Factor.
9q3+9q2–2q–2​

A circle inside a semicircle is depicted in the diagram. The circle measures 10 cm in diameter. The semicircle has a 20 cm diameter. Calculate the shaded area. Give a precise response to the nearest decimal point.

The area of the shaded region is 39.3\(cm^{2}\).

Given the diagram shows a circle inside a semicircle.

Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the center. All lines that cross the circle join together to produce the line of reflection symmetry. Every angle also possesses rotational symmetry about its center.

Area of a circle = \(\pi r^{2}\).

Semicircle is when a line travelling through the center of a circle reaches its two ends, a semicircle is created. Thus, a circle can be formed by combining two semicircles.

Area of a semicircle = \(\frac{1}{2} \pi r^{2}\).

The circle has a diameter of 10 cm. The semicircle has a diameter of 20 cm.

Semicircle:

\(r_{1}=\frac{d_{1} }{2}=\frac{20}{2}=10cm\\S_{1}=\frac{ \pi r_{1}^{2} }{2} =\frac{ \pi \times 10^{2} }{2} =50\pi cm^{2}\)

Circle:

\(r_{2}=\frac{d_{2} }{2}=\frac{10}{2}=5cm\\S_{2}=\pi r_{2}^{2} = \pi \times 5^{2} =25\pi cm^{2}\)

So,

\(S=\frac{S_{1} -S_{2}}{2} \\S=\frac{50\pi -25\pi}{2}\\S=\frac{25\pi}{2} \\S=39.3cm^{2}\)

Therefore, The area of the shaded region is 39.3\(cm^{2}\).

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Answer:

S= 5, L= 12

Step-by-step explanation:

To find the value of L and S, we need to first label the 2 equations.

L +S= 17 -----(1)

3L +2S= 46 -----(2)

From (1):

L= 17 -S -----(3) (-S on both sides)

Subst. (3) into (2):

3(17-S) +2S= 46

3(17) -3S +2S= 46 (expand)

51 -S= 46

-S= 46 -51 (-51 on both sides)

-S= -5

S= 5 (divide by -1 throughout)

Subst. S=5 into (3):

L= 17 -5

L= 12

Answer:

sorry i didn't get it

Step-by-step explanation:

Answer: She wants it written down because she does not like Mr. Pearson's attitude. He can't call her by a nickname if she can't call him by a nickname.

Step-by-step explanation:

Answer:

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

We can observe it is a special form of the difference of squares identity:

where a = 3x and b = 5y

Therefore the polynomial is:

Answer:

\(9x^2 - 25y^2\)

Step-by-step explanation:

\(\sf (3x + 5y)(3x - 5y) = (3x)^2 - (5y)^2\)

\(\sf (a^2 - b^2) = (a + b)(a - b)\)

\(\sf (3x + 5y)(3x - 5y) \\\\ (3x)^2 - (5y)^2 \\\\ 9x^2 - 25y^2\)

\(\sf (3x + 5y)(3x - 5y) = 9x^2 - 25y^2\)

e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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Answer:

C. ED

Step-by-step explanation:

The center of the angle is the point E, so it would be written first.

Answer:

Point A

Step-by-step explanation:

Look along the x axis (horizontal) and find -1. Then look on the y axis and find 1 and 1/4. Finally, find where the two coordinates meet and that's your point - A.

Hope this helps!

Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.

As given in the question,

Perimeter of the rectangular area encloses for fencing = 3200 yards

Let 'x' and 'y' be the length and width of the rectangle.

2( x + y ) = 3200

⇒ x + y = 3200/2

⇒y = 1600 - x

Area of rectangular field 'A' = xy

⇒ A = x ( 1600 - x )

⇒ A = 1600x - x²

Differentiate both the side of the equation we get,

dA/dx = 1600 - 2x

For Maximum Area dA/dx = 0

1600 -2x =0

⇒ 2x = 1600

⇒ x= 800 yards

Now, y = 1600 - 800

          = 800 yards

Maximum area = (800) (800)

                        = 640,000 square yards

Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.

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Hello!

\(\large\boxed{B. \text{ } One}\)

2x - y = 6

3x + 5y = -17

Solve systems of equations by elimination.

