What is the surface area of a sphere with a radius of 13 units?
OA. 676 units²
OB. 1014 units²
OC. 845 units²
OD. 507 units²

A factorization of the quadratic function 81x² - 36x + 4 is (9x - 2)².

First of all, we would rearrange the given quadratic function as follows;

4 - 36x + 81x²

81x² - 36x + 4

By using the sum-product pattern, we have the following:

81x² - 18x - 18x + 4

By writing the common factor from the two pairs, we have the following:

(81x² - 18x) + (-18x + 4)

9x(9x - 2) - 2(9x - 2)

By rewriting in factored form, we have the following:

(9x - 2)(9x - 2)

Lastly, we would combine to a square as follows;

81x² - 36x + 4 = (9x - 2)².

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Complete Question:

Factorize each of the following expressions completely.

(a) 4 - 36x + 81x²

Answer:

A) It wasalso claimed by the country of Spain.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

5 1/4 =5.25

42/5.25 = 8

8×5.25 = 42

Answer:

5 1/4 of 800 is 42

Step-by-step explanation:

Change 5 1/4 into a decimal = .0525

(.0525)x =42

divide both sides by 0.0525:

x = 42 / .0525

x = 800

5¼% of 800 is 42

For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June

Mean = sum of data / Number of data

The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,

Only the top 200200200 longest streaks worldwide in June will win.

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An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

r=-4

Step-by-step explanation:

\(gradient = \frac{change \: in \: y}{change \: in \: x} \\ - 5 = \frac{r - - 9}{6 - 7} \\ - 5 = \frac{r + 9}{ - 1} \\ - 5 \times - 1 = r + 9 \\ 5 = r + 9 \\ 5 - 9 = r \\ r = - 4\)

Hope that this is helpful.

Answer:

Step-by-step explanation:

sin A = \(\frac{a}{c}\)

sin 9.4° = \(\frac{20.5}{c}\) ⇒ c = (20.5) / (sin 9.4°) ≈ 125.52

tan A = \(\frac{a}{b}\)

tan 9.4° = \(\frac{20.5}{b}\) ⇒ b = (20.5) / (tan9.4°) ≈ 123.83

m∠B = 90° - 9.4° = 80.6°

m∠C = 90°

Part 1: An increase in the price of fertilizer per pound will affect the supply curve for avocados.

The supply function for avocados is given by Q = 58 + 15p - 20pf, where p is the price of avocados and pf is the price of fertilizer. When the price of fertilizer rises by $1.60 per pound, it means that the value of pf in the supply function increases by $1.60. Consequently, the equation for the new supply curve becomes Q = 58 + 15p - 20(pf + 1.60). This adjustment reflects the decrease in supply resulting from the higher cost of production due to the increased fertilizer price.

Part 2: To determine how the supply of avocados changes in response to the price increase of $1.60 per pound of fertilizer, we need to evaluate the change in quantity supplied (ΔQ) at each price level. By substituting the new value of pf = original pf + $1.60 into the supply function, we can find the difference in quantity supplied.

For example, if the supply of avocados at a particular price was initially Q1, the new supply with the increased fertilizer price would be Q2. The change in supply can be calculated as ΔQ = Q2 - Q1, expressed in avocados per month. This value will indicate the magnitude and direction of the supply shift resulting from the change in fertilizer price.

The supply curve for avocados is influenced by the cost of production, including the price of inputs like fertilizer. When the price of fertilizer increases, it directly affects the production costs for avocado growers. The supply function reflects this relationship by incorporating the price of fertilizer (pf) as a factor.

As the price of fertilizer per pound rises, the term -20pf in the supply equation causes a decrease in the quantity supplied at each price level. This implies a leftward shift of the supply curve, indicating a reduction in the overall supply of avocados in the market. The magnitude of the shift can be determined by calculating the change in quantity supplied (ΔQ) using the new value of the fertilizer price. The supply curve is dynamic and changes in input prices can lead to significant shifts in the quantity of avocados supplied.

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Answer:

9.553×10^-26

Step-by-step explanation:

m= 9.1 ×10 ^-31

v = 3 × 108

= ( 9 .1 × 10 ^- 31) × ( 3 × 108 ) ^2

= 9 .552816 × 10 ^ -26

approximately

9.553×10 ^26

To find the number of people who like all three fruits, we can use the principle of inclusion-exclusion.In a group of 6 people, 45 like apples, 30 like bananas, and 15 like oranges.

