true or false ? is (b^9)^3 = b^27

1) (f - g) (x) = f(x) - g(x) = x ≤ 1/4  

Domain of the function is : [1/4, infinity)

2) → [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]        

Domain of the function : (1/4, infinity)

We have the function are as follows:

f(x) = -x + 4

g(x) = [tex]\sqrt{4x+1}[/tex]

To find the f - g and f/g and also their domains using interval  notation.

Now, (f - g) (x) = f(x) - g(x)

                       = [tex]-x+4-\sqrt{4x+1}[/tex]

                       = 4x + 1 ≤ 0

                       = x ≤ 1/4            

Domain of the function is : [1/4, infinity)

→ [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]

=> 4x - 1 > 0

=> x > 1/4

Domain of the function : (1/4, infinity)

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Answer:

Step-by-step explanation:

No

Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.

a. The 95% confidence interval for the proportion of teenagers using video streaming services daily is (0.5579, 0.6221). This means we're 95% confident that 55.79% to 62.21% of US teenagers use such services daily.

b. The results demonstrate that the proportion is not 0.5 because the full confidence interval is higher than 0.5.2. We obtain a t-value of roughly 2.51 with 108.52 degrees of freedom using a two-sample t-test.

At a significance level of 0.05, the critical t-value for a one-tailed test is approximately 1.66.

Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.

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The height of the person on the ferris wheel can be modeled by the equation:

h = 20sin(π/4*t) + 21

where h is the height in meters above the ground, t is the time in minutes, and 21 meters is added to account for the height of the platform.

The volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.

We shall calculate for the volumes of the cone and the cylinder, the sum of each volume will give the volume of the composite figure

The cone have;

radius = 7 ft

height = 34ft - 16ft = 18ft

Volume of the cone = 1/3 × 22/7 × 7ft × 7ft × 18ft

Volume of the cone = (22 × 7 × 6) ft³

Volume of the cone = 924 ft³

The cylinder have;

radius = 7 ft

height = 16 ft

Volume of the cylinder = 22/7 × 7ft × 7ft × 16ft

Volume of the cylinder = (22 × 7 × 16) ft³

Volume of the cylinder = 2464 ft³

Volume of the composite figure = 924 ft³ + 2464 ft³

Volume of the composite figure = 3388 ft³

Therefore, the volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.

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From Table 2, we can see that Georgia's income tax rate is 7%.

To find the amount of state income taxes Anthony will owe, we can multiply his income by the tax rate:

State income tax = (Anthony's income) x (Georgia's tax rate)

State income tax = $65,750 x 0.07

State income tax = $4,602.50

Therefore, Anthony will owe $4,602.50 in state income taxes. To find out how much money he will have left after he pays these taxes, we can subtract the tax amount from his income:

Money left after paying state income taxes = Anthony's income - State income tax

Money left after paying state income taxes = $65,750 - $4,602.50

Money left after paying state income taxes = $61,147.50

Therefore, Anthony will have $61,147.50 left after he pays state income taxes.

Sin A Cos A, and Tan A can be found respectively as follows:

1. 41.81°.

2. 44.19 degrees

2. 60 degrees

The angles can be found by following the rules for right-angled triangles. This can be achieved in the following ways:

1. sin A= opposite/hypotenuse

sin A = 6/9

Now we take the sine inverse:

sin^-1(6/9)

=  41.81°.

2. Cos 45° = Adjacent/hypotenuse

= cos 45° = x/4

x = cos 45° × 4

= 0.707 × 4

= 2.82

cos A = b2 + c2 – a2 ÷ 2bc

2.8² + 4² - a² ÷ 2×2.8×4

23.84 - 2.8² ÷ 22.4

23.84 - 7.84 ÷ 22.4

Cos A = 0.7142

= 44.19 degrees

3. tan A = Opposite/Adjacent

tan 60°  = 4/x

x = 4/tan 60°

x = 4/1.732

= 2.309

Tan A = 4/2.309

= 1.732

= 60 degrees

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Answer:

 50 cm

Step-by-step explanation:

To solve this answer you can find the area of the small triangle, and multiply it by 2 to get the area of the top part.

Then you can find the area of one of the bigger triangles and multiply it by 2.

Please could I get brainiest? I'm trying to get to the Expert level.

