Which of the following represents the distributive property?
A. a = b then bea
B. a(b+c)=ab+ac
C. if a = band b-c, then a = c
D. If a = b then ac- be

Answer:

A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us

Step-by-step explanation:

i may be wrong but I tried

The aforementioned equations have the following solutions: x = 0, x = 3. And the right response is B) x = 0, x = 3.

Replace the equation's variable with the given integer. The expressions on both sides of the issue should ideally be made simpler. Check the accuracy of the derived equation.

We must rearrange the terms to obtain a quadratic equation in standard form in order to solve the problem x2 - 2x = x:

x² - 2x - x = 0

x² - 3x = 0

Now we can factor out x:

x(x - 3) = 0

When x = 0 or x - 3 = 0, the equation is true. Hence, the equation's answers are x² - 2x = x are x = 0 and x = 3.

We can enter these answers into the initial equation and determine whether they satisfy it to verify that they work:

f(0) = 0² - 2(0) = 0

g(0) = 0

So, x = 0 is a solution.

f(3) = 3² - 2(3) = 3

g(3) = 3

So, x = 3 is also a solution.

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Question:

Given the function f(x) = x² - 2x and g(x) = x what is the solution for the equation x² - 2x = x?

A) X= 1, x = 3

B) x = 0, x = 3

C) x=-1,x=0

D) x = 0, x = 1

Answer:

Yes, there is a linear relationship between height and volume.

V = (12π)h. 12π is a constant.

If you rewrite this as y = (12π)x and graph it, you will notice that the graph is a line which goes through the origin.

Answer:

Measures of Central Tendancy

Mean: 429

Median: 344

Mode: 134,185,193,217,471,580,799,853

Range: 719

Step-by-step explanation:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

[tex]\mu = \frac{{\sum}x}{N}[/tex]

The formula for the mean of a sample is

[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:

[tex]\frac{3432}{8} = 429[/tex]

The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:

[tex]134, 185, 193, 217, 471, 580, 799, 853[/tex]

Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 217 and 471. The median is the average of these numbers. We have

[tex]{\frac{ 217 + 471 }{2}}[/tex]

Therefore, the median is

[tex]344[/tex]

The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are

[tex]134,185,193,217,471,580,799,853[/tex]

Answer:

Step-by-step explanation:

To find the range of a data set from a box and whisker plot, you can use the whiskers of the plot. The whiskers represent the minimum and maximum values of the data set, so the range can be calculated by subtracting the minimum value from the maximum value.

A whisker plot, also known as a box and whisker plot, is a graphical representation of the distribution of a set of data. It displays a summary of the minimum, maximum, median, and quartiles of the data set.

A typical whisker plot consists of a rectangular box with a vertical line inside, which represents the median of the data set. The lower and upper edges of the box represent the first and third quartiles, respectively. The length of the box thus represents the interquartile range (IQR), which is a measure of the spread of the middle 50% of the data.

In statistics, the range of a data set can be found from a box and whisker plot by looking at the endpoints of the whiskers.

The whiskers in a box and whisker plot extend from the box to the smallest and largest data points within a certain range of the median. The range of the data set is simply the difference between the smallest and largest data points.

To find the range of the data set from a box and whisker plot, simply identify the endpoints of the whiskers and find the difference between them. Note that the whiskers may be labeled with the actual values of the data points or labeled with a multiple of the interquartile range (IQR), which is the distance between the first and third quartiles of the data set.

It's worth noting that the range is a very basic measure of the spread or dispersion of a data set and is sensitive to outliers. Other measures of spread, such as the interquartile range, variance, or standard deviation, may provide more robust and informative summaries of the data.

Hence, the method to plot whiskers in a data range is provided.

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In the given differential equation, the general solution to the differential equation is: y = Ae^(√(1 - x²)), where A is any non-zero constant.

To solve this differential equation, we can start by using separation of variables.

√(1 - x²) y' = xy

We can rewrite this equation as:

y' / y = x / √(1 - x²)

Now we can integrate both sides:

∫ (y' / y) dy = ∫ (x / √(1 - x²)) dx

ln|y| = -√(1 - x²) + C

where C is the constant of integration.

