composite functions homework

Answer:

Bryce is 10 years old

Step-by-step explanation:

The age of Brice is given by B = 10 years old

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as B

Now , the value of B is

Substituting the values in the equation , we get

The age of Aida = 15 years

The age of Brice = 5 years younger than Aida

On simplifying the equation , we get

So , age of Brice = 15 - 5 = 10 years

The age of Henry = three years younger than Aida

So , the age of Henry = 15 - 3 = 12 years

Hence , the age of Brice is 10 years old

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Answer:

b. B, C, and E

Step-by-step explanation:

The lateral surface area is the sum of the areas of all the faces except for the base.

The value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².

In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a composite function is essentially applied to the output of another function.

Given that,

s(x)=x²

t(x) = 4x³

The value of the composite functions is given as:

(t + s)(x) = t(x) + s(x) = 4x³ + x²

(t.s)(x) = (4x³)x² = [tex]4x^5[/tex]

(t - s)(x) = t(x) - s(x) = 4x³ - x²

Hence, the value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².

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The GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.

What is Interest?

Interest is the income that is returned to the holder of capital. Different kinds of interest include gross interest and net interest.

To find GI (Gross Income), we add wages and interest:

GI = Wages + Interest = $145,000 + $2500 = $147,500

To find AGI (Adjusted Gross Income), we subtract the contributions towards retirement from GI:

AGI = GI - Contributions towards Retirement = $147,500 - $3000 = $144,500

To find TI (Taxable Income), we subtract exemptions and deductions from AGI:

TI = AGI - Exemptions - Deductions = $144,500 - $4100 - $2800 = $137,600.

Therefore, the taxable income is $137,600.

Hence, GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.

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Answer:

[tex]y=\pm2\sqrt{5}[/tex]

Step-by-step explanation:

[tex]4y^2=80\\y^2=20\\y=\pm\sqrt{20}\\y=\pm2\sqrt{5}[/tex]

The square root method for solving a quadratic equation involves isolating the squared term, and then taking the square root of both sides of the equation.

Starting with the equation 4y^2 = 80, we can isolate the squared term by dividing both sides of the equation by 4:

y^2 = 20

Next, we take the square root of both sides of the equation:

y = ±√20

The solution in radical form is y = ±√20. To simplify the radical, we can factor 20 into 2 * 10. Then, we can simplify the square root as follows:

y = ±√2 * √10 = ±2√10

So, the simplified solution is y = ±2√10.

Answer:

c = 8

Step-by-step explanation:

4x³ + cx² + x + 2 ÷ x + 2 = ...

first we divide

4x³ + cx² by x + 2

and that is by doing 4x³/x = 4x².

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

now we need to find the remainder, as with regular number divisions :

4x² × (x + 2) = 4x³ + 8x²

which we need to subtract from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

----------------

0 cx² - 8x²

now we pull down the next position (x) and divide that by x + 2

4x³ + cx² + x + 2 ÷ x + 2 = 4x² + 1

- 4x³ + 8x²

----------------

0 cx² - 8x² + x

and the same again, to find the remainder, we have to subtract 1×(x + 2) = x + 2 from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

----------------

0 cx² - 8x² + x

- x + 2

-----------------------------

cx² - 8x² 0 0

the polynomial is divisible by x + 2, if the remainder is 0.

so,

cx² - 8x² = 0

cx² = 8x²

c = 8

The value of angle ABE is 52°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.

The sum of interior angle in a triangle is 180°

Angle EBD = 180-(90+27)

= 180-117

= 63°

angle ABE + EBD = ABD

ABE = ABD - EBD

ABE = 115-63

= 52°

Therefore the value of angle ABE is 52°

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A quotation isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2.

The option (a) is correct.

Famous people who discuss their opinions on a given subject often employ quotation marks around their words. The brief nature of a quotation allows it to share individuality. The citation served as a means of sharing ideas and serving as a source of historical information.

The quotation, which is sometimes referred to as "quote vomit," was cut off from the remainder of the text.

The sentences are directed at their objective. Understanding how the universe functions and how we fit into it can be done through the metaphor of weaving.

As a result, the quote isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2. Therefore, option (a) is correct.

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The equation for v is ±√k/m

Two or more expressions with an Equal sign is called as Equation.

The given equation is k=mv²

k equal to m times of v square.

Where k is a formula of kinetic energy.

We need to solve for v

To do this we have to isolate the variable v

To isolate the variable v we have to Divide both sides by m

v²=k/m

v square equal to k by m.

Square root on both sides.

v=±√k/m

v equal to plus or minus square root of k by m.

Hence, the equation for v is ±√k/m

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Answer:

(a)

smaller value = 125 ft

larger value = 250 ft

(b)

31250 ft²

Step-by-step explanation:

(a)

In total, the farmer used 875ft worth of fencing.

