DIVIDE. Show how you used partial quotients to find your answer.

1,562 ÷ 34

3 painters would take 3/4 hour (or 45 minutes) to complete the same job.

Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.

6 painters can paint the classrooms in 4 1/2 hours or 9/2 hours.

Therefore, we can write:

W = 1 job (painting the classrooms)

R = (6 painters) x (1 job / (9/2) hours) = 12/9 jobs per hour = 4/3 jobs per hour

T = unknown (what we're trying to find)

Where W = amount of work to be done

R = rate of work (number of classrooms painted per hour)

T = time to complete the work

Now we can use the formula:

time = (work) / (rate)

to solve for T:

T = W / R

T = 1 job / (4/3 jobs per hour)

T = 3/4 hour

Therefore, T = 3/4 hour.

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The integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is: \(8 * (1/3)tan^2\theta(1 + tan^2\theta)^(3/2) + C\), where θ is determined by x = 2tanθ, and C represents the constant of integration

What is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function.

To integrate the function \(\int(x^3/\sqrt(x^2+4))\) dx using a trigonometric substitution, we can use the substitution x = 2tanθ. Let's go through the steps:

Substitute x = 2tanθ. This implies \(dx = 2sec^2\theta d\theta.\)

Rewrite the integral in terms of θ:

\(\int((8tan^3\theta)/(\sqrt(4tan^2\theta+4))) * 2sec^2\theta d\theta.\)

Simplify the expression inside the square root:

\(\int((8tan^3\theta)/(2sec\theta)) * 2sec^2\theta d\theta.\\\\\int(8tan^3\theta) * sec\theta d\theta.\)

Simplify further:

\(16\int tan^3\theta sec\theta d\theta.\)

Apply the trigonometric identity: \(sec^2\theta = 1 + tan^2\theta\). Rearranging, we get: \(sec\theta = \sqrt(1 + tan^2\theta).\)

Substitute \(sec\theta = \sqrt(1 + tan^2\theta)\) in the integral:

\(16\int tan^3\theta * \sqrt(1 + tan^2\theta) d\theta.\)

Let u = tanθ, which implies \(du = sec^2\theta d\theta\). We can rewrite the integral in terms of u:

\(16\int u^3 * \sqrt(1 + u^2) du.\)

Now we have a rational power of u. We can use the substitution \(v = 1 + u^2\) to simplify it:

\(v = 1 + u^2\), which implies dv = 2u du.

Rewrite the integral using v:

\(16\int (u^3 * \sqrt v) * (1/2u) dv.\\\\8\int (u^2\sqrt v) dv.\)

Simplify and integrate:

\(8\int (u^2\sqrt v) dv = 8\int(u^2 * v^{(1/2)}) dv = 8\int u^2v^{(1/2)} dv.\)

Integrate \(u^2v^{(1/2)\) with respect to v:

\(8 * (1/3)u^2v^{(3/2)} + C.\)

Replace v with \(1 + u^2\):

\(8 * (1/3)u^2(1 + u^2)^{(3/2)} + C.\)

Substitute u = tanθ back into the expression:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C.\)

So, the integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C,\)

where θ is determined by x = 2tanθ, and C represents the constant of integration

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Answer:

C. 150 miles.

Step-by-step explanation:

By multiplying the scale by 3 to get the value for 6 inches, you can find that 6 inches on the map is equal to 150 miles.

Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

Domain: (-6, -1]

This is where the graph lines up with the x-axis.

Range: [-6, 4)

This is where the graph lines up with the y-axis.

See the two pictures for a visual reason why.

Answer:

1300.62

Step-by-step explanation:

thank me later lolol.

Answer:

To find the circumference you need to use C= 2πr but since you started with the diameter you need to divide it by 2 and you will get 3963.2. After you get the radius use the formula C= 2πr and you will get 24901.52

The equation would be written as 2 x π x 3963.2 = 24901.52

The equation which represents a cost function with a greater hourly rate than these charges is; C > 28 + 35h. The table required is therefore the table which represents the given function.

According to the question;

On this note, for one hour, the charge is; $63.

In essence, the table represents a cost function with a greater hourly rate than these charges will be;

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In a rigid body motion, we have that the angle ABC is still the same, the midpoint of AB is mapped to the midpoint of A'B', and the length of BC is equal the length of B'C'.

So the only option that is not always true is that AB is parallel to A'B'.

So the correct option is (1).

The equation relating x and y when they vary inversely is y = 75/x. (option-a)

When two variables are said to vary inversely, it means that as one variable increases, the other decreases, and vice versa, so their product remains constant. In this case, we are told that x and y vary inversely. Therefore, we can write:

\(x \times y\)= k

where k is a constant.

Given that x = 15 when y = 5, we can substitute these values into the above equation to solve for the constant k:

\(15 \times 5\) = k

k = 75

Now we can substitute the value of k into the equation to get:

\(x \times y\) = 75

Dividing both sides of this equation by x, we get:

y = 75/x

So, the answer is: y = 75/x.(option-a)

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Given the following question:

Your exact solutions are...

\( \rm9(a + 4b + 3c) \\ 9(a) + 9(4b) \rm+ 9(3c) \\ \rm 9a + 36b + 27c \\ \therefore \tt9(a + 4b + 3c) = 9a + 36b + 27c\)

Answer:

15.3

Step-by-step explanation:

Half the result.

Answer:

28 is equal to 28/100. Therefore, it is 28 percent.

