Find a polynomial function whose graph passes through (7,13), (9,- 11), and (0,3).

The equation which represents exponential growth is y = (1.2)* and equation which represents exponential decay is y = (.71)*,  y = 0(6.3)* represents a constant function.

Consider the function:

[tex]y = a(1\pm r)^m[/tex]

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is plus sign, then there is exponential growth happening by r fraction or 100r %

If there is negative sign, then there is exponential decay happening by r fraction or 100r %

We are given that;

c. y = (1.2)*

d. y = 0(6.3)*

e. y = (.71)*

a.) The equation and graph that show exponential growth is y = (1.2)x. This is because the base of the exponent (1.2) is greater than 1, so as x increases, the value of y increases at an increasing rate. The graph of y = (1.2)x is an upward-curving curve that gets steeper as x increases.

b.) The equation and graph that show exponential decay is y = (0.71)x. This is because the base of the exponent (0.71) is between 0 and 1, so as x increases, the value of y decreases at a decreasing rate. The graph of y = (0.71)x is a downward-curving curve that flattens out as x increases.

Therefore, exponential growth shows y = (1.2)* whereas y = (.71)* show exponential decay.

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Answer:

DE = 3

Step-by-step explanation:

A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of [tex]\frac{1}{2}[/tex] means that the new shape is half the size of the original.

To solve for a missing length, we can use this expression:

Inserting our numbers into the expression:

Subtract 64 from each side:

Therefore, the missing side length is 6.

Looking at the side CB, it is 10 units long. If the new shape is 5 units long, that means that the scale factor from shape 1 to 2 is [tex]\frac{1}{2}[/tex], meaning it is half its size. If the new shape is half its size, we can use this expression to solve for the missing length:

Therefore, the measure of DE is 3.

Answer:

The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.

Plugging x=0 into the given function, we get:

f(0) = 320(0.90)^0 = 320(1) = 320

Therefore, the initial price of the store item was $320.

The volume of the composite solid is 5104 cubic ft.

A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.

The area of a triangular prism is given as:

V = 1/2(bhl)

Here, h = 22 - 12 = 10 ft.

Substituting the values we have:

V = 1/2(13)(10)(32)

V = 2080 cubic ft.

The volume of the rectangular prism is given as:

V = lwh

V = (28)(9)(12)

V = 3024 cubic ft.

The volume of the composite solid is:

V = V1 + V2

V = 2080 + 3024

V = 5104 cubic ft.

Hence, the volume of the composite solid is 5104 cubic ft.

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After 21 minutes the location of BO in the wheel is EO

The location of BO after 21 minutes is solved using the data:

It takes 4 minutes for the wheel to make one complete rotation

hence in 21 minutes the rotation covered is

= 21 / 4

= 5.25

This is 5 complete rotations and 0.25 (a quarter rotation).

0.25 rotation is

=0.25 * 360

= 90

Each gap in the wheel is

360 / 12 = 30 degrees

hence three steps from B which is EO

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Jimmy will leave a $33.32 tip for the great service.

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

To calculate the tip, we need to first find 20% of the total cost of the meal (before sales tax):

20% of 166.60 = 0.20 x 166.60 = 33.32

Therefore, Jimmy will leave a $33.32 tip for the great service.

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The value of k that makes the remainder of the polynomial equal to -6 when divided by x + 1 is k = 5.

To find the value of k that makes the remainder of the polynomial P(x) = kx3 - 4x2 + x + 4 equal to -6 when divided by x + 1, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial P(x) is divided by x - a, the remainder is P(a).

In this case, we are dividing by x + 1, so we can rewrite this as x - (-1). Therefore, a = -1 and we can plug this value into the polynomial to find the remainder:

P(-1) = k(-1)3 - 4(-1)2 + (-1) + 4

Simplifying this equation gives us:

P(-1) = -k - 4 - 1 + 4

P(-1) = -k - 1

Since we want the remainder to be -6, we can set P(-1) equal to -6 and solve for k:

-k - 1 = -6

-k = -5

k = 5

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The values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.

To find k so that when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2, the remainder is 0, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x-a, the remainder is f(a).

So, if we let f(x) = x^(3)+kx^(2)+k^(2)x+14 and a = -2, we can find the value of k that makes the remainder 0.

f(-2) = (-2)^(3)+k(-2)^(2)+k^(2)(-2)+14 = 0

Simplifying the equation, we get:

-8 + 4k - 2k^(2) + 14 = 0

-2k^(2) + 4k + 6 = 0

Dividing by -2, we get:

k^(2) - 2k - 3 = 0

Factoring the equation, we get:

(k-3)(k+1) = 0

So, k = 3 or k = -1.

