QUESTION 15
What are the domain and range of the real valued function?

The value of the equation that defines f(x) is [tex]f(x) = 5(2^\frac x2)[/tex]

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

The graph

Where, we have

A = (2, 10)

B = (4, 20)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

Using the points, we have

ab² = 10

ab⁴ = 20

Divide the equations

So, we have

b² = 2

So, we have

[tex]b = 2^\frac12[/tex]

Recall that

ab² = 10

So, we have

2a = 10

Evaluate

a = 5

This means that

[tex]f(x) = 5(2^\frac x2)[/tex]

Hence, the equation defining f is [tex]f(x) = 5(2^\frac x2)[/tex]

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Answer:

9pi/4 and 17pi/4

Step-by-step explanation:

Using the unit circle, we can easily find coterminal angles that coincide with a given angle. This includes across the y-axis and the x-axis, making sure to stay within the guidelines of [-2pi, 2pi]. The reference angle for 29pi/4 is pi/4. Coterminal angles are found my making a full rotation around the circle (by adding 2pi). In this case, make sure to have a common denominator before adding. These coterminal angles should not surpass -2pi or 2pi. pi/4+8pi/4=

9pi/4 +

8pi/4=17pi/4

. 9pi/4 and 17pi/4 are coterminal angles.

Hello!

width = x

length = 3x

so:

2(x + 3x) = 132

2x + 6x = 132

8x = 132

x = 132/8

x = 16.5

so:

width = 16.5 inches

length = 3*16.5 = 49.5 inches

Answer:

length is 49.5 inches

Step-by-step explanation:

length: l = 3w

perimeter: p = 2(l + w) = 132

2(l + w) = 132

l + w = 66

3w + w = 66

4w = 66

w = 66/4 = 16.5

l = 3w = 3 x 16.5 = 49.5

Answer: C because it went left 9 and up 2 so it is C. Hope this helps!

Step-by-step explanation:

The two numbers that satisfy the given conditions are 61 and 11. Their sum is 72, and their difference is 50.

Let's assume the two numbers as x and y. We can set up a system of equations based on the given information.

From the first statement, "The sum of two numbers is 72," we can write the equation:

x + y = 72

From the second statement, "Their difference is 50," we can write the equation:

x - y = 50

Now we have a system of two equations with two variables. We can solve this system by using the method of substitution or elimination.

Let's solve the system using the method of elimination:

Add the two equations:

(x + y) + (x - y) = 72 + 50

2x = 122

Divide both sides by 2:

x = 61

Now substitute the value of x into one of the original equations, let's use the first equation:

61 + y = 72

Subtract 61 from both sides:

y = 11

Therefore, the two numbers are 61 and 11.

To verify the solution, we can check if the numbers satisfy both conditions:

61 + 11 = 72 (sum condition)

61 - 11 = 50 (difference condition)

Both conditions are satisfied, confirming that the solution is correct.

Hence, the two numbers are 61 and 11.

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Note the complete and correct question is

The sum of two numbers is 72 and their difference is 50. Find the two numbers​ ?

Answer:  2 hours and 5 minutes

Step-by-step explanation:

I know trust

Multiplying the slope by -4 will result in a negative slope. The correct answer is option Y.

Based on the given information, the slope of the function will be multiplied by -4, and the y-value of the y-intercept will be decreased by 1 unit.

Looking at the graphs, we can determine that the slope of the original function is positive, as it rises from left to right. Therefore, multiplying the slope by -4 will result in a negative slope. This immediately eliminates options X and Z, as they still have positive slopes.

Next, we need to consider the change in the y-intercept. The y-intercept represents the point where the graph intersects the y-axis. Decreasing the y-value of the y-intercept by 1 unit means the graph will shift downward.

Comparing the remaining options, Y and W, we can see that option Y best represents the new function. It has a negative slope and is shifted downward compared to the original function. Option W has a positive slope and does not reflect the shift in the y-intercept as described.

