Need help solving this

Answer:

B) \(x^{2} -16x+64=-21+64\)

Step-by-step explanation:

The first step to completing the square is by dividing "b" by 2, squaring that number, and adding it on both sides. In this case, 16/2 = 8 and 8 squared = 64. In answer choice B, this is correctly added to both sides of the equation.

See the full steps for completing the square below. If you're still stuck on this, I suggest watching the completing the square video on Tutors.com. It is very helpful!

Have a great day!

The value of the triple integral over the solid E lying beneath the paraboloid z=1−x²−y² in the first octant is 1/20. It is evaluated using cylindrical coordinates.

The solid E lies beneath the paraboloid z=1−x²−y² in the first octant, so we can describe it using cylindrical coordinates

x = rcosθ

y = rsinθ

z = z

0 ≤ r ≤ √(1-z)

0 ≤ θ ≤ π/2

0 ≤ z ≤ 1 - r²

Then, the integral becomes

∫θ=0^(π/2) ∫r=0^(√(1-z)) ∫z=0^(1-r²) (r³cos³θ + r⁴cosθsin²θ) dz dr dθ

We can first evaluate the innermost integral with respect to z

∫z=0^(1-r²) (r³cos³θ + r⁴cosθsin²θ) dz = z(r) = (1-r²)(r³cos³θ + r⁴cosθsin²θ)

Then, we integrate this expression over r from 0 to √(1-z)

∫r=0^(√(1-z)) (1-r²)(r³cos³θ + r⁴cosθsin²θ) dr = (1/10)cos³θ - (1/7)cosθsin²θ

Finally, we integrate this expression over θ from 0 to π/2

∫θ=0^(π/2) [(1/10)cos³θ - (1/7)cosθsin²θ] dθ = 1/20

Therefore, the value of the triple integral is 1/20.

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--The given question is incorrect, the correct question is given

" Evaluate ∫∫∫E(x³+xy²)dV, where E is the solid in the first octant that lies beneath the paraboloid z=1−x²−y².

Triple Integrals

The integral of f(x,y,z)

over the region given in Cartesian coordinates as

E={(x,y,z)|a≤x≤b,u₁(x)≤y≤u₂(x),v₁(x,y)≤z≤v₂(x,y)}

is ∬Ef(x,y,z)dV

and evaluated iteratively as

∫ba∫u₂(x)u₁(x)∫v₂(x,y)v₁(x,y)f(x,y,z)dzdydx.

If the region is easier to be described in Cylindrical coordinates,

x=rcosθ,y=rsinθ,z=z,

as

E={(r,θ,z)|θ₁≤θ≤θ₂,g₁(θ)≤r≤g₂(θ),h₁(r,θ)≤z≤h₂(r,θ)}

then the integral is

∫θ₂θ₁∫g₂(θ)g₁(θ)∫h₂(r,θ)h₁(r,θ)r f(r,θ,z)dzdrdθ"--

Answer:

The answer is

Step-by-step explanation:

5m+8n-2(3m-n)

Expand the terms in the bracket

That's

5m + 8n - 6m + 2n

Group like terms

We have

8n + 2n + 5m - 6m

Simplify

The final answer is

10n - m

Hope this helps you

The equivalent operation is: b = (a < 5) ? 12 : (d = 30);

The original if/else statement is:

if (a < 5)

   b = 12;

else

   d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true (i.e., if the value of a is less than 5), then the statement b = 12; is executed. Otherwise, if the condition is false (i.e., if the value of a is greater than or equal to 5), then the statement d = 30; is executed.

The equivalent operation using the conditional (ternary) operator is:

b = (a < 5) ? 12 : d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true, the value 12 is assigned to b. This is indicated by ? in the statement. The : separates the true and false cases.

If the condition is false (i.e., if the value of a is greater than or equal to 5), the value 30 is assigned to d. This is the value assigned after the : in the statement.

The ternary operator statement (a < 5) ? 12 : d = 30; achieves the same outcome as the original if/else statement, providing an alternative way to write the logic based on the condition a < 5.

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Answer:

120 peices of candy

Step-by-step explanation:

24/3

so one peice of candy is 8 cal, then 960/8 equals 120

A sample size of 76 would be required to estimate the population mean with a margin of error of 4 and a 98% level of confidence.

To determine the sample size required to estimate the population mean with a specific margin of error and level of confidence, we can use the formula:

n = (Z * σ / E)²

where

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = standard deviation of the population

E = desired margin of error

here, we have that

the standard deviation (σ) is given as 15,

the margin of error (E) is 4 and

the level of confidence is 98% and For a 98% confidence level, the Z-score is approximately 2.33.

Plugging the values into the formula:

n = (2.33 * 15 / 4)²

n = (8.7375)²

n ≈ 76.34

n = 76

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The equation of the circle centered at (3,5) and passing through point (-2,9) is given by:

(x - 3)² + (y - 5)² = 41.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

For the circle graphed, we have that the circle is at (3,5), hence \(x_0 = 3, y_0 = 5\).

