Question 4
A is at -6 and B is at 9. Find the point, T, so that T is three-fifths of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2 3 4 5 6 7 8 9 10

By analyzing the end behavior of the function we can see that the correct options are A and D.

Here we have the exponential function:

[tex]F(x) = 2^x[/tex]

This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:

as x → ∞, f(x) → ∞

And when x is a really large negative number, the function tends to zero, then we have:

as x →-∞, f(x) → 0

Then the correct options are A and D.

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Answer:3

Step-by-step explanation: Initial value = y-intercept

Answer:

The probability of guessing the first genre correctly is 1/10. After guessing the first genre, the probability of guessing the second genre correctly is 1/9. Similarly, the probability of guessing the third genre correctly is 1/8. Therefore, the probability of guessing the top 3 genres correctly and in the correct order is:

1/10 * 1/9 * 1/8 = 1/720

So the exact probability is 1/720, which is already reduced to its simplest form.

The line is a vertical line, then the correct option is D, the slope is undefined.

A general linear equation can be written as:

y = a*x + b

Where a is the slope, b is the y-intercept, and x is the variable.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the two points are (2, -4) and (2, 4)

Replacing that we would have a problem, that is because we have the same x-value in both points.

Then we have a vertical line at x = 2.

That line has no defined slope, thus, the correct option is D.

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Answer:

t = 6.8

Explanation:

We know that A is at 1, B is at 10, so that is where we place those two.

First, we need to know what 2/3 of 10 is because the distance between A and B is 10.

Solving 2/3 of 10:

_____________________

- Divide 10 by the denominator, 3

         10 ÷ 3 = 3.3333......

- Multiply 3.3333..... by 2

         3.3333..... x 2 = 6.6666666666667

            or about 6.8 if we round up, which is prefered in these scenarios

Now that we know what 2/3 of 10 is, we can use that number as where to put it on the number line.

So t = 6.8

Hope this helps :)

Between Weeks 3 and 4, the water level varied the greatest.

To determine which two weeks had the greatest change in water level, we need to find the difference between each pair of consecutive weeks and identify the largest difference.

Here are the differences between consecutive weeks:

Week 1 to Week 2: (1 3/8) - (-1 1/4) = 2 5/8

Week 2 to Week 3: 2 1/2 - 1 3/8 = 1 1/8

Week 3 to Week 4: (-1 5/8) - 2 1/2 = -4 1/8

Week 4 to Week 5: (-1 3/4) - (-1 5/8) = -1/8

The largest difference is between Week 3 and Week 4, with a difference of 4 1/8 inches.

Therefore, the water level changed the most between Week 3 and Week 4.

Note that the differences are calculated by subtracting the water level of the earlier week from the water level of the later week.

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Answer:

The total cost per month is $190.76 to the nearest cent.

Step-by-step explanation:

From the given table, the monthly service plan costing $52.00 is:

The base calling plan includes two lines.

Therefore, for 4 lines, we will need to pay for 2 additional lines per month:

⇒ $21.99 × 2 = $43.98 per month

If 3,487 minutes are used per month, then the overage of minutes is:

⇒ 3487 - 2000 = 1487 minutes per month

As the overage rate is $0.06 per minute, then the cost of the additional minutes is:

⇒ 1487 × $0.06 = $89.22 per month

Therefore, the total cost per month before tax is:

⇒ $52.00 + $43.98 + $89.22 = $185.20

To apply the federal tax of 3%, multiply the total cost by 1.03:

⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)

Therefore, the total cost per month is $190.76 to the nearest cent.

The match to A line that has a slope of 5/3 and a y-intercept of 4 is 2y - x = -4.

We are given that;

The four equations to match from

Now,

Using the slope-intercept form, we can plug in m = 3/2 and b = -8:

y = (3/2)x - 8

This equation matches with y = 3/2x - 5 if we multiply both sides by 2:

2y = 3x - 16

Therefore, the correct equation is 2y - x = -16.