Therefore, the values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.

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Answer:

24

Step-by-step explanation:

This is a division problem.

0.72/0.03 = 7.2/0.3 = 72/3 = 24

Answer:

  (a)  8 : 3

  (b)  1 7/8 cups

Step-by-step explanation:

Given a recipe that calls for 2 cups of flour and 3/4 cup of water, you want to know the ratio in simplest terms, and the amount of water for 5 cups of flour.

The ratio can be written and simplified as a fraction. Fractions are divided in the usual way.

  2/(3/4) = 2 ÷ 3/4 = 2 × 4/3 = 8/3 = 8 : 3

If we multiply each term in this ratio by 5/8, we can find the recipe that uses 5 cups of flour:

  (5/8)·8 : (5/8)·3 = 5 : 15/8 = 5 : 1 7/8

Naomi uses 1 7/8 cups of water with 5 cups of flour.

Answer:

Step-by-step explanation:

[tex](a)[/tex]

[tex]2:\frac{3}{4}[/tex]

Multiply both sides by 4 to remove fraction:

[tex]2\times4:\frac{3}{4} \times 4[/tex]

[tex]8:3[/tex]     (this is simplest form because no number goes into both 8 and 3)

[tex](b)[/tex]

5 cups of flower:

[tex]8 \times \frac{5}{8} : 3 \times \frac{5}{8}[/tex]   (I chose [tex]\frac{5}{8}[/tex] to turn the 8 into 5)

[tex]5:\frac{15}{8}[/tex]

5 cups flour needs [tex]\frac{15}{8}[/tex] ([tex]=1\frac{7}{8}[/tex]) cups water

The slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.

To find the y-intercept and slope of the linear equation x  +y=-6 1/2, we

need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's isolate y by subtracting x from both sides of the equation:

x + y = -6 1/2

y = -x - 6 1/2

Now we can see that the equation is in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is -6 1/2.

Therefore, the slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.

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Answer:

AAS

Step-by-step explanation:

Answered this question before on Acellus.

Binomial and Normal distributions are two different types of probability distributions that are commonly used in statistics. Both distributions involve a set of possible outcomes, and the probability associated with each outcome.

The Binomial Distribution is used for discrete data such as coin flips, the number of defective items in a production run, and the number of wins and losses in a series of games. It is used with the formula P(x;n,p) and the techniques of probability, permutations, and combinations.

The Normal Distribution is used for continuous data such as height, weight, IQ scores, and test scores. It is used with the formula P(x;μ,σ) and the techniques of statistics, standardization, and z-scores.

Both distributions have the same basic shape and the same basic idea of a probability of a certain outcome. The main difference between them is that the Binomial Distribution is discrete and the Normal Distribution is continuous.

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The probability of the spinner not landing on A is 0.47.

To find the probability that the spinner does not land on A, we need to add up the frequencies of the outcomes where A does not appear, which are (B,B), (B,C), (C,B), and (C,C):

Frequency of not landing on A = Frequency(B,B) + Frequency(B,C) +  Frequency(C,B) + Frequency(C,C)

Frequency of not landing on A = 15 + 17 + 13 + 14 = 59

The total number of outcomes is 125, so the probability of not landing on A is:

P(not A) = Frequency of not landing on A / Total number of outcomes

P(not A) = 59 / 125 = 0.47

Therefore, the probability of the spinner not landing on A is 0.47.

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Babe and Ruth are 675 miles apart and headed straight toward each

other. If Babe is traveling at 40 mph and Ruth is traveling at 35

mph, it will take 9 hours before they meet.

To determine the time it will take for Babe and Ruth to meet, we need to use the formula:

time = distance / rate

Since they are traveling towards each other, we can add their speeds to get the combined speed at which they are approaching each other.

combined speed = Babe's speed + Ruth's speed

combined speed = 40 mph + 35 mph

combined speed = 75 mph

Now we can plug in the values we have into the formula:

time = distance / combined speed

time = 675 miles / 75 mph

time = 9 hours

Therefore, it will take 9 hours before Babe and Ruth meet.

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This hypothesis test indicates that the team efficiency when working through distance working (e.g. with online meetings) is not generally more efficient than when working with physical presence.

The research question being examined is whether teams that work through distance working (e.g. with online meetings) are generally more efficient than those that work with physical presence. To answer this question, a hypothesis test can be used with a 1% level of significance.

The null hypothesis (H0) is that there is no difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence. The alternative hypothesis (H1) is that there is a difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.

To test this hypothesis, a two-tailed independent t-test was used. The mean score for the team that had used online meetings was 2.63 with a standard deviation of 0.92 and for the team that had worked with physical presence the mean was 2.35 with a standard deviation of 0.81. The t-statistic obtained was 1.71 and the corresponding p-value was 0.093.