The solution to each of the given polynomials are:

1)  x² + 3x - 4

2) x² - 4x + 4

3) x² - 7x + 8

4) x² - 13 - (15/(x + 3)

1) We want to divide the polynomial. Thus:

          x² + 3x - 4

x + 2| x³ + 5x² + 2x - 8

     -   x³ + 2x²

                 3x² + 2x

               - 3x² + 6x

                        - 4x - 8

                      -  -4x - 8

                                0

2) We want to divide the polynomial. Thus:

        x² - 4x + 4

x - 2| x³ - 6x² + 12x - 8

     -  x³ - 2x²

              - 4x² + 12x

              - -4x² + 8x

                         4x - 8

                      -  4x - 8

                                0

3) We want to divide the polynomial. Thus:

         x² - 7x + 8

x + 3| x³ - 4x² - 13x + 24

      -  x³ + 3x²

              - 7x² - 13x

              - -7x² - 21x

                         8x + 24

                      -  8x + 24

                                0

4) We want to divide the polynomial. Thus:

        x² - 13

x + 3| x³ + 3x² - 13x - 15

      -  x³ + 3x²

              - 0x² - 13x

              - -7x² - 13x

                       0 - 15

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My own multi-step combination problem is given below:

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

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Answer:

Step-by-step explanation:

The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is  (9.7, 14.7).

Here, we have,

1. Identify the given information:

 - Confidence level (c) = 0.95

 - Sample mean (x) = 12.2

 - Sample standard deviation (s) = 3.0

 - Sample size (n) = 8

2. Determine the degrees of freedom (df) for the t-distribution:

 - df = n - 1 = 8 - 1 = 7

3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:

 - You can use a t-table or an online calculator for this.

 - The t-value for a 0.95 confidence level and 7 df is approximately 2.365.

4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):

 - ME = t-value * (s / sqrt(n))

 - ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5

5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):

 - Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7

 - Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7

So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).

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Answer: -8

Step-by-step explanation:

Simple math. Your welcome glad to help

Answer:

To find the value of y, we can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

We know that the slope is 5, and the two points on the line are (5,y) and (4,1). We can substitute these values into the slope formula to get:

5 = (y - 1) / (5 - 4)

Simplifying this equation gives:

5 = y - 1

Adding 1 to both sides gives:

y = 6

Therefore, the value of y is 6.

Step-by-step explanation:

Answer:

The first spinner has a 1/3 chance of not showing an odd number, and the second spinner has a 1/4 chance of showing a 3. The probability of both events happening is:

1/3 x 1/4 = 1/12

Therefore, there is a 1/12 chance of an outcome showing a 3 on the second spinner and not showing an odd number on the first spinner. Since there are a total of 3 x 4 = 12 possible outcomes, the number of outcomes that meet the criteria is:

12 x 1/12 = 1

So there is only one outcome that meets the criteria.

The first equation of this system is y = 2x + 3, the second equation is y = 3x - 1, and the solution of the system is (4, 11).

a) The first equation of this system can be found by using the points given in the first table. We can use the two points (-1, 1) and (0, 3) to find the equation of the line passing through them using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

The slope of the line passing through (-1, 1) and (0, 3) is (3-1)/(0-(-1)) = 2/1 = 2.

Substituting one of the points in the slope-intercept form, we get 1 = 2(-1) + b, which gives us b = 3. Therefore, the equation of the line is y = 2x + 3.

b) Similarly, we can use the points given in the second table to find the equation of the second line. Using the points (0, -1) and (2, 5), we get the slope as

(5-(-1))/(2-0)

= 6/2

= 3.

Substituting one of the points in the slope-intercept form, we get

-1 = 3(0) + b, which gives us b = -1.

Therefore, the equation of the second line is y = 3x - 1.

c) To find the solution of the system, we need to find the point of intersection of the two lines. We can do this by solving the two equations simultaneously.

Substituting the second equation in the first, we get:

2x + 3 = 3x - 1

Simplifying, we get x = 4.

Substituting x = 4 in either of the equations, we get y = 11. Therefore, the solution of the system is (4, 11).

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Answer:

10

Step-by-step explanation:

When you think of the mean of a data set, think of the word average. 'Mean' and 'average' are the same thing when you're talking about a set of data.

To find the mean, you have to divide the sum of all values in your data set, by the number of values.