(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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Answer:

x = 10

Step-by-step explanation:

9 is to 45 as 2 is to x

9 ---- 45

2 ---- x

x = 2 . 45 / 9

x = 10

Answer:

The age of his son is 10 years

Step-by-step explanation:

Think x is the age of his son

The age of his son is

=>45/x=9/2

=>9x=90

=>x=90/9

therefore

x=10

The his of son is 10 years

Answer:

84.2%

Step-by-step explanation:

420 + 380 = 800

800 / 950 = .842

.842 * 100 = 84.2

84.2 = 84.2%

The length of the third side is BC ≈ 1315.5.

Let the two sides of the triangle with given altitudes be AB=1010 and AC=1515. Let h be the length of the altitude from A to BC.

Let D and E be the feet of the perpendiculars from A to BC and from B to AC, respectively. Then we have:

BD = AB - AD = 1010 - h

CE = AC - AE = 1515 - h

Since the length of the altitude from A to BC is the average of the lengths of the altitudes to the two given sides, we have:

h = (BD + CE) / 2

h = [(1010 - h) + (1515 - h)] / 2

2h = 2525 - h

3h = 2525

h = 2525 / 3

Now we use the Pythagorean theorem on the right triangle ABD:

\(AD^2 + BD^2 = AB^2\)

\(h^2 + (1010 - h)^2 = 1010^2\)

Expanding and simplifying, we get:

\(2h^2 - 2020h + 515 = 0\)

Solving for h using the quadratic formula, we get:

h = \((2020 ± sqrt(2020^2 - 4(2)(515))) / (2(2))\)

h ≈ 808.6 or h ≈ 1511.4

We take the smaller value of h since the altitude is shorter than the length of the side opposite to it. Therefore, h ≈ 808.6.

Now we can use the Pythagorean theorem on the right triangle ABC:

\(BC^2 = AC^2 - h^2\)

\(BC^2 = 1515^2 - (808.6)^2\)

BC ≈ 1315.5

Therefore, the length of the third side is BC ≈ 1315.5.

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Answer:

what you have ticked is correct :)

Answer:

Rectangle B

Step-by-step explanation:

Given the expression x^2+7x+6, to get the required rectangle we need to factorize first;

= x^2+7x+6

= x^2+6x+x+6

= x(x+6)  + 1 (x+6)

= (x+1)(x+6)

From line 2 we will see that the terms contains x², 6x, x and 6. The rectangle that contains all this terms is rectangle B. Hence option B is correct.

Answer:

75 miles

Step-by-step explanation:

If the bird flies for 90 minutes at 50 mph (miles per hour), we need to calculate how many hours 90 minutes is.

One hour is 60 minutes. Our equation will be: 90/60 = 1.5

This mean the bird flies 1.5 hours at 50 mph. To find the distance, we multiply 1.5 by 50.

1.5 × 50 = 75

The bird has flown 75 miles.

Answer:

8

Step-by-step explanation:

I think I'm not for sure but if not 8 then 9 and no it's not because you add 5+4

Answer:

\(\sqrt{41}\)

Step-by-step explanation:

Pythagorean Theorem: \(a^{2} + b^{2} = c^{2}\)

\(4^{2} + 5^{2} = c^{2}\)

\(16+25= c^{2}\)

\(c^{2} = 41\)

\(c = \sqrt{41}\)

Answer:

Step 1, she reversed the values of x. It should have been 4 - (-2) not -2 - 4.

Step-by-step explanation:

Fern made a mistake in writing equation [1] where she wrote  {-2 - 4} in the denominator in place of {4 -(-2)}.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept

Given is Fern who is finding the slope of the line that passes through (-2, 8) and (4, 6).

In order to find the slope of the line, the following formula is used -

m = (y₂ - y₁)/(x₂ - x₁)

So, the slope of the line passing through the given points can be calculated using the following steps -

m = (6 - 8)/{4 -(-2)}                       ..[1]

m = -2/6                              

m = -1/3

Fern made mistake in writing equation [1]. She should have written

{4 -(-2)} in the denominator in place of {-2 - 4}

Therefore, fern made a mistake in writing equation [1] where she wrote  {-2 - 4} in the denominator in place of {4 -(-2)}.

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Answer:

Extreme high or low so

Step-by-step explanation:

(6.7, 108)

A high - leverage point on a regression plot simply means an extreme data point on the regression graph, which point will most likely be the coordinate (5.1, 105) on the scatter plot drawn.

Therefore, the point (5.1, 105) is a high leverage point on the regression plot.

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The sample size is most affected by construct validity.

The larger the sample size, the better the construct validity.

Here's an explanation: Validity refers to the degree to which an instrument or test accurately measures the concept it is supposed to assess.

It is crucial to have a valid measure for any type of research, but one of the significant factors that can affect validity is the sample size.

A construct is a theoretical concept that cannot be directly measured, and researchers usually create measures that capture and assess the construct indirectly.

As such, the measures' construct validity ensures that the assessment instrument measures what it is supposed to measure.

Researchers use construct validity to evaluate the instrument's accuracy in measuring the construct's concept.

Construct validity has a more significant impact on sample size since the sample size is a crucial factor in measuring the construct.

It is because a larger sample size increases the likelihood of having diverse perspectives and differences in opinion. Having a large number of participants ensures that the measure covers all aspects of the concept and reduces the risk of bias due to individual differences.

Therefore, construct validity is most affected by sample size, and having a larger sample size enhances the construct validity of the study.

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What is most affected by sample size? Does It Primarily Affect Internal Validity?

Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

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