Find the volume and total surface area of the shape below. The base is a semi-circle. height 8 in, length 12 in​

the roots are 5/2, -5/2

Answer: To find the amount of border needed to put wallpaper around a rectangular bedroom, the formula for the perimeter of a rectangle is needed. The formula for the perimeter of a rectangle is:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width of the rectangle.

Step-by-step explanation:

I hope this helps but i am not sure about the last qn.

The probability that exactly 7 out of 10 people chosen at random favor the new building project is approximately 0.2010 or 20.10%.

To calculate the probability that exactly 7 out of 10 people chosen at random favor the new building project, we need to use the binomial probability formula, which is:

P(X = k) = [tex](n choose k) * p^k * (1-p)^(n-k)[/tex]

where:

n = 10 (the number of trials)

k = 7 (the number of successes we want to find)

p = 0.6 (the probability of success)

Using this formula, we can calculate the probability as:

P(X = 7) = (10 choose 7) * [tex]0.6^7 * (1-0.6)^(10-7)[/tex]

P(X = 7) = (10!/7!3!) * [tex]0.6^7 * 0.4^3[/tex]

P(X = 7) = 120 * 0.0279936 * 0.064

P(X = 7) = 0.2010 (rounded to four decimal places)

Therefore, around 0.2010 or 20.10% of people like the new building project, which is the probability that exactly 7 out of 10 randomly selected individuals will do so.

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The volume of the clay brick is 2.25 cubic inches and the weight of the clay brick is 0.1575 pounds

The volume of the clay brick, we need to use the dimensions provided. The length of the brick is 1 inch and the width is 2 [tex]\frac{1}{4}[/tex] inches. We can assume the height of the brick is also 1 inch since it is not specified.

The formula for the volume of a rectangular object is

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

Using the given dimensions, we can calculate the volume of the brick:

V = (1 inch) x (2 [tex]\frac{1}{4}[/tex] inches) x (1 inch)

V = (1 inch) x (2.25 inches) x (1 inch)

V = 2.25 cubic inches

V = 2.25 inches³

Since the density of the clay is given as 0.07 pounds per cubic inch, we can find the weight of the brick using the formula:

Weight = Volume x Density

Weight = 2.25 inches³ x 0.07 pounds/inches³

Weight = 0.1575 pounds

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To find the value of f(2), we need to use the equation of the normal to the curve at the point (2,-1). We know that the normal to the curve is perpendicular to the tangent at that point.

From the given equation of the normal, we can determine the slope of the tangent line, which is -1/2.

Now we can use the point-slope form of a line to find the equation of the tangent line to the curve at (2,-1): y + 1 = (-1/2)(x - 2).

To solve for f(2), we need to find the y-coordinate of the point on the curve that lies on this tangent line. We can substitute x=2 into the equation of the tangent line to find the y-coordinate: y + 1 = (-1/2)(2 - 2) => y = -1.

Therefore, f(2) = -1.

The length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.

what is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Let's denote the length of the shorter leg by "x".

According to the problem statement, the length of the longer leg is 22cm more than six times the length of the shorter leg, so:

longer leg = 6x + 22

Also, the length of the hypotenuse is 23cm more than six times the length of the shorter leg, so:

hypotenuse = 6x + 23

Now, we know that this is a right triangle, so we can use the Pythagorean theorem to relate the side lengths:

shorter leg² + longer leg² = hypotenuse²

Substituting the expressions we found earlier, we get:

x² + (6x + 22)² = (6x + 23)²

Expanding the squared terms and simplifying, we obtain:

x² + 36x² + 264x + 484 = 36x² + 276x + 529

Subtracting 36x² + 276x + 529 from both sides, we get:

x² - 12x - 45 = 0

Now, we can solve for x by factoring the quadratic equation:

(x - 15)(x + 3) = 0

So, either x = 15 or x = -3. Since we're dealing with lengths, we discard the negative solution and take x = 15.

Therefore, the length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.

So the side lengths of the right triangle are 15cm, 112cm, and 113cm.

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The table graph X: -3, -2, -1, 0, 1; Y: 2, 8, 2, 1/2, 1/8 identify an exponential function.

To determine if the function represented by this table is linear, quadratic, or exponential, we can look for a pattern in the ratios of consecutive y-values to consecutive x-values.

Furthermore, the ratios decrease or increase depending on the direction of the movement, suggesting that the function is an exponential function.

Hence, we can conclude that the function represented by this table is an exponential function.

