(From Unit 7, Lesson 3. )


The Colorado state flag consists of three horizontal stripes of equal height. The


side lengths of the flag are in the ratio 2 : 3. The diameter of the gold-colored disk is


equal to the height of the center stripe. What percentage of the flag is gold?

The annual growth rate is 23.81%

The annual growth rate is the percentage increase of the production or an investment over a year. It's the annualized growth rate of the output.The formula for the annual growth rate is given as:

Annual Growth Rate = (1 + r)^(1 / n) - 1

Where,‘r’ is the growth rate, and‘n’ is the number of periods considered.

The percentage increase in the output over seven years is given as 21.6%.

The annual growth rate can be calculated as:

(1 + r)^(1 / n) - 1 = 21.6 / 7Or (1 + r)^(1 / 7) - 1 = 0.031

Therefore, (1 + r)^(1 / 7) = 1 + 0.031r = [(1 + 0.031)^(7)] - 1 = 0.2381

The annual growth rate is 23.81% (approx) in percent terms.

Therefore, the answer is "The annualized growth rate is 23.81%."

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Step-by-step explanation:

1. 35.7/0.07=510

2. 486.12/0.6=810.2 approximately 810

3. 3.43/0.035=98

4. 5418.54/0.009=602,060

5. 812.5/1.25=650

6. 17.343/36.9=0.47 approximately 1

Answer:

Approximately 6.642 years

Step-by-step explanation:

The given parameters are;

The amount in the deposit account = $6,000

The time in which the money will have trebled at 11% compound interest, is given as follows;

\(A = P\times \left (1 + \dfrac{r}{n} \right )^{n\cdot t}\)

Where;

A = The amount at the end of the period

P = The amount in the deposit = $6,000.00

r = The rate of interest = 11%

t =  The periods that elapsed

n = The number of times the interest is applied per period of time, t = 1

For the money to have trebled, the amount generated at the end of the period will be 200% the amount deposited

Therefore, we have;

Amount, A, at the end of period = 200/100× $6,000 = $12,000

Substituting the values into the formula for the formula, we have;

\(\$ 12,000 = \$ 6,000\times \left (1 + \dfrac{0.11}{1} \right )^{1\times t}\)

Which gives;

\(\$ 12,000 = \$ 6,000\times \left (1 + {0.11} \right )^{t}\)

\(\left (1 .11} \right )^{t} = \dfrac{ \$ 12,000}{\$ 6,000} = 2\)

t = ㏒(2)/(㏒(1.11)) ≈ 6.642 years which is approximately 6 years, 7 months and 24 days

To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted. The true value of 59k is 44k after the test.

In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.

It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.

When we analyze the  given question, we find that,

The total number of students were 49,The true average was found to be 59k,and the Sample average is found to be 44k.

Thus, in  the present question we will use the One- sample T-test.

We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.

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Answer:

$13

Step-by-step explanation:

multiply 65 by 80 then divide by 100, you get 52, so subtract 65 from 52 you get 13

The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:

Step-by-step explanation:

It should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity.

It should be noted that an identity simply means an equation that is always true no matter the values that are substituted.

In this case, should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity. It's simply the inverse of the sine function.

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The absolute values of the three integer roots of the given polynomial are |a| = 0, |b| = 2011, and |c| = 2011.

The given polynomial is x³ - 2011xᵐ.

We are asked to find the absolute values of the three integer roots of this polynomial, denoted as a, b, and c.

To find the roots, we can set the polynomial equal to zero and solve for x:

x³ - 2011xᵐ = 0

Factoring out an x gives us:

x(x² - 2011xᵐ⁻¹) = 0

From this equation, we can see that one of the roots is x = 0.

Now let's focus on the second factor, x² - 2011xᵐ⁻¹ = 0.

This quadratic equation has two roots, which we can find using the quadratic formula:

x = (-b ± √(b² - 4ac))/(2a)

For this equation, a = 1, b = -2011, and c = 0. Substituting these values into the quadratic formula, we get:

x = (-(-2011) ± √((-2011)² - 4(1)(0)))/(2(1))
x = (2011 ± √(4044121))/(2)

Simplifying further, we have:

x = (2011 ± √(2011²))/(2)
x = (2011 ± 2011)/(2)

This gives us two possible values for x:

x = (2011 + 2011)/(2) = 2011
x = (2011 - 2011)/(2) = 0

Now we have three potential roots: x = 0, x = 2011, and x = 2011.

To find the absolute values of these roots, we take the absolute value of each:

|0| = 0
|2011| = 2011
|2011| = 2011

Therefore, the absolute values of the three integer roots of the given polynomial are |a| = 0, |b| = 2011, and |c| = 2011.

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This sample would be considered A. Cluster sample. In a cluster sample, the researcher divides the population into groups or clusters, and then randomly selects some of these clusters to include in the sample.

In this case, the researcher is selecting nine counties as the clusters, and surveying all shoulder surgery patients within those counties. This is different from a stratified sample, in which the population is divided into subgroups or strata based on certain characteristics, and a representative sample is selected from each stratum. It is also different from a convenience sample, in which the researcher simply selects the individuals who are easiest to reach or who happen to be available at the time of the study. And it is different from a simple random sample, in which every member of the population has an equal chance of being selected for the sample.

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Answer:

Step-by-step explanation:

14.

(1.25)² +EF ² = 3²; subtract (1.25)² from both sides

EF²= 3² - (1.25)²; square root both sides and calculate

√EF² = √10.5625

EF = 3.25

15.

