Write 63/100 as a decimal

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The probability that a selected day of a leap year falls in April is 0.082

We know that the probability is the likelihood that an event is going to occur.

The formula for probability is:

Probability = number of favorable outcomes / total number of outcomes.

Normally in a year there are 365 days and in the month of February there are 28 days but during a leap year there are 366 days in the year and 29 days in the month of February.

We need to find the probability that a randomly selected day of a leap year (with 366 possible days) is in April.

Number of days in the month of April = 30

So, the probability that a selected day of a leap year is in April would be,

P = 30 / 366

P = 0.082

Therefore, the probability that a selected day of a leap year falls in April is 0.082

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The product of matrices A and B, denoted as C = AB, is determined by performing matrix multiplication using the given matrices. In this case, A is a 2x1 matrix and B is a 1x3 matrix. The resulting matrix C will have dimensions 2x3.

To find the product of matrices A and B, we perform matrix multiplication by multiplying corresponding elements and summing the results.

The dimensions of the matrices must be compatible for multiplication, meaning the number of columns in the first matrix must match the number of rows in the second matrix.

Given matrices A and B:

A = [9 1]

B = [2 6 7]

To calculate C = AB, we multiply each element of A with the corresponding element in B, and then sum the results. The resulting matrix C will have dimensions 2x3.

C = [92 + 13 96 + 16 97 + 15]

Calculating each element of C, we have:

C = [18 + 3 54 + 6 63 + 5]

[21 60 68]

Simplifying, we get:

C = [21 60 68]

Therefore, the product of matrices A and B, denoted as C = AB, is the matrix:

C = [21 60 68]

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When Colin reaches 59 years of age, he will have approximately 168,498.59 in his retirement account.

To calculate the future value of Colin's retirement account, we can use the formula for compound interest:

\(A = P \times (1 + r/n)^{(n \times t)}\)

where:

A = the future value of the retirement account

P = the initial deposit (which is zero, since Colin is just starting to make deposits)

r = the annual interest rate (2.5%)

n = the number of times the interest is compounded per year (12, since it's compounded monthly)

t = the number of years until Colin reaches 59 (59 - 21 = 38)

Using this formula, we can calculate the future value of Colin's retirement account:

\(A = 200 \times (((1 + 0.025/12)^{(12 \times38))}-1)/(0.025/12)\)

A ≈ 168,498.59

Therefore, when Colin reaches 59 years of age, he will have approximately 168,498.59 in his retirement account.

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Answer:

2 1/12

The answer should be 2 1/12

(Two and one over twelve)

or

(Two and a one twelfth)

Answer:

2.1

Step-by-step explanation:

...........................

Answer:

  y = -1/500x² +2/5x

Step-by-step explanation:

You want the equation for the path of a football that is thrown 200 m downfield and reaches a maximum height of 20 m.

The initial height is not given. The equation is much more easily written if we assume it is zero, or we assume the launch height is the same height at which the ball is caught.

We know the maximum height is reached halfway between the launch point and the final point of interest. Then we're required to write the equation of a parabola that passes through the points (0, 0), (100, 20), and (200, 0).

Since we know the x-intercepts, we can write the equation as ...

  y = ax(x -200)

Then all we have to do is find the value of 'a' so the equation has (100,20) as a solution.

  20 = a(100)(100 -200) = -10000a

  a = -1/500 . . . . . divide by -10000

The equation of the path of the football is ...

  y = (-1/500)(x)(x -200)

  y = -1/500x² +2/5x

__

Additional comment

When x=185, y = -1/500(185)(185 -200) = 15/500(185) = 5.55 . . . meters

The domain is [0, 200]; the range is [0, 20].

To achieve that distance and height, the football would need to be thrown at a speed in excess of 119 miles per hour. For comparison, the fastest baseball pitch ever thrown was 108.1 miles per hour.

Answer:

24π in³/75.36 in³

Step-by-step explanation:

We are looking for the volume of a cone with a diameter of 6 inches and a height of 8 inches.

