which statement is true regarding the graphed functions?
a- f(0) = 2 and g(-2) = 0
b- f(0) = 4 and g(-2) = 4
c- f(2) = 0 and g (-2) =0
d- f(-2) = 0 and g(-2) = 0

Using the Elimination and Extensions Theorems, we can simplify the given system of equations and solve it. There are three solutions in C3: (1, 0, 0), (0, 1, 0), and (0, 0, 1).

To solve the system of equations x³ + y³ - z³ = 1, x² + y² + z² = 1, and x+y+z = 1, we can apply the Elimination and Extensions Theorems.

1. Elimination Theorem:

By subtracting the second equation from the first equation, we eliminate the terms involving z and obtain x³ + y³ - z³ - (x² + y² + z²) = 1 - 1, which simplifies to x³ + y³ - x² - y² - z³ - z² = 0.

2. Extensions Theorem:

We consider the equation obtained from the Elimination Theorem and add the third equation x+y+z = 1 to it. This yields x³ + y³ - x² - y² - z³ - z² + x + y + z = 0 + 1. Simplifying further, we have x³ - x² + x + y³ - y² + y + z³ - z² + z = 1.

To find the solutions, we can use computer algebra software or solve the equation manually. In this case, the solutions are (1, 0, 0), (0, 1, 0), and (0, 0, 1). These values satisfy all three original equations, and thus, they are the solutions to the given system in C3.

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Answer:

43

Step-by-step explanation:

43 is the answer as

33+20+9=62

105-62=43

Step-by-step explanation:

The perimeter of a quadrilateral is the distance around it

first add all the sides and then equate to the total that they have given you

x+9+33+20=105

x+62=105

x=105-62

x=43

the answer is 43 in

Answer:

Timmy has been working at Monster Burger longer than Susie, which explains why he earns more money. Monster Burger employees are given a 50 cent raise each year, so Susie's salary will likely increase over time as she continues to work there.

Step-by-step explanation:

It is possible to determine how long Susie has been working at Monster Burger by using the information given. Since Timmy makes 720 dollars working 40 hours and Susie makes 600 dollars working the same hours, we can calculate their hourly wages:

Timmy's hourly wage: 720 / 40 = 18 dollars

Susie's hourly wage: 600 / 40 = 15 dollars

Since Monster Burger employees are given a 50 cent raise a year, this means that Susie's hourly wage has increased by 50 cents * x years, where x is the number of years Susie has been working there. Thus, we have:

15 + (0.50 * x) = 18

Solving for x, we get:

x = (18 - 15) / 0.50 = 6 years

Therefore, Susie has been working at Monster Burger for 6 years.

The total amount needed to be saved to meet the cost at 18 years is $235,531.75.

To calculate the total amount needed to be saved, we can use the timeline method. We know that the payments will begin in exactly 18 years and will be made in four installments on the child's 18th, 19th, 20th, and 21st birthdays. We also know that the cost of the child's education will be $80,000 per year.

Using the future value formula, FV = PV * \((1 + r)^n\), where FV is the future value, PV is the present value, r is the interest rate, and n is the number of periods, we can calculate the future value of each installment:

FV1 = $80,000 *\((1 + 0.05)^0\) = $80,000

FV2 = $80,000 * \((1 + 0.05)^1\) = $84,000

FV3 = $80,000 * \((1 + 0.05)^2\) = $88,200

FV4 = $80,000 * \((1 + 0.05)^3\)= $92,610

The total amount needed is the sum of the future values of all installments:

Total amount = FV1 + FV2 + FV3 + FV4

Total amount = $80,000 + $84,000 + $88,200 + $92,610

Total amount = $344,810

Since the total amount needed is in the future, we need to adjust it to its present value. We can use the present value formula, PV = FV / \((1 + r)^n\), to calculate the present value:

PV = $344,810 / \((1 + 0.05)^1^8\)

PV = $235,531.75

Therefore, the total amount needed to be saved to meet the cost at 18 years is $235,531.75.

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Answer:

26.4

Step-by-step explanation:

I had the same question once

The given expressions can be written in the complex form a + bi as follows,
1. log(1) = 0 + 0i
2. log(-1) = 0 + πi
3. log(i) = 0 + (1/2)πi
4. ii = e^(-π/2) + 0i

The given expressions can be written in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

1. log(1)
Since log(1) = 0, we can write it as 0 + 0i.

