Solve for the variable. (g + 6)/3 = 11

Answer:

If the two alternate exterior angles are from two parallel lines cut by a transversal, angle 8 would be 30 degrees.

Explanation:

Alternate exterior angles resulting from two parallel lines cut by a transversal are congruent.

Answer:

1.54 × 10-4m²

Step-by-step explanation:

Unit Conversion,

r = 7 × 10-3m

Solution,

A = πr2 = π · (7 × 10-3)² ≈ 1.54 × 10-4m²

Answer:

154 mm²

Step-by-step explanation:

Given : -

Radius ( r ) = 7 mm

The value of π = 22/7

To find : Area of a cirlce

Formula : -

A = πr²

A = 22/7 * 7²

= 22/7 * 7 * 7

= (22 * 7 * 7)/7

= 22 * 7

A = 154 mm²

Hence,

the Area of the Circle is 154 mm².

Answer:

0.67

Step-by-step explanation:

Edge 2021

The probability that Mrs. Barnes does not check homework if the students take a pop quiz will be 0.77. Then the correct option is D.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42.

They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9.

Then the probability that Mrs. Barnes does not check homework if the students take a pop quiz will be

\(\rm P = 0.42 \times 0.60 + 0.58\times 0.90\\\\P = 0.252 + 0.522\\\\P = 0.774 \approx 0.77\)

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Answer:

Y =-2.5X +3.5

Step-by-step explanation:

x1 y1  x2 y2

-1 6  3 -4

(Y2-Y1) (-4)-(6)=   -10  ΔY -10

(X2-X1) (3)-(-1)=    4  ΔX 4

slope= -2  1/2    

B= 3  1/2    

Y =-2.5X +3.5    

The correct answer would be -3/8 or in decimal form -0.375 :)

Answer:

Its a

Step-by-step explanation:

Answer:

n = 72

Step-by-step explanation:

Multiply both sides of the equation by  8

\(8*\frac{n}{8}=8*9\)

Simplify/Solve.

\(n=72\)

hope this helps :)

The quadrilateral that has four congruent sides is option D. square. A square is a special type of rectangle and rhombus, characterized by having all four sides of equal length.

A parallelogram (option A) is a quadrilateral with opposite sides that are parallel. While the opposite sides of a parallelogram are congruent, it does not guarantee that all four sides are equal.

A rectangle (option B) is a quadrilateral with four right angles. While opposite sides of a rectangle are congruent, it does not necessarily have four congruent sides unless it is also a square.

A rhombus (option C) is a quadrilateral with all sides of equal length. While a rhombus does have four congruent sides, it is not the only quadrilateral with this property.

Therefore, among the given options, the quadrilateral that has four congruent sides is the square (option D).

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The probability that all three M&M's are brown is (0.5)^3 = 0.125.

The probability that the third M&M is the first one that's red is (0.2)^2 * 0.8 = 0.032.

The probability of the first two M&M's being non-red is (0.8)^2, and the probability of the third one being red is 0.2.

The probability that none of the M&M's are yellow is (0.8)^3 = 0.512.

Explanation: The probability of each M&M not being yellow is 0.8, so we multiply this probability for all three M&M's.

The probability that at least one M&M is green is 1 - the probability that none of them are green. The probability that none of them are green is (0.1)^3 = 0.001, so the probability that at least one is green is 1 - 0.001 = 0.999.

The probability of each M&M not being green is 0.9, so we multiply this probability for all three M&M's. Then, we subtract this probability from 1 to get the probability that at least one M&M is green.

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If the graphs of the linear equations are identical, then there are infinitely many solutions.

If the graphs are not identical, then there are not infinitely many solutions. In this case, there may be either no solutions (lines are parallel but not collinear) or one solution (the lines are not parallel but they intersect).

All the solution of the blank words are given below.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Figure ABCD is the pre-image.

And A'B'C'D' is the image.

The line of the reflection is y = 0.

The coordinates of the output:

A'(3, -6), B;(1, -1), C'(11, - 1) and D'(6, -6)

Therefore, all the blank words are given above.

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The price that that club members pay for the computer is $465.92.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

Since the selling price was first at 728, but then the store advertised a 20% markdown on the system and members of the store's loyalty club get an additional 20% off their computer purchases.

