Suppose the longest side in a right triangle has the measure 7√15. If the acute angles have the measure of 30° and 60°, which is the exact measure of the longer leg?

The critical values of the function are x = 0 and x = 64

The critical values of a function f(x) are the values of x for which f'(x) = 0.

Given,

f(x) = \(\frac{x^{4} }{5(x-8)^{2} }\)

The derivative is found as follows, applying the quotient rule:

f'(x) = \(\frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2} }\)

     = \(\frac{2x^{3}(x-64) }{5(x-8)^{3} }\)

The zeros of the function are the zeros of the numerator, thus:

\(2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\\)

x - 64 = 0------------->x = 64

The critical values are x = 0 and x = 64

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Answer:

12b+1

Step-by-step explanation:

-4 + 4b + 5 + 8b

12b+1

Answer: The remainder is 0.

Step-by-step explanation:

We are given:

Dividend polynomial = \(6x^5+4x^4-27x^3-7x^2+27x+\frac{3}{2}\)

Divisor polynomial = \(2x^2-3\)

We divide the dividend by the divisor using the long division method.

In this method, the final answer written in the bottom is considered as remainder and the uppermost polynomial is considered as the quotient.

The long division of the two polynomials is attached in the image below.

From the image, we can say that the remainder of the two is 0

Answer:47r64765

Step-by-step explanation:no

Answer : 52

Explaination :

(5x+2)+(2x+18)+90=180

5x+2x+2+18+90=180

7x+110=180

7x = 180-110

7x = 70

x = 70÷7

x = 10

Angle CDF

= 5(10)+ 2

=52

Instead of performing repeated two-mean comparisons, we conduct an analysis of variance to compare means because doing so reduces the likelihood of Type I errors. Here option A is the correct answer.

ANOVA is preferred over multiple two-mean comparisons because it reduces the Type I error probability and offers several benefits over conducting multiple t-tests.

When conducting multiple two-mean comparisons, the likelihood of making a Type I error (i.e., rejecting a true null hypothesis) increases with each comparison made. This is known as the multiple comparison problem, and it can lead to an inflated false positive rate.

In contrast, ANOVA uses a single test to compare multiple means simultaneously, reducing the likelihood of making a Type I error. ANOVA achieves this by partitioning the total variation in the data into different sources of variation and estimating the amount of variation due to random chance.

Additionally, ANOVA offers several benefits over multiple t-tests. One advantage is that it provides a statistical significance test for the overall difference among the groups, not just for pairwise comparisons. ANOVA also allows for the testing of interactions between factors that influence the mean differences. Furthermore, ANOVA calculations can be more efficient than conducting multiple t-tests, especially when the number of groups is large.

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Complete question:

The reason why we perform an analysis of variance for comparing means rather than conducting multiple two-mean comparisons is

A. Because multiple two-mean comparisons increase the Type I error probability.

B. Simply because ANOVA has simpler calculations but otherwise offers no benefit over the multiple t-tests.

C. Power is compromised when using t-tests.

From the details that we have here we can say that the amount of vinegar that is mixed with 1 milliliter of soy sauce is 0.67

the vinegar is given as 100

the soy sauce is given to be 150

The ratio would be

100 / 150

= 0.67

hence we can say that the amount of vinegar that is mixed with 1 milliliter of soy sauce is 0.67

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For the first expression: b - (d-c) = 5

For the second expression: b - (c-d) = 15

For the first expression, we are given the values of four variables:

a=4, b=3, c=-1, and d=-3.

We are asked to evaluate the expression b² - (d-c)² using these values.

To do this, we first need to substitute the given values into the expression:

b² - (d-c)² = 3² - (-3-(-1))²

Next, we need to simplify what's inside the parentheses:

-3 - (-1) = -3 + 1 = -2

So we can further simplify the expression to:

b² - (d-c)² = 3²  - (-2)²

Now we can evaluate the squared term:

(-2)²  = 4

So we have:

b²  - (d-c)²  = 3²  - 4

Finally, we evaluate the remaining expression:

3² - 4 = 9 - 4 = 5

Therefore, when a=4, b=3, c=-1, and d=-3,

The value of the expression b²  - (d-c)²  is 5.

For the second expression, we follow the same steps.

We are given the values of four variables: a=2, b=4, c=-3, and d=-4.

We are asked to evaluate the expression b²  - (c-d)²  using these values.

First, we substitute the given values into the expression:

b²  - (c-d)²  = 4²  - (-3-(-4))²

Next, we simplify what's inside the parentheses:

-3 - (-4) = -3 + 4 = 1

So we can further simplify the expression to:

b²  - (c-d)²  = 4² - 1²

Now we evaluate the squared term:

1²  = 1

So we have:

b²  - (c-d)²  = 4²  - 1

Finally, we evaluate the remaining expression:

4 - 1 = 16 - 1 = 15

Therefore, when a=2, b=4, c=-3, and d=-4,

The value of the expression b²  - (c-d)²  is 15.