The total number of people who like only two fruits is 22, and they like at least one of the fruits.

Let's break it down:
- The number of people who like apples only is 45 - 22 = 23.
- The number of people who like bananas only is 30 - 22 = 8.
- The number of people who like oranges only is 15 - 22 = 0 (since there are no people who like only oranges).
To find the number of people who like all three fruits, we need to subtract the number of people who like only one fruit from the total number of people in the group:

6 - (23 + 8 + 0)

= 6 - 31

= -25.
Since we can't have a negative number of people, there must be an error in the given information or the calculations. Please check the data provided and try again.

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There are no people in the group who like all three fruits. In a group of 6 people, 45 like apples, 30 like bananas, and 15 like oranges. We need to find the number of people who like all three fruits. To solve this, we can use a formula called the inclusion-exclusion principle.

This principle helps us calculate the number of elements that belong to at least one of the given sets.

Let's break it down:

1. Start by adding the number of people who like each individual fruit:
  - 45 people like apples
  - 30 people like bananas
  - 15 people like oranges

2. Next, subtract the number of people who like exactly two fruits. We know that there are 22 people who fall into this category, and they also like at least one of the fruits.

3. Finally, add the number of people who like all three fruits. Let's denote this number as "x".

Using the inclusion-exclusion principle, we can set up the following equation:

    45 + 30 + 15 - 22 + x = 6

Simplifying the equation, we get:

    68 + x = 6

Subtracting 68 from both sides, we find that:

    x = -62

Since the number of people cannot be negative, we can conclude that there are no people who like all three fruits.

In conclusion, there are no people in the group who like all three fruits.

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SOLUTION:

Case: Parallelograms

Method:

Sketch the parallelogram

The angles mHence the angle J is 45 degrees

The angles mHowever,

Final answers:

1. J= 45 degrees {Opposite angles are equal in a parallelogram}

2. K= 135 degrees {Adjacent angles sum up to 180 degrees in a parallelogram}

Step-by-step explanation:

we see here :

when ordering 0 shirts, it costs about $10 basic price, that will always be added, no matter how many shirts are ordered.

then we look at the points directly at gridline intersections (we don't need to guess about the values).

we see, 20 shirts cost $50.

and 120 shirts cost $250.

if we consider the $10 basic fee and deduct it from the price, we see that 20 shirts cost shirt-specific $40 and 120 shirts $240. we see a 1:2 relationship.

so, the equation is seemingly

cost(x) = y = 2x + 10

so, 100 shirts cost

cost(100) = 2×100 + 10 = $210

the ordered pair is (x, y) = (100, 210)

Answer:

4,100

Step-by-step explanation:

1000+1000+1000+1030=4030

20+20+30=70

4030+70=4100

Answer:

Well add them up and you get 4100

The area of the surface is 8π.

Given, r(s, t) = (t sinh(s), t cosh(s), t)

Taking partial derivative with respect to s

\(\frac{\hat{a}r}{\hat{a}s}\) = (t cosh(s), t sinh(s), 0)

Taking partial derivative with respect to t

\(\frac{\hat{a}r}{\hat{a}t}\) = ( sinh(s), cosh(s), 1)

The cross product of these partial derivatives is given by

\(|\frac{\hat{a}r}{\hat{a}s} \times\frac{\hat{a}r}{\hat{a}t} |\) = | (t sinh(s), t cosh(s), t)|

= t √(sinh²(s) + cosh²(s) + 1)

= t √(cosh²(s) - 1 + 1)

= t cosh(s)

So, the area of the surface is given by the integral:

A = ∫∫\(|\frac{\hat{a}r}{\hat{a}s} \times\frac{\hat{a}r}{\hat{a}t} |\) ds dt

= 2 Ï \(\hat{a_0}^{\hat{a} tcosh(s)ds}\)

(Integrating over s)

= 2 Ï \(\hat{a_0}^{\hat{a} t(\frac{e^s+e^{-s}}{2} ) ds}\)

=  2 Ï \(\hat{a_0}^{\hat{a} \frac{t}{2} (e^s+e^{-s}) ds}\)

= 2 Ï \([\frac{t}{2}e^s]_0^\hat{a}\)

= 2π (∞ - 0)

= 8π

Therefore, the area of the surface is 8π.

