Apply the distributive property to factor out the greatest common factor. 24a−18b

Answer:

Step-by-step explanation:

[tex]x = \frac{68}{13}[/tex]

[tex]y = \frac{1}{13}[/tex]

To solve the system of equations by substitution method, we can use one equation to solve for x or y, and then substitute that expression into the other equation to solve for the other variable.

From the second equation, we have:

x - 3y = 5

Solving for x, we get:

x = 3y + 5

Now we can substitute this expression for x into the first equation and solve for y:

2x + 7y = 11

2(3y + 5) + 7y = 11

6y + 10 + 7y = 11

13y = 1

y = 1/13

Now that we have solved for y, we can substitute this value back into one of the original equations to solve for x:

x - 3y = 5

x = 3y + 5

x = 3(1/13) + 5

x = 5 6/13

Therefore, the solution to the system of equations is:

x = 5 6/13 and y = 1/13.

The assumptions include that the path of the ball can be modeled by a parabolic function, that data on the trajectory of the ball is needed, and that matrices can be used to solve for the constants a, b, and c. Finally, the inverse of the matrix can be computed using matrix algebra.

A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are organized in rows and columns. In addition to representing and transforming data in statistics, physics, and computer science, matrices are also used to represent and convert linear equations and transformations in linear algebra.

We need to make some assumptions and approximations in order to develop an equation for the flight of the golf ball because the actual path of the ball is influenced by a number of variables, including wind, temperature, humidity, and spin. The idea that a parabolic function may simulate the ball's trajectory is one that is frequently held.

We would need information on the ball's trajectory, such as height and distance at various points along the trip, in order to perform regression. Regression analysis cannot be used to derive an equation for the trajectory of the golf ball in the absence of this data.

To use matrices, we can set up a system of equations based on the parabolic function:

[tex]y = ax^2 + bx + c[/tex]

where x is the distance traveled by the ball, y is the height of the ball, and a, b, and c are constants to be determined.

We can set up three equations based on the following assumptions:

At the starting point (x=0), the height of the ball is zero.

At the point where the ball hit the tree (x = d), the height of the ball is the height of the tree (90 feet).

At the landing point on the green (x = D), the height of the ball is zero.

Using these assumptions, we can set up the following system of equations:

c = 0 (from assumption 1)

[tex]ad^2 + bd + c[/tex] = 90 (from assumption 2)

[tex]aD^2 + bD + c[/tex] = 0 (from assumption 3)

To solve for the constants a, b, and c, we can use matrix algebra to write the system in matrix form:

[tex][0 0 1] [c] [0][/tex]

c[tex][d^2 d 1] * [b][/tex] = [90]

[tex][D^2 D 1][/tex] [a] [0]

Multiplying the matrices, we get:

[0 0 1] [c] [0]

[tex][d^2 d 1][/tex] * [b] = [90]

[tex][D^2 D 1][/tex] [a] [0]

Simplifying, we get:

[c] [0]

[b] = [90] * [tex][d^2 d 1]^-1 * [d^2 d 1][/tex]

[a] [0]

where the inverse of the matrix [tex][d^2 d 1][/tex] can be computed using matrix algebra. Once we have the values of a, b, and c, we can plug them into the equation [tex]y = ax^2 + bx + c[/tex] to get the equation for the path of the golf ball.

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The estimated total number of moles in the local area is 4.

The farmer needs to use the capture-recapture method to estimate the total number of moles in the local area. This involves tagging a population sample, releasing them back into the population, and then capturing another sample to determine the proportion of tagged individuals in the second sample. Using this proportion, the total population can be estimated using the following formula:

total population = (number in first sample * number in the second sample) / number of tagged individuals in the second sample

In this case, the farmer tagged 30 moles in the first sample and found that half of the second sample had tags. We can use these values to estimate the total number of moles:

total population = (30 * 2) / 15

total population = 4

Note that the actual population size may be larger or smaller than this estimate due to factors such as migration, birth, and death rates.

To correctly estimate the number of moles in a substance, the farmer needs to use the grams to moles formula, which is:

n = m / M

where n is the number of moles, m is the mass of the substance in grams, and M is the molar mass in grams per mole . To calculate the molar mass of a substance, the farmer can sum the molar masses of its component atoms

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The probability that an irs auditor will catch only 2 income tax returns with illegitimate deduc-tions = 0.24

Let us assume that X be the number of returns containing illegitimate deductions in the sample.

Here, X has a hypergeometric distribution.

We need to find the probability that an IRS auditor will catch only 2 income tax returns with illegitimate deduc-tions.

Here, N = 15, r = 9, n = 5

So, P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

We know that the combination formula:

⁹C₂ = 9! / (2! × 7!)

     = 36

⁶C₃ = 6! / (3! × 3!)

     = 20

¹⁵C₅ = 15! / (5! 10!)

