Let
x = −4, y = 0,
and
z = 7
and evaluate the expression.

B) The domain for #1 and #2 is  ≥ -7 and the domain for #3 is -∞ ≤  ≤ ∞.

1. [tex](f + g)(x) = f(x) + g(x)[/tex]

The domain of [tex](f + g)(x)[/tex] is the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex] (since we can't take the square root of a negative number), the domain of [tex](f + g)(x)[/tex] is [tex]x > = -7[/tex].

2. [tex](f - g)(x) = f(x) - g(x)[/tex]

The domain of [tex](f - g)(x)[/tex] is also the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for[tex]x > = -7[/tex], the domain of [tex](f - g)(x)[/tex] is also [tex]x > = -7[/tex].

3. [tex](fg)(x) - > (f(g(x))[/tex]

The domain of [tex]f(g(x))[/tex] is the set of all values of  [tex]x[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex]. Since the domain of [tex]f[/tex] is all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex]  is defined only for [tex]x > = -7[/tex], the domain of [tex]f(g(x))[/tex] is [tex]x > = -7[/tex].

Therefore, the correct answer is option:

B) The domain for 1) and 2) is [tex]> = -7[/tex] and the domain for 3) is -∞ ≤ [tex]x[/tex] ≤ ∞.

The probability that someone with a credit score of 650 or below defaulted on the loan is 0.14.

The probability that someone with a credit score of 650 or below defaulted on the loan is calculated below:

Probability = number of defaulters/ number of loan recipients

From graph:

The total number of defaulters = 30 + 30 + 30

The total number of defaulters = 90

The total number of loan recipients = 120 + 240 + 270

The total number of loan recipients = 630

Probability to default = 90/630

Probability to default = 0.14

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The polynomial function with the given properties is:[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]

A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a  quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.

Since the polynomial has real coefficients and one of its zeros is complex, the complex conjugate of 4+ i, which is 4-i, must also be  zero. So the three zeros of the polynomial are -1, 4+i and 4-i.  To form a polynomial with these zeros, we start by writing  the factors of the polynomial:

(x + 1) (x - 4 - i) (x - 4 + i)

We can simplify this expression by multiplying  the factors:

[tex](x + 1) (x^2 - 8x + 17)[/tex]

Expanding this, we get:

[tex]x^3 - 7x^2+ 9x - 17[/tex]

Thus, the polynomial function with the given properties is:  

[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]

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The polynomial function is p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16

A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a  quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.

If -1 is a zero of the polynomial function, then x+1 is a factor of the polynomial. Similarly, if 4+i is a zero, then 4-i is also a zero, because complex roots always occur in conjugate pairs. Therefore, (x+1) and (x - 4 - i)(x - 4 + i) = (x - 4)² + 1 are factors of the polynomial. We can then construct the polynomial function by multiplying these factors:

p(x) = A(x+1)(x - 4 - i)(x - 4 + i)

where A is a constant that we need to determine, and p(x) is the desired third-degree polynomial function.

To determine A, we can use the y-intercept given in the problem. The y-intercept is the value of p(0), so:

p(0) = A(0+1)(0 - 4 - i)(0 - 4 + i) = A(17+4i)

But we also know that p(0) = -17, so:

-17 = A(17+4i)

Solving for A:

A = -17/(17+4i) = (-17/5) + (68/5)i

Therefore, the polynomial function we seek is:

p(x) = [(-17/5) + (68/5)i](x+1)(x - 4 - i)(x - 4 + i)

Expanding the product and simplifying, we get:

p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16

This is a third-degree polynomial with only real coefficients, -1 and 4+i are two of the zeros, and the y-intercept is -17.

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answer:

17%

I hope this helps

A statistical question would be:  What is the average salary of teachers in this school district?

When a question can be answered statistically, it can be done so by gathering and analysing data, for example. This particular question aims to comprehend a population or a phenomenon by using numerical data. In contrast to non-statistical questions, which are more concerned with acquiring information or opinions, statistical questions are more concerned with getting and analysing data. Statistical procedures including sampling, data analysis, and inference are frequently used to answer statistical issues.

A statistical question would be:  What is the average salary of teachers in this school district?

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Answer:

the required answer are -8,0,4

1) The length of the segments BC =√53   FG =√53  JK =√53

2) The statements that are true are;

BC ≅ FG

BC ≅ JK

FG ≅ JK

To find the lengths of the segments, we use the formula d = √((x2 - x1)² + (y2 - y1)²)

For BC, it would be √((1 - (-6))² + (2 - 4)²) = √53.