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Answer:

should be acute

Step-by-step explanation:

hypotenuse is smaller than both sides combined

Answer:

a Hitachi 50 plasma tv at 495 per month for 6

The angle between the two planes with normals 1=⟨1,0,1⟩ and 2=⟨8,9,5⟩ is approximately 32.9 degrees.

To find the angle between two planes with normal vectors, we can take the dot product of the two vectors and divide it by the product of their magnitudes. The result of this calculation gives us the cosine of the angle between the planes.

Taking the inverse cosine of this value gives us the angle in radians, which can then be converted to degrees. In this case, the normal vectors are 1=⟨1,0,1⟩ and 2=⟨8,9,5⟩, and the angle between their corresponding planes is approximately 32.9 degrees.

Understanding the dot product and its applications is essential in many areas of mathematics and physics, as it allows us to solve problems related to angles, distances, and projections.

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Answer:

If A is the distance from the center of the dilation to a vertex of the pre-image, and B is the distance from the center of the dilation to the corresponding vertex on the image, then B/A is the scale factor of the dilation.

Step-by-step explanation:

The rule about the distance from the center of dilation to the vertices of the pre-image and image is \((x,y) \to (kx,ky)\)

Dilation involves changing the size of a shape.

Assume the image is shape B, and the pre-image is shape A

The scale factor would be to divide the side length of the image, by the corresponding side length of the pre-image

So, the scale factor (k) is:

\(k = \frac BA\)

Hence, the rule of dilation is:

\((x,y) \to (kx,ky)\)

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The prime factorization of 64 :

64 divided by 2 = 32

32 divided by 2 = 16

16 divided by 2 = 8

8 divided by 2 = 4

4 divided by 2 = 2

2 divided by 2 = 1

So,

64 = 2 x 2 x 2 x 2 x 2 x 2

Question options :

a. They should be between 64 and 76 inches tall.

b. They should be close to the height that is 95% of the mean. That is, 66.5 inches, plus or minus 2 standard deviations.

c. They should be at or below the 95th percentile, which is 74.92 inches.

d. None of the above.

Answer: a. They should be between 64 and 76 inches tall.

Step-by-step explanation:

Given the following :

Assume men's height follow a normal curve ; and :

Mean height = 70 inches

Standard deviation= 3 inches

According to the empirical rule ;

Assuming a normal distribution with x being random variables ;

About 68% of x-values lie between -1 to 1 standard deviation of the mean. With about 95% of the x values lying between - 2 and +2 standard deviation of mean. With 99.7% falling between - 3 to 3 standard deviations from the mean.

Using the empirical rule :

95% will fall between + or - 2 standard deviation of the mean.

Lower limit = - 2(3) = - 6

Upper limit = 2(3) = 6

(-6+mean) and (+6+ mean)

(-6 + 70) and (6+70)

64 and 76

The range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches

According to the given data

The mean height for adult males in the U.S. is about 70 inches

The standard deviation of heights is about 3 inches.

Considering the data to be normally distributed

According  to the empirical rule for normal distribution we can write that

95.45% of the data lies with in the range of

\(\rm \mu - 2\sigma \; to \; \mu +2\sigma\\\\where \\\mu = Mean\\\sigma = Standard \; deviation\)

We have to to determine that  using the Empirical Rule 95% of adult males should fall into what height range

According to the given data

\(\rm \mu = 70\\\rm \sigma = 3 \\\)

\(\rm Lower \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 - 2(3) = 64\)

\(\rm Upper \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 +2(3) = 76\)

So we can conclude that the range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches

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a)The individual in this scenario is the person thinking about purchasing a cell phone.

b. The variables that are categorical are whether the plan includes access to the internet and the required length of the service contract.

c. The variables that are quantitative are the cost of the phone itself and the average cost per month.

a. The individuals are the major service providers in the area that the person contacted to obtain information about the cost of the phone, length of the service contract, internet access, and average monthly cost.

b. The categorical variables are whether the plan includes access to the internet and the length of the service contract. These variables are not numerical in nature and cannot be measured in terms of quantity.

c. The quantitative variables are the cost of the phone itself and the average cost per month. These variables are numerical in nature and can be measured in terms of quantity, such as dollars or euros.

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Answer:

The probility is hight .

Step-by-step explanation:

because there are more pennies then quarters so there's about a 85 to 75% chance

Answer: x + 1

Hope this helps :)

Answer:

x+1

Step-by-step explanation:

I hope you have a merry christmas!