      = 3003

P (X = 2) = (⁹C₂ × ⁶C₃) / (¹⁵C₅)

              = (36 × 20) / (3003)

              = 0.24

Therefore, the required probability is: 0.24

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A rectangular pyramid is a pyramid with a rectangular base and four triangular faces that meet at a single point at the top, called the apex. It is a three-dimensional solid with five faces, including the base, and is a type of pyramid with a rectangular base.

No, we do not have enough information to find the surface area of the rectangular pyramid.

To find the surface area of a rectangular pyramid, we need to know the lengths of all four sides of the base, as well as the slant height and height of each triangular face.

In this case, we only have two sides of the rectangular base (5 ft and 7 ft) and the height of one of the triangular faces (4 ft). We do not have enough information to find the length of the other two sides of the base or the slant height and height of each triangular face.

Therefore, we cannot find the surface area of the rectangular pyramid with the given information.

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Answer:

Step-by-step explanation:

Answer:

m = 2/3

Step-by-step explanation:

Given two points on a line, we can find the slope, m, of a linear equation using the slope formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point and x2 and y2 are the other point.

The order of the points don't matter as long you pair the points already together (e.g., if you choose 7 as x1, you have to choose -2 as y2, and if you choose 1 as x1, you have to choose -6 as y2).

Thus, if we allow the first point to be x1 and y2 and the second point to be x2 and y2, our slope is:

[tex]m=\frac{-6-(=2)}{1-7}\\ \\m=\frac{-6+2}{-6}\\ \\m=\frac{-4}{-6}\\ \\m=\frac{2}{3}[/tex]

To write an absolute value Equation for a given solution set, we need to use the appropriate formula depending on the nature of the solution set.

To write an absolute value equation for a given solution set, we need to first understand what absolute value is. Absolute value is a mathematical function that returns the positive value of a given number, irrespective of its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. Now, let's consider the given figures and their respective solution sets:

Figure 1: The solution set for this figure is {2, -2}. To write an absolute value equation for this solution set, we can use the formula |x| = a, where a is the value of the solution set. Therefore, the absolute value equation for this figure is |x| = 2.

Figure 2: The solution set for this figure is {5}. To write an absolute value equation for this solution set, we can use the formula |x - b| = a, where b is the midpoint of the solution set and a is the distance from the midpoint to one of the solutions. Therefore, the absolute value equation for this figure is |x - 5| = 0.

Figure 3: The solution set for this figure is {-3, 3}. To write an absolute value equation for this solution set, we can again use the formula |x| = a, where a is the value of the solution set. Therefore, the absolute value equation for this figure is |x| = 3.

In conclusion, to write an absolute value equation for a given solution set, we need to use the appropriate formula depending on the nature of the solution set.

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Answer:

the ruler showed 7 inch segment

Step-by-step explanation:

have an amazing weekend

Answer:

7÷2= 3.5

Step-by-step explanation:

The length of each part is 3.5

Step-by-step explanation:

When x -5 is a positive

   x -5  = 2

    x = 7

when x -5 is a negative

    x-5 = -2

       x = 3

Using the median, which is not affected by outliers, would provide a better representation of the typical or central value of the data.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude. To find the median, you need to arrange the values in order from smallest to largest and then find the middle value.

Based on the given information, the median is the best measure of center because there are outliers present. The reason for this is because the presence of outliers can greatly affect the mean and make it a less representative measure of central tendency.

In this case, the dots above 6, 7, and 3 may be considered as outliers since they are far from the other data points.

Therefore, using the median, which is not affected by outliers, would provide a better representation of the typical or central value of the data.

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The probability that Karen's second card will be a black card is 3/650.

After Sandra deals Karen a red seven, there are 51 cards remaining in the deck, of which 26 are black cards. So the probability of Karen drawing a black card on her second draw depends on whether or not the first card she drew was black or red:

If the first card Karen drew was black, then there are 25 black cards left in the deck out of 50 cards, since one card has already been drawn. So the probability of Karen drawing a black card on her second draw is 25/50 = 1/2.

If the first card Karen drew was red, then there are still 26 black cards left in the deck out of 50 cards, since one card has already been drawn. So the probability of Karen drawing a black card on her second draw is 26/50 = 13/25.

Since there are 26 red cards and 26 black cards in a standard deck of playing cards, the probability of Karen being dealt a red seven by Sandra is 2/52 = 1/26.

To find the overall probability of Karen being dealt a red seven and then drawing a black card on her second draw, multiply the probability of these two events occurring:

P(red seven and black card) = P(red seven) × P(black card on second draw | red seven)

P(red seven) = 1/26

P(black card on second draw | red seven) = 13/25

P(red seven and black card) = (1/26) × (13/25) = 13/650

Therefore, the probability of Karen's second card being a black card, given that Sandra dealt her a red seven, is 13/650.

