Which of the following is equal to the expression listed below?

(18 × 24) - (18 × 9)

a.(24 - 18) × (18 - 9)
b.24 × (18 - 9)
c.18 × (24 - 9)
d.18 - (24 × 9)

A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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The value of secant XY is 37.5 units.

The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

VZ * VW = VX * VY

30 * 45 = 22.5 * VY

22.5VY = 1350

VY = 1350/22.5

VY = 60 units

Since VY = VX + XY. We have:

60 = 22.5 + XY

XY = 60 - 22.5

XY = 37.5 units

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The margin of error for the confidence interval for a population is 0.71 ± 0.1.

The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

The margin of error is given as:

MOE = U - L / 2

MOE = 0.81 - 0.61 / 2

MOE = 0.2 / 2

MOE = 0.1

The interval is:

Interval = P ± 0.1

Interval = (0.61 + 0.1) ± 0.1

Interval = 0.71 ± 0.1

Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.

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Finance charge be on a $500 balance for just 1month is equal to $20.79.

APR   stands for the annual percentage rate on a loan which is the interest rate on a one year loan.  To calculate the monthly rate r, we know that:

49.9 / 100 / 12 * $500 = $20.79

The finance charge is $20.79.

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

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Answer:

I can't see the graph

Step-by-step explanation:

The amount that she owes after she factors in interest will be $33,455.64.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.

Then the amount is given as,

A = $25,000 x (1 + 0.06)⁵

A = $25,000 x (1.06)⁵

A = $25,000 x 1.3382

A = $33,455.64

The amount that she owes after she factors in interest will be $33,455.64.

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The Remainder in the Synthetic division is three, for given problem

1 |__1___2__-3__3 is 3.

So, the correct option is option(c).

The Synthetic Division:

It is defined as the method of dividing the polynomial by the binomial is known as the synthetic division. It stands for polynomial division. Here, the division principle is performing in the coefficient of the polynomial.

We have given that the synthetic division is

1 |__1___2__-3__3

We find out the remainder in the synthetic division :

Multiply the carry-down value (i.e 1) by the test zero on the left, and carry the result(i.1×1 = 1) up into the next column inside:

1 | 1 2 -3 3

|______________

1

Add down the column( 2+1 = 3) :

1 | 1 2 -3 3

|____1_________

1 3

Multiply the previous carry-down value (i.e 3) by the test zero, and carry the new result up into the last column:

1 | 1 2 -3 3

|____1____3____

1 3 0

1 | 1 2 -3 3

|____1____3___0_

1 3 0 3

three, last carry-down value is the remainder.

Therefore, the remainder is 3. The option c is correct.

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Complete question:

What is the remainder in the synthetic division problem below?

a. 6

b. 4

c. 3

d. 5

timer--;  //This statement uses the auto-decrement operator to decrease the value of the variable timer by 1.

The auto-decrement operator -- is used to decrease the value of a variable by 1. In this case, the variable is called timer. The statement which uses the auto-decrement operator is timer--;. This statement will take the current value of the timer variable and decrease it by 1. For example, if the current value of timer is 5, the statement timer--; will decrease the value to 4. This is a very useful and efficient way to decrease a variable's value by 1. It is also much shorter than having to write out a statement such as timer = timer - 1;. The auto-decrement operator can be used with other types of variables as well, such as strings or characters.

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To determine the number of solutions, let us first solve for h.

We will also need to find b using the sine law.

Here we see that a = 26, b = 29, and h = 12.6.

When h < a < b, then are 2 solutions or 2 triangles.

Next, we solve for the 2 solutions.

For the first solution, we already calculated B to be 71.07 degrees. We know that A = 58 degrees. So to find C, we simply subtract their sum from 180.

Again, using the sine law, we can solve for c.

The other solution is when B = 180 - 71.07 = 108.93. We do this because there are 2 angle measurements that have the same sine (in this case, it's 0.946).

Again, the other possible value of B is 180 - 71.07 or 108.93. That will give us C = 180 - (53 + 108.93) = 18.07 degrees.

Again, we use the sine law to solve for the corresponding c.

So the answers are:

1. There are 2 possible triangles.

2. Triangle 1: B = 71.07 degrees, C = 50.93 degrees, and c = 23.80.

3. Triangle 2: B = 108.93 degrees, C = 18.07 degrees, and c = 9.51

Answer:

8.2

Step-by-step explanation:

We can use the distance formula: \(\sqrt{((x_2 - x_1)^2 + (y_2-y_1)^2}\)

\(\sqrt{(10-2)^2 + (7-9)^2} = \sqrt{8^2 + (-2)^2} = \sqrt{64+4} = \sqrt{68} = 2\sqrt{17} = 8.2\)

Answer:

The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.