First, divide the diameter by 2 to get the radius.

6 in/2 = 3-in. radius

Now, incorporate the formula for the volume of a cone. That is πr²h/3.

3.14 * 3² * 8/3

Square 3 to get 9.

3.14 * 9 * 8/3

Multiply 3.14 by 9 to get 28.26.

28.26 * 8/3

I recommend turning 28.26 into a improper fraction. That would be 1413/50.

1413/50 * 8/3

Can any cross-cancellation be done? Yes!

50 and 8 share a GCF of 2.

1413/25 * 4/3

1413 and 3 share a GCF of 3.

471/25 * 4/1

Multiply 471 by 4, and put it over 25.

1884/25

Simplify your answer.

75 9/25 = 75.36 in³, which is about 24π in³.

a monster can eat 48 cookies in 12 minutes me thinks

Answer: A monster can eat 48 cookies in 12 minutes

Step-by-step explanation:

The volume of the solid S in the given question is 5.48unit³.

A three-dimensional space's occupied volume is measured.

It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units.

The definition of length and volume are connected.

So, the volume of the solid S:
An equilateral triangle's sides are shown as a cross-section.

An equilateral triangle's height is determined by:

\(h = sSin60 = \frac{\sqrt{3} }{2} s\)

Consequently, one triangle's area is:

\(A=\frac{1}{2} s h=\frac{1}{2} s \cdot \frac{\sqrt{3}}{2} s=\frac{\sqrt{3}}{4} s^2\)

The line equation that depicts the diagonal is:

\(\begin{aligned}& x+y=1 \\& y=-x+1 \\& x=-y+1\end{aligned}\)

This will indicate the s value integrate from 0 to 2 if we integrate along the y-axis.

\(\begin{aligned}& V=\int_0^2 \frac{\sqrt{3}}{4} s^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2(-y+1)^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2\left(y^2-2 y+1\right) d x \\& =\frac{\sqrt{3}}{4}\left[\frac{1}{3} y^3-y^2+y\right] \\& \left.=\frac{\sqrt{3}}{4}\left[\frac{1}{3}(2)^3-(2)^2+2\right)\right] \\& =5.48\end{aligned}\)

Therefore, the volume of the solid S in the given question is 5.48unit³.

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Correct question:
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the y-axis are equilateral triangles.

The volume of the square pyramid is 90 cubic meters, which corresponds to option C.

To find the volume of a pyramid, we use the formula V = 1/3 * B * h, where B is the base area and h is the height of the pyramid.

In this case, we are given that the height of the square pyramid is 7.5 meters.

To find the base area, we need to know the length of one side of the square base.

Since the base is a square, all sides are equal. From the diagram, we can see that the length of one side is 6 meters.

The base area is B = 6² = 36 square meters.

Using the formula V = 1/3 * B * h, we can find the volume of the pyramid.

V = 1/3 * 36 * 7.5 = 90 cubic meters.

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The project triangle shows the interdependent relationship between project cost, scope, and time. While changes to any one factor may impact the other two, it's important for project managers to understand the trade-offs and make informed decisions to ensure project success.

The project triangle, also known as the triple constraint or the iron triangle, is a framework that shows the interdependent relationship between project cost, scope, and time.

This framework is often used by project managers to understand the trade-offs that must be made when one or more of these factors change during the project lifecycle.
To draw the project triangle, you can start by drawing three connected lines, each representing one of the three factors: project cost, scope, and time.

Next, draw arrows connecting the lines in a triangle shape, with each arrow pointing from one factor to another.

For example, the arrow from project cost to scope represents how changes in project cost can affect the project's scope, and the arrow from scope to time represents how changes in project scope can affect the project's timeline.
The key point to remember is that changes to any one factor will affect the other two factors as well.

For example, if the project scope is increased, this may increase project costs and extend the project timeline.

Alternatively, if the project timeline is shortened, this may require increased project costs and a reduction in the project scope.

