We want to evaluate the integral X +34 +16 dx, we use the trigonometric substitution X and dx = do and therefore the integrar becomes, in terms or o, de The antiderivative in terms of 8 is (do not forget the absolute value) 1 = + Finally, when we substitute back to the variable x, the antiderivative becomes T Use for the constant of integration

To find the derivative of y = cos(sin(14x-13)), we will use the chain rule.

Let's start by defining two functions:

u = sin(14x-13)
v = cos(u)

We can now apply the chain rule:

dy/dx = dv/du * du/dx

First, let's find dv/du:

dv/du = -sin(u)

Next, let's find du/dx:

du/dx = 14*cos(14x-13)

Now we can put it all together:

dy/dx = dv/du * du/dx
dy/dx = -sin(u) * 14*cos(14x-13)

But we still need to substitute u = sin(14x-13) back in:

dy/dx = -sin(sin(14x-13)) * 14*cos(14x-13)

So the derivative of y = cos(sin(14x-13)) is:

dy/dx = -14*sin(sin(14x-13)) * cos(14x-13)

To find the derivative of the function y = cos(sin(14x - 13)), we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Let u = sin(14x - 13), so y = cos(u). Now we find the derivatives:

1. dy/du = -sin(u)
2. du/dx = 14cos(14x - 13)

Now, using the chain rule, we get:

dy/dx = dy/du × du/dx

dy/dx = -sin(u) × 14cos(14x - 13)

Since u = sin(14x - 13), we can substitute back in:

dy/dx = -sin(sin(14x - 13)) × 14cos(14x - 13)

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The price of the medium pizza without the coupon is approximately $14.74.

To find the original price of the pizza without the coupon, we can use the following formula:

Original Price = Discounted Price / (1 - Discount Percentage)

In this case, the discounted price is $10.32 and the discount percentage is 30% or 0.3. Plugging the values into the formula:

Original Price = $10.32 / (1 - 0.3)

Original Price = $10.32 / 0.7

Original Price ≈ $14.74

So, the price of the medium pizza without the coupon is approximately $14.74.

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The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0

From the question, we have the following parameters that can be used in our computation:

The statement that x = -3

The above value implies that we substitute -3 for x in an inequality and solve for the variable y

Take for instance, we have

y < x + 3

Substitute the known values in the above equation, so, we have the following representation

y < -3 + 3

Evaluate

y < 0

This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0

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Answer:

Length: 22 inches × 3.5 = 77 inches

Width: 10 inches × 3.5 = 35 inches

Answer:

The three equivalent equations are x+1=4, -5+x=-2, and 2+x=5. The x equals 3.

Step-by-step explanation:

The scale factor used in the dilation of the triangles is 1/2

From the question, we have the following parameters that can be used in our computation:

The scale factor is calculated as

Scale factor  = X'/X

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (4, 1)/(8, 2)

Evaluate

Scale factor = 1/2

Hence, the scale factor is 1/2

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The equation of the circle in this problem is given as follows:

x² + y² = 49.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle. As this distance is of 7 units, it is then given as follows:

r = 7 -> r² = 49.

The center of the circle is at the origin, hence:

[tex](x_0, y_0) = (0,0)[/tex]

Thus the equation of the circle is given as follows:

x² + y² = 49.

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The volume of foam in the model is approximately 27,211.5 cubic centimeters

The radius of the circular base can be found by dividing the diameter by 2:

radius = diameter / 2 = 48 cm / 2 = 24 cm

The formula for the volume of a cone is:

V = (1/3) * π * r² * h

where π is approximately 3.14, r is the radius of the circular base, and h is the height of the cone.

Substituting the values we have:

V = (1/3) * 3.14 * 24² * 12

V = 27,211.52 cm³

Rounding this to the nearest tenth, we get:

V ≈ 27,211.5 cm³

Therefore, the volume of foam in the model is approximately 27,211.5 cubic centimeters

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Answer:

Step-by-step explanation:

5 6 7

The most responsible choice for Nick regarding his birthday money would be option C, which is to use all the money to pay down his credit card debt.