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Answer:

To find the probability of numbers lying between 500 and 900 inclusive with exactly two consecutive figures that are identical, we can use the following steps: Step 1: Count the total number of three-digit numbers between 500 and 900 inclusive. There are 400 three-digit numbers between 500 and 900 inclusive. Step 2: Count the number of three-digit numbers between 500 and 900 that have exactly two consecutive figures that are identical. We can break this down into cases based on the middle digit of the three-digit number. Case 1: The middle digit is not 0 or 9. In this case, there are 8 possible digits that can be used for the middle digit (i.e., 1, 2, 3, 4, 5, 6, 7, or 8). For each possible middle digit, there are

Margo will pay $21.28 in interest for the loan. The formula I = Prt is used to calculate the interest for a loan.

It is expressed as a percentage of the total amount borrowed and is typically noted as an annual percentage rate (APR).

The interest that Margo will pay can be calculated by using the formula I = Prt, where I is the interest, P is the principal (the initial amount borrowed), r is the interest rate, and t is the length of time.

In this case, the principal is $200, the interest rate is 8%, and the time is 16 months.

Therefore, the interest that Margo will pay is

I = 200 x 8% x (16/12)

 = $21.28

Therefore, Margo will pay $21.28 in interest for the loan.

The formula I = Prt is used to calculate the interest for a loan.

Here, I is the interest, P is the principal (the initial amount borrowed), r is the interest rate, and t is the length of time.

This formula can be used to calculate interest for any loan, no matter the principal, interest rate, or length of time.

By simply substituting the values into the formula, the interest can be easily calculated.

Therefore, in this case, Margo will pay $21.28 in interest for the loan.

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Answer:

O 20

Step-by-step explanation:

when you add 1 and 5 the mean only changes by a little.

but, once you add the 20 it makes your answer go up drastically which makes

O 20

your correct answer.

(a) A quadratic equation is in the form: y = -12.87x² + 42.22x + 1.18

(b) The height of the rocket after 3 seconds would be 12.01 feet.

A quadratic equation is a polynomial equation with a maximum degree of two. Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation.

Here, we have

Given: A rocket is launched upwards from the ground.

(a) A quadratic equation is in the form:

y = -12.87x² + 42.22x + 1.18

(b) When x = 3 seconds

y = -12.87(3)² + 42.22(3) + 1.18

y = 12.01 feet

Hence, the height of the rocket after 3 seconds is 12.01 feet.

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Answer:

5 boxes

Step-by-step explanation:

We Know

There are 40 apples packed into boxes.

There are 8 apples in each box

How many boxes are there?

We take

40 / 8 = 5 boxes

So, there are 5 boxes.

Answer:(2I3O-9247)

Step-by-step explanation:

Using trigonometric equation, we can find that on January 25th, 218 days after June 21st, there will be 11 hours of sunlight.

The trigonometric equations can be linear, quadratic, or polynomial equations and are conceptually related to algebraic equations. Trigonometric equations substitute the Sin, Cos, and Tan trigonometric ratios for the variables found in a typical polynomial equation. Sinθ, Cosθ, or Tanθ are the trigonometric ratios that are employed in trigonometric equations.

The number of daily sunlight hours of a particular location is modelled by the trigonometric equation,

l(t) = 12 + 3.5sin (2/365t)

L(t) denotes the number of hours of sunlight in a day.

t is the number of days after June 21st.

In order to find the day during the first 365 where there are 11 hours of sunlight, we must know the value of "t" for which L(t) = 11 hours. The result of solving for t in the given equation with L(t)=10 is as follows:

l(t) = 12 + 3.5sin (2/365t)

11 = 12 + 3.5sin (2/365t)

11-12 = 3.5sin (2/365t)

-1 = 3.5sin (2/365t)

-1/3.5 = sin (2/365t)

-0.285 = sin (2/365t)

For the inverse function of y = sin x

sin ⁻¹(y) =x + 2n

Given that we must determine the day with 11 hours of sunlight in the first 365 days, we get the following results when we set n=0: t = -35.3521 or t =217.9422.

Now, t cannot be negative since we want to discover that the day after June 21st will have 10 hours of sunlight. therefore, ignoring t=-35.3521. We now have t=217.9422.

By rounding, we arrive at the necessary response, t=218.

So, it will have 11 sunlights on January 25th—218 days after June 21st.

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the total number of doctors that were registered was about 154,744.

In a recent year, 27.4% of all registered doctors were female. If there were 42,400 female registered doctors that year,

Let's call the overall number of licensed physicians "x". We know that there were 42,400 female registered doctors in that year, making up 27.4% of all registered doctors.