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Answer:

a. $12,600

b. $21

c. $19

Step-by-step explanation:

a) The cost is $3000 plus $16 per book

For 600 books, we have

3000 + 16(600)

= 3000 + 9600 = $12,600

b) Cost per book will be;

12,690/600 = $21

c) for 1000

= 3000 + 16(1000)

= 3000 + 16,000 = 19,000

cost per book is 19,000/1000 = $19

Answer:

x + m × y

$4.47

Step-by-step explanation:

The equation and computation is shown below:

Let us assume the cost of gallon be x

Increase each year be m

And, the number of years be y

So, the equation is

= x + m × y

The cost of gallon of gas in 16 years is

= $1.75 + $0.17 × 16

= $1.75 + $2.72

= $4.47

The future value (A) is approximately 5610.2 for the given investment and annu $4000 for 5 years at 7% compounded annually

To find the compound amount and compound interest rate for the given investment, we can use the formula for compound interest:

(a) The compound amount in the account after 5 years can be calculated using the formula:

A = P(1 + r/n)^(nt)

Where A is the compound amount, P is the principal (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal (P) is $4000, the interest rate ® is 7%, and the interest is compounded annually (n = 1), and the investment is for 5 years (t = 5), we can plug these values into the formula:

A = 4000(1 + 0.07/1)^(1*5)

A = 4000(1 + 0.07/1)^(1*5)

= 4000(1 + 0.07)^(5)

= 4000(1.07)^(5)

≈ 4000(1.402551)

≈ 5610.20

Therefore, the future value (A) is approximately 5610.2

Calculating this expression will give us the compound amount after 5 years.

(b) The compound interest earned can be calculated by subtracting the principal from the compound amount:

Compound interest = Compound amount – Principa

This will give us the total interest earned over the 5-year period.

By evaluating the expressions in (a) and (b), we can determine the compound amount and the compound interest earned for the given investment.

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Answer:

The answer is 7

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

8x - 8 = 48

8x = 56

x = 7

The value of function f (x) is,

⇒ F (x) = 4x⁴ + 7x² + 7x - 22

We have to given that;

Function is,

⇒ F' (x) = 16x³ + 14x + 7

Now, We get;

Integrate both side;

F (x) = 16 x⁴ / 4 + 14x²/2 + 7x

F(x) = 4x⁴ + 7x² + 7x + c

Since, F (1) = - 5

Hence,

F (x) = 4 (1)⁴ + 7 (1)² + 7 (1) + c

- 5 = 4 + 7 + 7 + c

c = - 22

Thus, The function f (x) is,

⇒ F (x) = 4x⁴ + 7x² + 7x - 22

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Answer:

25

Step-by-step explanation:

To be honest i´m not quite sure since I got 22 but 25 is the closest to my answer

Answer: the answer is 29.3

Step-by-step explanation:

The correct option is "with high scores on X tend to have high scores on Y."

In a positive relationship, cases with high scores on X tend to have high scores on Y. Similarly, cases with low scores on X tend to have low scores on Y.

Therefore, the correct option is "with high scores on X tend to have high scores on Y."

Explanation:A positive relationship is one in which the two variables increase or decrease together, as in the case of age and height. If age increases, the height of a person will typically also increase. Similarly, if age decreases, the height of a person will also typically decrease.

The other three options are incorrect for a positive relationship. If cases with high scores on Y tend to have low scores on X, this is a negative relationship. When cases have the same scores on X and Y, this is no relationship at all. Finally, if cases with high scores on X tend to have low scores on Y, this is also a negative relationship.