This is because credit card debt  generally comes with high- interest rates, and it can be  grueling  to pay off the debt if the interest keeps adding up. By using the$ 500 to pay down his credit card debt, Nick can reduce the  quantum he owes and, as a result, pay  lower interest in the long run.   Options A and D suggest  unyoking the  plutocrat between paying down debt and investing/ saving, which may not be the stylish choice given Nick's current  fiscal situation.

Option B suggests putting all the  plutocrat into a savings  regard with a lower interest rate, which would not be as effective in reducing his credit card debt. thus, option C is the most responsible choice for Nick.

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probability that Regina plays tennis and/or basketball during her 8th grade year at Redland Municipal Middle School, we first need to know the total number of sports offered and the number of students participating in each sport. However, based on the information provided in your question, we do not have sufficient data to determine the probability.

In general, to determine the probability, we would follow these steps:

1. Determine the total number of sports offered at the school (let's call this S).
2. Find out the number of students participating in tennis (T) and basketball (B).
3. Calculate the probability of Regina playing tennis (P_T) by dividing T by S.

4. Calculate the probability of Regina playing basketball (P_B) by dividing B by S.
5. Use the formula P(T or B) = P_T + P_B - P(T and B) to calculate the probability that Regina plays tennis and/or basketball. Here, P(T and B) is the probability of her playing both sports.

Without the specific numbers, we cannot provide a precise probability. Please provide more details about the sports and participation at Redland Municipal Middle School to help us calculate the probability accurately.

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The expression to find the number of events is: (1 event) / (1/8 side) = (n events) / (1/4 sides).

Devonte is studying for a history test and uses 1/8 of a side of one sheet of paper to write notes for each history event. He fills 2 full sides of one sheet of paper. To find out how many events he wrote notes for, you can set up an expression using the given information.

Since Devonte uses 1/8 of a side for each event, and he fills 2 sides, you can calculate the total amount of space he used by multiplying the fractions: (1/8) * 2. This simplifies to 2/8 or 1/4. Now, you can set up a proportion to find the number of events (n) that Devonte wrote notes for:

(1 event) / (1/8 side) = (n events) / (1/4 sides)

Cross-multiply to solve for n:

1 * (1/4) = n * (1/8)

1/4 = n/8

To find n, multiply both sides by 8:

(8) * (1/4) = n

2 = n

So, Devonte wrote notes for 2 history events using the 2 full sides of one sheet of paper. The expression to find the number of events is: (1 event) / (1/8 side) = (n events) / (1/4 sides).

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Complete Question:

Devonte is studying for a history test. He uses 1/8 of a side of one sheet of paper to write notes for each history event. He fills 2 full sides of one sheet of paper. Which expression could be used to find how many events Devonte makes notes for?

The measure of angle ABC is 30 degrees.

To find the measure of angle ABC, we need to use the fact that the sum of angles in a triangle is always 180 degrees. Since we know that angle ABD is a right angle (90 degrees) and angle CBD is 60 degrees, we can find the measure of angle ABC as follows:

angle ABD + angle CBD + angle ABC = 180 degrees

Substituting the given values, we get:

90 degrees + 60 degrees + angle ABC = 180 degrees

Simplifying, we get:

150 degrees + angle ABC = 180 degrees

Now we can solve for angle ABC by subtracting 150 degrees from both sides:

angle ABC = 180 degrees - 150 degrees

angle ABC = 30 degrees

Therefore, angle ABC measures 30 degrees.

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The cost of a similar carpet in the client's bedroom is $225 when the area of the bedroom is 120  square feet.

Given Data:

Cost of Carpet = $576

length of office room =  16

Width of office room = 19.2

length of Bedroom = 12

Width of Bedroom = 10

We need to determine the area of the office and the bedroom. we can determine it by using the Area of a rectangle formula which is given as,

Area of a rectangle = length × width

Area of Office  = length  of office room × width of office room

= 16 × 19.2

= 307.2 square feet

Area of Bedroom = length of Bedroom × width of Bedroom

= 12 × 10

= 120  square feet

Therefore, the area of the office is 307.2 square feet, and the area of the Bedroom is 120  square feet.

From the above data, the area of the office is 307.2 square feet and the carpet will cost $576 for the office. we need to find the cost of the carpet for the 120 square feet bedroom, let's assume the cost as x, and cross multiply we get,

x = 120 × 576 / 307.2

x = 69120 / 307.2

x = $225

Therefore, the cost of the bedroom carpet is $225.

