Simplify.
21. 5t(2)(3)
24. 9(8n)
22. 7(a-b+5)
25. 3k+ 6k-12
23. 9y+ 15y-10y
26. 2t + 5m+7t-4m

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=471 \end{cases}\implies 471=2\pi r\implies \cfrac{471}{2\pi }=r \\\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \implies A=\pi \left( \cfrac{471}{2\pi } \right)^2\implies A=\pi\cdot \cfrac{471^2}{4\pi^2} \implies A=\cfrac{471^2}{4\pi }\)

\(\textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ A=\frac{471^2}{4\pi } \end{cases}\implies \cfrac{471^2}{4\pi }=s^2\implies \sqrt{\cfrac{471^2}{4\pi }}=s \implies \cfrac{471}{2\sqrt{\pi }}=s \\\\\\ \stackrel{\textit{perimeter of a square}}{4s\implies 4\left( \cfrac{471}{2\sqrt{\pi }} \right)}\implies \cfrac{942}{\sqrt{\pi }}~~ \approx~~531.47\)

Answer:

1 hour and 45 mins

Step-by-step explanation:

I am not sure I am right but I think I am

Hope this helps!

Answer:

1 hour and 25 minutes

Step-by-step explanation:

Answer:

\( \sqrt{9 } = 3 \)

The distance between two points can be calculated using the formula;

For points;

Given the points;

The distance between the two points can be calculated using the above formula;

The distance between the two points is;

Answer:

C: 200

Step-by-step explanation:

Just multiply 12.5 x 8 x 2 to get the answer.

Answer:

C. 200 in.^3

Step-by-step explanation:

The volume is given by

V = l*w*h

V = 12 1/2 * 8*2

V = 25/2 *8*2

  = 25*8

  = 200 in ^3

Answer:

10

Step-by-step explanation:

Step-by-step explanation:

 This problem expects us to model the equation for the total cost of the services of the plumber given the conditions stated.

Say the fixed amount charged for coming to your house is $10

say the fix amount charged per is $3

and the time spent to do the job is X

Hence the scenario can be modeled as

\(Y= 3x+10\)

the equation is similar to the equation of a straight line

\(Y= mx+c\)

Answer:

  7/15

Step-by-step explanation:

Given 3 of 10 counters are blue, you want the probability that randomly drawing 2 without replacement will result in drawing exactly one blue counter.

The probability of drawing a counter that is blue is the ratio of the number of blue counters to the total number of counters. The probability of drawing one that is not blue is the same: the ratio of not-blue counters to the number of counters.

The probability of drawing a particular sequence of counters is the product of the probabilities of the members of that sequence.

There are two ways to get exactly one blue:

The respective probabilities of these events are ...

  (blue, not-blue) = (3/10)×(7/9) = 7/30

  (not-blue, blue) = (7/10)×(3/9) = 7/30

The probability of one or the other of these is the sum of their probabilities:

  p(only one blue) = 7/30 +7/30

  p(only one blue) = 7/15

__

Additional comment

There are other ways this can be computed.

For example, there are 3·7 = 21 ways to have one blue and one not-blue counter. There are 10·9/(2·1) = 45 ways to draw 2 counters out of 10. So the probability of one blue in a draw of two is 21/45 = 7/15.

Answer:

2 over 9 can be expressed as a repeating decimal.

Step-by-step explanation:

Answer:

The equation of the line that passes through the given points is ;

7y = -x + 12

Step-by-step explanation:

Here, we want to get the equation of the line that passes through the given points

The general equation form

is;

y = mx + b

where m is the slope and b is the y-intercept

Now, let us substitute the x and y coordinate values of each of the points;

for (-2,2); we have

2 = -2m + b

b = 2m + 2 •••••(i)

for F;

1 = 5m + b

b = 1-5m ••••••(ii)

Equate both b

1-5m = 2m + 2

1-2 = 2m + 5m

7m = -1

m = -1/7

Recall;

b = 2m + 2

b = 2(-1/7) + 2

b = -2/7 + 2

b = (-2 + 14)/7 = 12/7

The equation of the line is thus;

y = -1/7x + 12/7

Multiply through by 7

7y = -x + 12

First you will get 4dz

The region E, such as its boundaries or any other relevant details, so that we can proceed with the evaluation of the integral and compute the final flux value.