The correlation coefficient, denoted by r, measures the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

The formula for the correlation coefficient r between two variables x and y is:

r = Cov(x, y) / (sqrt(Var(x)) * sqrt(Var(y)))

where Cov(x, y) is the covariance between x and y, Var(x) is the variance of x, and Var(y) is the variance of y.

Using the given information, we can substitute the values into the formula to get:

r = -50 / (sqrt(36) * sqrt(81))

r = -50 / (6 * 9)

r = -50 / 54

r = -25/27

Therefore, the correlation between x and y is -25/27. This indicates a strong negative linear relationship between the two variables.

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The solution to the system of given linear equations is x = 0 and y = 2.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

The system of equations is given in the question, as follows:

2x + 2y = 4  .....(i)

8x - 2y = -4  .....(ii)

To eliminate y, add the two equations together:

2x + 8x = 4 - 4

10x = 0

Solve for x:

x = 0

Now that we have x, we can substitute it back into one of the original equations to find y:

2x + 2y = 4

2(0) + 2y = 4

2y = 4

y = 4/2

y = 2

Thus, the solution is x = 0 and y = 2.

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The firm's optimal quantity, price, and profit can be determined using two methods. Firstly, by using the profit and marginal profit equations, and secondly, by setting marginal revenue (MR) equal to marginal cost (MC).

The inverse demand curve is given by P = 120 - 0.5Q, and the cost equation is C = 420 + 60Q + Q^2.Using the profit and marginal profit equations, we can start by calculating the total revenue (TR) by multiplying the price (P) by the quantity (Q): TR = P * Q. To find the optimal quantity, we differentiate TR with respect to Q and set it equal to zero.

The resulting value of Q is the optimal quantity. Once we have the optimal quantity, we can substitute it into the inverse demand curve to find the corresponding price. Finally, we can calculate the total cost (TC) +by substituting the optimal quantity into the cost equation. Subtracting TC from TR gives us the profit.

On the other hand, setting MR equal to MC involves differentiating the total revenue with respect to Q to find the marginal revenue (MR). Then, we differentiate the cost equation to find the marginal cost (MC). By setting MR equal to MC, we can solve for Q, which gives us the optimal quantity. Similarly, we can substitute the optimal quantity into the inverse demand curve to find the price, and calculate the profit as TR minus TC.

To graphically represent the marginal revenue and marginal cost, we plot them on the same graph with quantity (Q) on the x-axis and price (P) on the y-axis. The MR curve will have the same intercept as the inverse demand curve, but with twice the slope. The MC curve will be obtained by differentiating the cost equation with respect to Q. The optimal quantity is where the MR curve intersects the MC curve.

In the case where the firm can sell its output at a fixed market price of P = 120, the optimal output is simply the quantity that maximizes the firm's profit. We can find this by substituting the fixed price into the cost equation and differentiating it to find the marginal cost. By setting the marginal cost equal to zero, we can solve for the optimal output.

In summary, the firm's optimal quantity, price, and profit can be determined by using the profit and marginal profit equations or by setting MR equal to MC. Graphically, the intersection of the MR and MC curves represents the optimal quantity. When the firm can sell its output at a fixed market price, the optimal output is obtained by setting the marginal cost equal to zero.

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Answer: x ≥ $5

Step-by-step explanation:

Given expression

1500 + 200x ≥ 2500

Subtract 1500 on both sides

1500 + 200x - 1500 ≥ 2500 - 1500

200x ≥ 1000

Divide 200 on both sides

200x / 200 ≥ 1000 / 200

\(\boxed{x\geq 5}\)

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29,060,000

When writing this out, it is important to make sure you include the commas and the exact amount of zero's by the way.

Answer:29,060,000

Step-by-step explanation:

with every three zeros your number grows bigger 100,00= One hundred thousand. 29,000,000 = thwenty-nine million

Answer:

SAS, because vertical angles are congruent.

A C - chart is used for Number of defects per unit.

What is C - chart?

In statistical quality control, the c-chart is a sort of control chart used to track "count"-type data, often the total number of nonconformities per unit. On rare occasions, it is also used to keep track of all the events that take place in a given period of time.

C-charts are used to assess if a process is predictable and stable as well as to track the results of process improvements before and after they have been made. The C - chart is particularly useful when there are few actual flaws in the subgroup but many potential for defects exist.

Count type data, such as the number of non-conformities per unit, are monitored using a statistical quality control chart known as a C-Chart.

Hence, a C - chart is used for Number of defects per unit.

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