2. log(-1)
Using the complex logarithm, log(-1) can be expressed as πi, so it is 0 + πi.

3. log(i)
The complex logarithm of i is (1/2)πi, so we can write it as 0 + (1/2)πi.

4. ii
To find ii, we first need to express i in exponential form. i = \(e^{\frac{i\pi }{2} }\), so:
ii = \((e^{\frac{i\pi }{2} })^{i}\)
Using the power rule for exponentials (a^(mn) = (a^m)^n):
ii = \(e^{\frac{-\pi }{2} }\)
This can be written as \(e^{\frac{-\pi }{2} }\) + 0i.

So, the given expressions can be written in the form a + bi as follows:
1. log(1) = 0 + 0i
2. log(-1) = 0 + πi
3. log(i) = 0 + (1/2)πi
4. ii = \(e^{\frac{-\pi }{2} }\) + 0i

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Answer:

Because they fit in a larger box for transport and the boxes form a stronger structure for added crush resistance

Hope this helps

Answer: m and n

8(m+n)= 8m + 8n

The absolute maximum and minimum values of the function f(x, y) = x^2 + y^2 - 2y on the set R = {(x, y): x^2 + y^2 ≤ 9} can be found by analyzing the critical points and the boundary of the region R.

To find the critical points, we take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero. Solving these equations, we find that the critical point occurs at (0, 1).

Next, we evaluate the function f(x, y) at the boundary of the region R, which is the circle with radius 3 centered at the origin. This means that we need to find the maximum and minimum values of f(x, y) when x^2 + y^2 = 9. By substituting y = 9 - x^2 into the function, we obtain f(x) = x^2 + (9 - x^2) - 2(9 - x^2) = 18 - 3x^2.

Now, we can find the maximum and minimum values of f(x) by considering the critical points, which occur at x = -√2 and x = √2. Evaluating f(x) at these points, we get f(-√2) = 18 - 3(-√2)^2 = 18 - 6 = 12 and f(√2) = 18 - 3(√2)^2 = 18 - 6 = 12.

Therefore, the absolute maximum value of f(x, y) is 12, which occurs at (0, 1), and the absolute minimum value is also 12, which occurs at the points (-√2, 2) and (√2, 2).

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The recursive formula for the given geometric sequence is:\(\(a(n) = \frac{3}{5} \cdot a(n-1)\)\)

To find the recursive formula of the geometric sequence 10, 6, 3.6, 2.16, ..., we can observe that each term is obtained by multiplying the previous term by a common ratio of\(\(\frac{3}{5}\).\) Let's denote the first term\(\(a(1)\).\)

The recursive formula for a geometric sequence is typically given by\(\(a(n) = r \cdot a(n-1)\),\)where\(\(a(n)\)\) represents the\(\(n\)\)th term of the sequence.

For this particular sequence, we have:

\(\(a(1) = 10\)\) (the first term)

To obtain the subsequent terms, we multiply each term by\(\(\frac{3}{5}\):\(a(2) = \frac{3}{5} \cdot a(1)\)\)

\(\(a(3) = \frac{3}{5} \cdot a(2)\)\)

\(\(a(4) = \frac{3}{5} \cdot a(3)\)\)

\(\(\ldots\)\)

So, the recursive formula for the given geometric sequence is:

\(\(a(n) = \frac{3}{5} \cdot a(n-1)\)\)

Note: The recursive formula alone does not give the value of\(\(a(1)\)\), the first term of the sequence. It only represents how each subsequent term is related to the previous term. In this case,\(\(a(1)\)\) is explicitly given as 10.

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As per the given statement The recursive formula for the given geometric sequence is \(\[ a_n = a_{n-1} \times 0.6 \]\).

The given geometric sequence can be expressed using the recursive formula:

\(\[ a_n = a_{n-1} \times r \]\)

where \(\( a_n \)\) represents the \(\( n \)\)th term in the sequence and \(\( r \)\) is the common ratio.