Taking the exponential of both sides:

|y| = e^(-√(1 - x²) + C) = e^C / e^(√(1 - x²))

Since we only care about the magnitude of y, we can drop the absolute value signs and write:

y = Ae^(√(1 - x²))

where A = ± e^C is another constant of integration.

Therefore, the general solution to the differential equation is:

y = Ae^(√(1 - x²))

where A is any non-zero constant.

Note that the solution only holds for |x| ≤ 1, since otherwise the expression inside the square root would become negative, and the solution would not be real-valued.

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Answer:25% interest or $5,000

5\100= .05

.05 / 20= .0025

5,000/1,000=0.5

0.5 / 20=.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the implied interest rate in this scenario, we can use the concept of present value (PV) and future value (FV).

If Jochebed decides to pay the full amount of R20 000 cash right now, then the PV is R20 000 and the FV is also R20 000. Therefore, the implied interest rate on this option is 0%.

If Jochebed decides to pay in five annual installments of R5 000 each, then the PV of the land is equal to the sum of the present values of each installment. Using the formula for present value of an annuity, we can calculate the PV as:

PV = R5 000 x ((1 - (1 + r)^-5) / r)

where r is the implied interest rate. Solving for r, we get:

r = 7.18%

Therefore, the implied interest rate on the installment plan is 7.18%.

The quadratic equation on the graph can be written as:

y = x² + 6x + 8

Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:

y = a*(x - h)² + k

Here we can see that the vertex is at (-3, -1), replacing that we will get:

y = a*(x + 3)² - 1

Now we can also see that it passes through the point (-2, 0), replacing these values we will get:

0 = a*(-2 + 3)² - 1

0 = a - 1

1 = a

Then the quadratic is:

y  = (x + 3)² - 1

Expanding that we get:

y = x² + 6x + 9 - 1

y = x² + 6x + 8

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The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -

experimental probability = number of on-time trains / total number of trains

From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -

number of on-time trains = 15

total number of trains = 20

Substituting these values into the equation, we get -

experimental probability = 15 / 20

Simplifying the fraction, we get -

experimental probability = 3/4

Therefore, the experimental probability value is obtained to be 3/4 or 0.75.

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Okay so hopefully. I got the equation right. But I believe this is it

Answer:

If we change the value of 82° to 94°, the new data set becomes:

58, 61, 71, 77, 91, 100, 105, 102, 95, 94, 66, 57

IQR:

To find the new interquartile range (IQR), we first need to find the new values of the first quartile (Q1) and the third quartile (Q3). The median of the original data set is 84°, which is between the 6th and 7th values when the data is ordered. So, the first half of the data set consists of the values 58, 61, 71, 77, 82, and 91, and the second half consists of the values 94, 95, 100, 102, 105.

The new Q1 is the median of the first half of the data set, which is (71 + 77) / 2 = 74. The new Q3 is the median of the second half of the data set, which is (100 + 102) / 2 = 101.

The new IQR is Q3 - Q1 = 101 - 74 = 27.

Range:

The range is simply the difference between the largest and smallest values in the data set. Before the change, the range was 105 - 57 = 48. After the change, the range is 105 - 58 = 47.

Mean:

To find the new mean, we add up all the temperatures and divide by the number of temperatures. Before the change, the sum was 980 and there were 12 temperatures, so the mean was 980/12 = 81.7° (rounded to one decimal place). After the change, the sum is 982 and there are still 12 temperatures, so the new mean is 982/12 = 81.8° (rounded to one decimal place).

Median:

The median is the middle value in the data set when it is ordered. Before the change, the median was 84°. After the change, the median is still 84°, since only one value was changed and it did not affect the position of the median.

Therefore, the IQR changes the most, increasing from 34° to 27°. The new value of the IQR is 27.

AB has a length of 15, angle A is approximately 36.87 degrees and angle B is approximately 53.13 degrees.