Step-by-step explanation:

Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing

In this case:

Probability of Winning = 0.05

Payout for Win = $5

Cost of Playing = $1

Expected Value = (0.05 * $5) - $1

Expected Value = $0.25 - $1

Expected Value = -$0.75

Answer:

45 degrees

Step-by-step explanation:

DBC: 180 - 135

DBC: 45 degrees

Hope that helps!

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

Hi 

let call "a number" X.

then we have: 4-13X = X + 8 ..

It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

The annual interest rate of jessica's loan is 6%.

Interest rate is the amount a lender charges a borrower and is a percentage of the principal.

To calculate the annual interest rate of Jessica's loan, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the annual interest rate is 6%.

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Answer:

c) 8r - 19

Step-by-step explanation:

Subtract    6r - 7

              -  -2r + 12

  = 8r - 19

Answer:8r-9 or c

Step-by-step explanation:

Answer:

D. 1/3

Step-by-step explanation:

The point at the top of the dashed figure is 3 units from the origin. The solid figure is 1 unit from the origin.

Answer:

it would be 2 because if you take the scale factor of both of the figures it would be x2

Answer: The cost of each new uniform is $89.

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

Explained below.

Step-by-step explanation:

The complete question is:

A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries. a. If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? b. If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? c. If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? d. If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? e. If 6 bottles are randomly selected, what is the probability that all of them are the same variety?

Solution:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

\({n\choose k}=\frac{n!}{k!(n-k)!}\)

Permutation is the number of ways to select k items from n distinct items in a specific order.

The formula to compute the permutation or arrangement of k items is:

 \(^{n}P_{k}=\frac{n!}{(n-k)!}\)

(a)

The number of ways to serve 3 bottles of zinfandel, with a specific order is:

\(^{8}P_{3}=\frac{8!}{(8-3)!}=\frac{8\times7\times6\times5!}{5!}=336\)

(b)

The number of ways to select 6 bottles from the 30 is:

\({30\choose 6}=\frac{30!}{6!(30-6)!}=\frac{30!}{6!\times 24!}=593775\)

(c)

The number of ways to select two bottles of each variety is:

\({8\choose 2}\times {10\choose 2}\times {12\choose 2}=\frac{8!}{2!\times6!}\times \frac{10!}{2!\times8!}\times \frac{12!}{2!\times10!}\)

                         \(=\frac{12!}{(2!)^{3}\times 6!}\\\\=83160\)

(d)

Compute the probability of selecting two bottles of each variety if 6 bottles are selected:

\(P(\text{2 bottles of each})=\frac{83160}{593775}=0.14\)

(e)

Compute the probability of selecting the same variety of bottles, if 6 bottles are selected:

\(P(\text{Same Variety})=\frac{{8\choose 6}+{10\choose 6}+{12\choose 6}}{{30\choose 6}}\)

                           \(=\frac{28+210+924}{593775}\\\\=0.0019570\\\\\approx 0.002\)

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Total quantities of plant-produced pollutants:

\(=(10.88+15.82+0.92) \ L\\\\=27.62\ L\)

We are three medicinal plants here, Pinecrest, Macon, and Ogala. The average number of contaminants produced by plants would be

\(\to 27.62\div 3 \\\\\to \frac{27.62}{3} \\\\ \to 9.206 \ L\)

The statement that best describes the graph is the second one, this is because the standard deviation defines the graph on the x-axis, and it can be observed that both have the same extension in x, and the mean defines the height of the distribution, therefore differing by 8 units makes one higher than the other.

Answer:

The answer is 83

Step-by-step explanation:

You have to mutiply them all then divide

Answer:

23

Step-by-step explanation:

So you want to add 7x degrees and (x-4) degrees. And it will be 8x - 4 = 180 degrees because it's 180 degrees in a straight line. And you want to + the 180 by 4 because there is -4 on the other side. so it will be 8x = 184 and you just divide 184 by 8 and it will be 23 easy. if you want to my help again you can text me on instargram jason_lee093

hope this helps!!!:)) just follow the steps and the answer is 56!

The area of the rectangle formed by extending the square backyard rink is x² + 7x + 10 square meters.

To find the area of the rectangle formed by extending a square backyard rink, you will need to use the formula for the

area of a rectangle, which is:

A = lw

Where A is the area,

l is the length, and

w is the width.

Since we know that the backyard rink is square, we can set the length and width to be equal to the length of one side (x).

After extending the rink, the length and width of the rectangle are x + 2 and x + 5, respectively.

Therefore, we can substitute these values into the area formula to get:

A = (x + 2)(x + 5)

Simplifying this expression gives:

A = x² + 7x + 10

Therefore, the area of the rectangle formed by extending the square backyard rink is x² + 7x + 10 square meters.

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