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a) The probability distribution of x is  

P(x = 0) = 1/16

P(x = 1) = 4/16

P(x = 2) = 6/16

P(x = 3) = 4/16

P(x = 4) = 1/16

b) the probability distribution for x follows a binomial distribution with n = 4, and the expected number of even digits is 2.

To find the probability distribution for the random variable x, which represents the number of even digits in the new telephone number, we can use the binomial distribution.

a) The probability of a single digit being even is 1/2 since there are 5 possible digits (0, 2, 4, 6, 8) and 2 of them are even. Therefore, the probability of success (p) is 1/2, and the probability of failure (q) is also 1/2.

The probability distribution for x can be calculated using the binomial distribution formula:

P(x) = C(n, x) * p^x * q^(n-x)

where n is the number of trials (which is 4 in this case).

For x = 0, 1, 2, 3, 4, the probability distribution is as follows:

P(x = 0) = C(4, 0) * (1/2)^0 * (1/2)^(4-0) = 1/16

P(x = 1) = C(4, 1) * (1/2)^1 * (1/2)^(4-1) = 4/16

P(x = 2) = C(4, 2) * (1/2)^2 * (1/2)^(4-2) = 6/16

P(x = 3) = C(4, 3) * (1/2)^3 * (1/2)^(4-3) = 4/16

P(x = 4) = C(4, 4) * (1/2)^4 * (1/2)^(4-4) = 1/16

b) The expected number of even digits in the new telephone number can be calculated by summing the product of each possible value of x and its corresponding probability, i.e., E(x) = Σ(x * P(x)).

E(x) = (0 * 1/16) + (1 * 4/16) + (2 * 6/16) + (3 * 4/16) + (4 * 1/16) = 2

Therefore, the expected number of even digits in the new telephone number is 2.

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Answer:

The given equation is:

-4√x - 3 = -12

Add 3 to both sides:

-4√x = -9

Divide both sides by -4:

√x = 9/4

Square both sides:

(√x)² = (9/4)²

x = (81/16)

Thus, the solution of the equation is x = 81/16.

It is not an extraneous solution because it satisfies the original equation.

After evaluating the integral, you'll obtain a numerical value, which represents the result of the line integral over the given circle C.

To evaluate the given line integral ∮C (3y - e^sinx)dx + (7x + √(y^4 + 1))dy, where C is the circle x^2 + y^2 = 9, we need to parameterize the curve C and compute the integral using the parameterization.

Let's parameterize the circle C as x = 3cos(t) and y = 3sin(t), where t is the parameter. Differentiating with respect to t, we get dx = -3sin(t)dt and dy = 3cos(t)dt.

Substituting these parameterizations into the integral, we have:

∮C (3y - e^sinx)dx + (7x + √(y^4 + 1))dy

= ∫(t_initial to t_final) [(3(3sin(t)) - e^sin(3cos(t))) * (-3sin(t)) + (7(3cos(t)) + √((3sin(t))^4 + 1)) * (3cos(t))]dt

Now we can compute this integral by substituting the parameterization and evaluating it over the appropriate range of t, which depends on the starting and ending points of the circle C. The range of t typically spans from 0 to 2π for a complete circle.

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Answer:

Step-by-step explanation:

Answer:

  16 square units

Step-by-step explanation:

You want the area of the triangle bounded by the x- and y-axes and the line y = -2x +8.

The line has a y-intercept of +8, and an x-intercept of +4. This means the triangle height is 8 units and its base is 4 units.

The area is ...

  A = 1/2bh

  A = 1/2(4 units)(8 units) = 16 square units

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To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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Step-by-step explanation:

To find the distance the train will travel in 5 hours, we need to convert the time from hours to minutes and then use the given rate of 4/5 km per minute.

There are 60 minutes in an hour, so 5 hours is equal to 5 x 60 = 300 minutes.

