Find the average (mean) of the following test scores
83,92,47,78,80
A.76
B.70
C.72
D.83
E.68

The indefinite integral of ∫x√(9 - x²) dx is (1/3)(9 - x²)\(^(3/2)\)+ C.

To evaluate the indefinite integral ∫x√(9 - x²) dx, we can use the substitution method. Let u = 9 - x². Taking the derivative of both sides, du = -2x dx. Rearranging, we have dx = -(1/2x) du.

Substituting these values into the integral, we get ∫x√(9 - x²) dx = ∫-x(1/2x)√(u) du = -1/2 ∫√(u) du.

Now we integrate with respect to u: -1/2 ∫√(u) du = -(1/2)(2/3)(u\(^(3/2)\)) + C = -(1/3)(9 - x²)\(^(3/2)\) + C.

Therefore, the indefinite integral of ∫x√(9 - x²) dx is given by (1/3)(9 - x²)\(^(3/2)\) + C.

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Answer:

8 days

Step-by-step explanation:

it takes her two days to make 8 liters so for every 8 liters you add on two more days. 8:2, 16:4, 24:6, 32:8

Answer:

Angle DFC is complementary to angle BFC

Step-by-step explanation:

AD is a straight line passing line EB. DFE, EFA, AFB and BFD are right angles as the lines are perpendicular.

DFB is divided into 2 angles by the segment FC

therefore

DFC + BFC = 90 degrees

B

Step-by-step explanation:

The answer is B 60 in.^2.

10*12= 120

120/2 = 60

I hope this helps and have a great day!

Answer:

No

Step-by-step explanation:

From the information provided, we can say that he is not correct. This is because the depth of the water is the only measurement that he is using to make his estimate. Comparing the depth of the aquarium and the bucket is one measurement, but both the aquarium and bucket are most likely of different shapes and sizes. Therefore, this equates to more buckets for the same amount of depth in the aquarium. To get a proper estimate on how long it will take he needs to calculate the volume of water in the bucket and compare it to the volume of water needed to fill the aquarium.

Answer:

Step-by-step explanation:

455

Answer:

the answer is 43%

Step-by-step explanation:

The buyer for the retail store ordered 83 dozen pairs of shorts. To determine the total number of pairs of shorts, we need to multiply the number of dozens by 12 buyer ordered 996 pairs of shorts.

To calculate the number of pairs of shorts, we can use the following formula:

Number of pairs of shorts = Number of dozens * 12

In this case, the number of dozens is 83, so substituting it into the formula, we have:

Number of pairs of shorts = 83 * 12

Evaluating the expression, we find:

Number of pairs of shorts = 996

Therefore, the buyer ordered 996 pairs of shorts.

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Answer:

7 feet long

Step-by-step explanation:

This set up will give a right angle triangle where;

Length of the ladder is the hypotenuse = x

The distance of the ladder to the house is the adjacent = 3 feet

Angle of elevation theta = 72 degrees

Using the CAH in trigonometry identity;

cos theta = adjacent/hypotenuse

cos 72 = 3/hyp

hyp = 3/cos72

hyp = 3/0.4258

hyp = 7.05 feet

Hence the ladder is approximately 7 feet long

The Total surface of triangular prism  is 112 inches.

To calculate the surface area of a triangular prism, you need the measurements of the base and the height of the triangular faces, as well as the length of the prism.

The given measurements are;

Base ; 5 inches and  4 inches

height is 8 inches

Length of the prism is 2 inches.

To find the total surface area, we sum up the areas of all the faces:

Total surface area = area of triangular  faces + area of rectangular faces + area of lateral faces.

area of triangular faces = 5 inches × 4 inches = 20 inches.

area of the two faces = 20 ×2 =40

Area rectangular faces = 5 inches × 8 inches/ 2 = 40 inches.

Area of lateral faces = 8 inches ×2 = 16 square inches

for the two lateral faces is 16 × 2 = 32 square inches.

Total surface area = 40 square inches + 40 inches + 32 square inches = 112 square inches.

The Total surface of triangular prism  is 112 inches.

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On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

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Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A.

Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A. This is due to the fact that for any symmetric matrix A, the image (column space) and kernel (null space) are orthogonal subspaces. Since v is in the image of A and w is in the kernel of A, their dot product must be zero, indicating orthogonality.