In terms of x, the total fencing used is: 2x + x + x + x + 2x = 7x

This means 7x=875ft. Dividing both sides by 7, we find x=125ft

The dimensions of the rectangular enclosure in terms of x are "x and 2x". Subbing in 125ft for x, these dimensions become "125ft and 2(125ft)" or "125ft and 250ft".

(b)

Since we know the enclosure is 125ft long and 250ft wide, and since the area of a rectangle is its length times its width, the are of the enclosure is:

125ft * 250ft = 31250 ft²

Answer:

(a)

smaller value =125 ft

larger value = 250 ft

(b)

31250 ft?

Answer: To find the monthly rent during the 11th year, we need to calculate the total increase in rent over the course of 10 years and then add that to the original monthly rent of $900.

The total increase in rent over 10 years is $120 per year * 10 years = $1200.

So, the monthly rent during the 11th year would be $900 + $1200 = $2100.

Therefore, the monthly rent during the 11th year would be $2100.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the number of solutions for a system of linear equations, we can use the method of substitution or elimination. Here, we'll use the method of substitution.

We'll start by solving for x in one of the equations and then substitute that expression into the other equation. If the resulting equation has a unique solution, then the system has a unique solution. If the resulting equation has no solution, then the system has no solution. If the resulting equation has infinitely many solutions, then the system has infinitely many solutions.

Let's start by solving the first equation for x:

y = -7/2 x + 11

To solve for x, we'll isolate x by subtracting 11 from both sides of the equation:

y - 11 = -7/2 x + 11 - 11

y - 11 = -7/2 x

Next, we'll multiply both sides of the equation by -2/7 to cancel out the fraction on the right side:

-2/7 (y - 11) = -2/7 (-7/2 x)

-2/7 y + 22/7 = 7/2 x

Now, we have an expression for x in terms of y. We can substitute this expression into the second equation:

7x + 2y = 20

7 (-2/7 y + 22/7) + 2y = 20

Substituting -2/7 y + 22/7 for x, we get:

7 (-2/7 y + 22/7) + 2y = 20

Expanding the left side of the equation, we get:

-2y + 22 + 2y = 20

0y = -2

Since 0y is never equal to -2, this equation has no solution.

Therefore, the system of equations has no solution, and there are no values of x and y that satisfy both equations simultaneously.

So, the system of equations y = -7/2 x + 11 and 7x + 2y = 20 has no solutions.

Answer: 1,652.8 calories

Step-by-step explanation:

620 divided by 6 = 103.3 calories per inch

103.3 times 16 inches = 1,652.8 calories

Answer: 68.82

Step-by-step explanation:

74 * (1- 7%) and solve

= 68.82

Answer:

x(f)- this is the correct answer

The x-intercepts of the graph of the given polynomial function as described is; 2, 3 and -5.

The x-intercepts of a polynomial function are otherwise termed, roots, solutions or zeroes of the polynomial function.

On this note, the x-intercepts of the polynomial function which is as described in this scenario are;

x - 2 = 0; x = 2.

x - 3 = 0; x = 3.

x + 5 = 0; x = -5.

Ultimately, the x-intercepts of the polynomial function in discuss are; 2, 3 and -5.

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Work Shown:

4.5% of 125 = 0.045*125 = 5.625

That rounds to 5.63

Answer:

5.625

Step-by-step explanation:

The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

(3/5) (30x - 15) = 72

Solve the linear equation with a single variable for 'x', then we have

(3/5) (30x - 15) = 72

3(6x - 3) = 72

18x - 9 = 72

18x = 81

x = 4.5

The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.

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Answer:

-$48.39

Step-by-step explanation:

The answer choice which is true about the given equation; y = -2x as required to be determined is; It is a linear function because its graph is a straight line.

It follows from the task content that the given function y = -2x as required be identified as being a linear equation or not and why?

On this note, since the graph of the equation is such that g

it yields a straight line, it follows that the given function; is a linear function because its graph is a straight line.

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Answer:

is not a solution to the system of equations.

Step-by-step explanation:

Sure! Here's a step-by-step solution to determine if the point (-6, 3) is a solution to the system:

Substitute the x and y values into the first equation:

y = 1/2x + 6

3 = 1/2(-6) + 6

Simplify the right side of the equation:

3 = -3 + 6

Solve for the value of y:

3 = 3

The first equation is satisfied, so now let's substitute the x and y values into the second equation:

2y = -x - 3

2 * 3 = -(-6) - 3

6 = +6 - 3

Simplify the right side of the equation:

6 = -3

The second equation is not satisfied, so the point (-6, 3) is a not solution to the system.

Step-by-step explanation:

the volume of such a regular cylinder is (as for any regular object) :

base area × height

and for a cylinder the base area is a circle, and its area is

pi×r²

so, combined, the volume of our cylinder is

pi×r²×height = pi×9²×26.5 = pi×81×26.5 =

= 6,743.428631... cm³

≈ 6,743 cm³

Answer:

0.209.