Then:

(x - 3)² + (y - 5)² = r²

The line passes through point (-2,9), that is, when x = -2, y = 9, hence the radius is found as follows:

(x - 3)² + (y - 5)² = r²

r² = (-2 - 3)² + (9 - 4)²

r² = 41.

Hence the equation is:

(x - 3)² + (y - 5)² = 41.

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The probability of getting an Ace is 1/13.

Probability of an event = number of favorable outcomes for the event/number of all possible products.

First, let's calculate the number of all possible outcomes. Randomly picking the cards could result in each of the 52 being selected. So, there are 52 possible outcomes.

But if you want an Ace in your desired event, you have four options—ace of Spades, Ace of Clubs, Ace of Hearts, and Ace of Diamonds. Therefore, the number of favorable outcomes for Aces = 4.

Therefore,

The probability of getting an Ace with a deck of 52 cards = 4/52 = 1/13.

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Answer: i think its 17

Step-by-step explanation:

Answer:

\(\frac{10}{3}\)

Step-by-step explanation:

each circle is composed of 3 sectors

The first 3 are completely shaded representing 3 + 3 + 3 = 9 sectors

the last one has 1 sector of 3 shaded representing  1 sector

sectors shaded = 9 + 1 = 10

improper fraction is then \(\frac{10}{3}\)

Answer:

-2x(6x⁴ - 7x² + x - 5)

= -12x⁵ + 14x³ - 2x² + 10x

Answer:

See screenshot

Step-by-step explanation:

Answer:

I am not completely sure but it should be the first one

Step-by-step explanation:

Answer:

\(t = \frac{3 - 4p}{p + 2}\)

Step-by-step explanation:

Given

\(P = \frac{3 - 2t}{4 + t}\)

Required

Make t the subject

\(P = \frac{3 - 2t}{4 + t}\)

Cross Multiply

\(P * (4 + t) = 3 - 2t\)

\(4p + tp = 3 - 2t\)

Collect Like Terms

\(tp + 2t = 3 - 4p\)

Factorize:

\(t(p+2) = 3 - 4p\)

Make t the subject

\(t = \frac{3 - 4p}{p + 2}\)

The probability that none of the 5 calls reaches a person is 0.32768 for the general case and 0.659081 for the New York City case.

The probability that a call reaches a live person is 0.2, so the probability that a call does not reach a live person is 1 - 0.2 = 0.8.

a) If a telemarketer places 5 calls, the probability that none of them reaches a person is 0.8^5 = 0.32768.

b) When calls are made to New York City, the probability of reaching a person is only 0.08, so the probability of not reaching a person is 1 - 0.08 = 0.92. The probability that none of 5 calls made to New York City reaches a person is 0.92^5 = 0.659081.

Therefore, the probability that none of the 5 calls reaches a person is 0.32768 for the general case and 0.659081 for the New York City case.

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Answer:

she earned a total of 1190 in 5 years. I don't know if this helps.

Step-by-step explanation:

The rate of interest with the given parameters is 6.8%.

Given that, Principal =$3,500, time period =5 years and the amount =$4,690.

We need to find the rate of interest.

The interest rate formula helps in calculating the amount of money to be repaid towards a loan taken and the interest over the investment on fixed deposits, mutual funds, etc. The interest rate formula also helps in calculating the interest on credit cards. The interest rate for a given amount on simple interest can be calculated by the following formula,

Interest Rate = (Simple Interest × 100)/(Principal × Time)

Now, SI=Amount-Principal=4690-3500=1,190

rate of interest=(1,190×100)/(3,500×5)=6.8%

Therefore, the rate of interest with the given parameters is 6.8%.

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Answer:        $8.25 is your answer.

Step-by-step explanation:

12 x 3 = 36

2.75 for 12 so 2.75 times 3 = 8.25

Answer:

$8.25

Explanation:

If 12 eggs cost £2.75,

3 x 12 = 36,

$2.75 x 3 = $8.25.

There would be about 12 pieces of fruit in the bag.

a. Yes, the individual scores can be rediscovered.

b. No, this is not possible with four players because there will not be enough information to solve the equations.

a. Let the individual scores of the three players be a, b, and c respectively. Since we know the total of the scores for players 1 and 2 is x, the total of the scores for players 2 and 3 is y, and the total of the scores for players 3 and 1 is z,

\(a + b = xb + c = yc + a = z2a + 2b + 2c = x + y + zWe can subtract x + y + z from both sides of the equation to get:2a + 2b + 2c - x - y - z = 02(a + b + c) - (x + y + z) = 02*(total of all 3 scores) - (total of 1 & 2 + total of 2 & 3 + total of 3 & 1) = 0a + b + c = (x + y + z)/2Then subtract x and y from both sides a + b - x - y = (z - x - y)/2a = (z - x - y)/2 + x\)

Since we know z, x, and y, we can plug these values in to solve for a. Similarly, we can use the same method to solve for b and c.

b. With three players, there were three equations with three unknowns. With four players, there will be four equations with four unknowns, so the equations will be underdetermined and there will not be enough information to solve them.