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Answer:

[tex]-2a^{4}b^{6} c^{3}[/tex]

Step-by-step explanation:

(2a² b c³) (-a² b⁵)

distribute amongst each other

-2a²bc³a²b⁵

rearrange

-2a²a²bb⁵c³

combine like terms

[tex]-2a^{4}b^{6} c^{3}[/tex]

Hope this helps!

Answer:  -2[tex]a^{4}[/tex][tex]b^{6}[/tex]c³  

Step-by-step explanation:

Given:

(2a² b c³) (-a² b⁵)

Rules:

>Multiply numbers first

>If a number with an exponent is multiplied to another, you can combine if the bases are the same(lower number)  

>If they have the same base, you can add the exponents

Solution:

(2a² b c³) (-a² b⁵)       >multiply the - and 2

-2(a² b c³) (a² b⁵)      > combine the a's by adding the expnents 2+2

-2[tex]a^{4}[/tex]( b c³) ( b⁵)           > combine b, there is an invisible 1 by the first b 1+5

-2[tex]a^{4}[/tex][tex]b^{6}[/tex]c³                   >c stays as is because nothing to combine with

The surface area of Dante's tent is approximately 180 square feet.

To find the surface area of Dante's tent, we need to find the area of each of its faces and then add them up. Since the tent is in the shape of a triangular prism, it has three rectangular faces and two triangular faces.

First, let's find the area of each rectangular face. We know that the tent is 8 feet long and 4.3 feet tall. To find the width of each face, we need to use the Pythagorean theorem since the base of the tent is equilateral. So, we can use a triangle with sides of 5 feet (the base of the tent) and 4.3 feet (the height of the triangular face) to find the width of each rectangular face.

a^2 + b^2 = c^2
5^2 + 4.3^2 = c^2
25 + 18.49 = c^2
43.49 = c^2
c = √43.49
c ≈ 6.6 feet

Now that we know the width of each rectangular face, we can find the area of each face:

Area of rectangular face = length x width
Area of rectangular face = 8 x 6.6
Area of rectangular face ≈ 52.8 square feet

Next, let's find the area of each triangular face. Since the base of the tent is equilateral, each triangular face has a base of 5 feet and a height of 4.3 feet. The area of each triangular face is:

Area of triangular face = (base x height) / 2
Area of triangular face = (5 x 4.3) / 2
Area of triangular face ≈ 10.8 square feet

Now we can add up the areas of all five faces to find the total surface area of the tent:

Surface area of tent = 3 x area of rectangular face + 2 x area of triangular face
Surface area of tent = 3 x 52.8 + 2 x 10.8
Surface area of tent = 158.4 + 21.6
Surface area of tent ≈ 180 square feet

Therefore, the surface area of Dante's tent is approximately 180 square feet.

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Answer:

22.25

Step-by-step explanation:

8x+ (11*2)=200

first, multiply 11 and 2 =22

that leaves 8x+22=200

so now let's subtract the 22 from both sides

8x=178 now divide the 8

x= 22.25 so that is the most the jackets could have cost

The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.

We can use trigonometry to find the x and y components.

x3 = 12 * cos(15°) ≈ 11.59 km (east)

y3 = -12 * sin(15°) ≈ -3.10 km (south, hence the negative sign)

Leg #4: 14 km [South]

x4 = 0 km (no east/west movement)

y4 = -14 km (south, hence the negative sign)

Now, let's find the total x and y displacements:

x_total = x1 + x2 + x3 + x4 ≈ 0 + 10 + 11.59 + 0 ≈ 21.59 km

y_total = y1 + y2 + y3 + y4 ≈ 8 + 0 - 3.10 - 14 ≈ -9.10 km

Now, we can find the distance and direction he needs to ride to get back to the starting point:

Distance=  

[tex]\sqrt{21.59^2 + (-9.10)^2}[/tex])

23.21 km

Direction:

angle =

arctan(9.10 / 21.59)

= 23.13°

The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.

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The number 71.38 can be written in word form as "seventy-one and thirty-eight hundredths." The correct answer is option D.