∠I = 180-46-90 = 44°

Answer:

there are 100 centigrams in a gram

Step-by-step explanation:

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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The scale factor used in the dilation is 3

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

Image = 9

Pre-image = 3

The scale factor is calculated as

Scale factor  = Image/Pre-Image

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = 9/3

Evaluate

Scale factor  = 3

Hence, the scale factor is 3

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Answer:

21/3+3(4)

21/3+12

21/15

7/5, 1 & 2/5, or 1.4

Answer:

19

Step-by-step explanation:

s/3+3w

21/3+3x4

7+12

19

The required value of  polynomial is f(x) = x² - 35x + 219.

To find the smallest possible value of the polynomial f(x), we need to consider the smallest possible values for x. Given that f(7) = 23 and f(8) = 3, we can use these equations to form a system of equations.

Let's write the system of equations:
f(7) = 23, which means a(7²) + b(7) + c = 23
f(8) = 3, which means a(8²) + b(8) + c = 3

Simplifying these equations, we get:
49a + 7b + c = 23
64a + 8b + c = 3

To solve this system of equations, we can subtract the second equation from the first:
(49a + 7b + c) - (64a + 8b + c) = 23 - 3
49a - 64a + 7b - 8b = 20
-15a - b = 20

Now, we need to find the smallest possible value for a. Since a is an integer, we want the coefficient of a to be as small as possible. If we let a = 1, the coefficient becomes -15. This means that the absolute value of b will be minimized, resulting in the smallest possible value of the polynomial.

Plugging in a = 1 into the equation, we have:
-15(1) - b = 20
-15 - b = 20
-b = 20 + 15
-b = 35
b = -35

Now, we can substitute the values of a and b back into one of the original equations to find c:
a(7²) + b(7) + c = 23
(1)(49) + (-35)(7) + c = 23
49 - 245 + c = 23
-196 + c = 23
c = 23 + 196
c = 219

Therefore, the polynomial is f(x) = x²- 35x + 219.

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The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

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The correct answer is: "The UpdateTime method is called, and the local Euler angle is passed onto the Y transform of the hour hand of the clock.

 When clicking on a collider within the clock-face, the clock's hour hand needs to update its position to reflect the current time. To achieve this, the UpdateTime method is called which passes the local Euler angle onto the Y transform of the hour hand. This ensures that the hour hand rotates to the correct position on the clockface based on the current time."
                                     When clicking on a collider within the clock-face to update the time, the correct sequence is: The UpdateTime method is called, and the local Euler angle is passed onto the Y transform of the hour hand of the clock.

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The values that represent the possible distance, d, in miles, between Lincoln, NE, and the third city are given as follows:

300 < d < 699.

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements for this problem are given as follows:

Then if 500 miles is the largest distance, we have that:

x can be between 300 and 500.

If x is the largest distance, we have that:

x can be between 501 and 699.

Then the range of possible distances is given as follows:

300 < d < 699.

(which are the distances for each case).

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Answer:

see picture

Step-by-step explanation:

Answer:

1. 256 bacteria cells 2. y=2^x 3. 2 bacteria cells

Step-by-step explanation:

Answer:

along the edge of tectonic plate

Using a graph, the orthocenter for this triangle has a coordinate at (x, y) are (-0.46, 0.2)

The intersection of a triangle's three elevations is called the orthocenter. It is the intersection of the three lines that run perpendicular to the triangle's three sides. Due to its several intriguing characteristics, the orthocenter is a crucial place in the study of triangles..

In this problem, we need to use a graphing calculator and plot each of the coordinates and then find the orthocenter which is an equidistant position from all the coordinates.

In this particular problem, the orthocenter for this triangle is (-0.46, 0.2)

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Answer:1a

Step-by-step explanation:

Answer:

f(2)= -2

g(2)= 12

Step-by-step explanation:

To solve this we use the substitution method. Since f(2) is your variable, we will plug the x-value of 2 into each equation

f(2)= 2(2)^2-5(2)

f(2)=8-10

f(2)= -2

If the same variable is used for both equations then g(x) would be g(2) as well leaving you with

g(x) = 3x^2

g(2)= 3(2)^2

g(2)=12

Answer:

A narrow majority of U.S. adults (53%) now describe their personal financial situation as excellent or good, up from 47% in April 2020. The share saying their finances are in only fair or poor shape now stands at 46%, compared with 52% earlier in the pandemic.

Step-by-step explanation:

The change in units of measurement from centimeters to feet would not affect the linear correlation coefficient, as it is independent of the units used for the variables.

Hence option C is correct.

Assume that it's referring to the scenario where the distance calculation was changed from centimeters to feet.

In this case, the linear correlation coefficient, r, will not change due to the change in units of measurement.

It's important to note that the correlation coefficient is not dependent on the units of measurement used for the variables.

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables, and it just describes the degree of association between them.

Therefore, regardless of whether the distance is measured in centimeters or feet, the value of the correlation coefficient is unaffected since the underlying relationship between the variables remains the same.

As a result, the correct answer is C. It would likely not change at all.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

The correct answer is 5.

If we consider the vector z = [7 8 9 3 4], the length of z can be determined by counting the number of elements in the vector. In this case, z has five elements: 7, 8, 9, 3, and 4. Therefore, the length of z is 5.

In general, the length of a vector refers to the number of elements it contains. It is a fundamental property of vectors and is often denoted by the symbol "n" or "N." The length can be calculated by counting the number of entries in the vector.

In this specific example, z has five entries, so the length of z is 5. It is important to note that the length of a vector is different from its magnitude or norm, which typically refers to a measure of the vector's size or length in a geometric sense.

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