What is the answer to this question ?

Answer:

x = 45°

Step-by-step explanation:

It a transversal line intersect two parallel lines, then alternative interior angles are congruent.

From the below graph it is clear that the line m and n are two parallel lines and l is a transversal line.

[tex]\angle ABC\cong \angle BCD[/tex]          (Alternative interior angles)

[tex]m\angle ABC=m\angle BCD[/tex]          (Definition of congruent angles)

[tex]x+30^{\circ}=75^{\circ}[/tex]

Subtract 30° from both sides.

[tex]x+30^{\circ}-30^{\circ}=75^{\circ}-30^{\circ}[/tex]

[tex]x=45^{\circ}[/tex]

Therefore the measure of angle x is 45°.

The value V of a square glass varies directly as the square of its length X cm. This means that V is proportional to [tex]X^2[/tex], which can be expressed as:

[tex]\[ V = kX^2 \][/tex]

where k is the constant of proportionality.

Given that the value of a square glass with length 3 cm is $243, we can use this information to find the constant k:

[tex]\[ 243 = k(3)^2 \][/tex]

[tex]\[ 243 = 9k \][/tex]

[tex]\[ k = \frac{243}{9} \][/tex]

[tex]\[ k = 27 \][/tex]

Now that we have the value of k, we can find the value of a glass with length 5 cm by substituting X = 5 into the original equation:

[tex]\[ V = 27(5)^2 \][/tex]

[tex]\[ V = 27 \times 25 \][/tex]

[tex]\[ V = 675 \][/tex]

Therefore, the value of a glass with length 5 cm is $675.

The answer is: 675.

Final answer:

To find the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex], change the sign of each term to get  [tex]8c^3+10c^2-6c-5.[/tex].

Explanation:

The opposite of any algebraic expression is found by changing the sign of each term within the expression. To find the opposite of the expression  [tex]-8c^3-10c^2+6c+5[/tex], simply change the signs of each term:

Putting it all together, the opposite of the expression  [tex]-8c^3-10c^2+6c+5[/tex] is [tex]8c^3+10c^2-6c-5.[/tex]

In essence, each term in the original expression is multiplied by -1 to obtain its opposite. This operation changes all positive terms to negative and all negative terms to positive.

The concept of taking the opposite is fundamental in algebra and is often used in simplifying expressions, solving equations, and manipulating mathematical statements.

Using the map scale of 1cm equals 18 miles, the actual length of Clay's vacation route is calculated as 252 miles by multiplying 14 centimeters (the length on the map) by 18 miles (the scale conversion factor).

Clay is using a map scale to plan his vacation route. The scale of the map is given as 1cm equals 18 miles. To calculate the actual length of Clay's vacation route in miles, we can set up a simple proportion. Since 1cm on the map represents 18 miles in reality, we multiply the length on the map, which is 14 centimeters, by 18 to find out how many miles this length represents:

Length in miles = 14 cm * 18 miles/cm

After performing the multiplication, we get:

Length in miles = 252 miles

Therefore, Clay’s vacation route is 252 miles long according to the map's scale.

In this situation, because the project was handed in late, you lost a total of 9 points. The full score was 81, and you got 72 after a deduction.

The principal in this problem is understanding proportion. Given that handing in a project late results in receiving 8/9, or approximately 88.88%, of the total points, we'll figure out the total possible score by dividing the received points (72) by the portion of the full score you got for handing in the project late, which is 8/9. So, 72 ÷ 8/9 = 81. This would be the original points you could have received. You can then subtract the received points (72) from the original points (81) to ascertain the number of points lost. Therefore, 81 - 72 = 9. Consequently, you lost 9 points because the project was handed in late.

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Answer:

Part 1) The constant of variation is [tex]k=1/9[/tex]

part 2) The equation is [tex]y=\frac{1}{9}x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

x -----> the number of square feet

y ----->  the number of square yards

Three square yards are equivalent to 27 square feet

so

we have the point (27,3)

Part 1) What is the constant of variation?

The constant of variation or proportionality is equal to

[tex]k=y/x[/tex]

substitute the values

[tex]k=3/27[/tex]

Simplify

[tex]k=1/9[/tex]

Part 2) What is the equation representing the direct variation?

we know that

[tex]y=kx[/tex]

substitute the value of k

[tex]y=\frac{1}{9}x[/tex]

This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.

In direct variation, the relationship between two variables can be represented by the formula:

y = kx

Where:

- y represents one variable (in this case, the number of square yards).

- x represents the other variable (in this case, the number of square feet).

- k is the constant of variation, which remains the same for all data points in the direct variation.

In this specific case, you've mentioned that 3 square yards are equivalent to 27 square feet. You can use this information to find the constant of variation (k). You can choose one of the data points to solve for k. Let's use the point (3, 27):

3 = k * 27

Now, solve for k:

k = 3 / 27

k = 1 / 9

So, the constant of variation (k) is 1/9. The equation representing the direct variation is:

y = (1/9)x

This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.

Learn more about proportionality here

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The question asks to find the scale factor for given scale drawings and measurements. A scale factor is computed by creating a ratio comparing the measurement of the scale drawing to the actual measurement, simplifying that ratio to find the scale factor.

The subject of the question is concerned with finding the scale factor from a given scale drawing and measurements. In mathematics, particularly in geometry, a scale factor is used to transform the size of a figure without altering its shape.

To find the scale factor for each given scale drawing, you will need to create a ratio or a fraction that compares the scale measurement to the actual measurement. Here’s how you might solve one of the problems:

Example: What is the scale factor if 3 inches is equal to 12 feet?

