Write an equivalent expression for (3m - 6)(8m2 - 40m - 5).​

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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Answer:

f(x) = x/4

Step-by-step explanation:

To find the inverse of a function replace the positions of x and y. Then isolate y.

y = 4x

x = 4y

x/4 = y

f(x) = x/4

The point estimate of the mean of the population is 18.0.

The point estimate of the mean of a population is the sample mean, which is calculated by adding up the values in the sample and dividing by the sample size.

In this case, the sample consists of six values: 16, 19, 18, 17, 20, and 18. To find the sample mean, we add up these values and divide by 6, giving:

Sample mean = \((16 + 19 + 18 + 17 + 20 + 18) / 6 = 18\)

Therefore, the point estimate of the mean of the population is 18.0. This means that based on this sample, we estimate that the true population mean is 18.0.

However, we must be careful not to generalize this estimate beyond the population that was sampled.

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Therefore, the value of x is x = -2 / m + 3.

Supporting Answer: We have to find the equation of the line that passes through the point (3, 7) and has a slope of m. We use the point-slope form of the equation of the line, which is :y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line. Thus, the equation of the line is: y - 7 = m(x - 3). Now, we are given that point A(x, 5) lies on the line. Hence, we substitute y = 5 and solve for x:x - 3 = (5 - 7) / mx - 3 = -2 / mmx = -2 / m + 3.

Equations act as a scale of balance. If you've ever seen a balancing scale, you know that it needs to have an equal amount of weight on both sides in order to be deemed "balanced". The scale will tip to one side if we just add weight to one side, and the two sides will no longer be equally weighted. Equations use the same reasoning. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.

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Answer:

Amy is (21.6 - 14.4) 7.2 km/hr faster than Bill.

Distance = speed / time

Amy's speed

40 minutes = 40/60 = 2/3 hours

14.4 = speed / 2/3

Speed = 14.4 * 3/2 = 21.6 km/ hr

Bill speed

60 minutes = 1 hour

Speed = 14.4 km / hr.

The total amount Jamar spends during the rest of the year is $22620.

Given case states that,

Jamar earns a salary of $34,800 per year. His employer withholds 1/10 of this amount for federal taxes.

And Jamar puts 1/4 of his remaining salary in a savings account and spends the rest of his salary during the year.

We need to determine how much does Jamar’s employer withhold in 1 year, in dollars.

Here,

Jamar earns a salary of $34, 800 per year

Amount paid to the federal taxes (FT);

FT = 1/10 * 34800

FT= $3480

Jamar puts 1/4 of their salary in savings let it be SA;

SA = 1/4 * 34800

SA = $8700

The total amount Jamar spends during the rest of the year is

= Total salary - FT - SA

= 34800 - 3480 - 8700

= $22620

Thus, the total amount Jamar spends during the rest of the year is $22620.

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Step-by-step explanation:

Since the initial fee is fixed, we can assume it is a constant and the succeeding mile fee is the variable as it changes for every mile covered.

Let x = distance (mile)

let y = total charge (dollars)

Yellowcab company equation for cost calculation;  3.50 + 2.5x = y

laxicab company equation for cost calculation;  4.54+2.3x = z

the two companies charge the same amount when y = z

; 3.50 + 2.5x = 4.54+2.3x

x = 5.2 miles

COST CALCULATION

;3.50 + 2.5x = ?

if x = 5.2;

; 3.50 + 2.5(5.2) =$16.50

OR

; 4.54+2.3x = ?

; 4.54 + 2.3(5.2) = $16.50

Answer: same distance but different side

Step-by-step explanation:

We have the following:

therefore:

The margin the error that corresponds to a sample of size of 5 with mean 75.2 and a standard deviation of 21.2 at a confidence level of 98% is 35.52

Answer:

82(-x-5)=26

-82x-410=26

-410-26=82x

-436/82=x

x=-218/41

The area enclosed by the polar curve r = 6e^0.7θ on the interval 0 ≤ θ ≤ 1/4 and the straight line segment between its ends is approximately 2.559 square units.

To find the area, we can break it down into two parts: the area enclosed by the polar curve and the area of the straight line segment.

First, let's consider the area enclosed by the polar curve. We can use the formula for finding the area enclosed by a polar curve, which is given by A = (1/2)∫[θ1 to θ2] (r^2) dθ. In this case, θ1 = 0 and θ2 = 1/4.

Substituting the given polar curve equation r = 6e^0.7θ into the formula, we have A = (1/2)∫[0 to 1/4] (36e^1.4θ) dθ.

Evaluating the integral, we find A = (1/2) [9e^1.4θ] evaluated from 0 to 1/4. Plugging in these limits, we get A = (1/2) [9e^1.4(1/4) - 9e^1.4(0)] ≈ 2.559.

Next, we need to consider the area of the straight line segment between the ends of the polar curve. Since the line segment is straight, we can find its area using the formula for the area of a rectangle. The length of the line segment is given by the difference in the values of r at θ = 0 and θ = 1/4, and the width is given by the difference in the values of θ. However, in this case, the width is 1/4 - 0 = 1/4, and the length is r(1/4) - r(0) = 6e^0.7(1/4) - 6e^0.7(0) = 1.326. Therefore, the area of the straight line segment is approximately 1.326 * (1/4) = 0.3315.

Finally, the total area enclosed by the polar curve and the straight line segment is approximately 2.559 + 0.3315 = 2.8905 square units.

