evaluate the expression

The solutions of the inequalities are shown below

x [tex]\geq[/tex] 5

x< 13

x[tex]\geq[/tex]1

x> 1

Solving inequalities involves finding all possible values of a variable that make the inequality true. The process for solving an inequality depends on the type of inequality and the operations involved.

[tex]6^x + 4 \leq 6^{2x - 1} \\x + 4 \leq 2x - 1\\x - 2x\leq -1 - 4\\-x \leq -5\\x \geq 5[/tex]

[tex]2^{x + 3} > 4x^{x - 5} \\2^{x + 3} > 2^{2x - 10}\\x + 3 > 2x - 10\\x - 2x > - 10 - 3\\-x > - 13\\x < 13[/tex]

[tex]9^x \leq 9^{2x - 1}\\ x \leq 2x - 1\\x - 2x \leq -1\\-x \leq -1\\x \geq 1[/tex]

[tex]5^4 > 25^{2x} \\5^4 > 5^{4x} \\4 > 4x\\x > 1[/tex]

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Area of sector XYZ is 81.45 feet².

The area of a sector is a measure of the size of a portion of a circle enclosed by two radii and an arc between them. It is expressed in square units, such as square centimeters, square meters, or square inches.

To find the area of a sector, you need to know the radius of the circle and the central angle of the sector.

The formula for the area of a sector is:

Area of sector = (central angle / 360°) x π x r²

where r is the radius of the circle, π is the mathematical constant pi (approximately 3.14), and the central angle is measured in degrees.

n is the area of sector XYZ

n/360=115/255(X)

n/255=115/360(V)

(The same elements are proportional)

n=115/360×255

n=81.4583≈81.45 feet²

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The calculated value of the probability that the experiment results in exactly 1 success is 0.08719

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

n = 7

x = 1

p = 0.45

The probability is then calculated as

P(x = x) = nCr * p^x * (1 - p)^(n - x)

Substitute the known values in the above equation, so, we have the following representation

P(x = 1) = 7C1 * (0.45)^1 * (1 - 0.45)^(7-1)

Evaluate the expression

So, we have

P(x = 1) = 0.08719

Hence, the probability is 0.08719

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The trigonometric ratio cosA = [tex]\frac{3}{5}[/tex] which is in the lowest form.

Trigonometric ratios are the ratios of the sides of a right triangle. The sine, cosine, and tangent are three popular trigonometric ratios. (tan).

The given triangle is a right angle,

To find the cos angle we need to take the ratio of the length of the side which is next to the angle, it is also called an adjacent side to the length of the longest side of the triangle called the hypotenuse.

[tex]cosA = \frac{Length of the side next to the angle}{length of the longest side of the triangle} \\cosA = \frac{Adjacent side}{Hypotenuse} \\cosA = \frac{6}{10}\\ cosA = \frac{3}{5}[/tex]

Therefore [tex]cosA= \frac{3}{5}[/tex]

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Answer:

what arecrosses on line 2

The variables that Natalie used in the data collected was C. Number of flowers in each bouquet.

The bar graph that Natalie crafted utilized the variable "number of flowers in each bouquet." This particular type of graph reveals the frequency or count associated with every number of flowers contained within a single bouquet.

As an illustration, let us suppose there were 20 bouquets holding 5 flowers, 30 bouquets possessing 10 flowers, and 15 bouquets that had 15 flowers each; consequently, the bar chart would exhibit exactly three bars symbolizing the count for all three categories as outlined above.

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Answer:

distance = rate x time

where distance is 300 kilometers and time is t hours. Rearranging this formula to solve for rate, we get:

rate = distance / time

Substituting the given values, we get:

r = 300 / t

Therefore, the equation that represents the train's rate in kilometers per hour based on how many hours the trip takes is r = 300/t.

Step-by-step explanation:

The constant of proportionality of the line is slope m = 2/3

Given data ,

Let the line be represented as A

Now , the value of A is

Let the point on the straight line be P ( 2 , 3 )

Now , from the proportionality , we get

y = kx

Divide by x on both sides , we get

k = y/x

So , the slope of the line is k

k = 2/3

Hence , the proportion is y = ( 2/3 )x

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The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.

What is a sphere?

The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.

We are given diameter as 20 inches.

So, the radius is half of the diameter which comes out to be 10 inches.

From this, we get the volume as

⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]

⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]

⇒ Volume = [tex]\frac{4000}{3}[/tex] π

⇒ Volume = 4186.67 cubic inches

Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.