It would ordinarily be 7.3. However, since approximations are not needed, it has been left in the form of squareroot

For  FG: √((-5 - (-7))² + (-1 - 6)²) = √53.

The answers provided are based on the questions seen in the image

Here are the endpoints of the segment BC, FG and JK.

B (-6, 4)  C (1, 2)        F (-7, 6),  G (-5, -1)        J (1, -8), K (3, -1)

Find the length of each segment. give an exact answer (not a decimal approximate)

BC =     FG =      JK =

Check all the statement that are true below;

BC ≅ FG

BC ≅ JK

FG ≅ JK

None of these are true.

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Dimensions of the rectangle are 6 feet and 12 feet.

Rectangle is a quadrilateral whose each pair of opposite sides are equal in length and each two consecutive sides are in right angle to each other. In rectangle one pair of equal opposite sides is called Length and another one is called Width.  

If length of a rectangle is L and width of rectangle is W then the perimeter of that rectangle will be = 2(L+W)

Let W be the rectangle's width.

Here according to question the rectangle is twice as long as it is wide.

So, length of rectangle = 2W

Perimeter will be = 2(W+2W) = 2*(3W) = 6W

So, according to question,

6W = 36

W = 36/6 = 6

Thus the width of the rectangle is = 6 feet.

Then the length = 2*6 = 12 feet.

Hence dimensions of the rectangle are 12 feet and 6 feet respectively.

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Answer:

Step-by-step explanation:

Greetings!Answer:[tex]\sqrt{85} or 9.22

Answer:

Step-by-step explanation:

The length of the Hypotenuse should be [tex]\sqrt{45}[/tex] , 6.70.

By Pythagoras' Theorem, [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].

so, Let a =6cm, b =3cm

[tex]6^{2}[/tex] + [tex]3^{2}[/tex] = 45

Therefore,

The length of the hypotenuse will be either [tex]\sqrt{45}[/tex]

We can compare and contrast the primary differences between the Job costing and Process costing processes as follows:

Job costing process:

Process costing:

We can classify the cost types by understanding their usage in the accounting industry. Process costing is used for calculating the costs for mass-produced materials while job costing is used for calculating the cost for customized products.

Process costing is used for accumulating costs and to ascertain the flow of costs through accounts. Job costing is the main document for tracking costs.

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Answer:

(m-3)^2

Step-by-step explanation:

(m^2-6m+9) is factored by using this formula:
(a-b)^2=a^2-2ab+b^2.

Therefore, we can substitute the values into this equation.

m^2=a^2,

-6m=-2ab,

9=b^2.

Solving for b in the third equation, b is equal to 3 or -3. However, as this equation is negative, then it must be -3.

(m-3)^2

Answer: The height of the cone is [tex]12 \text{ units}.[/tex]

Step-by-step explanation:

We are given that [tex]L = \pi r \sqrt{r^2+h^2}.[/tex] Plugging in the given values of [tex]L[/tex] and [tex]r[/tex] yields:

[tex]65 \pi = 5 \pi \sqrt{25+h^2} \implies 13 = \sqrt{25+h^2}.[/tex]

Now, squaring each side of the equation, and then isolating [tex]h^2[/tex] gives us [tex]h^2=144[/tex], so [tex]\boxed{h=12}.[/tex] Note that [tex]h[/tex] cannot take any negative values because it is a side length.

The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.

Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:

x(t) = 2 - t

y(t) = (t+3)²

To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.

When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.

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Answer:

Part A:

To find the total length of the two sides of the triangle, we need to add Side 1 and Side 2:

Side 1: 3x² - 4x - 1

Side 2: 4x - x² + 5

Total length: (3x² - 4x - 1) + (4x - x² + 5)

Simplifying and combining like terms, we get:

Total length: -x² + 7x + 4

Therefore, the total length of the two sides of the triangle is -x² + 7x + 4.

Part B:

To find the length of the third side of the triangle, we need to subtract the sum of Side 1 and Side 2 from the perimeter of the triangle:

Length of Side 3 = Perimeter - (Side 1 + Side 2)

Length of Side 3 = (5x³ - 2x² + 3x - 8) - (3x² - 4x - 1 + 4x - x² + 5)

Simplifying and combining like terms, we get:

Length of Side 3 = 2x³ - 2x² + 7x - 12

Therefore, the length of the third side of the triangle is 2x³ - 2x² + 7x - 12.

Part C:

The answers for Part A and Part B show that the polynomials are closed under addition and subtraction. The sum of Side 1 and Side 2 is a polynomial (-x² + 7x + 4), and the difference between the perimeter of the triangle and the sum of Side 1 and Side 2 is also a polynomial (2x³ - 2x² + 7x - 12). In both cases, the result is a polynomial, which means that the set of polynomials is closed under addition and subtraction.

