\sqrt{(~~ 1- 3~~)^2 + (~~ -1- 1 ~~)^2} \\\\\\ ~\hfill QR=\sqrt{( -2)^2 + ( -2)^2} \implies \boxed{QR=\sqrt{ 8}} \\\\\\ R(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill RS=\sqrt{(~~ -2- 1~~)^2 + (~~ -1- (-1)~~)^2} \\\\\\ ~\hfill RS=\sqrt{( -3)^2 + ( 0)^2} \implies RS=\sqrt{ 9}\implies \boxed{RS=3}[/tex]

[tex]S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad P(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) ~\hfill SP=\sqrt{(~~ 1- (-2)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill SP=\sqrt{( 3)^2 + ( 4)^2} \implies SP=\sqrt{ 25}\implies \boxed{SP=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{8}+\sqrt{8}+3+5} ~~ \approx ~~ \text{\LARGE 13.7}[/tex]

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta = \frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }6^2 ~~}{2}\implies A=12\pi \stackrel{ using~\pi =3.14 }{\implies A=37.68}[/tex]