A line that contains the points (0,-2) and (4,0)

m = (0 - (-2)) / (4 - 0) m = 2 / 4 m = 1/2

Then we can plug in m = 1/2 and any of the given points to find b. For example, using (0, -2), we have:

-2 = (1/2)(0) + b -2 = b

Therefore, the equation is:

y = (1/2)x - 2

This equation matches with -5x - 3y = -12 if we multiply both sides by -6:

6y = -3x + 12

Therefore, the correct equation is -5x - 3y = -12.

A line that contains the y-intercept (0-2) and the slope of -3/4

Using the slope-intercept form, we can plug in m = -3/4 and b = -2:

y = (-3/4)x - 2

This equation matches with y = -3/4x - 2.

A line that has a slope of 5/3 and a y-intercept of 4

Using the slope-intercept form, we can plug in m = 5/3 and b = 4:

y = (5/3)x + 4

This equation matches with 2y - x = -4 if we multiply both sides by 3:

3y = (5/3)x + 12

Therefore, the correct equation is 2y - x = -4.

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Answer:

Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.

Step-by-step explanation:

The simplified expression for the difference in the area of circle A and B is 12π/(x+2)²

A circle is simply a round shape that has no corners or line segments. The area of a circle is expressed as;

A = πr²

The circumference of a circle = 2πr

for circle A;

8π/x+2 = 2πr

r = 8π/x+2 × 1/2π

r = 4/x+2

area = πr² = (4/x+2)²π

for circle B

4π/x+2 = 2πr

r = 4π/x+2 × 1/2π

r = 2/2x+2

area =( 2/2x+2)²π

difference = (4/x+2)²π - ( 2/x+2)²π

= π/(x+2)²( 4²-2²)

= π/(x+2)²(16-4)

= 12π/(x+2)²

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The probability of getting two numbers whose sum is greater than 9 = 5/36

We know that the probability is nothing but the number of favourable outcomes divided by the total number of outcomes.

Here, a single die is rolled twice.

and we get the set of 36 equally likely outcomes.

so, the total number of outcomes n(S) = 36

Let us assume that event A: getting two numbers whose sum is greater than 9

A = {(4, 6), (5,5), (5, 6), (6, 4), (6, 5)}

n(A) = 5

Using above formula of probability,

P(A) = n(A)/n(S)

P(A) = 5/36

Thus the required probability = 5/36

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Answer: B. 4

Step-by-step explanation: The interquartile range is just the distance in between the upper and lower quartiles. Therefore, to find the interquartile range, the equation in this case is 7 - 3, which equals 4.

Answer:

Step-by-step explanation:

down 1

compress 1/2

The calculated value of x if ∠A and ∠B are vertical angles is 13 degrees

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

∠A = (2x − 2)

∠B = (3x − 15)

Since the ∠A and ∠B are vertical angles, then they are congruent angles

So, we have

3x - 15 = 2x - 2

Evaluate the like terms

So, we have

x = 13

Hence, the solution is x = 13

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Answer:

3t^2i + 2tj is the correct answer.

The choices that are equivalent to the expression 4√3 will be ✓48 and ✓24.✓2.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

4✓3 will be:

= ✓4² × ✓3

= ✓48

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that would be 5 pieces of cardboard needed

The probability of observing an income between $70,000 and $90,000 for engineers at this computer company is 0.6217, or about 62.17%.

To solve this problem, we need to standardize the given income range using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by using the formula:

z = (x - μ) / σ

where x is the income, μ is the mean income, and σ is the standard deviation.

For the lower bound of $70,000, we have:

z₁ = (70,000 - 83,422) / 8,278 = -1.62

For the upper bound of $90,000, we have:

z₂ = (90,000 - 83,422) / 8,278 = 0.79

We can now find the probability of observing an income between $70,000 and $90,000 by calculating the area under the standard normal curve between z₁ and z₂.

We can use a standard normal distribution table or a calculator to find this probability, which turns out to be approximately 0.6217. This means that about 62.17% of engineers at this company earn an income within this range.

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Complete question is:

The salaries of engineers at a computer company are normally distributed with mean $83,422 and standard deviation $8,278. What is the probability of observing an income between $70,000 and $90,000?