The cost will be calculated thus:

582.40 - (20% × $582.40)

= $582.40 - $116.48

= $465.92

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a) To determine if the treatment has a significant effect, we can perform a hypothesis test using the sample mean. The null hypothesis (H0) states that the treatment has no effect, while the alternative hypothesis (H1) states that the treatment does have an effect. In this case, we are conducting a two-tailed test with α = 0.05, meaning we are looking for extreme values in both tails of the distribution.

b) Using the same approach as in part a, we can calculate the z-score with a population standard deviation of σ = 12. Given M = 54, μ = 50, σ = 12, and n = 16, the z-score is calculated as z = (54 - 50) / (12 / √16) = 1.

To perform the test, we can calculate the z-score using the formula: z = (M - μ) / (σ / √n), where M is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, M = 54, μ = 50, σ = 8, and n = 16.

Plugging these values into the formula, we get z = (54 - 50) / (8 / √16) = 2. Using a z-table or a statistical calculator, we find that the critical z-value for a two-tailed test with α = 0.05 is approximately ±1.96.

Since our calculated z-value of 2 is greater than the critical value of 1.96, we reject the null hypothesis. This means that the sample mean of 54 is statistically significant and provides evidence that the treatment has a significant effect.

Comparing the calculated z-value of 1 to the critical z-value of 1.96, we see that the calculated value is less than the critical value. Therefore, we fail to reject the null hypothesis.

In other words, the sample mean of 54 is not statistically significant when the population standard deviation is 12, and we do not have sufficient evidence to conclude that the treatment has a significant effect.

The magnitude of the standard deviation (σ) plays a crucial role in hypothesis testing. A larger standard deviation indicates that the data points are more spread out from the mean, resulting in a wider distribution. As a result, it becomes more challenging to detect a significant effect of the treatment, as the variability in the data increases. This is evident when comparing parts a and b of the question.

In part a, where the population standard deviation is σ = 8, the calculated z-value of 2 exceeds the critical value of 1.96. This indicates that the sample mean of 54 is statistically significant, suggesting a significant effect of the treatment.

On the other hand, in part b, where the population standard deviation is larger at σ = 12, the calculated z-value of 1 is smaller than the critical value.

Consequently, we fail to reject the null hypothesis, implying that the sample mean of 54 is not statistically significant, and we cannot conclude that the treatment has a significant effect.

Thus, a larger standard deviation reduces the ability to detect a  significant effect in a hypothesis test.

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Answer:

1 is divided by 3z with difference 2

Answer:

1/5

Step-by-step explanation:

because multiply any different copies by 1/5 to get the cost of the print shop

There are 840 ways for the person to get 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die.

To calculate the number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die, we can use the formula for combinations with repetition.

The number of ways to choose 6 rolls to be fives out of 10 is given by the combination formula:

C(10, 6) = 10! / (6! * (10 - 6)!) = 210

Similarly, the number of ways to choose 3 rolls to be ones out of the remaining 4 rolls is:

C(4, 3) = 4! / (3! * (4 - 3)!) = 4

Finally, there is only one way to choose the remaining roll to be a two.

Therefore, the total number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die is:

210 * 4 * 1 = 840.

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The complex power is 1920 ∠ (-45°) VA, the average power is approximately 1357.1 W, and the reactive power is approximately -1357.1 VAR.

To find the complex power, average power, and reactive power, we need to calculate the complex power S, which is the product of the voltage and current phasors.

Given:

v(t) = 160 cos(377t) V

i(t) = 12 cos(377t + 45) A

The complex power is given by:

S = V * I*

where V is the phasor representing the voltage and I* is the complex conjugate of the phasor representing the current.

In phasor form:

V = 160 ∠ 0° V

I = 12 ∠ 45° A

Taking the complex conjugate of I:

I* = 12 ∠ (-45°) A

Now, we can calculate the complex power:

S = V * I*

S = (160 ∠ 0° V) * (12 ∠ (-45°) A)

Multiplying the magnitudes and adding the angles:

S = (160 * 12) ∠ (0° - 45°) VA

S = 1920 ∠ (-45°) VA

Therefore, the complex power is 1920 ∠ (-45°) VA.

To find the average power, we take the real part of the complex power:

Average Power = Re(S) = Re(1920 ∠ (-45°) VA)

Average Power = 1920 * cos(-45°) W

Average Power ≈ 1357.1 W

The reactive power can be found by taking the imaginary part of the complex power:

Reactive Power = Im(S) = Im(1920 ∠ (-45°) VA)

Reactive Power = 1920 * sin(-45°) VAR

Reactive Power ≈ -1357.1 VAR (Note: The reactive power is negative in this case.)

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Answer:

0.20x + 5 ≤ 12

Step-by-step explanation:

The parametric equations for the motion of the particle in the xy plane that traces the counterclockwise ellipse are x = 6cos(t) and y = 4sin(t), where t is the parameter. The parameter interval for the motion is 0 ≤ t ≤ 2π.