Given that the train travels 4/5 km in 1 minute, we can calculate the distance it will travel in 300 minutes (5 hours) using the following equation:

Distance = Rate x Time

Distance = (4/5) km/minute x 300 minutes

Distance = (4/5) x 300 km

Distance = 240 km

Therefore, the train will travel a distance of 240 kilometers in 5 hours.

Answer:

To calculate the value of Z using the inverse normal distribution function (invNorm), we can use the cumulative probability associated with the desired Z-score. In this case, we want to find the Z-score that corresponds to a cumulative probability of 0.92.

Z = invNorm(0.92)

Using a standard normal distribution table or a statistical calculator, we can find that invNorm(0.92) is approximately 1.4051.

Therefore, Z ≈ 1.4051.

Answer:

B. 5,083,662.2 ft³

Step-by-step explanation:

The question asks us to calculate the volume of a cone in cubic feet, but it has provided the measurements of height and radius in metres.

Therefore, we have to first convert the given measurements into units of feet using the provided conversion factor:

• height = 65 m

             = 65 m × 3.2808 ft/m

             = 213.252 ft

• radius = 46 m

             = 46 m × 3.2808 ft/m

             = 150.9168 ft

Now that we have the measurements in the required units, we have to calculate the volume of the cone.

The formula for the volume of a right-circular cone is:
[tex]\boxed{V = \frac{1}{3}\pi r^2 h}[/tex],

where:

V = volume of the cone

r = radius of the circular base

h = perpendicular height of the cone

Substituting the required values into the formula above, we get:

[tex]V = \frac{1}{3} \times 3.14 \times (150.9168)^2 \times 213.252[/tex]

       [tex]= 5083662.17[/tex]

      [tex]= \bf 5083662.2[/tex]       [Rounding to the nearest tenth]

Therefore, the correct option is B.

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

The calculated equation of the line is y = -3x

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

The graph

Where, we have

(0, 0) and (-3, 9)

The equation of the line is calculated as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx

Using the points, we have

-3m = 9

So, we have

m = -3

This means that

y = -3x

Hence, the equation of the line is y = -3x

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Answer:

Step-by-step explanation:

30 lbs - 12 lbs = 18 lbs

8 oz - 5 oz =  3 oz

18 lbs and 3 oz

Answer:

4 1/2"

Step-by-step explanation:

3 5/8" + 7/8" = 3 12/8" = 4 4/8" = 4 1/2"

The relation R can be represented as R = {(-8, 0), (8, 0), (-6, 2), (-6, -2), (-5, √(39)), (-5, -√(39)), (-4, 4), (-4, -4), (-3, √(55)), (-3, -√(55)), (-2, 6), (-2, -6), (-1, √(63)), (-1, -(63)), (0, 8), (0, -8), (1, √63)), (1, -√(63)), (2, 6), (2, -6), (3, √(55)), (3, -√(55)), (4, 4), (4, -4), (5, √(39)), (5, -√(39)), (6, 2), (6, -2)}.

The relation R is defined as R = {(x, y) : x and y are integers and x^2 + y^2 = 64}. To find the elements in R, we need to determine all the integer solutions (x, y) that satisfy the equation x^2 + y^2 = 64.

One way to approach this is by listing all possible integer values of x and finding the corresponding values of y that satisfy the equation. Since x^2 + y^2 = 64, we can consider values of x from -8 to 8 and find the corresponding values of y.

By substituting the values of x, we can calculate y as follows:

For x = -8, y = ±sqrt(64 - (-8)^2) = ±sqrt(64 - 64) = ±sqrt(0) = 0. So we have (-8, 0) and (8, 0).

For x = -7, y = ±√(64 - (-7)^2) = ±√(64 - 49) = ±√(15). Since sqrt(15) is not an integer, there are no integer solutions for x = -7.