Answer: 17/24 for both jobs

Step-by-step explanation:

Answer: n>5

Step-by-step explanation:

The area of the forest after 11 years will be 298 km².

To calculate the area of the forest after 11 years, we need to decrease the initial area of 1700 km² by 7.5% each year for 11 years.

First, let's calculate the decrease in area for one year:

Decrease in area for one year = 7.5% of 1700 km²

7.5% of 1700 km² = (7.5/100) × 1700 km²

= 127.5 km²

Now, we can calculate the total decrease in area over 11 years:

Total decrease in area over 11 years = 11 × 127.5 km² = 1402.5 km²

Finally, we can subtract the total decrease in area from the initial area to get the area of the forest after 11 years;

Area of the forest after 11 years = Initial area - Total decrease in area

= 1700 km² - 1402.5 km²

= 297.5 km²

Therefore, Rounding to the nearest square kilometer, the area of the forest after 11 years will be approximately 298 km².

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Answer:

  h(x) = 3·2^x

Step-by-step explanation:

You want the equation of the exponential curve h(x) = a·b^x when it goes through the points (0, 3) and (1, 6).

When x=0, the equation is ...

  h(0) = a·b^0 = a

We know that h(0) = 3, so a = 3.

When x=1, the equation is ...

  h(1) = 3·b^1 = 3b

We know that h(1) = 6, so 3b = 6, or b = 2.

The equation is h(x) = 3·2^x.

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A graph of triangle TOW is shown below.

A graph of triangle T'O'W, the image of ΔTOW after a reflection in the y-axis is shown below.

The coordinates of ΔT'O'W are: T' (5, 6), O' (-1, 8), and W' (4, -2).

In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

Next, we would apply a reflection over or across the x-axis;

(x, y)                →      (-x, y)

T (-5, 6)       →      (-(-5), 6) = T' (5, 6)

O (1, 8)       →      (-(-1), 8) = O' (-1, 8)

W (-4, -2)       →      (-(-4), -2) = W' (4, -2)

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107 over 103 times 101 over 100 would result in 10807/10300.

In order to multiply the fractions 107/103 and 101/100, we can simply multiply their numerators together and their denominators together:

(107/103) x (101/100) = (107 x 101) / (103 x 100)

Now we can simplify this fraction by finding the greatest common factor of the numerator and denominator and dividing both by it:

(107 x 101) / (103 x 100) = 10807 / 10300

Therefore, 107/103 times 101/100 simplifies to 10807/10300.

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Step-by-step explanation:

1/3 ÷ 3

=  1/3 ÷ 3/1

= 1/3  X  1/3  =  1/9

Similarly

1/4 ÷ 5   =   1/4  X  1/5 = 1/20

The new vertices of the triangle after moving the triangle 5 units down, are A(1,-7), B(9,-7), and C(5,-3). So, correct option is B.

To determine the coordinates of the triangle after it is translated 5 units down, we need to subtract 5 from the y-coordinates of each vertex.

Let's start with vertex A(1,-2). If we subtract 5 from -2, we get -7. Therefore, the new coordinates of vertex A are (1,-7).

Next, let's look at vertex B(9,-2). Again, if we subtract 5 from -2, we get -7. So the new coordinates of vertex B are (9,-7).

Finally, let's consider vertex C(5,2). If we subtract 5 from 2, we get -3. So the new coordinates of vertex C are (5,-3).

In this case, we are moving the triangle 5 units down, which means that we are subtracting 5 from the y-coordinates of each vertex. This is a common transformation in geometry, and it's important to be familiar with it when working with shapes and figures in the Cartesian plane.

So, correct option is B.

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The students error is in step 3 and the correct solution is g(x) = 2x² + 4x - 4

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

The steps to solve the expression

From step 2 to step 3, we have

g(x) = 2(x + 1)(x + 1) - 6

g(x) = 2(x² + 1x + 1) - 6

The step 3 is incorrect

Because when the expression is expanded, we have

g(x) = 2(x² + 2x + 1) - 6

This gives a solution of

g(x) = 2x² + 4x - 4

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