In this case, the common ratio \(\( r \)\) can be found by dividing any term by its preceding term. Let's use the second term (6) and the first term (10):

\(\[ r = \frac{6}{10} = 0.6 \]\)

Therefore, the recursive formula for the given geometric sequence is:

\(\[ a_n = a_{n-1} \times 0.6 \]\)

This means that each term in the sequence is obtained by multiplying the preceding term by 0.6.

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(3x+2)(x+2)

Step-by-step explanation:

How to solve your problem

3x² + 8x + 4

1. Grouping

Use the sum-product pattern

3x² + 8x + 4

3x² + 6x + 2x + 4

2. Common factor from the two pairs

3x² + 6x + 2x + 4

3x(x+2)+2(x+2)

3. Rewrite in factored form

3x(x+2)+2(x+2)

(3x+2)(x+2)

Solution

(3x+2)(x+2)

Answer:

(x+2) x (3x+2)

Answer: \(f(a^2)=2a^2-4\)

Step-by-step explanation:

Substituting \(a^2\) for \(x\), \(f(a^2)=2a^2-4\).

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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A nurse researcher may choose to assign subjects randomly to groups in a study for various reasons.

Random assignment of subjects to groups is a fundamental technique in research design, particularly in experimental studies. Here are some reasons why a nurse researcher would choose to assign subjects randomly to groups:

1. Minimizing bias: Random assignment helps minimize selection bias by ensuring that each participant has an equal chance of being assigned to any group. This helps create comparable groups and reduces the influence of confounding variables.

2. Enhancing internal validity: Random assignment strengthens the internal validity of a study by increasing the likelihood that any observed differences between groups are due to the intervention or treatment being studied, rather than preexisting differences between individuals.

3. Facilitating statistical analysis: Random assignment allows for the use of inferential statistics, as it provides a basis for making generalizations and drawing conclusions about the population from the sample data.

4. Ensuring generalizability: Random assignment increases the generalizability or external validity of the findings, as it helps create groups that are representative of the target population, making it easier to apply the study's results to a broader context.

By employing random assignment, nurse researchers can enhance the rigor, reliability, and validity of their studies, thereby contributing to evidence-based practice and improving patient care.

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Answer:

..............................

The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

The given data is

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

(a) calculate mean value of x:

μ = E(x)

  = ∑(xi.P(xi))

 = 4.13

(b)  calculate variance of x:

σ² = ∑(xi - E(x))².P(xi)

   = 1.81331

(c)  calculate standard deviation of x:

σ = √σ²

σ = √1.831

σ = 1.3539

The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:

P(μ  - σ < x < μ  + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)

                                = P(2.7761 < x < 5.4839)

                                = P(x = 3) + P(x = 4) + P(x = 5)

                                = 0.13 + 0.30 + 0.31

                                = 0.74

Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

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The complete question is-

Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

Answer:

\(y = {1}^{2} + 1 = 1 + 1 = 2\)

Answer:

lily - 5

5+8= 13

James - 13

13+5= 18

18-75= 57

Michael - 57

Answer:

Step-by-step explanación

0.02

When the mean number of points scored per game next season is 60, the model predicts that the mean home attendance will be 11902

The function that predicts the attendance is given as:

\(y = -7628+325.5x\)

When the mean number of points scored per game next season is 60, it means that the value of x is 60

i.e. x = 60

Substitute 60 for x in the function

So, we have:

\(y = -7628+325.5 \times 60\)

Evaluate the product

\(y = -7628+19530\)

Add -7628 and 19530

\(y = 11902\)

Hence, the model predicts that the mean home attendance will be 11902

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when inserted to the equation it equals 4

(-3×-6)-(7×2)=4

answer =(-6,2)

Answer:

1. 5- (-8) = 13

2. -3 1/2 - 4 1/2 = -7 1/2

3. -7 - 4 = -11

4. -0.5 - 3.5 = -4

Step-by-step explanation:

1. 5- (-8) =

5 + 8

13

2. -3 1/2 - 4 1/2 =

-7 1/2

3. -7 - 4 =

-11

4. -0.5 - 3.5 =

-4

Answer:

C is the answer

Step-by-step explanation:

There are three major forms of linear equations:

Point slope form:

The point-slope form, as its name suggests, identifies a point on a line and its slope. Not frequently is this form provided to assist with line graphing. To get from a verbal or visual representation of a line to its slope-intercept or standard form, however, is where it is more frequently utilized.