The easiest variable to eliminate would be y since we can simply multiply the first equation by 5:

5(2x - y = 6)

3x + 5y = -17

10x - 5y = 30

3x + 5y = -17

Eliminate y by adding both equations to each other:

10x - 5y = 30

3x + 5y = -17

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

13x + 0y = 13

13x = 13

13x/13 = 13/13

x = 1

Therefore, there is only ONE solution to this system of equations because we only could derive one solution.

Answer:

x ≤ 2

Step-by-step explanation:

The number line graph corresponds to

x ≤ 2

hello

to solve this problem, let's represent the first consecutive number with x and the second with x + 2

from the information on the question, we can set out an equation here

let's solve this equation

step 1

collect like terms

step two

divide both sides by the coefficient of x

1. A graph of two similar, but not equal, right triangles using segments of line AB as the hypotenuse of each triangle is shown below.

2. The three pair of corresponding angles and sets of proportionate sides include:

ΔACE ≅ ΔBDF, ΔAEC ≅ ΔBFD, and ΔCAE ≅ ΔDBF.

AC = BD, EC = FD, and AE = BF

3. Yes, the slope of line is the same between any two points on the line.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Part 1.

In this exercise, we would use an online graphing tool to create two similar, but not equal, right triangles by using line segments AB as the hypotenuse of each triangle.

Part 2.

Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent (similar) triangles and sets of proportionate sides:

Part 3.

In Mathematics and Geometry, the slope of any straight line can be determined by using this formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope AC = (0 + 1)/(-3 + 5)

Slope AC = 1/2.

Slope BD = (3.5 - 2)/(4 - 1)

Slope BD = 1/2.

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Answer:

y=1

x=3

Step-by-step explanation:

Multiply 2x by three because if you substitute to y, you would have the multiply.

Write what is left. 6y+4y=10

Combine like terms   10y=10

y=1

x=3

Check      3=3(1)

                     6+4=10

So this solution is correct

Answer and Step-by-step explanation:

The answer you chose is correct:

D. 2(5w + 5)

This is equivalent to 10w + 10.

This is because the 2 is a factor of 10, so when distributed out of the 10's, we get 5.

#teamtrees #PAW (Plant And Water)

Answer:

Explanation:

The given polynomial is expressed as

16x^2 - 1

The standard form of a quadratic polynomial is expressed as

ax^2 + bx + c

By comparing both polynomials,

a = 16

b = 0

c = - 1

Answer:

The answer should be 10:7.

Hey there!

40:28

= 40 ÷ 2 : 28 ÷ 2

= 20 : 14

= 20 ÷ 2 : 14 ÷ 2

= 10 : 7

Therefore, your answer is: 10:7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The algebraic expression for total hours that represents the number of hours per week the theater is open is 4 x + 3 y

Number of hours the theatre is opened on Monday to Thursday = x hours.

Number of hours the theatre is opened on Friday to Sunday = y hours.

Number of hours from Monday to Thursday = 4 x hours.

Number of hours from Friday to Sunday = 3 y hours.

Total hours will be represented by the algebraic expression:

Total hours = 4 x + 3 y.

Therefore, the algebraic expression for total hours that represents the number of hours per week the theater is open is 4 x + 3 y

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Answer:

D c+364=500

Step-by-step explanation:

Answer:

A. C + 364 = 500

Step-by-step explanation:

The initial amount and rate of change given a table for a linear function are $65 and $86, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 476) and (10, 736)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (736 - 476)/(10 - 6)

Evaluate

Rate = 65

This means that the rate of change is $65

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 65

So, we have

y = 65(x - x1) + y1

Using one of the points, we have

y = 65(x - 6) + 476

Set x = 0

So, we have

y = 65(0 - 6) + 476

Evaluate

y = 86

Hence, the initial amount and rate of change given a table for a linear function are $65 and $86, respectively

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Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

The correlation that demonstrates the weakest correlation between two variables is option a) +.20.

Among the given options, the correlation that demonstrates the weakest correlation between two variables is option b) -50.

In correlation coefficients, the value ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation or a very weak correlation.

Let's analyze the options provided:

a) +.20:

This indicates a positive correlation, but the value is relatively small (0.20).