The cosine of angle B is: cos(B) = AC / AB = 20/29

The Pythagorean Theorem, a well-known geometric theorem that states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse (the opposite side of the right angle) - that is, in familiar algebraic notation. , a2 + b2 = c2 .

In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to its hypotenuse. In this case, angle B is the angle we are interested in, and the adjacent side is side AC. Using the Pythagorean theorem, we find the length of side AC:

AC² = AB²+ BC²

AC² = 29² - 21²

AC² = 400

AC = 20

Therefore, the cosine of angle B is:

cos(B) = AC / AB = 20/29

Other trigonometric ratios of angle B can be found using the following formulas:

sin(B) = BC / AB = 21/29

tan(B) = BC / AC = 21/20

csc(B) = AB / BC = 29 / 21

sec(B) = AB / AC = 29/20

bed (B) = AC / BC = 20 / 21  

Thus, the trigonometric ratios of angle B are:

sin(B) = 21/29

cos(B) = 20/29

tan(B) = 21/20

csc(B) = 29/21

sec(B) = 29/20

crib(B) = 20/21

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according to the question the sample mean used to obtain the confidence interval was 173.

The arithmetic means (in contrast to the geometrical mean) of a dataset is the average of all values split by the total amount of values. The most popular way to measure central tendency is with the "mean," which is widely utilised. This is obtained by dividing the number of values in the dataset by the total number of all the values. Either raw information or information that has been included in frequency tables can be used for calculations. The average of a number is known as the average. Simple math can be used to determine: After summing up all the digits, divide by the number of digits. the sum divided by the number.

given,

The confidence interval's midpoint is determined by the sample mean. Therefore, to find the sample mean, we add the lower and upper bounds of the confidence interval and divide by 2:

Sample mean = (Lower bound + Upper bound)/2

Sample mean = (168.685 + 177.315)/2

Sample mean = 173

Therefore, the sample mean used to obtain the confidence interval was 173.

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Answer:

3.15%

Step-by-step explanation:

To find the expected return and standard deviation of a portfolio that is invested in two assets A and B, we need to know the expected returns and standard deviations of those assets, as well as the correlation between them.

Let's assume that the expected return and standard deviation of asset A are 10% and 5%, respectively, and that the expected return and standard deviation of asset B are 8% and 3%, respectively. Let's also assume that the correlation between the two assets is 0.5.

To find the expected return of the portfolio, we can use the following formula:

Expected return of portfolio = weight of A * expected return of A + weight of B * expected return of B

where the weights are the proportions of the portfolio invested in each asset:

weight of A = 40% = 0.4

weight of B = 60% = 0.6

Expected return of portfolio = 0.4 * 10% + 0.6 * 8%

Expected return of portfolio = 9.2%

Therefore, the expected return of the portfolio is 9.2%.

To find the standard deviation of the portfolio, we can use the following formula:

Standard deviation of portfolio = sqrt(weight of A^2 * variance of A + weight of B^2 * variance of B + 2 * weight of A * weight of B * correlation * standard deviation of A * standard deviation of B)

where the variances are the square of the standard deviations of each asset:

variance of A = (5%)^2 = 0.0025

variance of B = (3%)^2 = 0.0009

Standard deviation of portfolio = sqrt(0.4^2 * 0.0025 + 0.6^2 * 0.0009 + 2 * 0.4 * 0.6 * 0.5 * 0.05 * 0.03)

Standard deviation of portfolio = 0.0315 or 3.15% (rounded to two decimal places)

Therefore, the standard deviation of the portfolio is 3.15%.

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The area of the shaded region = 30.903 in²

From the attached figure we can observe that the radius of the circle R is r = 6 in.

Using the forula for the area of circle, the area of circle R would be,

A₁ = πr²

A₁ = π × 6²

A₁ = 36π

A₁ = 113.097 in²

So, the diameter would be d = 6 × 2 = 12 in.

The circle R is inscribed in a square.

So, the side length of square is equal to the diameter of the circle.

This means the side length 'a' os square = 12 in.

Using the formula of the area of square,

A₂ = side²

A₂ = a²

A₂ = 12²

A₂ = 144 in²

so, the area of the shaded region would be,

A = A₂ - A₁

A = 144 -113.097

A = 30.903 in²

This is the required area.

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Answer:

5,500 ft²

Step-by-step explanation:

Easiest way is to find the area of the entire 100 x 80 square, then subtract the footprint of the house (50 x 50):

Backyard area = (100 x 80) - (50 x 50) = 8000 - 2500 = 5500 ft²

Looking at the table, If Bridget has 10 animals in total with 30 legs, it only means she has 5 chicken.