The Divergence Theorem states that the flux of a vector field across a closed surface is equal to the volume integral of the divergence of the vector field over the region enclosed by the surface.

Find The Absolute Maximum And Minimum Values Of The Following Function On The Given Region R. F(X,Y)=7x2+7y2−14x+23;R=

Let's compute the divergence of F:

div(F) = ∂/∂x(2yz) + ∂/∂y(x² + z²/(1 + arctan(x² + z²y))) + ∂/∂z(xcos(y²))

After taking the partial derivatives and simplifying, we get:

div(F) = 2z + 2x/(1 + arctan(x² + z²y)) - (2z²y)/(1 + (x² + z²y)²) - sin(y²)

Now that we have the divergence of F, we can evaluate the flux by integrating the divergence over the region E:

Flux = ∭E (2z + 2x/(1 + arctan(x² + z²y)) - (2z²y)/(1 + (x² + z²y)²) - sin(y²)) dV

Please provide additional information about the region E, such as its boundaries or any other relevant details, so that we can proceed with the evaluation of the integral and compute the final flux value.

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Answer:

here's how you calculate sales tax after a discount.

Sale Price = original price – (% of discount * original price)

Sales Tax = Sales Tax rate * Sale Price.

Sales Tax = 0.05 * $17.21 = $0.8605 = $0.86.

Step-by-step explanation:

Answer:

x = 23°

Step-by-step explanation:

\(94 + x = 117 \\ \\ x = 117 - 94 \\ \\ x = 23\)

Answer:

x=23˚

Step-by-step explanation:

So, 117˚ is the measurement of the whole angle. 94˚ is the measurement for the angle it's on. To get x˚, subtract 94 by 117.

117˚-94˚=23˚

So, x=23˚

Answer:

Total charge

=

$

4.25

+

$

1.50

(

m

−

1

)

Total charge for 12 miles  

=

$

20.75

Explanation:

Building the rule

The trick with algebra is to think what you would do with numbers, then substitute letters.

Mile number 1 costs

$

4.25

The rest of the miles

⇒

(

total miles

−

1

)

×

$

1.50

Putting this all together we have:

$

4.25

+

(

total miles

−

1

)

×

$

1.50

The question instructs that we are to use the letter m for the total miles so we now have:

$

4.25

+

(

m

−

1

)

×

$

1.50

This would be written as:

$

4.25

+

$

1.50

(

m

−

1

)

So

 Total charge

=

$

4.25

+

$

1.50

(

m

−

1

)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Determine the charge for 12 miles

Total charge

=

$

4.25

+

$

1.50

(

12

−

1

)

Total charge

=

$

4.25

+

$

1.50

(

11

)

Total charge for 12 miles

=

$

4.25

+

$

16.50

=

$

20.75

Hope this helps you...

:)

Answer:

133 miles

Step-by-step explanation:

3.75 + 3 = 6.75

round to 6.80

20 - 6.80 = 13.2

13.2 / 0.1  = 132

132 + 1 the first mile that you payed $3.75

The value of the given integral, ∬_R arctan(y/x) dA, when changing to polar coordinates, is π/8.

To evaluate the given integral using polar coordinates, we need to express the region R in terms of polar coordinates. The region R is defined by the inequalities 1 ≤ \(x^{2}\) + \(y^{2}\) ≤ 4 and 0 ≤ y ≤ x.

In polar coordinates, we have x = rcos(θ) and y = rsin(θ), where r is the distance from the origin and θ is the angle.

Converting the inequalities for R into polar form, we have 1 ≤ \(r^{2}\) ≤ 4 and 0 ≤ rsin(θ) ≤ rcos(θ). Simplifying the second inequality, we get 0 ≤ sin(θ) ≤ cos(θ), which corresponds to the region where the angle θ satisfies 0 ≤ θ ≤ π/4.

The integral becomes ∬_R arctan(y/x) dA = ∫∫_R arctan(rsin(θ)/rcos(θ)) r dr dθ.

Simplifying further, the integral becomes ∫∫_R arctan(tan(θ)) r dr dθ = ∫∫_R θ r dr dθ.

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(a) the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

(b) the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

What is riemann sum?

