Evaluate the following definite integral •b I so " f(x)dx a where f(x)=5x2+3x, a=3 and b=5. Round your answer to two decimal places. Evaluate the following definite integral b I ronde L f(x)dx a where f(x)=3x (4x^2+2)^3, a=0 and b=4. Round your answer to two decimal places. + Evaluate the following definite integral [" f(x)dx a where f(x)= 3x e(3x2-1), a=-1 and b=1. Round your answer to two decimal places. 1

Answer:

71 miles in 1 hour

Step-by-step explanation:

divide the total amount of miles by the total amount of hours: 335/5

you get 71 mph

Answer:

71 miles per hour

Step-by-step explanation:

355 divided by 5 is 71

71 x 5 = 355

355 divided by 71 is 5

Answer:

y = x/2 - 1

Step-by-step explanation:

Just throw everything to the right till only y is on the left side

X-2y-2=0

- 2y =-x+2

2y = x - 2

y = x/2 - 1

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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As seen in the simulations, when a population is extremely skewed, such as in the case of an exponential distribution, the sampling distribution of x (the sample mean) for random samples of 40 observations is roughly normal.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. Therefore, even if the population distribution is extremely skewed, the sampling distribution of x tends to become approximately normal as the sample size increases. This is observed in the simulations, where the sampling distribution of x becomes more symmetric and bell-shaped as the sample size increases.

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The points (–2, 8) and (2, –8) are reflections of each other across both axes. This can be seen by taking their coordinates and plugging them into the reflection formula, which is (x, y) → (–x, –y).

When we plug in the coordinates for the first point, we get (–2, 8) → (–(–2), –(8)) = (2, –8). This is the coordinates of the second point, so they are reflections of each other.

The points (–7, –1) and (–7, 1) are also reflections of each other across both axes. Using the same reflection formula, we get (–7, –1) → (–(–7), –(–1)) = (7, 1), which are the coordinates of the second point.

The points (5, –6) and (–5, –6) are reflections of each other across both axes. Applying the reflection formula, we get (5, –6) → (–(5), –(–6)) = (–5, 6), which are the coordinates of the second point.

Finally, the points (4, –3) and (–3, 4) are reflections of each other across both axes. Using the reflection formula, we get (4, –3) → (–(4), –(–3)) = (–4, 3), which are the coordinates of the second point.

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The volume of the cube is 1,000 units³.

The volume of a cube is calculated by raising the length of one of its edges to the power of 3 or multiplying the length, width and breadth.

For a cube, the  length, width and breadth are equal.

The volume of a cube is calculated as follows;

V = L³

where;

V = 10³

V = 1,000 units³

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The best approach to provide an answer to the question would be: Calculate a confidence interval using t*

The confidence interval is often used to obtain the true population mean. The question asks us to identify evidence that points to the fact that the mean amount of water drank by each teenager is more than 1.5 liters.

We are here searching for the true population mean. We calculate a confidence interval using t when the population variance is not known as is the case here. So, to solve this question, we would calculatethe confidentce interval using t*.

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Answer:

y_2 is 8 units

Step-by-step explanation:

Given that

The distance between the point is 13 units

x_1 is 5

y_1 is 3

x_2 is -7

We need to find out the y_2

So, the following formula should be used

\(d = \sqrt({x_2 - x_1})^2 + (y_2 - y_1)^2\\\\13 = \sqrt({-7-5})^2 + (y_2 - 3)^2\\\\169 = 144 + (y_2)^2 + (-3)^2 - 2(y_2) (-3)\\\\25 = (y_2)^2 + 9 - 6y_2\\\\16 = (y_2)^2 -6y_2\\\\(y_2)^2 -6y_2 - 16 = 0\\\\(y_2)^2 - 8y_2 + 2y_2 - 16 = 0\\\\y_2 (y_2 - 8) + 2(y_2 - 8) = 0\\\\y_2 = 8\)

hence, y_2 is 8 units

Step-by-step explanation:

The area of the floor of the scale drawing and the scale factor are 72 in² and 1/4 respectively

Actual Length = 36 feets

Actual width = 32 feets

Model width = 9 inches

The scale factor = 9 / 36 = 1/4

The length of the model canbe calculated thus :

Actual Length × scale factor

Model width = 32 × 1/4 = 8 inches

The Area of a rectangle can be calculated using the relation :

Area = Length × width

Area of floor = 8 inches × 9 inches = 72 inch²

Therefore, the area of the floor of the scale drawing is 72 in²

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The area of the rectangular floor in the scale drawing is A = 156 inches²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular floor in the scale drawing be A

Let the length of the rectangular floor be L = 26 feet

Now , the length of the rectangular floor in scale drawing = 13 inches = L/2

And , the width of the rectangular floor be W = 24 feet

So , the width of the rectangular floor in scale drawing = W/2 = 12 inches

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

The area of the rectangular floor in the scale drawing A = 13 x 12

The area of the rectangular floor in the scale drawing A = 156 inches²

Hence , the area of rectangle is 156 inches²

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Answer:

a) thousands:  1 (to the right of the 8)

b) ten millions:  3

c) hundreds: 9

d) millions: 1 (to the right of the 3)

Step-by-step explanation:

a) thousands:  1 (to the right of the 8)

b) ten millions:  3

c) hundreds: 9

d) millions: 1 (to the right of the 3)

The correct answer is (c) No, since the sample mean of 298.3 ml is in the confidence interval.