To find the parametric equations for the counterclockwise motion of the particle along the given ellipse, we can start by parameterizing the ellipse equation  \(16x^2 + 9y^2 =\) 144. We divide both sides of the equation by 144 to normalize it, giving us  \((x^2/9) + (y^2/16\)) = 1. By comparing this equation with the standard form of an ellipse, we can see that a = 3 and b = 4.

We can then use the trigonometric parametrization of an ellipse to obtain the parametric equations. Letting x = acos(t) and y = bsin(t), where t is the parameter, we substitute the values for a and b, resulting in x = 6cos(t) and y = 4sin(t). These equations represent the motion of the particle along the ellipse.

Since we want the particle to trace the ellipse counterclockwise, we need to cover the full circumference of the ellipse. This corresponds to a parameter interval of 0 ≤ t ≤ 2π, which completes one full revolution around the unit circle. Therefore, the parametric equations for the motion of the particle are x = 6cos(t) and y = 4sin(t), with a parameter interval of 0 ≤ t ≤ 2π.

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The car's horizontal distance from the building's base, to two decimal places, is roughly 64.24 m.

Let x be the horizontal distance between the car and the base of the building, and θ be the angle of depression of the car from the man on top of the building. The ratio of one side to the other in a right triangle is known as the tangent of the angle. Therefore, tan θ = opp/adj

Here, the opposite side is the height of the man plus the height of the building, and the adjacent side is x. Hence, tan θ = (h + 52)/x

where h is the height of the man, which is 1.75 m.

Substituting θ = 43°, h = 1.75 m, and solving for x:x = (h + 52) / tan θx = (1.75 + 52) / tan 43°x ≈ 64.24

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We can solve this problem by using some properties of centroids of the triangle and the fact that the centroid divides each median in a 2:1 ratio.

The centroid of a triangle is the point intersection of the three medians of the triangle.

First find the value of MR. The centroid divides each median in a 2:1 ratio, so we have:

MR = 2/3 * R + 1/3 * M

R is the centroid, so R = (P + V + M)/3.

Substituting, we get: MR = 2/3 * [(P + V + M)/3] + 1/3 * M

= 2/9 * P + 2/9 * V + 5/9 * M

Now, substitute the given values of PV and M to find MR:

MR = 2/9 * (3w+7) + 2/9 * (12y-9) + 5/9 * (5x-9) = (2w/3 + 8y/9 + 25x/9) - 1

Simplifying the expression: MR = (2w + 24y + 25x - 27)/9

Next, let's find the value of RP using the centroid. Since R is the midpoint of PV:

RP = 2/3 * R + 1/3 * P

Substituting the values of R and P:

RP = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (3w+7)

= (2w/9 + 8y/9 + 5x/3 + 7/3) + (w+7)/3

= (5w/3 + 8y/9 + 5x/3 + 10)/3

Simplifying this:

RP = (5w + 8y + 5x + 30)/9

Next, find the value of RV using the centroid. R is the midpoint of PV:

So, RV = 2/3 * R + 1/3 * V

Substituting R and V values:

RV = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (12y-9) = (2w/9 + 8y/9 + 5x/3 + 7/3) + 4y/3 - 3

Simplifying: RV = (5w + 20y + 5x - 18)/9

Find the value of RW using the centroid. R is the midpoint of VW, so: RW = 2/3 * R + 1/3 * W

Substituting the values of R and W:

RW = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * 1.75x = (2w/9 + 8y

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The type of triangle it is C. equilateral.

Since the triangle has sides measuring 4 cm, 4 cm and 4 cm, all its sides are equal.

Also, two of its angles measure 60°.

We need to determine the third angle.

Let the third angle be x.

So, 60° + 60° + x = 180° (Sum of angles in a triangle)

120° + x = 180°

x = 180° - 120°

x = 60°

Since the third angle is 60°, it implies that all its angles are 60°.

So, a triangle haing all its angles as 60° and sides equal is an equilateral triangle.

So, the type of triangle it is C. equilateral.

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Answer:

Step-by-step explanation:

Opposite sides are parallel and congruent. Opposite angles are congruent. Adjacent angles are supplementary. ... If one of the angles of a parallelogram is a right angle then all other angles are right and it becomes a rectangle.