A Riemann sum is a method used in calculus to approximate the area under a curve or the value of an integral. It involves dividing the region under the curve into smaller subintervals and approximating the area of each subinterval using a specific rule.

To find the Riemann sum using left endpoints and n equals 4, we need to divide the interval [2, 14] into four equal subintervals. The width of each subinterval, denoted as Δx, is calculated as (b - a) / n, where b is the upper limit (14) and a is the lower limit (2).

So, Δx = (14 - 2) / 4 = 12 / 4 = 3.

Now, we evaluate the function at the left endpoint of each subinterval and multiply it by the width (Δx).

The left endpoints for n = 4 are: x₀ = 2, x₁ = 5, x₂ = 8, x₃ = 11.

The Riemann sum using left endpoints is given by:

L₄ = f(x₀) Δx + f(x₁) Δx + f(x₂) Δx + f(x₃) Δx.

Now, let's substitute the given function f(x) = 2x² + 4x + 2 into the Riemann sum equation:

L₄ = (2x₀² + 4x₀ + 2) Δx + (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx.

L₄ = (2(2)² + 4(2) + 2) (3) + (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3).

L₄ = (8 + 8 + 2) (3) + (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3).

L₄ = (18)(3) + (72)(3) + (162)(3) + (288)(3).

L₄ = 54 + 216 + 486 + 864.

L₄ = 1620.

Therefore, the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

To find the Riemann sum using right endpoints and n equals 4, the process is similar. However, this time we evaluate the function at the right endpoint of each subinterval.

The right endpoints for n = 4 are: x₁ = 5, x₂ = 8, x₃ = 11, x₄ = 14.

The Riemann sum using right endpoints is given by:

R₄ = f(x₁) Δx + f(x₂) Δx + f(x₃) Δx + f(x₄) Δx.

Substituting the function into the Riemann sum equation:

R₄ = (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx + (2x₄² + 4x₄ + 2) Δx.

R₄ = (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3) + (2(14)² + 4(14) + 2) (3).

R₄ = (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3) + (392 + 56 + 2) (3).

R₄ = (72)(3) + (162)(3) + (288)(3) + (450)(3).

R₄ = 216 + 486 + 864 + 1350.

R₄ = 2916.

Therefore, the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

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Answer:

1 inch to 20 miles

Step-by-step explanation:

Answer:

$0.70

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

Answer:

Step-by-step explanation:

The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side.

What is the bisector about?

A bisector is known to be a kind of straight line that cut or divide an angle or a line segment.

Note that The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side as it is the right step to take.

The correct answer to this question is letter b.There are only three steps in constructing a circle circumscribed by a triangle. He is done with the first step.  Use the compass to find the perpendicular bisector for side DF. I hope I have helped you.

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

$3,425

Step-by-step explanation:

Net income is the income made after all expenses and cost of goods are deducted.

Last quarter income $9000

All expenses are goods ($575) + total expenses ($5000) = $5575

Net income = $9000 - $5575

Net income = $3,425

Answer:

15

Step-by-step explanation:

If CD and DE equal, then x+6 = 4x -21

So if you subtract x from both sides and plus 21 to both sides, that would be 3x = 27. Divide by 3 on both sides and you get 9.

Plug in x+6 with 9 and you get 15.

Answer:

Step-by-step explanation:

Total frequencies:

Median group is the containing the middle - 25th and 26th frequencies. This is the 11-15 interval.

Estimated median formula:

Substitute values and work out the number:

Answer:

A. and F. and B.

:)

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Based on the given information, if the observed price (p) exceeds the price expected by the producers (pe), then we can infer the following:

Demand exceeds supply: When the observed price is higher than the price expected by the producers, it suggests that there is greater demand for the product than initially anticipated. This could be due to various factors such as increased consumer demand, scarcity of supply, or other market dynamics.

Potential increase in profitability: If the observed price is higher than the expected price, it implies that producers can potentially generate higher profits. This situation may incentivize producers to increase production to meet the higher demand and take advantage of the higher prices.

Market equilibrium may shift: When the observed price surpasses the price expected by the producers, it indicates an imbalance between supply and demand. This could lead to a new market equilibrium where the price adjusts to reflect the increased demand and potentially influence the producers' pricing strategies in the future.

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