Similarly, by continuing this process for values of x from -6 to 6, we find the following solutions:

(-6, ±2), (-5, ±√(39)), (-4, ±4), (-3, ±√(55)), (-2, ±6), (-1, ±√(63)), (0, ±8), (1, ±√(63)), (2, ±6), (3, ±√(55)), (4, ±4), (5, ±√(39)), (6, ±2).

Therefore, the relation R can be represented as R = {(-8, 0), (8, 0), (-6, 2), (-6, -2), (-5, √(39)), (-5, -√(39)), (-4, 4), (-4, -4), (-3, √(55)), (-3, -√(55)), (-2, 6), (-2, -6), (-1, √(63)), (-1, -(63)), (0, 8), (0, -8), (1, √63)), (1, -√(63)), (2, 6), (2, -6), (3, √(55)), (3, -√(55)), (4, 4), (4, -4), (5, √(39)), (5, -√(39)), (6, 2), (6, -2)}.

This set includes all the integer pairs (x, y) that satisfy the equation x^2 + y^2 = 64.

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The solutions to the system of equations are (2 - 2√2, 2√2) and (2 + 2√2, -2√2).

To solve the given system of equations algebraically, we can substitute the value of y from the second equation into the first equation.

This substitution will eliminate the variable y and allow us to solve for x.

First, let's substitute the expression for y from the second equation into the first equation:

[tex]x + (-1/4x^2 + 3) = 2[/tex]

Simplifying the equation, we get:

[tex]x - 1/4x^2 + 3 = 2[/tex]

Next, we rearrange the equation to have a quadratic equation in standard form:

[tex]-1/4x^2 + x + 1 = 0[/tex]

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula.

Let's solve it using the quadratic formula:

[tex]x = (-b\pm \sqrt{(b^2 - 4ac))} / (2a)[/tex]

For our equation, a = -1/4, b = 1, and c = 1.

Plugging these values into the quadratic formula, we get:

x = (-1 ± √(1 - 4(-1/4)(1))) / (2(-1/4))

Simplifying further, we have:

x = (-1 ± √(1 + 1)) / (-1/2)

x = (-1 ± √2) / (-1/2)

Now, let's consider the two possible values of x:

For x = (-1 + √2) / (-1/2):

x = (-1 + √2) [tex]\times[/tex] (-2) = 2 - 2√2

For x = (-1 - √2) / (-1/2):

x = (-1 - √2) [tex]\times[/tex] (-2) = 2 + 2√2

So the solutions to the system of equations are x = 2 - 2√2 and x = 2 + 2√2.

To find the corresponding values of y, we substitute these x-values into the second equation:

For x = 2 - 2√2:

[tex]y = -(1/4)(2 - 2\sqrt{2} )^2 + 3[/tex]

Simplifying, we get:

y = -(1/4)(4 - 8√2 + 8) + 3

y = -(1/4)(12 - 8√2) + 3

y = -3 + 2√2 + 3

y = 2√2

For x = 2 + 2√2:

[tex]y = -(1/4)(2 + 2\sqrt{2} )^2 + 3[/tex]

Simplifying, we get:

y = -(1/4)(4 + 8√2 + 8) + 3

y = -(1/4)(12 + 8√2) + 3

y = -3 - 2√2 + 3

y = -2√2

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The solution to the equation x/4 = -45 is x = -180

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

x/4 = -45

Multiply both sides of the equation by 4

So, we have

4 * x/4 = -45 * 4

Evaluate the products

x = -180

Hence, the solution to the equation is x = -180

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Answer:

$284,586.00

Step-by-step explanation:

To calculate the total interest paid on a home loan, we need to use the formula for calculating the monthly payment and then multiply it by the number of months in the loan term. The formula for calculating the monthly payment is:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Loan principal (amount borrowed)

r = Monthly interest rate (APR divided by 12 and converted to decimal)

n = Total number of payments (number of years multiplied by 12)

Let's calculate the monthly payment first:

Loan principal: P = $330,000

Annual interest rate: 6.375%

Monthly interest rate: r = 6.375% / 12 / 100 = 0.0053125

Loan term: 25 years

Total number of payments: n = 25 * 12 = 300

Now, we can calculate the monthly payment:

M = 330,000 * 0.0053125 * (1 + 0.0053125)^300 / ((1 + 0.0053125)^300 - 1)

Using a calculator or spreadsheet, this monthly payment comes out to be approximately $2,048.62.