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Answer:

k=2 should be the correct answer!

Answer:

\( - 4n - 8 = 4( - 3n + 2) \\ - 4n - 8 = - 12n + 8 \\ 12n - 4n = 8 + 8 \\ 8n = 16 \\ n = \frac{16}{8} \\ = 2 \\ thank \: you\)

Answer:My best guess is B or C

Step-by-step explanation:

im not the best at solving this but I feel certain it’s either of those

Let A be the set {cosx,sinx,cos(2x),sin(2x),...}. That shows that A is a non-complete orthogonal set over [−π,π] is (B) cos(3x). To find the main answer, we need to show that one pair of elements of A is not orthogonal. For that, we compute the inner product between two arbitrary elements of A.

Consider cos(x) and sin(x) as two elements of A.In order to show that A is not orthogonal, it is enough to find some non-zero value for this inner product.

cos(x) sin(x) =∫−ππ cos(x) sin(x) dxThe integral is nonzero, as the integrand is an odd function over the interval [−π,π], and hence the integral from −π to π is zero. Since cos(x) sin(x) is odd, the integral from 0 to π is zero and the integral from −π to 0 is zero. Thus, the value of this inner product is zero on each of these subintervals. We can conclude that the set A is not orthogonal. So, the main answer is (B) cos(3x).b) The answer is False because the given set is not a complete orthogonal set. To prove that it is not complete, we need to find a function that cannot be written as a linear combination of functions in the set.To show that {sin(πx/25),cos(25/πx),sin(25/2πx),cos(25/2πx),...} is not complete over [0,50], we must find a function that cannot be expressed as a linear combination of this set of functions. Let f(x) = x^2. This function is not a linear combination of {sin(πx/25),cos(25/πx),sin(25/2πx),cos(25/2πx),...}. Therefore, the given set is not complete and hence the answer is False.

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\( {6x}^{2} - 24 = 0 \\ = > 6( {x}^{2} - 4) = 0 \\ = > 6 {((x)}^{2} - {(2)}^{2} ) = 0 \\ = > 6(x - 2)(x + 2) = 0 \\ = > 6(x - 2) = 0 \: \: \: or \: \: 6(x + 2) = 0 \\ = > 6x - 12 = 0 \: \: \: or \: \: \: 6x + 12 = 0 \\ = > x = 2 \: \: \: or \: \: \: x = - 2\)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer: p = 4 for (0, p) and (p, 20)

p = 20 for (4, p)

Step-by-step explanation: To find the value of p in each ordered pair, we need to plug in the given values into the function f(x) = x^2 + 4 and solve for p.

(0, p)

When x = 0, we have:

f(0) = 0^2 + 4 = 4

So the ordered pair is (0, 4), which means p = 4.

(p, 20)

When x = p, we have:

f(p) = p^2 + 4

We are also given that f(p) = 20, so we can set up the equation:

p^2 + 4 = 20

Subtracting 4 from both sides, we get:

p^2 = 16

Taking the square root of both sides, we get:

p = ±4

Since the ordered pair (p, 20) lies on the graph of f(x) = x^2 + 4, we can eliminate the negative root and conclude that p = 4.

(4, p)

When x = 4, we have:

f(4) = 4^2 + 4 = 20

So the ordered pair is (4, 20), which means p = 20.

Therefore, the values of p are:

p = 4 for (0, p) and (p, 20)

p = 20 for (4, p)

Answer:

rteiyykykkucouyrilhk,dkrbbvvbnkl

Answer:

15x,-x,33x

Step-by-step explanation:

This is the set of like terms

To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

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Answer: The total cost would be $780.00

The expression for the total cost of fencing is $52x , where x is a variable representing the number of feet in one section.

An expression in one variable is a statement formed by the using constants and an unknown variables and mathematical operators but sign is equal to is not used. Expression in one variable is linear if the power of the unknown variable is equal to one .

Given that number of feet in one fence section be x

No of feet in 8 such fence section = 8x

Given , Perimeter = 8 fence sections = 8x feet

Cost of fencing of one foot = $6.50

Cost of fencing 8x feet = 8x * 6.50

Therefore , the total cost of the fencing can be given by = 8x*6.50

                                                                                                  = $ 52 x

Thus, the expression for the total cost of fencing is $52x

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The length of the rectangle is 6m - 2.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area = 30m² - 20m - 10

Width = 5m - 5

Now,

Area = Length x Width

30m² - 20m - 10 = Length x (5m - 5)

10(3m² - 2m - 1) = Length x (5m - 5)

10(3m² - (3 - 1)m - 1 = Length x (5m - 5)

10 (3m² - 3m + m - 1) = Length x (5m - 5)

10 (3m(m - 1) + 1(m - 1)) = Length x (5m - 5)

10 (3m + 1)(m - 1) = Length x 5(m - 1)

(m - 1) gets canceled.