Since the p-value (0.093) is not less than the level of significance (0.01), the null hypothesis cannot be rejected. Therefore, the data suggests that there is not a significant difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.

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The line passes through the x-axis at the point (13/2, 0).

To find where the line passes through the x-axis, we need to find the x-intercept of the line. The x-intercept is the point where the line crosses the x-axis, so the y-coordinate of this point will be 0.

We can use the slope-intercept form of a line, y = mx + b, to find the x-intercept. First, we need to find the slope of the line, m. The slope is given by the formula:
m = (y2 - y1)/(x2 - x1)

Plugging in the given points, we get:

m = (5 - 1)/(-1 - 5)

m = -2/3

Now we can plug in one of the points and the slope into the equation to solve for the y-intercept, b:
1 = -2/3(5) + b
b = -13/3

So the equation of the line is:
y = -2/3x + 13/3

To find the x-intercept, we set y to 0 and solve for x:
0 = -2/3x + 13/3
x = 13/2

So the line passes through the x-axis at the point (13/2, 0).

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The initial population is 4001 and the maximum population is 4000

The given population growth model is [tex]12000/3+e^{-0.02(t)}.[/tex]

To find the initial population, we need to plug in t=0 into the equation.

[tex]12000/3+e^{-0.02(0)}[/tex]

= [tex]12000/3+1[/tex]

= [tex]4000+1[/tex]

= [tex]4001[/tex]

So the initial population is 4001.

To find the maximum population, we need to find the limit of the equation as t approaches infinity.


= [tex]12000/3+0[/tex]

= [tex]4000[/tex]

So the maximum population is 4000.

In conclusion, the initial population is 4001 and the maximum population is 4000.

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We can use the two-point form to find the equation of the line passing through the two given points:

y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)

where (x1, y1) = (0, 4) and (x2, y2) = (5, 19).

Substituting the values, we get:

y - 4 = ((19 - 4)/(5 - 0))(x - 0)

Simplifying the equation, we get:

y - 4 = (15/5)x

y - 4 = 3x

Adding 4 to both sides, we get:

y = 3x + 4

Therefore, the equation of the line passing through the points (0, 4) and (5, 19) is y = 3x + 4.

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a) find slope

19-4/5-0 = 15/5 = 3

plug into equation

y = 3x + b

plug in coordinate pair to solve for b

4 = 3(0) + b

4 = 0 + b

b = 4

y = 3x + b

Answer:

First, subtract 10x on both sides so you get

12=10x-2

Then add 2 odd both sides

14=10x

Then divide both sides by 10

14/10= 10X/10

So you get x=1.4

When x = 4, y = 320/27.

If y varies directly as x, it means that y = kx, where k is a constant. To find k, we can use the given information:

When x = 3, y = 12

12 = k * 3

k = 4

Now that we know k, we can find y when x = 20:

y = k * x

y = 4 * 20

y = 80

Therefore, when x = 20, y = 80.

25. If y varies directly as the square of x, it means that y = k * x^2, where k is a constant. To find k, we can use the given information:

When x = 2, y = 16

16 = k * 2^2

k = 4

Now that we know k, we can find y when x = 8:

y = k * x^2

y = 4 * 8^2

y = 4 * 64

y = 256

Therefore, when x = 8, y = 256.

26. If y varies directly as the cube of x, it means that y = k * x^3, where k is a constant. To find k, we can use the given information:

When x = 3, y = 5

5 = k * 3^3

k = 5/27

Now that we know k, we can find y when x = 4:

y = k * x^3

y = 5/27 * 4^3

y = 5/27 * 64

y = 320/27

Therefore, when x = 4, y = 320/27.

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Answer:

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

Step-by-step explanation:

Assuming that the tape diagram shows the ratio of adult tickets to child tickets as 3:2, we can represent this as follows:

  AAA

  AAA

  AAA

  CCC

  CCC

In this diagram, each square represents a certain number of tickets. To determine how many tickets each square represents, we need to know the total number of squares in the diagram.

There are a total of 3 + 3 + 3 + 2 + 2 = 13 squares in the diagram. Since the theater sold 126 tickets in total, we can divide 126 by 13 to find out how many tickets each square represents:

126 ÷ 13 ≈ 9.69

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

It can be inferred that milk chocolate does have a lower melting point than dark chocolate and that the rate at which chocolate melts is influenced by a number of variables, including composition, temperature, as well as humidity.

According to the facts provided, it is anticipated that within 64 seconds, half of the milk chocolate brands will melt. According to their composition as well as melting point, different milk chocolate brands may melt sooner or later than 64 seconds.