To find x, we can construct the following equation:

0.274x = 42,400

x= 42,400 ÷0.274

x ≈ 154,744

Consequently, when rounded to the nearest whole number, the total number of doctors that were registered was about 154,744.

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As a result, none of the suggested solutions are the correct one. The doctor's total capital assets $761,743.

What are assets?

Assets are resources that belong to a person or a business, have value, and can be utilized to make money. Cash, investments, real estate, equipment, and inventory are a few examples of assets.

Assets are split into two groups in accounting: current assets and non-current assets. In contrast to non-current assets, which cannot be turned into cash in a year or less, current assets can be changed into cash in a year or less.

The capital assets of the doctor are:

- $589,674 for the home

- Work equipment owned: $51,797

- Vehicle Cost: $61,182

$59,090 was invested.

The value of all the capital assets owned by the doctor is:

$589,674 + $51,797 + $61,182 + $59,090

value of all the capital assets  = **$761,743

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Answer:

x=25/2 or 12.5

Step-by-step explanation:

8x=115-15

8x=100

x=100/8

x=25/2 or 12.5

Answer:

x = 12.5

Step-by-step explanation:

4x + 14 + 4x = 38+77 - 1

8x + 14 = 38 + 77 - 1

8x + 14 = 114

8x = 100

x = 12.5

We can solve this system of equations by substitution. Since both equations are solved for y, we can set them equal to each other and solve for x.

y = -x - 32 ...(1)

y = 5x ...........(2)

Substituting (1) into (2), we get:

-x - 32 = 5x

Simplifying and solving for x, we have:

6x = -32

x = -32/6

x = -16/3

Now that we know x, we can substitute it back into either equation to solve for y. Let's use equation (2):

y = 5x

y = 5(-16/3)

y = -80/3

Therefore, the solution to the system of equations is (x, y) = (-16/3, -80/3).

Answer:

Jake's father can carry 10 and 5/7 lb of wood.

Step-by-step explanation:

Jake carried 6 and 1/4 lb of wood.

Let's convert this to an improper fraction:

6 and 1/4 = (4 * 6 + 1)/4 = 25/4

So, Jake carried 25/4 lb of wood.

Jake's father can carry 1 and 5/7 times as much as Jake.

Let's convert this to a fraction:

1 and 5/7 = (7 * 1 + 5)/7 = 12/7

So, Jake's father can carry 12/7 times as much as Jake.

To find out how many pounds Jake's father can carry, we need to multiply Jake's weight by 12/7:

Jake's father can carry = (25/4) * (12/7)

= (25 * 12) / (4 * 7)

= 300/28

= 10 and 5/7 lb (when simplified to a mixed number)

The function which is represented by graph is y= √(-x-2) + 1. So correct option is C.

In mathematics, a function is a relation between two sets of objects in which each element of the first set (called the domain) is associated with exactly one element of the second set (called the range). The domain and range can be any sets, but they are usually subsets of the real numbers.

A function is typically denoted by a name, such as f(x), and is defined by an equation or a rule that specifies how the function operates on its inputs. The inputs to the function are typically denoted by x, and the outputs are denoted by f(x).

Functions can be represented graphically as well. The graph of a function is a visual representation of the relation between the input and output values. It is a plot of the input values on the x-axis and the output values on the y-axis.

Functions can be classified in various ways, such as linear, quadratic, exponential, trigonometric, etc. The behavior of a function can also be analyzed by looking at its domain and range, its symmetry, its intercepts, and its slope.

The function which is represented by graph is y= √(-x-2) + 1. So correct option is C.

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The function (fog)(x) is 4x² - x - 3.

In mathematics, a function is a rule that maps each element from a set (called the domain) to a unique element in another set (called the range or codomain).

In other words, a function is a mathematical object that takes one or more inputs, performs a specified operation on them, and produces an output. The input values of a function are called its arguments, and the output value is called the function value.

Starting with g(x):

g(x) = -4x² + x + 5

Now substituting g(x) into f(x):

f(g(x)) = -(g(x)) + 2

= -[-4x² + x + 5] + 2 (substituting g(x) into f(x))

= 4x² - x - 3

Therefore, (fog)(x) = 4x² - x - 3.

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The estimated mean age, sample variance, and sample standard deviation for a prehistoric extended family group of 84 members in the southwestern United States are 14.5 years, 83.5 square years, and 9.1 years, respectively.

To estimate the mean age, we need to calculate the weighted average of each age group's midpoint using their respective frequencies.

The midpoint of the first class (1-10 years) is 5.5, the midpoint of the second class (11-20 years) is 15.5, the midpoint of the third class (21-30 years) is 25.5, and the midpoint of the fourth class (31 and over) is 35.5.