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These are absolute value expressions evaluated under different conditions:

|x + 3| if x > 5:

Here x is greater than 5, so x + 3 will also be positive. In this case, |x + 3| = x + 3.

|x + 3| if x > 2:

Similar to the above, x is greater than 2, so x + 3 will be positive. Thus, |x + 3| = x + 3.

|x + 3| if x = 2:

In this case, x + 3 = 2 + 3 = 5, and the absolute value of 5 is just 5. Thus, |x + 3| = 5.

|x - 3| if x > 5:

If x is greater than 5, then x - 3 will be positive. Hence, |x - 3| = x - 3.

|120 + x| if x < -120:

Since x is less than -120, 120 + x will be negative. But the absolute value of a negative number is its positive counterpart, so |120 + x| = -(120 + x).

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The balance after 10 years is equal to: A. $1491.82.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]A(t) = P_{0}e^{rt}[/tex]

Where:

When time, t = 10 years, the future value can be calculated as follows:

[tex]A(t) = 1000e^{0.04 \times 10}\\\\A(t) = 1000e^{0.4}[/tex]

A(t) = 1000(1.49182469764)

A(t) = 1491.82469764 ≈ $1491.82.

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Answer:

C

Step-by-step explanation:

If it is perpendicular to the line y = ¾x+7 then the gradient if the line must be the negative reciprocal of 3/4. The gradient must be - 4/3. So A, B and D are rejected. Left is C

Let's replace now.

For C,

Let's take y=-4/3x-10 into consideration at the point (-12,6)

Y should be equal to 6 when we replace x by -12

Let's try

Y = -4/3(-12) - 10 = 16 - 10 = 6

Yup. C is your answer.

1. The coordinates of the vertices of the preimage in the first column of the table are; (2, 2), (-1, 2) (-1, 1) (-2, 1) (-2, -2) (1, -2) (1, -1) (2, -1).

2. The scale factor for the dilation is 3

3. The coordinates for the image are,  (6,6) (-3, 6) (-3, 3) (-6, 3)(-6, -6) (3, -6) (3, -3)(6, -3)

4. The sketch has been attached below;

5. The dilation multiplies the length of line segments by the scale factor.

6. The dilation did not affect the angle measures. The angles in the image are the same as the angles in the preimage.

To calculate the scale factor for the dilation, we look at what has been provided (x, y) → (3x, 3y)

x =1 x2 = 3

1 multiplied by what will give us 3

1×? = 3

1/1 = 3/1 = 3

If we multiply 3 to every vertices of the preimage, we will find the coordinated of the image.

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The surd forms are simplified to give;

21. 10√6 - 12√10

23. -56a  - 5√2a - 25

25. -4√15x - 25x + 3

Surds are described as values in square root that can no longer be simplified into whole numbers or integers

They are also seen as irrational numbers.

From the information given, we have that;

√15(2√10 - 4√6)

Expand the bracket and multiply the surd forms

2√150 - 4√90

Factorize the forms

2√25 ×√6 - 4√9 × √10

find the square root

10√6 - 12√10

23. (√2a - 5)(7√2a - 5)

expand the bracket

7√4a² - 5√2a - 35√4a² + 25

find the square root, we have;

7×2a - 5√2a - 35×2a + 25

collect the like terms

14a - 70a - 5√2a - 25

-56a  - 5√2a - 25

25. (√3 + √5x)(√3 - 5√5x)

expand the bracket

3 - 5√15x + √15x - 5√25x²

find the square root

3 - 5√15x + √15x - 25x

collect the like terms

-4√15x - 25x + 3

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The volume of the prism is 143.44 in³

A prism is a solid shape that is bound on all its sides by plane faces.

The general formula for the volume of a prism is expressed as;

V = base area × height

The prism is a rectangular prism, therefore the volume will be calculated as

V = l× w × h

where l is the length of the base and w is the width of the base

V = 8.5× 4.5 × 3.75

V = 143.44 in³

therefore the volume of the rectangular prism is 143.44 in³

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It is financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model, as it has a net benefit of $12,000 compared to continuing to use the old boat.

To determine whether Harris Fishing Tours should replace the old boat with the new fuel-efficient model, we need to compare the costs and benefits of each option.

Option 1: Replace the old boat with the new fuel-efficient model

If Harris replaces the old boat with the new fuel-efficient model, they will have to pay $80,000 for the new boat. They can sell the old boat for $32,000, so the net cost of the new boat will be $48,000 ($80,000 - $32,000).

The new boat is expected to be extremely fuel efficient, which means that the fuel costs will be $15,000 per year lower than the old boat. Over the remaining four years of the old boat's useful life, this represents a total savings of $60,000 ($15,000 x 4).