In decimal notation, the number 71.38 can be broken down into its whole number and decimal parts. The whole number part is 71, and the decimal part is 0.38.

In a decimal number, the digits to the right of the decimal point represent fractions of a whole. Each digit to the right of the decimal point has a place value that is a power of 10.

In word form, the decimal part 0.38 is read as "thirty-eight hundredths." Therefore, when combined with the whole number 71, the correct word form is "Seventy-one and thirty-eight hundredths."

Therefore option D is the correct answer.

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Answer:

360 cubes

Step-by-step explanation:

Answer: -403

Step-by-step explanation:

Answer:

147 mm^2

Step-by-step explanation: The surface area has to be more, but not double the smaller figures surface area therefore the answer is 147 mm^2

The requried surface area of the larger solid is approximately 147 mm². Option A is correct.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Let's call the larger solid's surface area S.

Since the two solids are similar, their volumes have a ratio of (side length)³. Let's call the ratio of the side lengths of the larger to the smaller solid as k. Then:

[tex](k^3)(540 mm^3) = 857.5 mm^3[/tex]

Simplifying the above equation, we get:

[tex]k = (857.5/540)^{(1/3)}[/tex] =7/6

So, the larger solid is about 7/6=1.183 times bigger than the smaller solid in terms of side length. Since the surface area has a ratio of [tex](side length)^2[/tex], we can find the surface area of the larger solid by:

[tex]S = (1.183^2)(108 mm^2) \approx 147 mm^2[/tex]

Therefore, the surface area of the larger solid is approximately 147 mm². Answer: A.

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The weight of the heaviest 20% of fruits can be estimated using the z-score corresponding to the 80th percentile, which is 0.84.

The weight can be calculated by adding the z-score multiplied by the standard deviation to the mean weight. Therefore, the weight of the heaviest 20% of fruits is approximately 405 grams.

To calculate this, we first need to find the z-score for the 80th percentile, which is 0.84. Then, we can use the formula z = (x - mu) / sigma, where x is the weight we want to find, mu is the mean weight, and sigma is the standard deviation.

Rearranging this formula to solve for x, we get x = z * sigma + mu. Plugging in the values we have, we get x = 0.84 * 20 + 374 = 405.2 grams. Rounding this to the nearest gram, we get the answer of 405 grams.

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The probability of selecting an Ace, not replacing it, and then selecting a King is 4/663 or approximately 0.006 or 0.6%.

The probability of selecting an Ace, not replacing it, and then selecting a King can be calculated using the rules of conditional probability.

First, we need to determine the probability of selecting an Ace from a standard deck of 52 cards. There are four Aces in the deck, so the probability of selecting an Ace is 4/52, which can be simplified to 1/13.

Next, we need to consider the fact that the Ace is not replaced before selecting the King. This means that the deck now contains 51 cards, with only three remaining Aces. Therefore, the probability of selecting a King after selecting an Ace without replacement is 4/51.

To determine the overall probability of selecting an Ace and then a King, we multiply the probability of selecting an Ace (1/13) by the probability of selecting a King after selecting an Ace without replacement (4/51).

The calculation is as follows:

(1/13) x (4/51) = 4/663

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The volume of the pool can be calculated as:

Volume = length x width x height

Volume = 10 ft x 20 ft x 5 ft

Volume = 1000 cubic feet

The mass of the water in the pool can be calculated as:

Mass = Volume x Density

Mass = 1000 cubic feet x 60 pounds/cubic foot

Mass = 60,000 pounds

Therefore, the approximate mass of water in the pool is 60,000 lb , which corresponds to option D.

The reasonable amount of weight of his cargo Mr. Jackers while transporting a giraffe from one zoo to another is 1 ton and 2 tons. Options C and D are correct.

To arrive at a reasonable estimate, we can consider the average weight of a giraffe, which ranges between 2,600 lbs and 4,250 lbs for adult males and females, respectively.

Therefore, a reasonable amount for the weight of Mr. Jackers' cargo would be between 2,600 lbs and 4,250 lbs, which translates to either 1 ton or 2 tons.

Thus, options c and d are the only reasonable answers, with d (2 tons) being the safer choice.

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