7 + 9 + 10 + 11 + 11 + 12 = 60

60/6 = 10

Therefore, the mean of this data set would be 10.

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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Answer:

8+(3)-9=8+3-9=11-9=2

Step-by-step explanation:

by using PEMDAS rule

Start with :

P : Paranthesis

E: exponents

M: Multiplication

D : division

A: Addition

S:Subtraction

You must measure 24 male students to estimate the mean height within one inch with 93% confidence.

Since we want to estimate the mean height within one inch, the margin of error (E) is 1 inch:

E = Z * (Standard deviation / √Sample size)

Now, we can rearrange the formula to solve for the Sample size (n):

1 = 1.81 * (2.7 / √n)

Solving for n:

n = (1.81 * 2.7 / 1)²

n ≈ (4.887)²

n ≈ 23.88

Since we cannot have a fraction of a person, we round up to the nearest whole number:

n ≈ 24

So, you must measure 24 male students to estimate the mean height within one inch with 93% confidence.

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The total surface area of this countertop is 522 square feet.Once all of these factors are taken into account, Mrs. Miller can then calculate the total cost of the countertop.

Surface area is the total area of the visible surface of an object, such as a cube or a sphere. It is measured in square units such as square inches, square feet, or square meters. It is important in mathematics, science, and engineering because it is used to calculate the amount of material needed to cover an object, the volume of a container, and other measurements. Surface area is also helpful in solving problems involving friction, heat transfer, and air flow.

Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen. The total surface area of this countertop is 522 square feet. This is calculated by multiplying the length of the countertop (34 feet) by the width of the countertop (15 feet), which yields 510 square feet. Then, the total surface area of the countertop is increased by adding the surface area of the 3-ft by 3-ft corner (9 square feet). Therefore, the total surface area of the countertop is 522 square feet.

Part B

To determine the cost of the countertop, Mrs. Miller would need to consider several factors, such as the material used, the labor required to install the countertop, and any additional fees associated with the purchase. Generally speaking, countertops made of granite, quartz, and marble tend to be more expensive than countertops made of laminate and solid surface. The installation labor cost will vary depending on the complexity of the installation, as well as the type of material used and the size of the countertop. Additionally, there may be additional fees associated with the purchase, such as the cost of delivery and taxes. Once Mrs. Miller has determined all of these factors, she can then calculate the total cost of the countertop.

Conclusion

In conclusion, Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen. The total surface area of this countertop is 522 square feet. To determine the cost of the countertop, Mrs. Miller would need to consider several factors, such as the material used, the labor required to install the countertop, and any additional fees associated with the purchase. Once all of these factors are taken into account, Mrs. Miller can then calculate the total cost of the countertop.

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The first step is to copy a segment and an angle, and the second step is to fix the width of the compass to the length of the segment. Then last, draw a perpendicular line.

What is geometry?

Geometry is a branch of mathematics that deals with the study of spatial relationships, shapes, sizes, positions, and dimensions of objects. It involves the study of points, lines, angles, planes, curves, surfaces, and solids, and how they relate to each other in space.

According to the given information:

Considering that, we must define the first stage, which is the process of copying a line segment in order to ensure that the new line segment is the same length as the original line segment. In a first stage, an angle and a segment must be replicated. The illustration depicts the copying construction.

The compass width must then be changed to match the section length. The new angle is now commensurate with the old angle. This is the following step.

The next step is to draw a perpendicular line. It is shown here how to draw a line perpendicular to the specified line across a point.

As a result, the first step is to copy a segment and an angle, and the second step is to set the width of the compass to the length of the segment. Then last, draw a perpendicular line.

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the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.

what is  rounded to the nearest  ?

"Rounded to the nearest" means finding the nearest value of a specified degree of accuracy. For example, rounding a number to the nearest whole number means finding the closest whole number to that number. If the number is equally close to two whole numbers, it is rounded up to the higher number.