We can use the Pythagorean theorem to find the length of AB:

AB² = AC² + BC²

AB² = 9² + 12²

AB² = 81 + 144

AB² = 225

AB = √225

AB = 15

So, AB has a length of 15.

To find angle A, we can use the inverse tangent function:

tan(A) = opposite/adjacent = AC/BC = 9/12 = 3/4

A = tan⁻¹(3/4) ≈ 36.87°

So, angle A is approximately 36.87 degrees.

To find angle B, we can use the fact that the three angles in any triangle add up to 180 degrees:

B = 90 - A = 90 - 36.87 ≈ 53.13°

So, angle B is approximately 53.13 degrees.

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Answer:

Step-by-step explanation:

It will take 50 minutes for the turtle and snail to meet.

because they are all moving at feet per minute we can create a formula

total feet = (turtle feet per minute) + (snail feet per minute)

300 = 5m +1m

combine like terms

300 = 6m

divide both sides by 6

50=m

Answer:

See below.

Step-by-step explanation:

Let's denote the distance the turtle walks by x. Then the distance the snail crawls would be 300 − x.

We can now set up an equation to represent the situation. Since distance = rate × time, we have

x/5 = (300 - x)/1

Solving for x, we get

x = 250

So the turtle walks 250 feet before meeting the snail, and the snail crawls the remaining 50 feet.

To find the time it takes for them to meet, we can use either of the two distances and its corresponding rate:

time = distance/rate

For example, using the turtle's distance

time = 250/5 = 50 minutes

Therefore, it takes 50 minutes for the turtle and the snail to meet.

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Step-by-step explanation:

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A sliced cylinder's cross section can be any shape that can be formed by intersecting a cylinder with a plane.

The shape of a sliced cylinder's cross section is determined by the angle and position of the slice.

If the slice is made parallel to the cylinder's base, the cross section is a circle.

If the slice is made at an angle to the cylinder's base, the cross section is an ellipse.

If the slice is made perpendicular to the cylinder's base, the cross section is a rectangle.

In general, a sliced cylinder's cross section can be any shape formed by intersecting a cylinder with a plane.

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Applying the angle addition postulate, the value of x in the image given is calculated as: 49.

The Angle Addition Postulate states that for any angle, the sum of its adjacent angles is equal to the angle formed by combining them.

Therefore, we have:

x + 11 + x + 23 = 132

Combine like terms to find the value of x:

2x + 34 = 132

2x = 132 - 34

2x = 98

2x/2 = 98/2

x = 49

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Answer:

x = 25

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

71° is an exterior angle of the triangle , then

x + 46 = 71 ( subtract 46 from both sides )

x = 25

The probability that a randomly selected member always works out alone or always works out with a personal trainer is 0.5393.

What is probability?

The idea of probability can be used to determine if an event is possible. It is solely useful for calculating the likelihood that an event will occur. a scale from 0 to 1, where 0 represents impossibility and 1 represents a specific occurrence.

We are given that  111 members work out alone, 67 work out with a personal trainer, and 41 sometimes work out alone and sometimes work out with a personal trainer.

So, the number of members who always work out alone is 111 - 41 = 70.

Similarly, the number of members who always work out with a personal trainer is 67 - 41 = 26.

Therefore, 96 members are there who either exercise alone or always exercise with a personal trainer.

Number of people surveyed = 111 + 67 - 41 = 137

Let A be the event where a member always exercises alone and B be the event where a member always exercises with a personal trainer.

From this, we get

P (A) = [tex]\frac{70}{137}[/tex]

P (B) = [tex]\frac{26}{137}[/tex]

P (A and B) = [tex]\frac{26}{137}[/tex]

So,

⇒ P(A or B) = P(A) + P(B) - P(A and B)

⇒ P(A or B) = [tex]\frac{70}{137}[/tex]+ [tex]\frac{26}{137}[/tex]- [tex]\frac{26}{137}[/tex]

⇒ P(A or B) = [tex]\frac{70}{137}[/tex]

Hence, the probability that a randomly selected member always works out alone or always works out with a personal trainer is 0.5393.