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The complete question:

Sandra and Karen are playing a game of cards with a standard deck of playing cards. Sandra deals Karen a red seven. What is the probability that Karen’s second card will be a black card?

The amount that Nancy can save each month and put in the savings account is $10.

Savings are funds that are not used right away but are instead set aside for unforeseen expenses or future needs. It is the gap between one's earnings (income) and their outlays (expenditures) (the amount of money spent). Regular income, investment profits, tax refunds, and gifts are just a few of the several ways that people might support their savings. You may save money in a variety of ways, such as by creating a budget and eliminating wasteful spending, opening a savings account, buying stocks or bonds, and making contributions to retirement plans like 401(k)s or IRAs.

The total income earned by Nancy is:

30 + 50 + 25 + 35 = $140

The total expenses are:

40 + 60 + 30 = $130

The amount remaining after expenses is:

Savings = 140 - 130 = $10

Hence, the amount that Nancy can save each month and put in the savings account is $10.

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For given triangles, Condition 3 and 6 are true.

What is a triangle's definition?

A triangle is a closed two-dimensional shape with three straight sides, three angles, and three vertices (or corners). It is formed by connecting three non-collinear points in a plane with straight lines. The sum of the interior angles of a triangle is always 180 degrees, and each exterior angle is equal to the sum of its two adjacent interior angles. Triangles can be classified based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

Now,

As we can see that ΔABC is rotated 90° clockwise to make

ΔDEF.

So, the angles follows these conditions

∠F=∠A

∠E=∠C

∠D=∠B

hence,

             Condition 3 and 6 are true.

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The bag contains $4.60 in coins.

What are coins?

Let's use P, N, D, and Q to represent the number of pennies, nickels, dimes, and quarters, respectively, in the bag.

We know that the total number of coins is 50, so:

P + N + D + Q = 50

We also know that 10% of the coins are pennies, so:

P = 0.1(50)

P = 5

There are 2 more nickels than pennies, so:

N = P + 2

N = 5 + 2

N = 7

Now we can use this information to find the number of dimes and quarters. Since there are 50 coins in total, we can substitute the values we have found for P and N into the first equation:

P + N + D + Q = 50

5 + 7 + D + Q = 50

12 + D + Q = 50

D + Q = 38

We also know the values of P and N, so we can find the total value of all the coins in the bag:

Total value = (value of pennies) + (value of nickels) + (value of dimes) + (value of quarters)

Total value = (5 cents x 5) + (7 cents x 5) + (10 cents x D) + (25 cents x Q)

Total value = 25 + 35 + 10D + 25Q

We can substitute D + Q = 38 into this equation to get:

Total value = 25 + 35 + 10(D + Q)

Total value = 60 + 10(38)

Total value = 460 cents, or $4.60

Therefore, the bag contains $4.60 in coins.

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Answer:

blank1: 9

blank2: 30°

blank3: 60°

blank4: 90°

blank5: half

Step-by-step explanation:

The 30°-60°-90° triangle has some great shortcuts associated with it (there are math reasons, trig reasons for these shortcuts)

One of these great shortcuts is that the short leg is half the hypotenuse (or the hypotenuse is double the short leg)

For your question, the kite string, 18ft, is the hypotenuse. The kite height is half that--9ft.

see image.

The surface area of a right circular cone can be found using the formula:

A = πr²+ πrl

where r is the radius of the base, l is the slant height, and π is approximately 3.14159.

In this case, the diameter of the base is 8 m, so the radius is 4 m. The slant height is 18.5 m. The height is not needed for this calculation.

Substituting the given values, we get:

A = π(4 m)² + π(4 m)(18.5 m)

A = π(16 m²) + π(74 m²)

A = π(90 m²)

Using the approximation π ≈ 3.14159, we get:

A ≈ 282.74 m²

Therefore, the surface area of the right circular cone is approximately 283 m² rounded to the nearest whole.

Answer: The statement that is not true is D.

Explanation:

We know that the area of the rectangle is 160 square inches. Let's assume that the length of the base is b inches. Then, the height of the rectangle would be 160/b inches (since area = base x height).

Now, we can check the given statements:

A. The base of the figure is 20 inches in length.

We do not know the length of the base, so we cannot say for sure whether this statement is true or false.

B. The formula A=b/8 could be used to determine the area.

This statement is false. The correct formula for the area of a rectangle is A = b x h.

C. The formula b=160/8 could be used to determine the length of the base.

This statement is true. We can solve for b as:

b = A/h = 160/(160/b) = 8

So, the length of the base is 8 inches.

D. The formula 160(b)(8) could be used to determine the length of the base.

This statement is false. The given formula does not make sense in the context of the problem, and it does not allow us to determine the length of the base.

Step-by-step explanation:

Answer:

The answer to your problem is, C. -2

Step-by-step explanation:

To solve : 4(y - 3) +19=8(2y + 3) + 7?