In the given question,

The trajectory of the package can be modeled using the equation:

y = -0.5 * g * x² / v² + tan(∅) * x + h

where:

y = height of the package above the ground at horizontal distance x

g = acceleration due to gravity (9.8 m/s²)

v = horizontal velocity of the drone (100 m/s)

theta = angle at which the package is released

h = initial height of the package above the ground (4500 meters)

To hit the target, we want the package to land on the ground, which means its final height should be zero. So, we can set y = 0 and solve for x to find the horizontal distance at which the package should be released. This gives:

0 = -0.5 * 9.8 * x² / 100² + tan(∅) * x + 4500

Simplifying and rearranging, we get:

0.049 * x² + tan(∅) * x - 4500 = 0

Using the quadratic formula, we can solve for x:

x = (-tan(∅) ± √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)

Since we want the package to land in front of the target, we take the positive root of the equation:

x = (-tan(∅) + √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)

Now, we need to find the value of theta that will make the package hit the target. Since the drone is traveling horizontally, the package will also have a horizontal velocity of 100 m/s when it is released. So, we can use trigonometry to find the angle at which the package should be released. This gives:

tan(∅) = 4500 / x

Substituting this into the equation for x, we get:

x = (-4500 / x + √((4500 / x)²+ 0.049 * 4500 * 4)) / (0.098)

Simplifying and rearranging, we get:

x² = 4500 * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x) / 0.098

Squaring both sides, we get:

x⁴ = 4500² * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x)² / 0.009604

Expanding and simplifying, we get:

x⁴ = 900000000 * (1 + 0.00012345679 * x² - 0.00012345679 * 4500 * x / √(x² + 202500)) / 0.009604

We can solve for x using numerical methods, such as using a graphing calculator or an online solver. Using such a method, we find that:

x ≈ 9,932 meters

Therefore, the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.

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Answer:

A.

circular: ≈ 795.77 square feet

square: 625

Step-by-step explanation:

the circular pen would have a larger area.

Solving for the radius, we have:

r = 100 / (2 × 3.14) = 15.92 feet (rounded to two decimal places)

Therefore, the area of the circular pen would be:

Area = πr^2 = 3.14 × (15.92 ft)^2 ≈ 795.77 square feet

For a square pen with side length s, the perimeter is given by:

4s = 100

s = 25

The area of a square pen with side length s is given by:

A = s^2 = 25^2 = 625

The other number is 156.

Let a and b be two numbers, with a = 24.

We know that the product of two numbers' HCF and LCM is equal to the product of the two numbers.

So, we have:

HCF × LCM = a × b

We are given that the reciprocal of HCF is 1/12.

So, HCF = 1 / (1/12) = 12.

We are also given that the reciprocal of LCM is 1/312.

So, LCM = 1 / (1/312) = 312.

12 × 312 = 24 × b

Simplifying, we get:

b = (12 × 312) / 24 = 156

Therefore, the other number is 156.

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The solution set for the inequality is x < -10

The different signs for representing inequalities are;

From the information given, we have that;

−4x−38<2

To solve for the value of x, take the steps;

collect the like terms

-4x> 2 + 38

Add the values

-4x> 40

Divide both sides by the coefficient of x, we have;

x > -10

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Answer:  Approximately the year 2006

Roughly 8 years after 1998

================================================

Work Shown:

A = 373 represents a population of 373 thousand.

Plug in this value of A and solve for t. We'll need natural logs (LN) to isolate the variable.

[tex]A = 252e^{0.049t}\\\\373 = 252e^{0.049t}\\\\373/252 = e^{0.049t}\\\\1.4801587 \approx e^{0.049t}\\\\[/tex]

Apply natural logs to both sides.

[tex]\text{Ln}(1.4801587) \approx \text{Ln}\left(e^{0.049t}\right)\\\\\text{Ln}(1.4801587) \approx 0.049t*\text{Ln}\left(e\right)\\\\\text{Ln}(1.4801587) \approx 0.049t*1\\\\\text{Ln}(1.4801587) \approx 0.049t\\\\t \approx \text{Ln}(1.4801587)/0.049\\\\t \approx 8.0030472\\\\[/tex]

It takes about 8 years for the population to reach 373 thousand.

Since t = 0 starts at 1998, we get to the year 1998+8 = 2006.

The team made approximately 773 runs in the match.

Let's start by setting up an equation to represent the information given in the problem.

Let's call the total runs made by the team "T".

37% of T = 286

To solve for T, we can start by converting the percentage to a decimal:

37% = 0.37

0.37T = 286

Now we can solve for T by dividing both sides of the equation by 0.37:

T = 286 ÷ 0.37

T ≈ 773.0

Therefore, the team made approximately 773 runs in the match.

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