Solution:

Final answer:

To rewrite the fraction 8/9 with a denominator of 63, multiply both the numerator and denominator by 7 to get 56/63.

Explanation:

To rewrite 8/9 with a denominator of 63, you need to find a number that you can multiply both the numerator (8) and the denominator (9) of the original fraction by, so that the denominator becomes 63. To do this, divide 63 by the original denominator, 9, which gives you 7. Thus, the number you need to multiply by is 7.

Multiply both the numerator and the denominator by 7:

Numerator: 8  times 7 = 56

Denominator: 9 times 7 = 63

Therefore, the fraction 8/9 with a denominator of 63 is 56/63.

i believe its the option A

To solve this problem, we make use of the binomial probability equation.

P = [n! / (n – r)! r!] p^r * q^(n – r)

where,

n is the total number of sample = 100,000

r is the number of people with rare blood disorder = 7 or more

p is success of having a disorder = 0.00004

q is 1- p = 0.99996

But since it is easier to solve for the sum of probabilities with 0 to 6 disorder then deduct it from 1.

So,

=> at r = 0

P (r = 0) = [100,000! / (100,000 – 0)! 0!] (0.00004)^0 * (0.99996)^(100,000 – 0)

P (r = 0) = 0.01831

=> at r = 1

P (r = 1) = [100,000! / (100,000 – 1)! 1!] (0.00004)^1 * (0.99996)^(100,000 – 1)

P (r = 1) = 0.07326

=> at r = 2

P (r = 2) = [100,000! / (100,000 – 2)! 2!] (0.00004)^2 * (0.99996)^(100,000 – 2)

P (r = 2) = 0.14652

=> at r = 3

P (r = 3) = [100,000! / (100,000 – 3)! 3!] (0.00004)^3 * (0.99996)^(100,000 – 3)

P (r = 3) = 0.19537

=> at r = 4

P (r = 4) = [100,000! / (100,000 – 4)! 4!] (0.00004)^4 * (0.99996)^(100,000 – 4)

P (r = 4) = 0.19537

=> at r = 5

P (r = 5) = [100,000! / (100,000 – 5)! 5!] (0.00004)^5 * (0.99996)^(100,000 – 5)

P (r = 5) = 0.15630

=> at r = 6

P (r = 6) = [100,000! / (100,000 – 6)! 6!] (0.00004)^6 * (0.99996)^(100,000 – 6)

P (r = 6) = 0.10420

So the total P is:

P (r = 0 to 6) = 0.01831 + 0.07326 + 0.14652 + 0.19537 + 0.19537 + 0.15630 + 0.10420

P (r = 0 to 6) = 0.88933

=> So the probability that 7 or more people will have the disease is:

P (r ≥ 7) = 1 - 0.88933

P (r ≥ 7) = 0.11067 = 11.067%

There is only 0.11067 or 11.067% probability that 7 or more will have the disorder.

To solve this problem, we can use the binomial probability formula. The probability of exactly x successes in n trials is given by the formula. In this case, the probability of success (p) is 0.00004, and the total number of trials (n) is 100,000. To find the probability that seven or more people will have the rare blood disorder, we need to calculate the sum of the probabilities for x = 7, 8, 9, ..., 100,000.

To solve this problem, we can use the binomial probability formula. The probability of exactly x successes in n trials is given by the formula:

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

where:

P(x) is the probability of x successes

C(n, x) is the number of combinations of n trials and x successes

p is the probability of success in a single trial

n is the total number of trials

In this case, the probability of success (p) is 0.00004, and the total number of trials (n) is 100,000.

To find the probability that seven or more people will have the rare blood disorder, we need to calculate the sum of the probabilities for x = 7, 8, 9, ..., 100,000. This can be done using the binomial probability formula or statistical tables.

the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels in the area will be more than $150 is approximately 0.0081, or 0.81%.

To find the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels will be more than $150, we can use the Central Limit Theorem. Here's how:

1. Calculate the standard error of the mean (SEM) which is the standard deviation of the sample mean:

SEM = standard deviation / sqrt(sample size)

SEM = $29.12 / sqrt(15) ≈ $7.52

2. Calculate the z-score for a mean of $150:

z = (sample mean - population mean) / SEM

z = ($150 - $131.80) / $7.52 ≈ 2.41

3. Look up the z-score in the standard normal distribution table to find the probability associated with this z-score. The area to the right of a z-score of 2.41 gives us the probability that the average cost will be more than $150.

4. From the standard normal distribution table, a z-score of 2.41 corresponds to a probability of approximately 0.0081.

Therefore, the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels in the area will be more than $150 is approximately 0.0081, or 0.81%.

it should be used on the higher priced item to get a bigger discount.

 So it should be used on the soccer ball

soccer ball: 22.50 * 0.30 = 6.75 discount

shin guards: 17.00 * 0.30 = 5.10 discount

6.75 is greater than 5.10

The volume of the cone will be 1526.8 cubic units. The area of the vertical cross-section A at level x = 6 will be 72 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The equation of the base circle is given below.

x² + y² = 81

x² + y² = 9²

Then the radius of the circle is 9 units. Then the height of the cone is the same as the diameter of the circle.

h = 2r

h = 2 x 9 = 18

The volume of the cone will be

V = (1/3)πr²h

V = (1/3) × π × 9² × 18

V = 1526.8 cubic units

The area of the vertical cross-section A at the level x = 6 will be

A = (1/2) x (18 - 6) x (18 - 6)

A = (1/2) x 12²

A = (1/2) x 144

A = 72 square units

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