It suggests a weak positive relationship between the variables.

b) -50:

This option appears to be a typographical error since the correlation coefficient cannot be negative 50.

Assuming it is meant to be -0.50, this indicates a moderate negative correlation.

c) +.75:

This option represents a strong positive correlation.

With a coefficient of 0.75, it suggests a relatively strong positive relationship between the variables.

d) -76: Similar to option b, this value appears to be a typographical error. A correlation coefficient cannot exceed the range of -1 to +1.

Assuming it is meant to be -0.76, this indicates a strong negative correlation.

Comparing the given options, the weakest correlation is option b) -50, assuming it was intended to be -0.50. A correlation coefficient of -0.50 represents a moderate negative correlation, which is weaker than the other options but still indicates some relationship between the variables.

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We are given radius, r = 7 inches

We know that :

Circumference = 2πr

⟹ Circumference = 2π × 7 inches

⟹ Circumference = 14π inches

Hence, circumference of circle is 14π inches.

Answer:

You don't like them

Step-by-step explanation:

definition: contemptuously  

ADVERB

contemptuously (adverb)

in a scornful way that shows disdain.

"he contemptuously dismisses his son's work"

Answer:

confusion

Step-by-step explanation:

The assumptions for the two proportions z-test that would not be a concern, in this case, are random sampling, independence, large sample size, and normality of the sampling distribution.

When comparing two proportions using a z-test, there are several assumptions that need to be met to ensure that the results are valid. In this case, the assumptions that would not be a concern are:

Random sampling: The sample of 50 mushrooms from each company is assumed to be a random sample from the population of mushrooms for each company. This assumption ensures that the sample is representative of the population and that the results can be generalized to the larger population.

Independence: The samples from each company are assumed to be independent of each other. This means that the mushrooms from one company do not influence the mushrooms from the other company in any way. This assumption is necessary for the validity of the z-test.

Large sample size: The sample size of 50 mushrooms from each company is sufficiently large. When the sample size is large, the sample proportion can be used as an estimate of the population proportion, and the sampling distribution can be assumed to be approximately normal. A general rule of thumb is that the sample size should be at least 30.

Normality: The z-test assumes that the sampling distribution of the difference between the two sample proportions is approximately normal. This assumption is valid when the sample size is large, as mentioned above.

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a)The mean of the sampling distribution is equal to the population mean, so it is 6.04 thousand dollars.

b)Standard deviation \(= 26.5 / \sqrt(15) = 6.830\) thousand dollars.

the probability that the mean daily commissions received is between \(\$561,116\)and \(\$697,016\) is approximately \(99.77\% - 0.01\% = 99.76\%.\)

To solve the given questions, we'll use the properties of the normal distribution.

1. Sampling Distribution:

a) Mean of the sampling distribution of the sample mean daily commissions received:

The mean of the sampling distribution is equal to the population mean, so it is 6.04 thousand dollars.

b) Standard deviation of the sampling distribution of the sample mean daily commissions received:

The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size:

Standard deviation\(= 26.5 / \sqrt(15) = 6.830\) thousand dollars.

2. Probability Calculations:

a) Probability that the mean daily commissions received is more than $581,652:

We'll calculate the z-score using the formula\(\[ z = \frac{{(\$581,652 - \$604)}}{{\left(\frac{{6.830}}{{\sqrt{15}}}\right)}} \approx -3.161 \]\)

Using a standard normal distribution table, we find that the probability is approximately 0.0008, or 0.08%.

b) Probability that the mean daily commissions received is between $561,116 and $697,016:

We'll calculate the z-scores for both values and find the probabilities associated with those z-scores:

\(z_1 = ($561,116 - $604) / (6.830 / \sqrt(15)) = -3.907\)

\(z2 = ($697,016 - $604) / (6.830 / \sqrt(15)) = 2.870\)

Using the standard normal distribution table, we find the probability associated with z1 as approximately 0.0001, or 0.01%, and the probability associated with z2 as approximately 0.9977, or 99.77%.

Therefore, the probability that the mean daily commissions received is between $561,116 and $697,016 is approximately 99.77% - 0.01% = 99.76%.