However, it is believed that none of the dark chocolate brands are expected to melt before 64 seconds have passed and that their melting time actually begins after 200 seconds.

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The transformation between the points is (x, y) = (x, -y + 10)

From the question, we have the following parameters that can be used in our computation:

G(9, 12), H(−2, −15), J(3, 8) and

G'(9, -2), H'(-2, 25), J'(3, 2)

We can see that the x coordinates of the image and the preimage are equal

However, the relationship between the y-coordinates is

y' = -y + 10

This means that

(x, y) = (x, -y + 10)

The above rule is a translation transformation

Translation transformation is a transformation that moves each point in a figure or object by a fixed distance in a specified direction.

Hence, the transformation is (x, y) = (x, -y + 10)

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Complete question

26. G(9, 12), H(−2, −15), J(3, 8) and G'(9, -2), H'(-2, 25), J'(3, 2)

Write out the transformation rule from GHJ to G'H'J'

Answer: 1,068 and wil

Step-by-step explanation:

Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).

To use synthetic division to find the result of the given polynomial division, we need to follow these steps:

1. Write the coefficients of the dividend polynomial in a row: 2 10 8 1 24
2. Write the constant term of the divisor with the opposite sign in front of the row: -2 | 2 10 8 1 24
3. Bring down the first coefficient: -2 | 2 10 8 1 24
         -----------
            2
4. Multiply the first coefficient by the divisor's constant term and write the result under the second coefficient: -2 | 2 10 8 1 24
         -----------
            2 -4
5. Add the second coefficient and the result from step 4: -2 | 2 10 8 1 24
         -----------
            2  6
6. Repeat steps 4 and 5 for the remaining coefficients: -2 | 2 10 8 1 24
         -----------
            2  6  4 -6
7. The last number in the row is the remainder. If it is 0, the division is exact. If not, we need to express the result in the form: quotient + (remainder)/(divisor)

In this case, the quotient is 2x^(3)+6x^(2)+4x-6 and the remainder is 36. So the result of the division is:
2x^(3)+6x^(2)+4x-6+(36)/(x+2)

Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).

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The probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826. The score the employer will use to decide job offers is 123.3 to decide job offers for potential "high flyers."

The IQ test is designed to have a mean of 100 and a standard deviation of 10. This means that the test follows a normal distribution with a mean of 100 and a standard deviation of 10.

(a) The probability that a randomly selected individual from the population will score between 90 and 110 on this test can be found using the standard normal distribution table. We need to find the z-scores for 90 and 110 and then use the table to find the corresponding probabilities.

The z-score for 90 is (90 - 100) / 10 = -1
The z-score for 110 is (110 - 100) / 10 = 1

Using the standard normal distribution table, we find that the probability for a z-score of -1 is 0.1587 and the probability for a z-score of 1 is 0.8413.

The probability that a randomly selected individual will score between 90 and 110 is the difference between these two probabilities:

0.8413 - 0.1587 = 0.6826

So the probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826.

(b) The employer wants to identify potential "high flyers" and intends to do this using the outcome of the IQ test. If the employer offers these positions to people with IQs in the top 1% of the population, we need to find the z-score that corresponds to the top 1% of the population.

Using the standard normal distribution table, we find that the z-score that corresponds to the top 1% of the population is 2.33.

Now we can use the z-score formula to find the corresponding IQ score:

z = (x - mean) / standard deviation

2.33 = (x - 100) / 10

Solving for x, we get:

x = (2.33 * 10) + 100 = 123.3

So the employer will use a score of 123.3 to decide job offers for potential "high flyers."

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Answer: the first quadrant : 12° i the second quadrant : 168° i

the third quadrant : -168° i the forth quadrant : 348°.

Step-by-step explanation:

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The matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].

Assuming that A is a matrix with three rows, we can find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= by following these steps:

1. Start with the identity matrix, I, which is a matrix with ones along the main diagonal and zeros everywhere else:
I = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

2. Apply the first row operation, 3R3​+R1​⇒R1​, to the identity matrix by adding three times the third row to the first row:
I = [[1+3(0), 0+3(0), 0+3(1)], [0, 1, 0], [0, 0, 1]]
I = [[1, 0, 3], [0, 1, 0], [0, 0, 1]]

3. Apply the second row operation, −7R2​⇒R2​, to the identity matrix by multiplying the second row by -7:
I = [[1, 0, 3], [0*(-7), 1*(-7), 0*(-7)], [0, 0, 1]]
I = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]

4. The resulting matrix, I, is the matrix B that we are looking for:
B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]

Therefore, the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].

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Answer:

(2,-3)

Step-by-step explanation: