Can any body help Me with Factoring this
(5a+5a)=

Answers for a) $53.2, b) z = 10x+0.07y and c) y =300

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a car rental company charges $7 a day and 9 a mile to rent one of its cars, then the cost z, in dollars, to rent a car for 2 days and drive y miles can be found from the equation

z = 7x + 0.09y

a) x = 4, y = 280

z = 7*4 + 280*0.09

z = 53.2

Therefore, the cost to rent a car for 4 days and drive it for 280 miles is $53.2

b) The equation that gives the cost z

z = 10x+0.07y

c) When the costs are equal, then,

10*2+0.07y = 7*2+0.09y

20+0.07y = 14+0.09y

0.02y = 6

y = 300

Therefore, the cost of renting the cars from each of the two companies will be equal when y = 300 miles.

Hence, Answers for a) $53.2, b) z = 10x+0.07y and c) y =300

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Answer:

14! i think :D

Step-by-step explanation:

im probly worngg TvT

To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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(a) The statement assumes that the population mean of radon in New Brunswick houses (β) is equal to the EPA cutoff of 4.

The null hypothesis can be written as:

H0: β = 4

(b) The alternative hypothesis can be written as:

Ha: β ≠ 4

This statement suggests that the population mean of radon in New Brunswick houses (β) is not equal to the EPA cutoff of 4.

(c) When testing this null hypothesis, a two-tailed test is used. This is because the alternative hypothesis does not specify a direction (greater than or less than), but instead allows for the possibility that the population mean can differ from the EPA cutoff in either direction.

(d) To test the null hypothesis, we need to use an estimator of β. In this case, the sample mean (x) will serve as the estimator of β. The formula for the variance of this estimator, assuming simple random sampling, is:

Var(x) = σ²/n

Here, σ represents the population standard deviation and n is the sample size. To estimate this variance formula, we need the sample standard deviation (s). The estimated variance formula becomes:

Var(x)≈ s²/n

To obtain a standard error for the estimator of β, we take the square root of the estimated variance:

SE(x) ≈ √(s²/n)

4. To test the null hypothesis using a t-test, we will compute the t-statistic using the formula:

t = (x-β) / (SE(x))

In this case, since β is known (4), the formula simplifies to:

t = (x- 4) / (SE(x))

To carry out the test at the 5% significance level (α = 0.05), we will compare the computed t-statistic to the critical value(s) from the t-distribution with appropriate degrees of freedom. The rejection rule is as follows: If the absolute value of the computed t-statistic is greater than the critical value(s), we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

The result of the test will indicate whether there is sufficient evidence to reject the null hypothesis or not.

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Answer:

Step-by-step explanation:

Top left

Top right

Bottom left

Bottom right

Answer:

AAS, HL, ASA, Not enough info

Step-by-step explanation:

Answer:

∴Given Δ ABC is not a right-angle triangle

a= AB = √45 = 3√5

b = BC = 12

c = AC = √45 = 3√5

Step-by-step explanation:

Given vertices are A(3,3) and B(6,9)

           AB =

Given vertices are  B(6,9) and C( 6,-3)

            =  

   BC = 12

Given vertices are  A(3,3) and C( 6,-3)

AC² = AB²+BC²

45  = 45+144

45  ≠ 189

∴Given Δ ABC is not a right angle triangle

Step-by-step explanation:

Therefore, all possible values of aa that satisfy the conditions are aa such that a<34a<43​.

To find all possible values of aa such that the quadratic equation ax2+(2a+2)x+a+3=0ax2+(2a+2)x+a+3=0 has two roots with a distance greater than 1 on the number line, we can use the discriminant.

The discriminant of a quadratic equation ax2+bx+c=0ax2+bx+c=0 is given by Δ=b2−4acΔ=b2−4ac. For the equation to have two distinct real roots, the discriminant must be greater than 0.

In our case, the discriminant is Δ=(2a+2)2−4a(a+3)=4a2+8a+4−4a2−12a=−4a+4Δ=(2a+2)2−4a(a+3)=4a2+8a+4−4a2−12a=−4a+4.

For the equation to have two distinct roots with a distance greater than 1, we want Δ>12Δ>12, which simplifies to −4a+4>1−4a+4>1.