3. Maximum average daily commissions receivable from the lowest 7.5% volume trading days:

We'll find the z-score corresponding to the lowest 7.5%:

Using a standard normal distribution table, we find the z-score corresponding to the lowest 7.5% as approximately -1.15.

Now we'll find the corresponding value in the original scale:

\(\[ z = \frac{{(x - \mu)}}{\sigma} \]\)

\(-1.15 = (x - 99.7) / 2.9\)

\(x - 99.7 = -1.15 * 2.9\)

\(x - 99.7 = -3.335\)

\(x = 96.365\)

Rounding to the nearest thousand dollars, the maximum average daily commissions receivable is approximately \(\$96,000.\)

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1. a) Mean = $6.04 thousand dollars
  b) Standard deviation = $6.823 thousand dollars
2. a) Probability = 100%
  b) Probability = 100%
3. Maximum average daily commissions receivable = $98,000

1. To determine the mean and standard deviation of the sampling distribution of the sample mean daily commissions received (in thousand dollars), we can use the following formulas:

a) Mean of the sampling distribution = Mean of the population = $6.04
b) Standard deviation of the sampling distribution = Standard deviation of the population / Square root of the sample size

= \(\frac{\$26.5}{\sqrt{15}} = \$6.823\)

2. To find the probabilities, we need to use the z-score formula:

a) To find the probability that the mean daily commissions received is more than $581,652, we first need to find the z-score.

The z-score formula is given by:

\(z = \frac{x - \mu}{\frac{\sigma}{\sqrt{n}}}\),

where x is the value we want to find the probability for, μ is the mean of the population, σ is the standard deviation of the population, and n is the sample size.

z = \(\frac{\$581,652 - \$6.04}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z = 21518.78

Using a standard normal distribution table or a calculator, we find that the probability is approximately 1.

b) To find the probability that the mean daily commissions received is between $561,116 and $697,016, we need to find the z-scores for both values.

z₁ = \(\frac{(\$561,116 - \$6.04)}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z₁ = 20618.03

z₂ = \(\frac{\$697,016 - \$6.04}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z₂ = 25618.23

Using the standard normal distribution table or a calculator, we find that the probability is approximately 1.

3. To find the maximum average daily commissions receivable from the lowest 7.5% volume trading days, we need to find the z-score that corresponds to a cumulative probability of 0.075.

Using the z-score formula and rearranging it to solve for x, we have: \(x = z \cdot \left(\frac{\sigma}{\sqrt{n}}\right) + \mu\)

First, we find the z-score using the standard normal distribution table or a calculator. For a cumulative probability of 0.075, the z-score is approximately -1.405.

Then, we plug in the values to find x:

x = \(-1.405 \cdot \left(\frac{$2.9}{\sqrt{29}}\right) + $99.7\)

x = $98.324

Rounding to the nearest thousand dollars, the maximum average daily commissions receivable from the lowest 7.5% volume trading days is $98,000.

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Answer:

well for starters

the answer you get when you factor it out is 3(x+3)(x+3)

i know that would mean x=-3 but i dont know how the big 3 would effect anything. hope this helps

a. The sample proportion is calculated by dividing the number of voters in favor of the school bond measure (281) by the total number of voters in the sample (1000). Therefore, the sample proportion is 0.281.

b. The margin of error for a 90% confidence level can be calculated using the formula: margin of error = 1.645 x sqrt[(sample proportion x (1 - sample proportion)) / sample size]. Plugging in the values, we get: margin of error = 1.645 x sqrt[(0.281 x 0.719) / 1000] = 0.028.
c. The margin of error for a 95% confidence level can be calculated using the same formula: margin of error = 1.96 x sqrt[(sample proportion x (1 - sample proportion)) / sample size]. Plugging in the values, we get: margin of error = 1.96 x sqrt[(0.281 x 0.719) / 1000] = 0.032.
d. The 95% confidence interval can be calculated using the formula: sample proportion +/- (margin of error x z-score), where the z-score for a 95% confidence level is 1.96. Plugging in the values, we get: 0.281 +/- (0.032 x 1.96) = [0.219, 0.343]. Therefore, the 95% confidence interval is [0.219, 0.343].

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