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The solution of the given integral  \(\int\{7sin(x)4sec(x)tan(x)} \, dx\) is 14sec(x) + C

To evaluate the integral of  \(\int\{7sin(x)4sec(x)tan(x)} \, dx\)  , follow these steps:

Step 1: Simplify the integrand
Using the property sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x), we can rewrite the integrand as: 7sin(x) * (4/cos(x)) * (sin(x)/cos(x))

Step 2: Simplify further
Combine terms and simplify to get: (28sin^2(x))/cos^2(x)

Step 3: Perform substitution
Let u = cos(x), then du = -sin(x) dx. Therefore, -1/2 du = sin(x) dx.
Substitute u in the integrand and replace sin(x) dx with -1/2 du:  \(\int (-1/2)(28/u^2) \, du\)

Step 4: Simplify the new integrand
Simplify to get: \(\int{(-14/u^2)} \, du\)

Step 5: Integrate with respect to u
Now, integrate the simplified integrand: \(\int{(-14/u^2)} \, du\) = -14\(\int {(1/u^2) } \, du\)= -14\(\int {(u^{-2})} \, du\)

Using the power rule for integration (integrating \(u^n\) gives \(u^{n+1}/(n+1)\), we get: \(-14(u^{-1}/(-1))\)+ C

Step 7: Substitute back x
Replace u with cos(x): \(-14 (cos^{-1}(x))/(-1)\) + C = 14/cos(x) + C

Step 8: Rewrite the final answer
Using the property sec(x) = 1/cos(x), the final answer is: 14sec(x) + C

Therefore, the value of the given integral is ∫7 sin(x) 4 sec(x) tan(x) dx = 14sec(x) + C, where C is the constant of integration.

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Answer:

9

Step-by-step explanation:

the median is 9 and to keep it the same you put 9

Hope this helps!!!

Answer:

1. 11.84722 ≈ 12

2. 116.61111 ≈ 117

Answer:It is 19.7,??

Step-by-step explanation:

Answer:

2 slices per person.

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

The diagonals are bisected so DE =EB

67 = 2x+7

Subtract 7

67-7 = 2x+7-7

60 =2x

Divide by 2

60/2 =2x/2

30 = x

Answer:

D

Step-by-step explanation:

The table has

x values 2,3,4,5 and

f(x) as 1, 14,20, 31

The statements A is true Intermediate value theorem, B is false mean value theorem, C is true extreme value theorem and D is true.

Given that,

The table has

x values 2,3,4,5 and

f(x) as 1, 14,20, 31

The function f is continuous.

A is true, From the figure.

Intermediate value theorem is let [a,b]be a closed and bounded intervals and a function f:[a,b]→R be continuous on [a,b]. If f(a)≠f(b) then f attains every value between f(a) and f(b) at least once in the open interval (a,b).

B is false because, mean value theorem, Let a function f:[a,b]→R be such that,

1. f is continuous on[a,b] and

2. f is differentiable at every point on (a,b).

Then there exist at least a point c in (a,b) such that f'(c)=(f(b)-f(a))/b-a

In the B part, the differentiability is not given do mean value theorem can be applied.

C is true because the extreme value theorem, if a real-valued function f is continuous on the closed interval [a,b] then f attains a maximum and a minimum each at least once such that ∈ number c and d in[a,b] such that f(d)≤f(x)≤f(c)∀ a∈[a,b].

D is true.

Therefore, The statements A is true, B is false, C is true and D is true.

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344865

Explanation

Use the following formula:

In this case, n=830, thus you get your answer by entering 830 in the formula like this:

so, the answer is

344865

Answer:

The area of the sector in circle G formed by segments \(\overline{AG}\), and \(\overline {GB}\) is approximately 125.66 square units

Step-by-step explanation:

The given parameters are;

The radius of the circle with center G, r = 15

The measure of the given angle, m∠AGB = 64°

The area of a sector is given as follows;

Area of a sector of a circle = (θ/360°) × π × r²

Therefore;

The area of the sector in circle G formed by segments \(\overline{AG}\), and \(\overline {GB}\) is given as follows;

The area of the sector in circle G  = (64°/360°) × π × 15² ≈ 125.66 square units

No, it is not possible to obtain a negative value for the ss, variance, or standard deviation. They represent the amount of spread in data, and the values are always positive or zero.

Sum of squares (SS) measures the deviation of each data point from the mean of the set, squared. The formula for SS is:

SS = Σ (X - μ)^2

Variance is the average of the sum of squares, and it is calculated by dividing the SS by the degrees of freedom (n-1), where n is the number of data points in the set:

Variance = SS / (n - 1)

Standard deviation is the square root of variance and it is a measure of how far each data point is from the mean of the set:

Standard deviation = √Variance

Since both variance and standard deviation are based on the sum of squares, which is always non-negative, variance and standard deviation are also always non-negative.

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Answer:

60 people

Step-by-step explanation:

Of means to multiply

3/8 * 160

Rewriting

3 * 160/8

3 * 20

60

Answer:

60 students gave their speeches

Step-by-step explanation:

divide 160 by 8 you get 20. Then you multiply the 20 by 3 because 20 is only 1/8 of the 160 students, and you get 60.

Answer:

Explanation:

Given:

5/8 = 0.625

2/3 = 0.667

60% = 0.6

0.59

0.70

Now, we sort the numbers from least to greatest.

0.59, 60%, 5/8, 2/3, 0.70

Therefore, the answer is:

0.59, 60%, 5/8, 2/3, 0.70

Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)