Consider the following figure where l1 and l2 are parallel and cut by transversals g1
and g2.

Part A: Determine the values of m, n, v, and r.

Part B: if m|o=8p-12, then determine the value of (p/1/4)


Help please

Hence,  when \(n=10\) the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.

So,

\(2(n + 2) < 5(n-1)\)

When

\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)

Hence,  when \(n=10\) the given inequality is true.

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Answer:

7 groups

Step-by-step explanation:

1 hour = 60 minutes

3/4 of an hour = 3/4(60) = 45 minutes

therefore, 1 3/4 hours is 105 minutes

105 divided by 15 is 7

=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

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To test if there is a difference between the means of the two populations, we can perform a two-sample t-test. The null hypothesis is that there is no difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.

Let's assume that the researcher has collected the following data:

Sample of families with no children: n1 = 30, sample mean = 4.5 hours per week, sample standard deviation = 1.2 hours per week.

Sample of families with children: n2 = 40, sample mean = 3.8 hours per week, sample standard deviation = 1.5 hours per week.

Using the critical value method, we need to calculate the t-statistic and compare it to the critical value from the t-distribution table with n1+n2-2 degrees of freedom and a significance level of α = 0.05.

The formula for the t-statistic is:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the numbers, we get:

t = (4.5 - 3.8) / sqrt((1.2^2/30) + (1.5^2/40)) = 2.08

The degrees of freedom for the t-distribution is df = n1 + n2 - 2 = 68.

Using a t-distribution table, we find the critical value for a two-tailed test with α = 0.05 and df = 68 is ±1.997.

Since our calculated t-statistic of 2.08 is greater than the critical value of 1.997, we can reject the null hypothesis and conclude that there is a statistically significant difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.

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The probability of a bulb lasting for at most 607 hours is 0.7517. To find the probability of a bulb lasting for at most 607 hours, we can use the standard normal distribution and standardize the value using the z-score formula.

The z-score measures the number of standard deviations an observation is from the mean. First, we need to calculate the z-score using the formula:

z = (x - μ) / σ

Where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, x = 607, μ = 590, and σ = √625 = 25.

Plugging these values into the formula, we get: z = (607 - 590) / 25 = 0.68

Next, we need to find the probability corresponding to this z-score. We can use a standard normal distribution table or a calculator to find the cumulative probability. Looking up the z-score of 0.68 in a standard normal distribution table, we find that the cumulative probability is approximately 0.7517.

Therefore, the probability of a bulb lasting for at most 607 hours is 0.7517 (rounded to four decimal places).

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Answer:

-2 inches per hour

Step-by-step explanation:

Finding the average rate of change is just like finding the slope. So, take the y values (height) and subtract them and divide that by the difference in the x values (time).

( 3 - 9 ) / ( 8 - 5 )

= -6 / 3

= -2 inches per hour

Answer:

Step-by-step explanation:

The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.

Diagonal = 5 * 2 = 10

P = 2√2 * 10

P = 20√2

Speed = Distance/Time

So, speed

= 300 km/2h

= 150km/h

= (150 × 1000m) / 3600s

= 150000m/3600s

= 41.66m/s [approximately]

The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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The two outliers in the scatter plot below are the points with shoe size 5 and shoe size 12.

These outliers are likely due to the fact that the data set includes people of all ages, and shoe size is not a linear function of height. For example, a 5-year-old child is likely to have a shoe size of 5, even though they are much shorter than an adult with a shoe size of 5. Similarly, an adult with a shoe size of 12 is likely to be much taller than a child with a shoe size of 12.

In order to get a more accurate representation of the relationship between height and shoe size, it would be necessary to remove the outliers and only consider data from people of similar ages.

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By using congruency definitions, we can show that corresponding parts of two triangles are congruent.

Congruent triangles have the same corresponding angle measures and side lengths.

Given two triangles,

We can show that corresponding parts of two triangles are congruent by showing both the triangles congruent, then by CPCT we'll get the corresponding parts of congruent triangles are congruent.

Hence, By using congruency definitions, we can show that corresponding parts of two triangles are congruent.