The confidence interval provides a range of plausible values for the true population mean amount of juice dispensed per bottle based on the sample mean and standard error. Since the confidence interval includes the sample mean of 298.3 ml, it suggests that the true mean amount of juice dispensed per bottle is likely to be around this value. Therefore, there is no reason to believe that the mean amount of juice in today's bottles differs from 300 ml based on this confidence interval.

Answer (a) and (b) are incorrect because they incorrectly suggest that the sample mean or the confidence interval being below 300 ml necessarily indicates a difference from the advertised value. Answer (d) is also incorrect because the fact that the advertised value falls within the confidence interval does not by itself indicate conformity with the label promise; the confidence interval includes a range of plausible values, and some of them may be quite different from the advertised value.

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Answer:

d) 0.25 divided by 0.42

Step-by-step explanation:

To find the percentage of students who passed the second test,given that they have already passed the first test, you can use the following formula:

\( \small\sf \: percentage \: who \: passed \: both \: tests = \frac{(percentage \: who \: passed \: both \: tests \: and \: first \: test) }{ (percentage \: who \: passed \: first \: test)} \\ \\ \)

Given that 25% of the class passed both tests and 42% of the class passed the first test,

percentage who passed both tests

→ (25%) / (42%)

→ 0.25/0.42

→ 0.595 or 59.5%

Therefore, 59.5% of the students who passed the first test also passed the second test.

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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Answer:

15.11 lb

Step-by-step explanation:

At a butcher​ shop, Hilda bought 4 17/20 lb of Beef and some pork. She left with 19 24/25 lb of meat. Express the number of pounds of pork she bought using a decimal

so Hilda bought ? lb of pork

Beef = 4 17/20 lb

Pork = x lb

Total Meat = 19 24/25 lb

Using decimal to express the pound of pork she bought, convert the pounds of beef and total meat she bought into decimal

Beef = 4 17/20 lb = 4.85 lb

Total Meat = 19 24/25 lb = 19.96 lb

Total meat = Beef + pork

19.96 lb = 4.85 lb + x lb

Subtract 4.85 from both sides

19.96 - 4.85 = 4.85 + x - 4.85

15.11 = x

x= 15.11 lb

Therefore, pounds of pork she bought = 15.11 lb

Answer:

This doesn't make sense

Step-by-step explanation:

This doesn't make sense please emphasize

The number of hours after which the candle is burned completely is

68 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Candle height = 11(1/3) inches

Each hour the height decreases by 1/6 inch.

Now,

The equation to find the number of hours x after which the candle is burnout is 11(1/3) - (1/6)x = 0

Solve for x.

11(1/3) - (1/6)x = 0

11(1/3) = (1/6)x

34/3 = (1/6)x

x = (34 x 6) / 3

x = 34 x 2

x = 68

Thus,

After 68 hours the candle is completely burnt.

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The capitalized cost for the solid waste treatment plant, based on a 6% MARR, is approximately $579 million.

To calculate the capitalized cost for the solid waste treatment plant, we need to determine the present value of all the costs over the project's lifespan.

The costs involved in the project are as follows:

Initial installation cost: $35 million.

Minor repair and renovation (R&R) after 10 years: $14 million.

Major R&R after 20 years: $18 million.

Operating and maintenance (O&M) costs each year, increasing at a compound rate of 6% per year.

First, let's calculate the present value of the O&M costs over the 20-year period: Using the TVM Factor Table calculator, the present value factor for a 6% MARR and 20 years is 10.206.

The total O&M costs over 20 years can be calculated as follows: O&M costs for the first year: $3 million. O&M costs for the subsequent years: $3 million * (1 + 0.06) + $3 million * (1 + 0.06)^2 + ... + $3 million * (1 + 0.06)^19.

Using the formula for the sum of a geometric series, the O&M costs over the 20-year period can be calculated as: O&M costs = $3 million * (1 - (1 + 0.06)^20) / (1 - (1 + 0.06)) = $3 million * (1 - 1.418519) / (-0.06) = $3 million * (-0.418519) / (-0.06) = $2.91038 million.

Now, let's calculate the present value of the costs: Present value of the initial installation cost: $35 million.

Present value of the minor R&R cost after 10 years: $14 million * 10.206 (present value factor for 6% MARR and 10 years) = $142.884 million. Present value of the major R&R cost after 20 years: $18 million * 10.206^2 (present value factor for 6% MARR and 20 years) = $371.001 million.