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Step-by-step explanation:

these angles will add to 90 deg

90 = 22 + 2x

solve for x

Answer:

x = 34°

2x = 68°

Step-by-step explanation:

Both angles are complementary (add up to the sum of 90°), so we can say;

22 + 2x = 90°

2x = 90 - 22

2x = 68

x = 68 / 2

x = 34°

Furthermore:

If you have to find the value of 2x it would be 68, since

2x = 2(34) = 68°

Hope this helps!

Answer:

$10 i think

Step-by-step explanation:

Answer:

first of all i need to know the fractions and answer choices to answer this question.

A two-dimensional form that occupies an area is called a shape.

Shapes can be various types such as rectangles, circles, triangles, and many others, and they are defined by their properties such as sides, angles, and vertices. They are defined by their boundaries or edges and exist within a plane. These forms have dimensions of length and width, but not depth. Shapes play a fundamental role in geometry and are studied extensively in mathematics and art. They can be simple or complex, symmetrical or asymmetrical, and are used to represent objects, patterns, or designs. Whether in the natural world or man-made creations, shapes are integral to our understanding and appreciation of visual compositions.

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Answer:

The theoretical probability of spinning a sum of 9 is 4/36 or 1/9.

Step-by-step explanation:

Answer: 0%

Step-by-step explanation:

The equation x^2 + y^2 + 12x + 4y + 15 = 0 represents a circle with center (-6, -2) and radius 5.

To find the center and radius of the circle represented by the equation x^2 + y^2 + 12x + 4y + 15 = 0, we need to complete the square for both x and y terms. First, we will focus on the x terms:

x^2 + 12x = (x + 6)^2 - 36

Next, we will focus on the y terms:

y^2 + 4y = (y + 2)^2 - 4

Substituting these into the original equation, we get:

(x + 6)^2 - 36 + (y + 2)^2 - 4 + 15 = 0

Simplifying, we get:

(x + 6)^2 + (y + 2)^2 = 25

Comparing this to the standard form of the equation of a circle, (x - h)^2 + (y - k)^2 = r^2, we can see that the center of the circle is (-6, -2) and the radius is √25 = 5..

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Answer:

y=-2(x-1)+6

Step-by-step explanation:

y=m(x-h)+k

y=-2(x-1)+6

Answer:

Step-by-step explanation:

A squiggly line can refer to a variety of different shapes or patterns. To create an equation using cosine that resembles a squiggly line, you can use a combination of sine and cosine functions with different frequencies and amplitudes. Here's an example equation that produces a squiggly pattern:

y = A * cos(B * x) + C * sin(D * x)

In this equation, A, B, C, and D are constants that you can adjust to modify the shape and characteristics of the squiggly line. By experimenting with different values for these constants, you can create various squiggly patterns. Keep in mind that the specific equation may vary depending on the exact shape and features you have in mind for the squiggly line.

Answer:

e

Step-by-step explanation:

8ml x 6= 48ml of oil

3ml x 6= 18ml of vineger

Answer:

the correct answer is B

Step-by-step explanation:

–2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction + 1

Answer:

–2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction + 1 aka B

Step-by-step explanation:

Answer:

"First, work out the difference (decrease) between the two numbers you are comparing. Decrease = Original Number - New Number. Next, divide the decrease by the original number and multiply the answer by 100. % Decrease = Decrease ÷ Original Number × 100. If the answer is a negative number, this is a percentage increase."

Answer:

A.y=|x|+7

Step-by-step explanation:

Answer:

6 quarters and 1 nickel

Step-by-step explanation:

6 quarters each worth 25 cents adding up to 1.50$ and then one nickel adding on .05 $ to get you too 1.55$

Answer:

6 nickels ($0.30)

5 quarters ($1.25)

Step-by-step explanation:

Answer:

There is one solution, x=2

Step-by-step explanation:

1/2x+6=4x-1

subtract 6 from both sides

1/2x=4x-7

subtract 4x from both sides

-7/2x=-7

multiply both sides by 2

-7x=-14

divide both sides by -7

x=2

Answer:

The leading term is 2x^7. Since n is odd and a is positive, the end behavior is down and up.