The fraction of the total number of math Matthew completed = 0

The fraction of the total number of science Matthew completed = 12/12

Information given requires getting the fraction of problems solved by Matthew

science problems solved = 12

math problems = 0

fraction of total number

for science = science problems solved / total number of problems solved

= 12 / (12 + 0)

= 12/12

for math = math problems solved / total number of problems solved

= 0 / (12 + 0)

= 0 / 12

= 0

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Answer:

i think its 12!

Step-by-step explanation:

Options

A. Caroline rents exactly 7 games each month.

B. Caroline rents exactly 6 games each month.

C. Caroline rents 6 or more games each month.

D. Caroline rents from 1 to 5 games each month.

Answer:

D. Caroline rents from 1 to 5 games each month.

Step-by-step explanation:

Given

Plan A:

\(C = 2n\)

Plan B:

\(C = n + 6\)

Required

Which options justifies A over B

The solution to this question is option (d).

In option d, n = 1,2,3,4,5

When any of the values of n is substituted in plan A and B, respectively; the cost of plan A is cheaper than plan B.

This is not so, for other options (A - C)

To show:

Substitute 1 for n in A and B

Plan A:

\(C = 2n\)  \(= 2 * 1 = 2\)

Plan B:

\(C = n + 6\) \(= 1 + 6 = 7\)

Substitute 5 for n in A and B

Plan A:

\(C = 2n\)  \(= 2 * 5 = 10\)

Plan B:

\(C = n + 6\) \(= 5 + 6 = 11\)

See that A < B

The 25th percentile of the sum total amount of time that all 40 individuals spent in grad school is approximately 205.0139 years. the closest value to 205.0139 is 205.0139, so the answer is:205.0139.

To find the 25th percentile of the sum total amount of time that all 40 individuals spent in grad school, we need to calculate the cumulative distribution function (CDF) of the sum total time and find the value at which it is equal to or greater than 0.25.

The sum total time is the product of the average time and the number of individuals, which is 5.2 years * 40 = 208 years.

The standard deviation of the sum total time can be calculated by multiplying the standard deviation of an individual's time by the square root of the sample size. So, the standard deviation of the sum total time is 0.7 years * sqrt(40) = 4.41596 years.

Using these values, we can calculate the z-score corresponding to the 25th percentile:

z = (x - μ) / σ

z = (x - 208) / 4.41596

To find the value of x corresponding to the 25th percentile, we need to solve for x when the cumulative distribution function (CDF) is equal to 0.25. Using a standard normal distribution table or a statistical software, we find that the z-score corresponding to a CDF of 0.25 is approximately -0.6745.

Substituting this value into the z-score equation:

-0.6745 = (x - 208) / 4.41596

Solving for x:

x = -0.6745 * 4.41596 + 208

x ≈ 205.0139

Therefore, the 25th percentile of the sum total amount of time that all 40 individuals spent in grad school is approximately 205.0139 years.

Among the given options, the closest value to 205.0139 is 205.0139, so the answer is:205.0139.

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Answer:

m<A = 39

Step-by-step explanation:

1. Approach

To solve this problem, one first has to find the value of "x", then one will substitute "x" back into the equation given for the value of m<A, to solve for m<A. In order to solve this problem, one has to know that the sum of angle measures in a triangle will always equal 180.

2. Solving for "x"

The sum of angle measure in a triangle will always equal 180 degrees, hence one can set up an equation,

m<A + m<B + m<C = 180

Substitute,

(10x - 1) + (18x + 2) + (15x + 7) = 180

Simplify,

43x + 8 = 180

Inverse operations,

43x + 8 = 180

        -8       -8

43x = 172

/43         /43

x = 4

3. Solve for m<A

Now all one has to do is substitute the value of "x" back in to solve for m<A

10x - 1

x = 4

10(4) - 1

40 - 1

39

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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Answer:

I hope this helps

Step-by-step explanation:

Answer:

The numbers are 27 and 30

Step-by-step explanation:

Assume that the even number is x and the odd number is y

∵ The even number is x

∵ The odd number is y

∵ Their sum is 57

→ Add them and equate the sum by 57

∴ x + y = 57 ⇒ (1)

∵ Their difference is 3

→ Subtract them and equate the difference by 3

∴ x - y = 3 ⇒ (2)

→ Let us solve the system of the equations by adding equations (1) and (2)

∵ (x + x) + (y - y) = (57 + 3)

∴ 2x + 0 = 60

∴ 2x = 60

→ Divide the two sides by 2

∴ x = 30

→ Substitute the value of x in equation (1) to find the value of y

∵ 30 + y = 57

→ Subtract 30 from both sides

∴ 30 - 30 + y = 57 - 30

∴ y = 27

∴ The numbers are 27 and 30