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Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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Answer: 11

Step-by-step explanation:

Based on te question in the picture (which is different from what you wrote)

x^2 - 3x  +  1

-2^2 - 3(-2) + 1

4 + 6 + 1 = 11

a) 26 teenagers are in the group.   21+3+2=26

b) 21 like to drink coffee or tea only.    (3 like both and 2 like neither, so 21 enjoy one or the other)

Answer;

Explanation;

Here we want to write an algebraic expression

The quotient of 24 and 6 less than m

Mathematically, 6 less than m means we are to subtract 6 from m

We can have this as;

Quotient means the result of a division

So, basically, we are to divide 24 by the expression

Mathematically, we have this as;

Answer:

12.5

Step-by-step explanation:

Answer:

In this case, there are 2 green marbles out of a total of 5 blue + 2 green + 4 pink marbles, which is 11 marbles in total. Therefore, the probability of selecting one green marble is 2 out of 11. The correct answer is A. 2/11.

Step-by-step explanation:

Answer:

A. 2/11

Step-by-step explanation:

We Know

There are 5 blue, 2 green, and 4 pink marbles in a bag.

5 + 2 + 4 = 11 marbles in the bag

What is the probability of randomly selecting one green marble from the bag?

We Take

(2 ÷ 11) = 2/11

So, the answer is A. 2/11

Answer:

2.7 and 3.4 is the answer

The approximate solution of the equation shown in the picture is x ≈ 39 / 8 (Right choice: B).

The solution of the equation is between x = 4 and x = 5. Now we begin by evaluating each side of the expression (f(x) = x² - 5 · x + 4, g(x) = 2 / (x - 1)) at the average of x = 4 and x = 5.

x = (4 + 5) / 2

x = 4.5

f(4.5) = 4.5² - 5 · 4.5 + 1

f(4.5) = - 5 / 4

g(4.5) = 2 / (4.5 - 1)

g(4.5) = 4 / 7

The solution of the equation is between x = 4.5 and x = 5, then we evaluate at the average:

x = (4.5 + 5) / 2

x = 4.75

f(4.75) = 4.75² - 5 · 4.75 + 1

f(4.75) = - 3 / 16

g(4.75) = 2 / (4.75 - 1)

g(4.75) = 8 / 15

The solution of the equation is between x = 4.75 and x = 5, then we evaluate at the average:

x = (4.75 + 5) / 2

x = 4.875

f(4.875) = 4.875² - 5 · 4.875 + 1

f(4.875) = 25 / 64

g(4.875) = 2 / (4.875 - 1)

g(4.875) = 16 / 31

The approximate solution of the equation shown in the picture is x ≈ 39 / 8 (Right choice: B).

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The volume obtained by rotating the region enclosed by the given curves about the y-axis is \(\frac{320\pi}{3}\).

To compute the volume using the Shell Method, we need to integrate the circumference of the shells multiplied by their height over the interval of rotation.

First, let's find the intersection points of the two curves:

\(y = (x^2 + 1)^{-2}\\ y = 2 - (x^2 + 1)^{-2}\)

Setting these two equations equal, we get:

\((x^2 + 1)^{-2} = 2 - (x^2 + 1)^{-2}\)

Multiplying both sides by (x^2 + 1)^2, we have:

\(1 = 2(x^2 + 1)^2 - 1\)

Expanding and rearranging the equation, we get:

\(2(x^2 + 1)^2 = 2\)

Dividing both sides by 2, we have:

\((x^2 + 1)^2 = 1\)

Taking the square root of both sides, we get:

\($x^2 + 1 = \pm 1$\)

Solving for x, we have two cases:

\(x^2 + 1 = 1\\ x^2 = 0\\ x = 0\)

\(x^2 + 1 = -1\) (extraneous solution)

\(x^2 = -2\) (no real solution)

Therefore, the intersection point is (0, 1).

Now, let's set up the integral using the Shell Method. We will integrate over the interval from y = 0 to y = 1.

The radius of each shell is given by the x-coordinate, which is x = 9.

The height of each shell is given by the difference in y-values, which is y \($2 - \left(x^2 + 1\right)^{-2} - \left(x^2 + 1\right)^{-2}$\)

The volume is given by the integral:

\($V = 2\pi \int_0^1 x(y) h(y) dy$\)

Substituting the values, we have:

\($V = 2\pi \int_0^1 9\left(2 - \left(9^2 + 1\right)^{-2} - \left(9^2 + 1\right)^{-2}\right) dy$\)

Simplifying further, we have:

\($V = 18\pi \int_{0}^{1} \left(2 - \left(82 + 1\right)^{-2} - \left(82 + 1\right)^{-2}\right) , dy$\)

Evaluating this integral will give the volume of the solid obtained by rotating the region enclosed by the given curves about the y-axis.