Solving this inequality, we have −4a>−3−4a>−3, which leads to a<34a<43​.

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Answer:

y = 5\(\sqrt{6}\)

Step-by-step explanation:

JLT forms the special 90-60-30 right triangle and the side length for the given measure follows as 2a-a\(\sqrt{3}\)-a

since the side length that sees 90 degrees is 10 then x = 5

according to Euclidian theorem :

y^2 = LK*KI (LK = 15 -x, KI = 15)

y^2 = 10*15

y^2 = 150 find the root for both sides

y = 5\(\sqrt{6}\)

Yes, you can reconstruct the 14 vertices tree , A, B, . . . , N using the given pre-order and post-order traversals.

Here is a step-by-step explanation of how to do it:

Start with the first vertex in the pre-order list (A). This vertex will be the root of the tree.
Find the position of A in the post-order list. All the vertices before A in the post-order list will be in the left subtree, and all the vertices after A will be in the right subtree.
Repeat the process for the left subtree and right subtree separately, using the same approach of finding the root (the first vertex in the pre-order list for that subtree) and splitting the post-order list into left and right subtrees accordingly.
Following these steps, you will reconstruct the tree as follows:
Root: A
Pre-order left subtree: B, D, E, H, L, M, I, F
  Post-order left subtree: D, L, M, H, I, E, F, B
Pre-order right subtree: C, G, J, K, N
  Post-order right subtree: J, N, K, G, C
Repeating the process for the left subtree:
  Root: B
  Pre-order left subtree: D, E, H, L, M, I
  Post-order left subtree: D, L, M, H, I, E
  Pre-order right subtree: F
  Post-order right subtree: F
Repeating the process for the right subtree:
  Root: C
  Pre-order left subtree: G, J, K, N
  Post-order left subtree: J, N, K, G
  Pre-order right subtree: None
  Post-order right subtree: None
Continuing this process for each subtree, you will reconstruct the original tree.

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Answer:

7.538461538

Step-by-step explanation:

To calculate the root square (vrms) of a sine wave, you need to follow these steps: Find the maximum value of the sine wave (Vmax): In this case, Vmax is given as 3 V.

Use the formula \(vrms = Vmax / √2\): Divide the maximum value by the square root of 2.
\(vrms = 3 V / √2\) Simplify the expression: To simplify the expression, multiply the numerator and the denominator by the conjugate of the denominator (√2).
\(vrms = (3 V / √2) * (√2 / √2)\)
\(vrms = (3 V * √2) / 2\)
Rationalize the denominator: To rationalize the denominator, multiply both the numerator and denominator by √2.
\(vrms = (3 V * √2) / 2 * √2\)
\(vrms = (3 V * √2) / 2√2\)
vrms = (3 V * √2) / 4

Simplify the expression: Multiply the constant (3 V) with the square root of 2.
\(vrms ≈ 4.24 V\)
The root mean square (vrms) of the sine wave with a period of 10 s and a maximum value (Vmax) of 3 V is approximately 4.24 V.

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It's important to note that vrms is different from the peak voltage (Vmax) of the waveform. The peak voltage is the maximum value that the waveform reaches, while vrms represents the effective value of the waveform.

To calculate the root mean square voltage (vrms) for a sine wave, we can use the formula:

vrms = (Vmax / √2)

Given that the maximum voltage (Vmax) is 3 V, we can substitute this value into the formula:

vrms = (3 / √2)

To simplify this further, we need to rationalize the denominator by multiplying the numerator and denominator by the square root of 2:

vrms = (3 / √2) * (√2 / √2)

This gives us:

vrms = (3√2) / 2

So, the vrms for the given sine wave is (3√2) / 2.

Now, let's talk about the meaning of vrms. The root mean square voltage (vrms) is a measure of the effective voltage of an alternating current (AC) waveform. It represents the equivalent direct current (DC) voltage that would produce the same amount of power dissipation in a resistive load.

In this case, with a sine wave function f(t) = 3 × sin(2π10t), the vrms is (3√2) / 2. This means that if we were to replace the AC waveform with a DC voltage, the DC voltage would need to be (3√2) / 2 V to generate the same amount of power in a resistive load.