Therefore, the total cost of replacing the old boat with the new fuel-efficient model is $48,000 - $60,000 = -$12,000, which means that this option has a net benefit of $12,000.

Option 2: Continue to use the old boat until it wears out

If Harris decides to continue using the old boat until it wears out, they will not incur the $80,000 cost of purchasing the new boat.

However, they will continue to pay $15,000 per year more in fuel costs than they would with the new boat. Over the remaining four years of the old boat's useful life, this represents a total cost of $60,000 ($15,000 x 4).

In addition, at the end of the four years, the old boat will have no salvage value since it will have reached the end of its useful life.

Therefore, the total cost of continuing to use the old boat until it wears out is $60,000, which means that this option has a net cost of $60,000.

Conclusion

Based on the analysis above, it is more financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model. This option has a net benefit of $12,000, while continuing to use the old boat until it wears out has a net cost of $60,000.

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The composite functions are:

a) f ∘ g = 3x² + 4, with domain of all real numbers.

b) g ∘ f = 9x² + 24x + 16, with domain of all real numbers.

c) f ∘ f = 9x + 16, with domain of all real numbers.

d) g ∘ g = x⁴, with domain of all real numbers.

To find the composite functions, we need to substitute the function g into the function f or vice versa, depending on the order of composition. The resulting composite function will have a domain that is restricted by the domains of the individual functions involved.

a) To find f ∘ g, we substitute g(x) = x² into f(x) = 3x + 4:

f(g(x)) = 3g(x) + 4 = 3x² + 4

The domain of f ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

b) To find g ∘ f, we substitute f(x) = 3x + 4 into g(x) = x²:

g(f(x)) = (3x + 4)² = 9x² + 24x + 16

The domain of g ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

c) To find f ∘ f, we substitute f(x) = 3x + 4 into f(x) = 3x + 4:

f(f(x)) = 3f(x) + 4 = 3(3x + 4) + 4 = 9x + 16

The domain of f ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

d) To find g ∘ g, we substitute g(x) = x² into g(x) = x²:

g(g(x)) = (x²)² = x⁴

The domain of g ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

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Answer:

Starting with the equation:

-2x + 6 = -x^2

First, we can rearrange it to put it in standard quadratic form:

x^2 - 2x - 6 = 0

To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:

x^2 - 2x + 1 - 1 - 6 = 0

The first three terms can be written as a perfect square:

(x - 1)^2 - 7 = 0

Add 7 to both sides:

(x - 1)^2 = 7

Now we can take the square root of both sides:

x - 1 = ±√7

Add 1 to both sides:

x = 1 ± √7

So the solutions to the equation are:

x = 1 + √7 or x = 1 - √7

mark me brilliant

An example of where past performance does predict future performance would be Mt. Kīlauea's eruption in 2018.

An example of where past performance does not predict future performance would be the eruption of Hualālai last happening in 1801.

Using past data, there was a prediction that Mt. Kīlauea would erupt in the year 2018 and it did happen ( even though it was not very serious ) at the Lower East rift zone of the volcano. Past performance therefore predicted the future.

However, the same prediction said that Hualālai would erupt in 1854 and yet the volcano has not erupted since 1801 which shows that the prediction was wrong.

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Out of 60 bikes in the repair department, 25 need two repairs and the range of bikes that need both tire and handlebar repairs without needing to fix the seat is 25 out of 60 bikes.

Let's use F, H, and S to represent the events that a bike has a flat tire, bent handlebars, and ripped seat, respectively. Then, we are given:

P(F) = 0.25

P(H) = 0.05

P(S) = 0.10

P(F ∩ H ∩ S) = 1/12

We want to find the number of bikes in the repair department and the number of bikes that need two repairs.

Let N be the total number of bikes in the repair department. Then, the number of repairs needed for each category is:

Flat tires: 0.25N

Bent handlebars: 0.05N

Ripped seats: 0.10N

The number of bikes that need all three repairs is:

P(F ∩ H ∩ S)N = (1/12)N

The number of repairs needed for these bikes is:

3P(F ∩ H ∩ S)N = (1/4)N

The number of repairs needed for bikes that need only two repairs is:

2[P(F ∩ H) + P(F ∩ S) + P(H ∩ S)]N = (5/12)N

The number of repairs needed for bikes that need only one repair is:

[P(F) + P(H) + P(S)]N = 0.4N

The total number of repairs needed is given as 101, so we have:

(1/4)N + (5/12)N + 0.4N = 101

Simplifying this equation gives:

N = 60

Therefore, there are 60 bikes in the repair department.