Open the bracket:

4y - 12 + 19 = 16y + 24 + 7 

Collect like terms

4y - 16y = 24 + 7 + 12 - 19

-12y = 24

Divide both sides by - 12 to isolate y

-12y / - 12 = 24 / - 12 

y = -2

Thus the answer to your problem is, C. -2

For first step you do not really need to “ open the bracket “ just solve it.

Answer:

20(x + 2) = 20x + 40 = 4(5x + 10)

Answer:

-4860

Step-by-step explanation:

The formula for finding the nth term (An) of a geometric sequence is;

An = a₁ * r^(n-1)

where a₁ is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we have;

An = 20 * (-3)^(6-1)

An = 20 * (-3)^5

An = 20 * (-243)

An = -4860

Therefore, the answer is (Ob) -4860

The probability of choosing a password with no Y's and O's is 20/30 = 2/3, or approximately 0.667. The two probabilities are the same, so neither is greater than the other.

Probability is a measure of the likelihood or chance that an event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In mathematical terms, probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 0.5, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

To calculate the probability of choosing a password with no Y's or no O's, we need to first count the number of valid passwords without Y's or O's and then divide it by the total number of possible passwords.

Number of valid passwords without Y's:

There are 5 choices for the first character (B, R, O, G, P), since Y is not allowed.

There are 4 choices for the second character (any of the remaining 5 letters except Y), since we cannot repeat the first letter.

So the total number of valid passwords without Y's is 5 x 4 = 20.

Number of valid passwords without O's:

There are 5 choices for the first character (Y, B, R, G, P), since O is not allowed.

There are 4 choices for the second character (any of the remaining 5 letters except O), since we cannot repeat the first letter.

So the total number of valid passwords without O's is 5 x 4 = 20.

The total number of possible passwords is the number of ways to choose 2 characters out of 6, without repetition. This is given by the formula:

6P2 = 6! / (6 - 2)! = 6 x 5 = 30

Therefore, the probability of choosing a password with no Y's is 20/30 = 2/3, or approximately 0.667.

Similarly, the probability of choosing a password with no O's is also 20/30 = 2/3, or approximately 0.667.

The two probabilities are the same, so neither is greater than the other.

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The answer is A. f(x) and g(x) are closed under addition because when added, the result will be a polynomial.

Addition is denoted using the plus sign (+) or a plus symbol. Addition can be used to find the total in a group of numbers, to combine two or more numbers, or to compare two numbers.

When two polynomials f(x) and g(x) are added, the result is also a polynomial. The degree of the resultant polynomial is equal to the highest degree of the two added polynomials.

Thus, when a polynomial is added to another polynomial, the result will always be a polynomial.

This is true because when two polynomials are added, the resulting polynomial will have the same form as the two polynomials that were added.

In other words, the sum of two polynomials will have the same coefficients and powers of x as the two polynomials that were added.

Therefore, f(x) and g(x) are closed under addition because when added, the result will always be a polynomial.

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There are 75 percent of Americans consume alcoholic beverages regularly. so, the correct answer is D).

According to a 2021 survey conducted by the National Institute on Alcohol Abuse and Alcoholism, approximately 75% of adults in the United States reported that they had consumed alcohol in the past year.

However, it's important to note that this does not necessarily mean that they consume alcohol regularly. The percentage of Americans who consume alcoholic beverages regularly may vary depending on how "regularly" is defined and the specific population being studied.

So, the correct option is D).

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The 95% confidence interval for the mean is (1.6048, 1.6352).Hence, option (d) is the correct answer.

As given, a machine that is programmed to package 1.60 pounds of cereal is being tested for its accuracy in a sample of 40 cereal boxes, the sample mean filling weight is calculated as 1.62 pounds. The population standard deviation is known to be 0.06 pounds. We are required to find the 95% confidence interval for the mean. Here are the steps to solve this problem:

The formula to find the confidence interval is as follows;

Lower limit = x - zα/2 (σ/√n)

Upper limit = x + zα/2 (σ/√n)

Where,

x= sample mean

zα/2 = z-value of the level of significance

σ = population standard deviation

n = sample size

We are given;

x = 1.62 pounds

σ = 0.06 pounds

n = 40

We need to find the z-value of the level of significance, which can be found using the z-table or by using the calculator.Using the z-table, we get the z-value at 95% confidence interval as zα/2 = 1.96

Substituting the values, we get

Lower limit = 1.62 - 1.96(0.06/√40)

Upper limit = 1.62 + 1.96(0.06/√40)

Lower limit = 1.6048, Upper limit = 1.6352

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Answer: There are 8 campers for every 1 counselor.

Step-by-step explanation:

A ratio is relation in number between two things. 8:1 means that there are 8 ___s for every 1 ____.