10(3m - 1) = Length x 5

2(3m - 1) = Length

Length = 6m - 2

Thus,

6m - 2 is the length of the rectangle.

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Answer:

0.85,8/9,0.92

Step-by-step explanation:

Answer:

-x^2+3x+3;  5

Step-by-step explanation:

polynomial is -x^2+3x+3

when x=2 then -2^2+3*2+3=-4+6+3=5

The solution is Option B.

The value of the equation is A = -x² + 3x + 3 , and when x = 2 , A = 5

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 A

Now , the value of A is

Substituting the values in the equation , we get

A = x + 3x² + 2x - 3 - 4x² + 6   be equation (1)

On simplifying the equation , we get

A = 3x² - 4x² + x + 2x - 3 + 6

A = -x² + 3x + 3

Now , when x = 2

Substitute the value of x = 2 in the equation , we get

A = - ( 2 )² + 3 ( 2 ) + 3

A = -4 + 6 + 3

A = 9 - 4

A = 5

Therefore , the value of A is 5

Hence , the equation is A = -x² + 3x + 3

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Answer:

2/10 = 1/5

Step-by-step explanation:

It landed five 2 times and you rolled it 10 times

ANSWER

(x - x0)² + (y - y0)² = r²

EXPLANATION

The equation of a circle with radius r and center at point (x0, y0):

is:

1. The prime cost per cleaning is $249,900 / 9,000 = $27.77

2. The conversion cost per cleaning is $243,600 / 9,000 = $27.07

3. The total variable cost per cleaning is $262,500 / 9,000 = $29.17

4. The total service cost per cleaning is $276,900 / 9,000 = $30.77

5. The fixed overhead cost would increase by $900.

1. Prime cost per cleaning:

Prime cost includes direct materials and direct labor.

Prime cost = Direct materials + Direct labor

Prime cost = $18,900 + $231,000

Prime cost = $249,900

Therefore, the prime cost per cleaning is $249,900 / 9,000 = $27.77 (rounded to the nearest cent).

2. Conversion cost per cleaning:

Conversion cost includes direct labor and variable overhead.

Conversion cost = Direct labor + Variable overhead

Conversion cost = $231,000 + $12,600

Conversion cost = $243,600

Therefore, the conversion cost per cleaning is $243,600 / 9,000 = $27.07 (rounded to the nearest cent).

3. Total variable cost per cleaning:

Total variable cost includes direct materials, direct labor, and variable overhead.

Total variable cost = Direct materials + Direct labor + Variable overhead

Total variable cost = $18,900 + $231,000 + $12,600

Total variable cost = $262,500

Therefore, the total variable cost per cleaning is $262,500 / 9,000 = $29.17 (rounded to the nearest cent).

4. Total service cost per cleaning:

Total service cost includes direct materials, direct labor, variable overhead, and fixed overhead.

Total service cost = Direct materials + Direct labor + Variable overhead + Fixed overhead

Total service cost = $18,900 + $231,000 + $12,600 + $14,400

Total service cost = $276,900

Therefore, the total service cost per cleaning is $276,900 / 9,000 = $30.77 (rounded to the nearest cent).

5. If the rent on the office increased by $900, it would affect HHH's fixed overhead cost. The fixed overhead cost would increase by $900. This would lead to an increase in the total service cost per cleaning, as the fixed overhead is a component of the total service cost.

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Answer:

Isn't specific

Step-by-step explanation:

The Fundamental Counting Principle states that if there are x ways to do something and y ways to another, you can multiply x and y to do both things.

While this is a fast way of determining how many possible outcomes there are, it is broad and can't help you determine what those outcomes are.

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Answer:

1/3

Step-by-step explanation:

There are 3 rectangles, so 1 rectangle is 1 out of 3 rectangles.  So the fraction would be 1/3.

Each rectangle is 1/3 fraction of the complete design.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

Given is a design drawn by Mai.

The design consists of three rectangles.

Also, given that each of the rectangle has the same area.

This means that if we find one of the rectangle's area, multiply it by 3 and we will get the whole area.

Or in other words, if we find the whole area, then divide it by 3 to get each of the rectangle's area.

So the required fraction is 1/3.

Hence the fraction is 1/3.

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Answer:

so that's how you plot their intersection

Answer:

The probability would be 30/52

Step-by-step explanation:

if there is 52 cards in a deck, there is 26 red card, plus 4 queens equals 30