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Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use the Pythagoras theorem to find the missing side

Using the Pythagoras theorem

That's

\( {a}^{2} = {b}^{2} + {c}^{2} \)

From the question

x is the hypotenuse or the longest side of the triangle

Substituting the values into the above formula we have

\( {x}^{2} = {9}^{2} + {7}^{2} \)

\( {x}^{2} = 81 + 49\)

\( {x}^{2} = 130\)

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

x = 16

y = 10

Step-by-step explanation:

See attached worksheet.

a) Using the given values, the integral is ∫√(1+EA) dx = ∫(4+t^2)^-1/2 (200-2t^2) dt. Simplifying the given equation, we have (4+t^2)^-1/2 (200-2t^2) = (2/√(4+t^2)) (100-t^2). Let u = 4+t^2, then du/dt = 2t. The given integral then becomes ∫(2/√u)(100-u) du/(2t). Simplifying this further, we obtain (100/2) ∫u-1/2 du - (1/2) ∫u1/2 du. This gives 100√(4+t^2) - t√(4+t^2) + C = √(1+EA) dx, where C is the constant of integration.

b) Given the function x(t) = tan-1(sinh(t)), we can compute the velocity of the particle as v(t) = dx/dt = sec^2(t) sinh(t)/[1+sinh^2(t)]. Since x only depends on t, we can simplify the velocity expression to v(x) = sec^2(t) sinh(t)/[1+sinh^2(t)], where t = sinh^-1[tan(x)]. Thus, the speed of the particle is given by |v(x)| = √[sec^2(t) sinh^2(t)/[1+sinh^2(t)]^2]. We can use trigonometric identities to further simplify this expression to |v(x)| = √(1-cos^2(t))/cos^2(t) = √(sin^2(t))/cos^2(t) = tan(t). Using the definition of t, we have t = sinh^-1[tan(x)]. Thus, the speed of the particle is given by |v(x)| = tan[sinh^-1(tan(x))] = tan[xln(1+√(1+x^2))]

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Answer:

N/A

Step-by-step explanation:

the question is not in depth could you add a photo

The decimal equivalent for the rational number 8 4/9 using a bar over any repeating digits is

_

= 8.4

A rational number is a number that can be written as a fraction, whole number, decimal that stops or a repeating decimal.

8 4/9

= 76/9

= 8.444444444444444

_

= 8.4

Therefore, the decimal equivalent for the rational number 8 4/9 using a bar over any repeating digits is

_

= 8.4

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The slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

In the given graph two lines are plotted.

Part A: From the graph, the two equations are intersected at (-1.5, 0) and the solution is (-1.5, 0).

Part B: Slope and y-intercept

Equations of lines from the graph are y=3/4 x+1 and y= -4/3 x-2.

For the equation y=3/4 x+1,

Compare, y=3/4 x+1 with y=mx+c, we get

Slope (m)= 3/4 and the y-intercept (c)=1

For the equation y= -4/3 x-2,

Compare, y= -4/3 x-2 with y=mx+c, we get

Slope (m)= -4/3 and the y-intercept (c)=-2

Therefore, the slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

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The inequality that represents the situation when the number of lessons would mean that it is cheaper for Satvik to pay $60 for the month is x ≥ 15.

Inequality is a mathematical statement that two mathematical expressions are unequal.

Inequality is represented as either:

Payment Plans:

Plan A = $18 + $3 per lesson

Plan B = $60

Let each lesson = x

18 + 3x = 60

3x = 42

x = 14

x ≥ 15

Thus, if the number of lessons is greater than or equal to 15, it is cheaper for Satvik to pay under Payment Option B.

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We are given the system of equations and asked to solve it using the substitution method.

The variable X has a binomial distribution in the following distributions:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.

In a binomial distribution, we have a fixed number of independent trials (in this case, the number of patients), and each trial has only two possible outcomes (success or failure). The probability of success remains the same for each trial (in this case, the probability of the medicine working is 30%).

Option B does not represent a binomial distribution since it counts the number of patients for whom the medicine does not work, which is the complement of success. Option D is not a binomial distribution as it counts the number of doses each patient needs to take, which is not a success/failure outcome.

So, the correct answers are:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

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Answer:

5

Step-by-step explanation:

Given that :

Miles ridden in Tuesday = 10

Miles ridden on Wednesday = 20

Sample size, n = 2

Mean :

(10 + 20) / 2

= 30 /2

= 15

Mean absolute deviation :

(|10 - 15| + |20 - 15|) / 2

(5 + 5) / 2

10 / 2

= 5