Based on the information on the table,

For the number of chicken legs, we say

9 x 2 = 18       3 x 2 = 6          7 x 2= 14       14 x 2 = 28

If we sum these number to the total number of legs in each row, it would be;  4 + 18 = 22   8+6 = 14   12 + 14 = 26     16+28 = 44

This means that all the values provided so far does not give us the accurate number of legs of the animals.

If 5p = 20L the number of hen should be 30- 20 = 10/2 = 5

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The geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

It should be noted that to find the geometric mean of two numbers, we multiply them together and then take the square root of the result. So, for each pair of numbers, we can follow these steps:

Multiply the two numbers together.

Take the square root of the product.

Using this formula, we get:

7.16 and 27:

Geometric mean = √(7.16 × 27) ≈ 14.85

5 and 36:

Geometric mean = √(5 × 36) = √180 ≈ 13.42

10.8 and 48:

Geometric mean = √(10.8 × 48) ≈ 22.94

Therefore, the geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

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None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.

what is rounding ?

Rounding is a mathematical process of approximating a number to a specified degree of accuracy. It involves replacing a number with a simpler, but close value that is easier to work with or understand.

In the given question,

The question asks us to find the annual premium for a $75,000 10-year term policy for a 25-year-old male, using the table of annual life insurance premiums per $1,000 of face value.

First, we need to find the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. Looking at the table, we can see that the premium for a 10-year term policy for a 25-year-old male is $4.79 per $1,000 face value.

To find the annual premium for a $75,000 policy, we need to multiply the premium per $1,000 face value by 75. So:

Annual premium = $4.79 per $1,000 x 75 = $359.25

Rounding this answer to the nearest cent gives us:

$359.25 ≈ $359.26

Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male is $359.26.

None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.

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Therefore, the lawnmower can cut grass for 2.5 hours on 5/6 of a gallon of fuel in the gas can

To find out how long the lawnmower can cut grass with 5/6 of a gallon of gas, we first need to figure out how many gallons of gas the lawnmower will use per hour:

1 hour of grass cutting = 1/3 gallon of gas

1 gallon of gas = 3 hours of grass cutting

So the lawnmower uses 1/3 gallon of gas per hour, which means that 1 gallon of gas will last for 3 hours of grass cutting.

Now we can use this conversion factor to figure out how long 5/6 of a gallon of gas will last:

5/6 gallon of gas * 3 hours of grass cutting per 1 gallon of gas = 15/18 hours of grass cutting

Simplifying this fraction by dividing the numerator and denominator by 3:

15/18=3/6

So 5/6 of a gallon of gas will last for 5/6 of 3 hours, which is equal to 2.5 hours of grass cutting.

As a result, 5/6 of a gallon of gas will last for 5/6 of 3 hours, or 2.5 hours of mowing the lawn.

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Answer:

4x + 2 > 10 and -3x-1 > 5 : No solution

| 3x | + 4< 10:  -2 < 2 x < 2

| x+2 | + 4< 3: No solution

|2x+4 | +2 > 4: x > -1 or x < -3

Step-by-step explanation:

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

We have,

The area of the whole circle.

= πr²

Where r = 8

So,

= 3.14 x 8 x 8

= 200.96

Now,

Area of the red shaded circle = πr²

Where r = 4

So,

= 3.14 x 4 x 4

= 50.24

Now,

The probability that a randomly selected point within the circle falls in the red-shaded circle.

= Area of the red shaded circle / Area of the whole circle

= 50.24 / 200.96

= 1/4

= 0.25

Thus,

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

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Answer:

x = 4√3 y = 8/√2 = 4√2

(4 rad 3) (4 rad 2)

The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. The input values are often called the independent variable, while the output values are called the dependent variable. Functions are commonly denoted using functional notation, such as f(x), where x is the input and f(x) is the output. Functions are used to describe relationships between variables, such as in algebraic expressions or equations. They can take many forms, including linear, quadratic, polynomial, exponential, trigonometric, and logarithmic functions. Functions are fundamental to many areas of mathematics, science, engineering, and economics, and have many applications in real-world situations.

Here,

A. The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. In other words, the function is not a straight line, because y is not directly proportional to x. Instead, it is a linear equation in two variables x and y, where the graph of the equation is a straight line.

B. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change. In a linear function, the rate of change of the function (slope) is always constant, meaning that for any two points on the line, the change in y over the change in x is always the same. However, in this case, the rate of change of the function depends on the value of x, and thus the graph of the function is not a straight line. Instead, it is a quadratic function, where the graph is a parabola.

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