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Question:

A health club surveyed its members to determine if they worked out alone or with a personal trainer. The survey shows that 111 members work out alone, 67 work out with a personal trainer, and 41 sometimes work out alone and sometimes work out with a personal trainer. Find the probability that a randomly selected member always works out alone or always works out with a personal trainer.

a. 0.03714

b.0.5393

c.0.6342

d.0.6531

e.0.8128

The inequality for the provided sentence is (x+9)/(-4) >-2, and x>-1 is the obtained inequality's solution.

In mathematics, inequality is a concept that describes a relationship between two values. It is commonly expressed using symbols such as ">", "<", "≥", "≤", or "≠", and can be used to compare two numbers, variables, expressions, or sets. Inequality can be used to describe a range of values, such as "x is greater than 0 but less than 10", or "x is not equal to 0". Inequality is an important concept in mathematics, and it is used in many areas, such as problem solving, analysis, and statistics.

Given that, a maximum of -2 results when a number multiplied by 9 and split by -4.

Let x be the unknowable integer.

x+9 is the result of adding 9 to an integer.

Divided by -4, the outcome is (x+9)/.(-4)

Up to a limit of -2

(x+9)/(-4) >-2

On both sides of the discrepancy, multiply -4 to get

x+9>8

Subtract  9 on both the sides of inequality, we get

x>-1

Therefore, the inequality for the given phrase is (x+9)/(-4) >-2 and the solution for the inequality obtained is x>-1.

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Answer:

Without a graph provided, it's difficult to determine which of the given functions represents the graph on the right. However, we can analyze each function to see if it has any characteristics that match the shape of the graph.

f(x) = x(x – a)(x – b)2

This function has one x-intercept at x = 0 and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with a single x-intercept, a double root, and a local maximum and minimum.

f(x) = (x – a)(x – b)2

This function has one x-intercept at x = a and a triple root at x = b. If b > a, then the function will have a local minimum at x = a and a local maximum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum and maximum.

f(x) = x(x – a)³(x – b)

This function has one x-intercept at x = 0 and a triple root at x = a. If a < b, then the function will have a local minimum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum.

f(x) = x²(x – a)²(x – b)²

This function has two x-intercepts at x = 0 and x = a and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with two x-intercepts, a double root, and a local minimum and maximum.

Based on these analyses, it's unclear which function represents the graph on the right, as all four functions have characteristics that could match the shape of the graph.

Answer:

It's A

Step-by-step explanation:

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The domain of f(x) is (-∞, -7) ∪ (-7, -3) ∪ (-3, ∞).

What is the domain of function?

The function f(x) is defined as:

f(x) = 1/√((3+X)(7+X))

For f(x) to be defined, the expression under the square root must be positive. Therefore, we need to find the values of x that make (3+x)(7+x) positive.

We can use a sign analysis to determine the signs of (3+x) and (7+x) for different intervals of x:

When x < -7, both (3+x) and (7+x) are negative, so their product is positive.

When -7 < x < -3, (3+x) is negative and (7+x) is positive, so their product is negative.

When -3 < x < -7, (3+x) is positive and (7+x) is negative, so their product is negative.

When x > -3, both (3+x) and (7+x) are positive, so their product is positive.

Therefore, the expression (3+x)(7+x) is positive when x < -7 or x > -3.

However, we also need to consider the denominator of f(x), which cannot be zero. Therefore, we need to exclude any values of x that make the denominator equal to zero. The denominator is equal to zero when:

(3+x)(7+x) = 0

This occurs when x = -3 or x = -7.

Therefore, the domain of f(x) is all real numbers except -3 and -7, or:

x < -7 or -7 < x < -3 or x > -3

In interval notation, the domain of f(x) is (-∞, -7) ∪ (-7, -3) ∪ (-3, ∞).

