The corresponding angles postulate states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are

1.

2.25x+4.50 = 31.50

2.25x = 27

x = 27 / 2.25 = 12

Answer is B 12 weeks

2.

-2(p-1) =15

-2p +2 = 15

-2p =13

p = 13 / -2 =  -13/2

Answer is D -13/2

Answer:

Step-by-step explanation:

The given function is a transformation of the base function [tex]y=|x|[/tex].

We can observe that was added 5 units to the x, that is, a negative translation through the horizontal axis. So, our function is located at x = -5, because a horizontal translation to the left is when we add to the x certain units.

Then, we observe that the function subtracted 6 units to the vertical variable, that is, the function is translated 6 units downside.

Therefore, our functions is locate in (-5;-6), it starts there, which is the vertex.

29/1

Improper fractions have a greater numerator.

29 > 1

To find the value of x and BC, set up the equation CB + BD = CD and solve for x. The value of x is 3 and BC is 3.

To find the value of x and BC, we can set up the equation CB + BD = CD and solve for x.

Substituting the given values CB = 4x - 9, BD = 3x + 5, and CD = 17, we get (4x - 9) + (3x + 5) = 17.

Combining like terms, we have 7x - 4 = 17. Solving for x, we find x = 3. Plugging this value back into CB = 4x - 9, we get BC = 4(3) - 9 = 12 - 9 = 3.

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The midpoint of the range of frequencies given is:

midpoint =  (82.4 + 659.2) / 2 = 370.8 Hertz

Then the difference from midpoint to the other end is:
370.8 - 83.4 = 288.4 Hertz

Therefore the inequality formula is
|f - 370.8| <= 288.4

Final answer:

The 55th derivative of y = cos(3x) is recognized by repeating the derivative patterns of cosine functions and is found to be -27cos(3x).

Explanation:

The 55th derivative of y = cos(3x) can be found by recognizing that the derivatives of sine and cosine functions repeat every four steps. Considering the pattern cos(x) -> -sin(x) -> -cos(x) -> sin(x) -> cos(x), and that the derivative of cos(3x) is -3sin(3x), we can determine that the pattern repeats every four derivatives with a factor of 3n, where n is the number of times the derivative is taken.

The 55th derivative will be the same as the third derivative in the cycle, but with an iteration count of 55/4, which leaves a remainder of 3, so the 55th derivative will be -27cos(3x).

The inequality 1.6n ≤ 150 represents the max number of necklaces you can make within budget. Solving this gives n ≤ 93.75, meaning you can sell up to 93 necklaces. Total earnings are represented by E = np. The maximum earnings are 93p. Profit is calculated by deducting costs from earnings.

For (a) given that the initial investment is $150 and the cost per necklace is $1.6, the number of necklaces you can make without exceeding this limit is represented by the inequality 1.6n ≤ 150, where n represents the number of necklaces.

For (b), to find the maximum number of necklaces you can make, divide the total investment by the cost per necklace. Solve the inequality 1.6n ≤ 150 by dividing both sides by 1.6: n ≤ 93.75. This means you can make and sell up to 93 necklaces without exceeding your investment. To graph this, draw a number line and mark a closed circle at 93 to indicate that this value is included in the solution.

For (c), if you let p be the price at which you sell each necklace, your total earnings will be represented as E = np, where E stands for earnings.

For (d), substituting n ≤ 93.75 into E = np, the maximum you can hope to earn is 93p.

For (e), the total profit will be E - $150 (initial investment) - $1.6n (cost of necklaces). This would lead to either making a profit or loss. The profit or loss would then be used in adjusting your business plans.

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Answer:

95%

Step-by-step explanation:

0.68% per cent of the cockroaches have weights between 76 and 84 grams.

Given that, the weights of laboratory cockroaches follow a normal distribution with mean 80 grams and a standard deviation 2 grams.

We need to find out what per cent of the cockroaches have weights between 76 and 84 grams.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

First of all let's find the z-score which is given by the formula;

z = (x' - μ)/σ

From the question, mean= μ = 80 g and standard deviation; σ = 2 g

Test score; x' = 85 g

Thus;

z = (83 - 80)/2

z = 3/2

z = 1.5

From the z-distribution table attached, at z = 1.5, the probability is:

P(z > 1.5) = 1 - 0.9932 = 0.0068 or 0.68%

Therefore, 0.68% per cent of the cockroaches have weights between 76 and 84 grams.

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Step 1

Find the slope of the given line

we have

[tex]3x+4y=15[/tex]

Isolate the variable y

Subtract [tex]3x[/tex] both sides

[tex]3x+4y-3x=15-3x[/tex]

[tex]4y=-3x+15[/tex]

Divide by [tex]4[/tex] both sides

[tex]y=-\frac{3}{4}x+ \frac{15}{4}[/tex]

the slope of the given line is

[tex]m=-\frac{3}{4}[/tex]

Step 2

Find the equation of the line that passes through  the point [tex](8,-2)[/tex] and is parallel to the given line

we know that

if two lines are parallel, then their slopes are equal

The equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{3}{4}[/tex]

[tex](x1,y1)=(8,-2)[/tex]

substitute in the equation

[tex]y+2=-\frac{3}{4}(x-8)[/tex]

[tex]y=-\frac{3}{4}x+6-2[/tex]

[tex]y=-\frac{3}{4}x+4[/tex]  or  [tex]3x+4y=16[/tex]

therefore

the answer is

[tex]y=-\frac{3}{4}x+4[/tex]

or

[tex]3x+4y=16[/tex]

Answer:

3x+4y=16

Clarifying because other explanation was confusing

Just took review

Step-by-step explanation:

The unit rate of 324 calories in a 3-ounce serving is

108 calories per 1 ounce.

Given,

There are 324 calories in 3 ounce

We need to find the unit rate which means how many calories in one ounce.

We have,

In 3 ounces there are 324 calories.

We can write it as,

3 ounce = 324 calories

Dividing both sides by 3,

We get,

1 ounce = 324 / 3

1 ounce = 108

So,

In 1 ounce we have 108 calories.

This is our unit rate.

Thus the unit rate of 324 calories in a 3-ounce serving is 108 calories per 1 ounce.

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1.50x+0.80y≤20 is inequality represents how many hot dogs and how much water you can buy

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given,

a hot dog costs $1.50 each and water costs $0.80 each.

Let  x be the amount of hot dog

y be the amount of water

As hot dog costs $1.50 each, 1.50x

water costs $0.80 each, so 0.80y

You want to buy food and water for yourself and your friends but do not want to spend more than $20

1.50x+0.80y≤20

Hence, 1.50x+0.80y≤20 is inequality represents how many hot dogs and how much water you can buy

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it pumps 8 gallons a minute so it is 8x ( 8 gallons times x minutes)

you then need to subtract that amount from 1200

 lets say it pumped for 10 minutes,  8 *10 = -80

1200 - 80 =1120

 now the answers you have to choose from are kind of tricky because they don't give you the easiet one

 so using the numbers above

 the formula would be

1120 = -80+1200 =

y =-8x +1200

Final answer:

The equation y = 1200 - 8x models the amount of water in the tank as it is being pumped out.

Explanation:

The equation that models the amount of water in the tank y after x minutes is:

y = 1200 - 8x

This equation represents the initial 1200 gallons of water in the tank decreasing by 8 gallons per minute as it is being pumped out over time.

Answer: a=-3b

                  2

Step-by-step explanation:

get all letters on the same side so:

7a-5a (because when you cross the = you do the opposite)=-b+2b

2a=b

you are solving for a so: 2a/2=b/2

so the 2 cancel out and you have a=1/2b