Step-by-step explanation:

The probability that someone files their taxes on time is 1 - 0.351 = 0.649.

To find the probability that 6 out of 10 people file their taxes on time, we can use the binomial distribution. The binomial formula for the probability of k success in n trials is given by:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Where (n choose k) is the number of combinations of n items taken k at a time, and p is the probability of success in a single trial.

So, for the problem at hand:

P(6) = (10 choose 6) * 0.649^6 * (1 - 0.649)^(10 - 6) = 0.209

Therefore, the probability that 6 out of 10 people file their taxes on time is approximately 0.209.

Answer:

y=b+5+k/2

Step-by-step explanation:

2y-k=b+5

2y=b+5+k

2y/2=b+5+k/2

y=b+5+k/2

Answer:

y = b+ 5 + k/2.

Step-by-step explanation:

2y - k = b + 5

the subject for y

[tex]2y - k = b + 5 \\ 2y = b + 5 + k \\ \frac{2y}{2} = \frac{b + 5 + k}{2} \\ y = \frac{b + 5 + k}{2}. [/tex]

Answer: a) Mean and standard deviation of the sampling distribution:

The mean of the sampling distribution, also known as the expected value or the population mean, is equal to the proportion of U.S. residents who receive a jury summons each year, which is 15%. So, the mean of the sampling distribution is:

µ = 0.15

The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:

σ = √(p(1 - p) / n)

where p is the population proportion of U.S. residents who receive a jury summons each year (0.15), and n is the sample size (500).

σ = √(0.15 * (1 - 0.15) / 500)

σ ≈ 0.03

So, the standard deviation of the sampling distribution is approximately equal to 0.03.

b) Interpretation of the standard deviation:

The standard deviation measures the spread of the sampling distribution, or how much the sample proportions deviate from the population proportion. A smaller standard deviation indicates that the sample proportions are more likely to be close to the population proportion, while a larger standard deviation indicates that the sample proportions are more likely to be further from the population proportion.

In this case, the standard deviation of 0.03 indicates that the sample proportions are expected to be within 0.03 of the population proportion (0.15) about 68% of the time.

c) Justification for the approximate normality of the sampling distribution:

According to the central limit theorem, the distribution of the sample proportions will be approximately normal as long as the sample size is large enough. In this case, with a sample size of 500, we can assume that the sampling distribution is approximately normal.

Step-by-step explanation:

The volume of the irregular figure is solved to be

The volume of the irregular figure is solved by the formula

= area of the figure * thickness

The area of the figure is solved by dividing the firue into regular shapes and this will result to two rectangles

Area of the first rectangle

= length x width

= 4 * (12 - 5)

= 4 * 7

= 28 square centimeters

Area of the second rectangle

= 10 * 5

= 50 square centimeters

Total area = 50 + 28 = 78

volume = 78 * 1 = 78 cubic centimeters

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Answer:

Both of them are correct.

Step-by-step explanation:

Let's review both of their methods and check their validity.

This method is the most straight forward and seems to be correct as we're simply calculating the total value of each, and then subtracting the difference. We can write the expression as: [tex]2.25(4.25)-2.25(2.85)[/tex] and this should give us the difference assuming the prices and math is done correctly.

While this method is a bit difference, it actually does work! Think of this way, we first calculate the difference in the prices and then for each pound we increase it by, the difference also increases by this amount. It also helps to look at our original expression: [tex]2.25(4.25)-2.25(2.85)[/tex], notice how we have a factor of 2.25 on both sides? Well we can just factor that out to get: [tex]2.25(4.25 - 2.85)[/tex] and this is essentially what Ariel's method is. This should give us the difference in prices and is likely easier than Kaylee's method as we do less multiplication and with smaller numbers.

Answer:

t = 21 + (-4)h

Step-by-step explanation:

t = temp. at hour h

h = # of hours past midnight

t = 21° + (-4°/hr)h

By using the substitution method, the value of x is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2y - 4x = 8                 .......equation 1.

3(x + 4) - 2y = 5          .......equation 2.

From equation 1, we have:

y = 2x + 4         .......equation 3.

By using the substitution method to substitute equation 3 into equation 2, we have the following:

3(x + 4) - 2(2x + 4) = 5

3x + 12 - 4x - 8 = 5

-x + 4 = 5

x = 4 - 5

x = -1.

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The required trigonometric ratios are as follows: sin t = 1/2 and cos t = √3/2.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

According to the given figure, we have a right triangle ΔABC which has:

AB = 1/2

BC = √3/2

CA = AB² + BC²

CA = √(1/2)² + (√3/2)²

CA = √1/4 + 3/4

CA = √4/4 = 1

As we know that the trigonometric ratios are as follows:

sin (180°- t) = AB/CA

sin t = (1/2)/1

sin t = 1/2

cos (180°- t) = BC/CA

cos t = (√3/2)/1

cos t = √3/2

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