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Answer:

To solve for x, we can start by cross-multiplying the equation to eliminate the denominators:

(a+bx)(c+d) = (c+dx)(a+b)

Expanding the terms on both sides:

ac + adx + bc + bdx^2 = ac + abx + cdx + bd

Simplifying and rearranging the terms:

adx + bdx^2 - abx - cdx = bd - ac

dx(ad - ab - c) = bd - ac

Now, since we know that cb=ad, we can substitute ad=cb into the equation:

dx(cb - ab - c) = bd - ac

dx(cb - ab - c) = b(cd - ac)

x = b(cd - ac)/(d(cb - ab - c))

Therefore, the solution for x is:

x = b(cd - ac)/(d(cb - ab - c))

Answer:

Step-by-step explanation:

To solve this problem, we need to calculate the present value of the cash flows in both cases - the case where the payments are made at the beginning of each year and the case where the payments are made at the end of each year - and compare the two values.

First, let's calculate the present value of the cash flows when payments are made at the end of each year. We can use the formula for the present value of an ordinary annuity:

PV = PMT x [(1 - (1 / (1 + r)n)) / r]

where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] = R141,798.06

Now let's calculate the present value of the cash flows when payments are made at the beginning of each year. To do this, we can use the formula for the present value of an annuity due:

PV = PMT x [(1 - (1 / (1 + r)n)) / r] x (1 + r)

where PV is the present value, PMT is the payment amount, r is the discount rate, n is the number of periods, and (1 + r) adjusts the formula for the fact that payments are being made at the beginning of each year.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] x (1 + 0.09) = R153,094.97

So the present value of the cash flows when payments are made at the beginning of each year is R153,094.97, and the present value of the cash flows when payments are made at the end of each year is R141,798.06. Therefore, the difference in present value is:

R153,094.97 - R141,798.06 = R11,296.91

So, receiving the payments at the beginning rather than at the end of each year would result in a present value that is R11,296.91 higher.

Answer:

Supplementary Angles: The angles 1 & 2 are supplementary angles, as, when combined together, their total angle measurement is 180°, or a straight line. Supplementary angles, by definition, is either two angles in which, when combined, the sum is equal to 180°.

Adjacent Angles: The angles 1 & 2 are adjacent angles, as they share a common side and vertex. Vertexes, by definition is the corner point.

Why it is not:

Complementary Angles: Complementary angles suggest that, when two angles are combined together, their total angle measurements is 90°, or it creates a right angle. In this case, the total measurements of the combination of ∠1 & ∠2 is a straight line, or 180°. Therefore, complementary angles is not your answer.

Vertical Angles: Vertical angles suggest that, when there are two angles, they are directly opposite of each other. Vertical angles would share the same angle measurements.

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The proof that ΔABC ≅ ΔDCB (congruent) in a parallelogram is because they are alternate interior angles.

If AABC is a parallelogram, then AB and AC are parallel. Therefore, angle BAC is equal to angle BDC since they are alternate interior angles.

Similarly, angle ABC is equal to angle ADC since they are also alternate interior angles.

Now, using the angle-angle-side (AAS) postulate to show that ΔABC and ΔDCB are congruent.

Since angle BAC = angle BDC and angle ABC = angle ADC, angle A = angle D, angle B = angle C, and side AB = side DC.

Therefore, ΔABC ≅ ΔDCB.

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Image transcribed:

8. Prove ΔABC≅ΔDCB (parallelogram)

The number of solutions to the system of equation; y = x and y = x - 7 are;

There are no solution to the equation system

A solution is a set of the variable values in the equation system that make the system true at the same time.

The equations are;

y = x and y = x - 7

Whereby the right hand side of both equations are equated, we get;

x = x - 7

Subtracting x from both sides, we get;

x - x = x - 7 - x = -7

0 = -7

Geometrically, the meaning of the equations is that the two lines representing the two equations do not intersect, and are parallel lines. This is shown by the slopes (the coefficient of x) of the two equations, which are the same (The slope is 1 in each equation)

The y-intercepts of the equations are however different (0 and -7), therefore, the two equations represent parallel lines with different y-intercepts

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Answer:

19.2 ft

Step-by-step explanation:

ANSWER: 27 because the less people there is the more longer it takes