Let's simplify the expression inside the integral:

\(V = 18\pi \int_0^1 \left(2 - \left(8^2 + 1\right)^{-2} - \left(8^2 + 1\right)^{-2}\right) dy\\\ = 18\pi \int_0^1 \left(2 - \frac{1}{81} - \frac{1}{81}\right) dy\\\ = 18\pi \int_0^1 \left(2 - \frac{2}{81}\right) dy\\\ = 18\pi \int_0^1 \frac{160}{81} dy\\\ = \left(18\pi\right)\left(\frac{160}{81}\right) \int_0^1 dy\\\ = \left(18\pi\right)\left(\frac{160}{81}\right)\left[y\right]_0^1\\\ = \left(18\pi\right)\left(\frac{160}{81}\right)\left(1 - 0\right)\\\ = \frac{320\pi}{3}\)

Therefore, the volume obtained by rotating the region enclosed by the given curves about the y-axis is 320π/3

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Answer:

x = 138

Step-by-step explanation:

The 2 arcs above the diameter form a semicircle = 180°

x + 42 = 180 ( subtract 42 from both sides )

x = 138

The function \(f(x) = 4x^3 - 4\) is a polynomial function. It takes an input value x and returns an output value f(x) based on the expression \(4x^3 - 4.\)So the value of f(-1/2) is -4.5.

When we evaluate f(-1/2), we substitute -1/2 for x in the expression for f(x). This gives us:

\(f(-1/2) = 4(-1/2)^3 - 4\)

The expression inside the parentheses, \((-1/2)^3,\\\) is the cube of -1/2. To simplify this expression, we need to first raise -1/2 to the power of 3:

\((-1/2)^3 = (-1/2) * (-1/2) * (-1/2) = -1/8\)

Next, we substitute this value back into the expression for f(-1/2):

f(-1/2) = 4(-1/8) - 4

Now we can simplify the expression by multiplying 4 and -1/8:

f(-1/2) = -1/2 - 4

Finally, we subtract 4 from -1/2 to get the final answer:

f(-1/2) = -4.5

So the value of f(-1/2) is -4.5.

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Given the function f(x) = 4x^3 - 4, find the value of f(- 1/2)?

This function is neither even nor odd.

We have

f(x) = 5x² + 2x + 1

f(-x) = 5 (-x)² + 2 (-x) + 1 = 5x² - 2x + 1

- f(x) = -5x² - 2x - 1

but neither f(-x) = f(x) nor f(-x) = -f(x).

Answer:

10)17.5

11)18

12)70

13)110

Problem 10

This is because the opposite sides of any parallelogram are congruent (PQ = RS and QR = PS)

======================================

Problem 11

Diagonal QS is cut in half (bisected) by the other diagonal PR. The smaller pieces QT and ST are the same length.

======================================

Problem 12

The angle QRS is given to be 110 degrees. Angle PQR adds to this to get 180, so we effectively solve x+110 = 180 to get x = 70. Any pair of adjacent angles of any parallelogram are supplementary.

======================================

Problem 13

Opposite angles of a parallelogram are congruent. Angle SPQ is opposite of angle QRS = 110.

When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when the advances are not given for shows. This is to ensure that the performer is fully committed to performing at the event and to cover any expenses that may be incurred in the process.

The advance fee is usually non-refundable and is paid by the promoter or venue operator to the booking agent. This is to show their commitment to the performer and to demonstrate that they are serious about booking them for the event. The remaining balance is then usually paid on the day of the performance or shortly after.

The booking agent should also ensure that all parties involved in the booking are aware of the terms and conditions and have signed a contract or agreement to confirm their agreement.

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The length of line segment ab is approximately 3.74 units.

Given that a(5, 2, 0) and b(6, 0, 3), we can calculate the length of line segment ab as follows;

We know that, the length of a line segment AB can be calculated as follows;

AB2=(xb−xa)2+(yb−ya)2+(zb−za)2AB = √(xb−xa)2+(yb−ya)2+(zb−za)2

Therefore, using the above formula, the length of line segment ab is given by;

AB = √(xb−xa)2+(yb−ya)2+(zb−za)2

Where xa = 5, xb = 6, ya = 2, yb = 0, za = 0, and zb = 3AB = √(6 - 5)2 + (0 - 2)2 + (3 - 0)2

AB = √1 + 4 + 9AB = √14 ≈ 3.74 units

Therefore, the length of line segment ab is approximately 3.74 units.

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Answer:

I don't know sir actually I didn't understand your question no need to reply to my answer bye

Answer:

13

Step-by-step explanation:

if you read through the paragraph and pot your data on the table, the answer will show and is 13