To calculate the total interest paid, we can subtract the principal amount from the total amount paid over the loan term. The total amount paid can be calculated by multiplying the monthly payment by the total number of payments.

Total amount paid = Monthly payment * Total number of payments

Total amount paid = $2,048.62 * 300

Using a calculator or spreadsheet, the total amount paid comes out to be $614,586.00.

Now, we can calculate the total interest paid:

Total interest paid = Total amount paid - Loan principal

Total interest paid = $614,586.00 - $330,000

Using a calculator or spreadsheet, the total interest paid comes out to be $284,586.00.

Therefore, the total interest paid on the 25-year home loan of $330,000 at an APR of 6.375% is $284,586.00.

Answer: 464 sq units

Step-by-step explanation:

An easy way to find the area of complex figures such as this is to split the figure into separate parts, such as A, B, C, and D, as shown in the file attached. We find the area of each, using the formula

Area = Length x Width

(A = lw),

and add them together to find the area of the entire figure.

Area of A:

8x16 = 128 sq units

Area of B:

24x8 = 192 sq units

Area of C:

4x12 = 48 sq units

Area of D:

4x24 = 96 sq units

Area of entire figure: 128 + 192 + 48 + 96 = 464 sq units

I hope this helps!

In 10 days, the quilt is estimated to measure approximately 33 inches.

Based on the given information, Genesis learned to knit two days ago and the size of the quilt has been increasing over the past few days.

The growth rate seems consistent, with an increase of 1.5 inches each day.

Yesterday, the quilt measured 15.5 inches, which means it grew by 2.5 inches compared to the initial size of 13 inches.

Today, the quilt measures 18 inches, indicating another growth of 2.5 inches from yesterday.

If the quilt continues to grow at a rate of 1.5 inches per day, we can estimate its size in 10 days.

Starting from today's measurement of 18 inches, we can add 1.5 inches for each of the next 10 days.

Adding 1.5 inches for each day, we get:

Day 1: 18 + 1.5 = 19.5 inches

Day 2: 19.5 + 1.5 = 21 inches

Day 3: 21 + 1.5 = 22.5 inches

...

Day 10: 31.5 + 1.5 = 33 inches.

Therefore, in 10 days, the quilt is estimated to measure approximately 33 inches.

However, it's important to note that this estimation assumes a consistent growth rate of 1.5 inches per day, and actual measurements may vary depending on factors such as knitting technique, tension, and other variables.

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One example of a monopoly is the dominance in the search engine market.

An example of a firm in a monopolistic competition market is the telecommunication industry.

A monopoly has a significant market power while a monopolistic market has multiple business competitors

A monopoly is characterized by a single dominant company that has significant market power, allowing it to set prices and limit competition.

Multiple businesses compete in monopolistic markets, but because they each have unique product offerings, they have some pricing flexibility.

In contrast to enterprises engaged in monopolistic competition, monopolies frequently experience little or no competition.

While companies engaged in monopolistic competition work to set themselves apart in order to draw customers, monopolies may potentially exploit consumers row operations on a matrix.

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Monopoly is a market where there is a single seller selling a unique products to many customers while a monopolistic competition market is where there are many sellers selling substitute goods.

Monopoly:

There is a single seller

They set prices

They enjoy economies of scale

There is no competition or substitute which can harm customer's interest.

There is entry barrier

Monopolistic competition:

There are many companies

Similar products are sold

There is little or no entry barrier

The decisions of one firm do not affect other firms.

Therefore, in monopoly, there is a single seller and there are many sellers in monopolistic competition.

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