To calculate the weighted average, we multiply each midpoint by its respective frequency, sum these products, and divide by the total number of individuals:

x = [tex]\frac{5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7}{84}[/tex] = 14.5 years

Therefore, the estimated mean age for this community is 14.5 years.

To calculate the sample variance and sample standard deviation, we first need to calculate the deviation of each observation from the mean. Then, we square each deviation, sum these squared deviations, and divide by n - 1 to get the sample variance.

Using the formula:

s2 = [tex]\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}[/tex]

sample variance as follows:

s2 = [tex]\frac{[(1-10-14.5)^2 \times 35 + (11-20-14.5)^2 \times 22 + (21-30-14.5)^2 \times 20 + (35.5-14.5)^2 \times 7]}{83}[/tex] = 83.5

Therefore, the estimated sample variance for this community is 83.5 square years.

Using the formula:

s = [tex]\sqrt{s2}[/tex]

The sample standard deviation can be calculated as follows:

s = [tex]\sqrt{83.5}[/tex] = 9.1 years

Therefore, the estimated sample standard deviation for this community is 9.1 years.

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Answer:

To determine the best course grade your friend can earn, we need to know how much the final exam is worth. Since the final counts for 30% of the course grade, the remaining 70% must be from the other work completed so far. Let's assume that there's only one final exam and that it's graded out of 100 points. If your friend's current average is 84%, then they have earned 84 points out of every 100 possible points so far. To find the best course grade your friend can earn, we can set up the following equation: 0.7(84) + 0.3(F) = G where F is the score your friend earns on the final exam, and G is the overall course grade. We can solve for G by plugging in F and simplifying the equation: 0.7(

Thus, an interval with such a 90% confidence level has a z-score of 1.645.

An interval estimate of the mean is what the confidence limits for mean are. Since the estimation of the mean differs from sample to sample, interval estimates are frequently preferred.

From the positive z score table:

As 0.90 falls perfectly between the 1.64 and 1.65 z-scores, I shall calculate the z-score as 1.645.

Thus, an interval with such a 90% confidence level has a z-score of 1.645.

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Complete question:

Assuming that the confidence coefficient is 90%, then Find the the z-value that would be used in the interval.

The quadrilateral ANDC is not cyclic because the four vertices of a quadrilateral ANDC do not lie on the circumference of the circle

A cyclic quadrilateral is a four-sided polygon where all four vertices of the quadrilateral lie on a common circle.

The circle is called the circumcircle, and it passes through all four vertices of the quadrilateral.

From the figure, we can see that only two vertices of ANDC lie on the circle

The other two are in the circle

Hence, the quadrilateral ANDC is not cyclic

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The portfolio should be invested as follows:

Stock A: $120,000 (12%)

Stock B: $220,000 (22%)

Stock C: $342,857 (34%)

Risk-free asset: $319,149 (32%)

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To create a portfolio equally as risky as the market, we need to calculate the portfolio's beta, which is the weighted average of the betas of the individual assets in the portfolio.

The beta of the market is 1, so we need to find the weights of each asset in the portfolio that will result in a beta of 1.

Let wA, wB, and wC be the weights of stocks A, B, and C in the portfolio, respectively. Since we want the portfolio to be equally as risky as the market, we have the following equation:

wA * 1.00 + wB * 1.20 + wC * 1.40 = 1.00

We also know that the total investment is $1,000,000, so we have:

wA * $120,000 + wB * $220,000 + wC * X + (1 - wA - wB - wC) * Y = $1,000,000

where X is the investment in stock C, and Y is the investment in the risk-free asset.

We have two equations and two unknowns, so we can solve for wC and Y:

wC = (1.00 - wA * 1.00 - wB * 1.20) / 1.40

$1,000,000 = wA * $120,000 + wB * $220,000 + wC * X + (1 - wA - wB - wC) * Y

Substituting the first equation into the second equation, we get:

$1,000,000 = wA * $120,000 + wB * $220,000 + [(1.00 - wA * 1.00 - wB * 1.20) / 1.40] * X + [1 - wA - wB - (1.00 - wA * 1.00 - wB * 1.20) / 1.40] * Y

Simplifying and solving for Y, we get:

Y = $319,149

Substituting this value back into the second equation and solving for X, we get:

X = $342,857

Therefore, the portfolio should be invested as follows:

Stock A: $120,000 (12%)

Stock B: $220,000 (22%)

Stock C: $342,857 (34%)

Risk-free asset: $319,149 (32%)

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