Slope intercept form:

A line's slope and y-intercept are communicated using the slope-intercept form. Technically speaking, it is an exception to the point-slope form.

Standard form:

An equation's conventional form is as follows:

Ax+By=C

Where A is not a negative number and B, C, and all three are whole numbers.

Hence we get the required answer.

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0.38 is 7/18 (filling space)

Answer:

0.388888889

Step-by-step explanation:

Answer:

  sum = 65

Step-by-step explanation:

You want the sum of the set of 5 consecutive positive integers such that the sum of the even integers in the set is 26.

The sum of even integers will be a multiple of 3 if the middle integer of the set is even. Here, that sum is 26, not a multiple of 3. Hence the middle integer of the set is 26/2 = 13, and the sum of the set is 13·5 = 65.

The sum of the five integers is 65.

__

Additional comment

When working "consecutive integer" problems, it is often useful to think in terms of the average of the integers, the middle one of an odd-length set, or the number halfway between the two middle ones of an even-length set.

A set of 5 integers will have either 3 odds and 2 evens, or 3 evens and 2 odds. The set here obviously does not have 3 even integers (whose sum would be 3 times the middle one).

The set is s = {11, 12, 13, 14, 15}. 10 is not in the set, but 11 is. The sum of evens is 12+14=26.

Let's start by finding the measure of angle EFP. We know that the sum of the measures of the angles in a quadrilateral is 360 degrees. Since EFGH is a trapezoid, angle EFG and angle EHG are supplementary angles. Therefore, angle EFG = 180 - angle EHG.

Given that arc GH is 70 degrees, we can say that angle EHG is also 70 degrees (since it is the central angle that intercepts arc GH). Therefore, angle EFG = 180 - 70 = 110 degrees

arc FG = 56 - 3x degrees

arc EPF = (x^2 - 2x) + (56 - 3x) = x^2 - 2x + 56 - 3x = x^2 - 5x + 56 degrees.

Finally, we double the measure of angle EFP to find the measure of arc EPF:

arc EPF = 2 * (x^2 - 5x + 56) = 2x^2 - 10x + 112 degrees.

Therefore, the measure of arc EPF is 2x^2 - 10x + 112 degrees.

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Answer:

-5m-3

Step-by-step explanation:

step 1 Collect like terms.

3(5m+2)-20m+(-14+5)

step 2 Simplify.

3(5m+2)-20m-9

step 3 Expand by distributing terms.

15m+6-20m-9

step 4 Collect like terms.

(15m-20m)+(6-9)

step 5 Simplify.

-5m-3

Answer:-5m - 3

Step-by-step explanation:

1) Distribute

3(5m + 2) - 20m - 14 + 5

15m+6 - 20m - 14+5

2) Add the numbers

15m+6 - 20m- 14+5

15m-3 - 20m

3) Combine like terms

15m - 3-20m

Answer

-5m - 3

Hope this helps

The statement that could be true for h for given function is Option C  h(2) = 16 is correct.

The set of all potential values for the independent variable (typically designated as x) for which the function is specified is known as the domain of a function. In other terms, it refers to the entire set of input values for which a function returns a result.

We can state that for any value of x between -3 and 11, the corresponding value of h(x) will be between 1 and 25 because the function h has a domain of -3 x 11 and a range of 1 h(x) 25.

Indicates that the function h is not fixed and that its values change depending on the value of x.

Now, evaluate your options:

Option A h(-3) = -1 - This statement is false because the range of h(x) is stated to be between 1 and 25, so h(-3) cannot be less than 1.

OptionB h(13) = 18 - This statement cannot be true because h(x) is specified to have a range between -3 and 11, so h(13) is not defined.

OptionC h(2) = 16 - The statement may be accurate given that the value of h(x) for any x between -3 and 11 could range from 1 to 25, and there is no evidence to the contrary.

OptionD h(8) = 21 - Since we know that h(8) = 19, this assertion is false.

Therefore, the statement that could be true for h is: h(2) = 16

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