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The required elementary matrix E such that EA = B is

\(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\).

Any matrix obtained by performing a single elementary row operation on the identity matrix is called an elementary matrix.

The elementary operations are as follows:

1. Interchange the two rows of a matrix

2. Multiply a row of a matrix by the non-zero scalar k.

3. Add k-times of a row into another row of the matrix.

Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.To perform an elementary row operation on A, an n×m matrix, take the following steps:

1. To find E, the elementary row operator, apply the operation to an n×n identity matrix.

2. To carry out the elementary row operation, premultiply A by E.

We want to interchange the first and second rows of A, a 3×3 matrix to  get B. To create the elementary row operator E, we interchange the first and second rows of the identity matrix I3:

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\) is changed to  \(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\).

So, \(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\)\(\left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right]\) = \(\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right]\)

Thus, the required elementary matrix E such that EA = B is

\(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\)

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The values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

Let's expand the expression:

(3 - 7i)(p + qi)i = (3 - 7i)(pi - q)

Using the distributive property, we have:

= 3pi - 7pi^2 - 3qi + 7qi^2

Since i^2 is equal to -1, we can substitute -1 for i^2:

= 3pi - 7p - 3qi - 7q

Now, equating the imaginary part to 58i:

-7p - 7q = 58

Dividing both sides by -7:

p + q = -8

From the given options, only p = 3 and q = -7 satisfy this equation:

3 + (-7) = -4

Therefore, the values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

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The solution to the given system of linear equations is x = 6 and y = -4

From the question, we are to solve the given system of equations using the elimination method

The given system of equations is

3x + 4y = 2

x + 2y = -2

Multiply the second equation by 2 and subtract the result from the first equation

2 × [ x + 2y = -2

2x + 4y = -4

Subtract from the first equation

 3x + 4y = 2

- 2x + 4y = -4

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

x = 2 -(-4)

x = 2 + 4

x = 6

Substitute the value of x into the second equation

x + 2y = -2

6 + 2y = -2

2y = -2 - 6

2y = -8

y = -8/2

y = -4

Hence, the value of x is 6 and the value of y is -4

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Hello !

9 times 4 added to the difference of 3 and 2

9    x     4     +                                        ( 3 - 2)

9 x 4 + (3 - 2)

Answer:

x = 5,-3

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

See attachments

Step-by-step explanation:

Hope this helps! (I hope you can open them)

The measure of a central angle of a regular polygon with 24 sides is 15 degrees.

A polygon is a two-dimensional geometric shape that is defined by a closed chain of line segments, also known as sides. These line segments must be joined end to end to form a closed shape, with no curves or self-intersections. The word "polygon" comes from the Greek words "poly" meaning "many" and "gon" meaning "angle".

To find the measure of a central angle of a regular polygon with 24 sides, we can use the formula:

central angle = 360 degrees / number of sides

Substituting the given value, we get:

central angle = 360 degrees / 24 = 15 degrees

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\(y =\begin{cases}x + 1 \: \: \: \: \: \: \: \: x >2\\x + 2 \: \: \: \: \: \: \: \: x \leqslant 2\end{cases}\)

According to the graph,

Let y = \({m_1}\)x + \(b_1\) [\(b_1\) = 2]

when x = -2 , y = 0

-2\(m_1\) + 2 = 0 [\({m_1}\) = 1]

→ So when x ≤ 2 , y = x + 2

Let y = \(m_2\)x + \(b_2\)

\(m_2 = \frac{4 - 3}{3 - 2} = 1 \: \: \: \: \: \: \: \: \: \: [m = \frac{y_2 - y_1}{x_2 - x_1} ]\)

when x = 2 , y = 3

3 = 2 × 1 + \(b_2\) , \(b_2\) = 1

→ So when x > 2 , y = x + 1

\(y =\begin{cases}x + 1 \: \: \: \: \: \: \: \: x >2\\x + 2 \: \: \: \: \: \: \: \: x \leqslant 2\end{cases}\)

Step-by-step explanation:

We need to write the sum of 2x - 7 and the opposite of 2x

Opposite of 2x is (-2x)

Sum means to add the number :

2x-7 + (-2x)

Remove parentheses,

2x-7 - 2x

Taking like terms together,

2x-2x-7= 0-7

= -7

Hence, the answer is -7.