The number of bikes that need two repairs is:

(5/12)N = 25

Next, we need to find the range of bikes that need both the tires and handlebars repaired without needing to fix the seat. Let's use T and H to represent the events that a bike needs tire and handlebar repairs, respectively. We want to find P(T ∩ H ∩ not S).

We know that P(T ∩ H ∩ S) = P(F ∩ H ∩ S) = 1/12. Also, P(S) = 0.10, so P(not S) = 0.90. Therefore:

P(T ∩ H ∩ not S) = P(T ∩ H) - P(T ∩ H ∩ S)

= 2[P(F ∩ H) + P(F ∩ H ∩ S) + P(H ∩ S)] - P(F ∩ H ∩ S)

= 2(5/12) - 1/12

= 5/12

So, less than half of all the bikes have a ripped seat, and the range of bikes that need both the tires and handlebars repaired without needing to fix the seat is 5/12 of all the bikes, or 25 out of 60 bikes.

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After the first quarter, the interest earned would be:

$1,000.00 * 0.02 = $20.00

So the new balance would be:

$1,000.00 + $20.00 = $1,020.00

After the second quarter, the interest earned would be:

$1,020.00 * 0.02 = $20.40

So the new balance would be:

$1,020.00 + $20.40 = $1,040.40

After the third quarter, the interest earned would be:

$1,040.40 * 0.02 = $20.81

So the new balance would be:

$1,040.40 + $20.81 = $1,061.21

After the fourth quarter, the interest earned would be:

$1,061.21 * 0.02 = $21.22

So the final balance after 4 years would be:

$1,061.21 + $21.22 = $1,082.43

Therefore, the balance after 4 years would be $1,082.43.

Note that the perimeter of the parallelogram is 42

recall that opposite sides of a parallelogram are congruent always

We have to to find the distance between the  points Q(6, 6 ) and R(1, -6) using the distance formula which is

d = √[(x2 - x1) ² + (y2 - y 1)²]

where d is the distance between two points with paris   (x1 , y1)

and (x2, y2).

PS = QR = √(6-1)²  + (6+6)²

    = √5² + 12²
= √(25+144

= √(169)

= 13

PQ = SR = 8

Perimeter  = 13 + 13 + 8 + 8
Perimeter = 42.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.

Answer:

(A)

[tex] - 4.9 {t}^{2} + 43t + 339 = 0[/tex]

[tex]49 {t}^{2} - 430t - 3390 = 0[/tex]

[tex]t = \frac{ - ( - 430) + \sqrt{ {( - 430)}^{2} - 4(49)( - 3390)} }{2(49)} = \frac{430 + \sqrt{849340} }{98} = 13.79[/tex]

The rocket splashes down after 13.79 seconds.

(B) h'(t) = -9.8t + 43 = 0

t = 43/9.8 = 215/49 = 4.39 seconds

h(4.39) = 433.34 meters

At t = 4.39 seconds, the rocket peaks at

433.34 meters above sea level.

a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

b) the average temperature of the water in the system is 1527.

c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

What is right Riemann sum formula?

The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.

a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt

= 10 + 2√7

g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt

= 2 - (4 + 0)

= -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.

The highest value of g is thus given by 10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.

a) To evaluate the  S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:

[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8

= 17,088

This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.

b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:

Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527

In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.

c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.

This can be done using the definite integral of the equation, which gives us the following:

Total Change = ∫1020-√2xe (√x²-100)/x dx

= -14,351

This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

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Step-by-step explanation:

This is a right triangle , so the Pythagorean theorem applies

c^2 = a ^2 + b^2        c  is the hypotenuse   a and b are the legs

15^2 = 9^2 + x^2

15^2 - 9^2 = X^2

x  = 12 ft

1) Line AB

2) Ray AB

3) Line segment AB

4)Ray BA

The first drawing is a line AB because a line passing through two different points A and B

The second drawing is ray AB because it started at A

The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints

The fourth drawing is ray BA

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Answer:

75%

Step-by-step explanation:

To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.

According to the information provided:

55% of the team does not like to run.

Of those who do not like to run, 70% enjoy cycling.

Of those who enjoy running, 80% also enjoy cycling.

To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.

Percentage of athletes who do not like to run and enjoy cycling:

= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)

= 55% * 70% = 38.5%

Percentage of athletes who enjoy running and enjoy cycling:

= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)

= (100% - 55%) * 80% = 45% * 80% = 36%

Total percentage of athletes who enjoy cycling:

= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling

= 38.5% + 36% = 74.5%

Therefore, the correct answer is:

74.5%

Answer:

[tex]m = \frac{10 - 7}{7 - 3} = \frac{3}{4} [/tex]