Therefore, it is possible to rediscover individual scores in a certain scenario. However, it is not feasible to do so with four players,

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Answer:

y=2x-5

Step-by-step explanation:

first because if a linear equation is graphed to be perpendicular has to have the same slop y=2x which is equivalent to going up two over one on agrao from the +1 point to pass through (3,1) start at the point (3,1) go down two over until you find the y intercept which in this is -5 five so y=2x-5 is the answer.

When the quadrilateral WXYZ is mirrored across the y axis to form the quadrilateral W' X' Y' Z', the coordinates of X' are (-1,6).

When the x value is reflected across the y-axis, it takes on the opposite sign.

A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or even more numbers, or coordinates.

A coordinate system is a framework for specifying the relative locations of objects in a specific area, such as an area here on earth's surface or the entire earth's surface. A geographic coordinate system determines locations on the world by using a three-dimensional spherical surface.

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The other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of  -3/2.

The general equation of a straight line is -

y = mx + c

Given in the question is a equation that describes the one side of a rectangular patio. From the question, we can write -

Equation representing a side of Patio - y = 2/3x + 5/3

If we compare the equation representing a side of Patio with the general equation of line, we get -

y = 2/3 x + 5/3      

[y] = [m] x + [c]

From this we can conclude that -

m = 2/3 = slope of line

c = 5/3 = y - intercept

The patio is in the shape of a rectangle. Therefore, the side opposite to the line of slope → 2/3 will be equal in length and parallel to it. We know, that the slope of two parallel lines are same. So, the slope of line parallel to  y = 2/3x + 5/3  will be 2/3.

The remaining two sides are perpendicular to both the side of slope → 2/3. The remaining sides are also parallel to each other, indicating they both have same slope. The slope of a line perpendicular to a given line (L) is given by -

m [p] x m [L] = -1

m [p] = - 1 / m [L]

m [p] = - 3/2

Therefore, the remaining two sides will have slope of  -3/2.

Therefore, the other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of  -3/2.

[Refer to the graph attached]

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Assuming QF is the full employment equilibrium then in the Figure, if the level of spending is equal to AD1, the AD shortfall would be greater than XZ. The answer is B.

The respective figure as referred in the question is as attached.

Full employment equilibrium refers to the equilibrium where all resources in the economy are fully utilized (employed). Full employment is a situation in which all available labor resources are being used in the most economically efficient way, so there is no cyclical or deficient-demand unemployment.

When the natural rate of unemployment is equal to the unemployment rate, this means the cyclical rate of unemployment is zero. So, when this relationship happens, the economy is considered to be at full employment.

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Answer:

Median: 9

1 3 6 6 9 10 11 12 31

Step-by-step explanation:

To find the median, you have to organize your terms from least to greatest. And then find the center of your terms, which would be 9.

Answer:

Alex has 3x dollars and an extra 15 dollars in his coat pocket. He buys a new Nike shoe for 84 dollars. How much money did Alex spend that was not in his pocket.

Step-by-step explanation:

Answer:

Part A: Word problem

Maria went to the store and purchased some books for her book club. Each book cost $3, and she also bought some bookmarks at $15 each. Maria's total purchase, including tax, amounted to $84. If Maria bought x books, write an equation to represent the situation.

Part B: Solution

To solve the equation 3x + 15 = 84, we need to isolate the variable x on one side of the equation.

Step 1: Subtract 15 from both sides of the equation to eliminate the constant term on the left side:

3x + 15 - 15 = 84 - 15

3x = 69

Step 2: Divide both sides of the equation by 3 to isolate x:

3x/3 = 69/3

x = 23

So, the solution to the equation is x = 23.

Part C: Explanation

In the given equation 3x + 15 = 84, the variable x represents the number of books Maria purchased. The equation states that the cost of x books at $3 each, represented by 3x, plus the cost of $15 for bookmarks, totals to $84. Thus, the value of x represents the number of books Maria bought in this scenario. In the solution, x = 23, it means Maria purchased 23 books for her book club.

Step-by-step explanation:

The triangles can be created with angle measures of 135 degree, 45 degrees, and 10 degrees is b. no triangles.

To create a triangle, the sum of the angle measures must equal 180 degrees. However, the given angle measures of 135 degrees, 45 degrees, and 10 degrees add up to 190 degrees, which is greater than 180 degrees.

Therefore, it is not possible to create a triangle with these angle measures.

Triangle: A geometric figure with three sides and three angles.

Angle: The amount of rotation between two lines that intersect at a common point.

Degrees: A unit of measurement for angles. There are 360 degrees in a circle.

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