Present value of the O&M costs: $2.91038 million * 10.206 = $29.721 million. Finally, the capitalized cost of the solid waste treatment plant is the sum of all the present values: Capitalized cost = $35 million + $142.884 million + $371.001 million + $29.721 million = $578.606 million.

Rounding the final answer to the nearest whole number, the capitalized cost for the solid waste treatment plant is $579 million.

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The complete question is:

A new solid waste treatment plant is to be constructed in Washington County. The initial installation will cost $35 million (M). After 10 years, minor repair and renovation (R&R) will occur at a cost of $14M will be required; after 20 years, a major R&R costing $18M will be required. The investment pattern will repeat every 20 years. Each year during the 20 -year period, operating and maintenance (O\&M) costs will occur. The first year, O\&M costs will total $3M. Thereafter, O\&M costs will increase at a compound rate of 6% per year. Based on a 6% MARR, what is the capitalized cost for the solid waste treatment plant? Click here to access the TVM Factor Table calculator. $ Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. The tolerance is ±25,000.

Answer:

a. The total charge for first restaurant (in dollars) = 16x + 8

The total charge for the second restaurant (in dollars) = 18x

b. 16x+8=18x models the equation when the charge would be same for both restaurants.

Step-by-step explanation:

Given that:

Delivery charges of first restaurant = $8

Price per pizza = $16

Let,

x be the number of pizzas bought

Total cost = 16x + 8

There are no delivery charges for the second restaurant.

Price per pizza = $18

Total cost = 18x

The charge will be the same when

Total cost of first restaurant = Total cost of second restaurant

16x + 8 = 18x

Hence,

a. The total charge for first restaurant (in dollars) = 16x + 8

The total charge for the second restaurant (in dollars) = 18x

b. 16x+8=18x models the equation when the charge would be same for both restaurants.

if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.

No, it is not possible to make two triangles that are not congruent and have three pairs of congruent angles. This is because if two angles of a triangle are congruent, then the third angle must also be congruent by the Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees. If two triangles have three pairs of congruent angles, then all three angles in each triangle are congruent, meaning they have the same measure. However, this does not guarantee that the sides of the triangles are congruent. In order for two triangles to be congruent, they must have the same angle measures as well as the same side lengths. Therefore, if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.

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Answer: 77,850,074

Step-by-step explanation:

Use a calculator when it’s not simple division.

Answer: D is 8

Step-by-step explanation: nothing

Answer:

Step-by-step explanation:

the triangle is a 30º-60º-90º triangle, there's a formula for the sides of this type of triangle which I will attach

x = d

9 = x√3

9/√3 = x

x = 3√3

d = 3√3

Answer: the answer is 48

Step-by-step explanation:

Answer: 48

Step-by-step explanation: A triangles formula is base x height divided by 2, therefore we will do first 8 x 12 which equals 96, and divide by 2, giving us 48.

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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To find the value of f(6), we can use the information given about the function f(x) and its derivative f'(x).The value of f(6) is 44/3.

Given that f'(x) is continuous, we can apply the Fundamental Theorem of Calculus. According to the theorem:

∫[a to b] f '(x) dx = f(b) - f(a)

In this case, we are given that:

∫[1 to 6] 6 f '(x) dx = 16

We can simplify the integral:

6 ∫[1 to 6] f '(x) dx = 16

Since f'(x) is the derivative of f(x), the integral of 6 f '(x) dx is equal to 6 f(x). Therefore, we have:

6 f(6) - 6 f(1) = 16

Substituting the given value f(1) = 12:

6 f(6) - 6(12) = 16

6 f(6) - 72 = 16

Next, we isolate the term with f(6):

6 f(6) = 16 + 72

6 f(6) = 88

Finally, we solve for f(6) by dividing both sides by 6:

f(6) = 88 / 6

f(6) = 44/3

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Answer:

Multiplying polynomials involves applying the rules of exponents and the distributive property to simplify the product. This multiplication can also be illustrated with an area model, and can be useful in modeling real world situations.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Make sure that you combine like terms!

The number of packs of hot dogs bought is 2 packs

The number of packs of hamburgers bought is 4 packs

Let x represent the number of hot dogs bought and y represent the number of hamburgers bought

x + y= 6.........equation 1

2.65x + 6.29y= 30.46.........equation 2

From equation 1

x + y= 6

x= 6 - y

Substitute 6 - y for x in equation 2

2.65(6-y) + 6.29y = 30.46

15.9 - 2.65y  + 6.29y = 30.46

3.64y = 30.46 - 15.9

3.64y= 14.56

y= 14.56/3.64

y= 4

Substitute 4 for y in equation 1

x + y= 6

x + 4= 6

x= 6 - 4

x= 2

Hence 2 packs of hot dogs and 4 packs of hamburgers were bought

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