The percentile score of 71 on test score is 27 and the score of victor is 71.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula

\(R_{100} =\frac{100(N < )+\frac{1}{2} }{N}\)

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60th percentile.

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

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To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.

Let the length of the rectangular auditorium be L, and its width be W.

The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.

The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.

Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60

Simplifying: 2L + 2W - 8r + πr = 45π + 60

Rearranging: 2L + 2W = 8r + 44π + 60

The area of the seating area is given by A = (L - 2r)(W - 2r).

We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.

Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60

Solving for L: L = (8r + 44π + 60 - 2W) / 2

Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)

Simplifying: A = (4r + 22π + 30 - W) (W - 2r)

Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.

dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0

Solving for W: 8r + 44π + 60 - W = W - 2r

Simplifying: 10r + 44π + 60 = 2W

W = 5r + 22π + 30

Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.

A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)

Simplifying: A = (r - 22π) (3r + 22π + 30)

Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π

Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.

dA/dr = 6r + 8π + 30 - 66π = 0

Simplifying: 6r - 58π + 30 = 0

6r = 58π - 30

r = (58π - 30) / 6

r ≈ 29π/3 - 5

Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

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we get that the measure is:

The equation that represents the sentence "28 is the quotient of a number and 4" is 28 = n/4.

In the given sentence, "28 is the quotient of a number and 4," we can break down the sentence into mathematical terms. The term "quotient" refers to the result of division, and "a number" can be represented by the variable "n." The divisor is 4.

1) Define the variable.

Let's assign the variable "n" to represent "a number."

2) Write the equation.

Since the sentence states that "28 is the quotient of a number and 4," we can write this as an equation: 28 = n/4.

The equation 28 = n/4 represents the fact that the number 28 is the result of dividing "a number" (n) by 4. The left side of the equation represents 28, and the right side represents "a number" divided by 4.

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The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8

To determine the values of a, b, and c in the matrix equation:

4 a  +  3  0    = 7  3

3 4      5  b       c   5

By addition operation, we have

a + 0 = 3

3 + 5 = c

4 + b = 5

When the equations evaluated, we have

a = 3

c = 8

b = 1

The above are the values of a b and c

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Complete question

Determine the values of a, b, and c in the following matrix equation.

4 a  +  3  0    = 7  3

3 4      5  b       c   5

Answer:

S= 121

HJ= 150

Step-by-step explanation:

pop quiz?

Data collected at the same, or approximately the same point in time are  Cross- sectional data

In statistics and econometrics, cross-sectional data, or a cross section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.

For instance, if we wanted to determine the prevalence of obesity in a population, we could randomly select a sample of 1,000 people (also referred to as a cross section of that population), measure their height and weight, and then determine what proportion of that sample falls under the definition of obesity. With the use of this cross-sectional sample, we are able to get a current picture of that group. Be aware that based on a single cross-sectional sample, we cannot determine whether the prevalence of obesity is rising or falling; we can only describe the current proportion.

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Answer:

20 units I believe

Step-by-step explanation:

20 units

Answer:   C. 20 units

2021 edg

Step-by-step explanation:

The area of the surface defined by the parametric equations x(p, q) = p+q, P-9, y(p, q), and z(p, q) = pq, where 1 ≤ p ≤ 2 and 0 ≤ q ≤ 1, is [10].

To calculate the area of this surface, we can use the concept of surface area in parametric form. The formula for the surface area of a parametric surface is given by:

A = ∬ ||(∂r/∂p) x (∂r/∂q)|| dp dq,

where r(p, q) = (x(p, q), y(p, q), z(p, q)) is the vector function that defines the surface. In this case, r(p, q) = (p+q, P-9, pq).

To find the partial derivatives, we differentiate each component of the vector function with respect to p and q:

∂r/∂p = (1, 0, q),

∂r/∂q = (1, 0, p),

Taking the cross product of these vectors gives:

||(∂r/∂p) x (∂r/∂q)|| = ||(0, -p, -q)|| = sqrt(p^2 + q^2).

Integrating this expression over the given limits of p and q will give us the area of the surface.

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