Calculator A circle has a radius of 4 ft. What is the area of the sector formed by a central angle measuring 260°? Use 3.14 for pi. Enter your answer, rounded to the nearest tenth in the box. ft² 3 4 5 6​

The value of x in the equation 1.5(4)²ˣ is equal to 12 is 3/4 after equation the power of same base.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an equation:

⇒ 1.5(4)²ˣ is equal to 12

Now, We can simplify as;

⇒ 1.5(4)²ˣ is equal to 12

⇒ 1.5(4)²ˣ = 12

⇒ (4)²ˣ = 12/1.5

⇒ (4)²ˣ = 8

⇒ (2²)²ˣ = 2³

⇒ 2⁴ˣ = 2³

By comparing,

⇒ 4x = 3

⇒ x = 3 / 4

Thus, the value of x in the equation 1.5(4)²ˣ is equal to 12 is 3/4 after equation the power of same base.

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The x- and y-intercepts of the graph are:

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

-4x + 2y = 28.

For the x-intercepts, we set y to 0

So, we have

-4x = 28

Evaluate

x = -7

For the y-intercepts, we set x to 0

So, we have

2y = 28

Evaluate

y = 14

Hence, the x- and y-intercepts of the graph are -7 and 14, respectively

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Answer:

56 inches

Step-by-step explanation:

The aspect ratio of a TV in elementary terms is width/height expressed as a ratio. A 4:3 aspect ratio means that the width:height is 4:3

The size of a TV is the diagonal measure of the TV

For the given TV we are given that the size is 70 inches. This means the diagonal is 70 inches in length

If we let W = width and H = height of TV
Aspect ratio 4:3 means W/H = 4/3

H = 3W/4  (height:width = 3:4)

The diagonal D can be calculated from the width and length of the TV using the Pythagorean theorem

D² = W² + H²

Substitute H = 3W/4

D² = W² + (3W/4)²
D² = W² + 9W²/16
D² = (16W² + 9W²)/16
D² = 25W²/16

D = √(25W²/16) = 5W/4
W= 4D/5

Given D = 70 inches
W = (4 x 70)/5
W = 280/5
W = 56 inches

A. The comparison of the periods using the five number summary are

B. The box and whisker plot of the periods is attached

The readings of the periods are given as

The distributions of the periods will be compared using the five-number summaries. This is because the five-number summaries give the following statistical measurements

For the 7th Period, the summaries are

For the 3rd Period, the summaries are

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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Leslie and Colton made in total are Leslie's total earnings: Revenue from sales + Tips = 20s dollars + $15,Colton's total earnings: Revenue from sales + Tips = 30s dollars + $25.

To find out how much Leslie and Colton made in total, we need to determine the revenue from selling cups of strawberry lemonade and the amount they earned in tips separately.

Let's start by calculating the revenue from selling cups of strawberry lemonade:

Leslie sold 20 cups, and Colton sold 30 cups. Since they both sold the same product at the same price, we can assume that the price per cup is s dollars.

Revenue from Leslie's sales: 20 cups * s dollars per cup = 20s dollars

Revenue from Colton's sales: 30 cups * s dollars per cup = 30s dollars

Next, let's calculate the amount they earned in tips:

Leslie made an additional $15 in tips.

Colton made an additional $25 in tips.

Now we can calculate the total earnings for Leslie and Colton:

Leslie's total earnings: Revenue from sales + Tips = 20s dollars + $15

Colton's total earnings: Revenue from sales + Tips = 30s dollars + $25

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Answer:

First, we arrange the values in ascending order. Given that the data set has 9 values, the median represents the middle value when the values are arranged in order.

In this case, the least value is 8 and the greatest value is 20. To find the median, we need to determine the middle value. Since there are an odd number of values (9), the median will be the value at the (9 + 1) / 2 = 5th position.

Arranging the values in ascending order: 8, x, x, x, 11, x, x, x, 20

From the given information, we know that the median is 11. Therefore, the middle value must be 11.

Arranging the values again: 8, x, x, x, 11, x, x, x, 20

Since the median is the middle value, the remaining values can be any numbers as long as they are greater than or equal to 8 and less than or equal to 20. There is no unique solution for the remaining values in the data set, as long as the conditions are met.
Here are some possible data sets that satisfy the given conditions:

There are many other possible data sets that satisfy the given conditions.

Farmers, like anyone else, may need to visit a drugstore for various reasons. One reason could be to obtain prescription medications if they fall ill or get injured. Additionally, over-the-counter medicines for minor ailments such as headaches, colds, and stomachaches can be found there. In addition, farmers may need to purchase first aid supplies like bandages, antibiotic ointment, and pain relievers in the event of injuries. Moreover, pharmacists can advise on various health topics, such as medication usage, health care, and injury prevention.

Farmers may visit a drugstore to buy pet medications, vitamins, supplements, baby products, beauty products like shampoo, conditioner, makeup, and personal care items such as deodorant, toothpaste, and soap.

a. Dividend is given to shareholder's while bonus are given from profit made in the revenue.

b. The shareholder's received a dividend of Rs. 10 per share

c. The bank shared 15% of it's profit.

(a) A dividend is a payment made to shareholders from a company's earnings. Employees may receive financial compensation in the form of bonuses in addition to their base pay. Bonuses are paid from a company's revenue, whereas dividends are paid from its profits. While bonuses are often given out on an annual basis, dividends are typically paid out weekly or annually. All stockholders receive dividend payments, however most employees only receive bonuses when they meet predetermined performance standards.

(b) The bank distributed 15% of its profit to the shareholders, which is equal to Rs. 6,00,00,000. This means that each shareholder received a dividend of Rs. 10 per share. Virochan has 1,580 shares, so he received a dividend of Rs. 15,800.

(c) The bank distributed 15% of its profit as dividend, which is equal to 15/100 = 0.15 = 15%.

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The tables that represent the values of a function are

A. Input (x) 1 2 3 4

    Output (y) 12 15 18 21

B. Input (x) 1 7 7 −8

    Output (y) 22 −30 18 2

C.  Input (x) 1 1 1 1

     Output (y) −2 −5 −12 1

The values that represent a function are those that apply the same rule with both the input and output values. This means that there should be a relationship between the input and output values as they follow a consistent rule.

The values in the selected list follow a consistent rule thus, we can classify them as representative of functions.

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The function A(d) = 27 + d represents a linear relationship where the number of puzzles increases by one each day.

The given function A(d) = 27 + d represents the relation between the number of puzzles, A, and the time, d, measured in days.

According to the function, the initial number of puzzles in Ken's account is 27 (when d = 0). As each day passes (increasing d by 1), one additional puzzle is downloaded into his account.

For example, after 1 day (when d = 1), the number of puzzles would be A(1) = 27 + 1 = 28. After 2 days (when d = 2), the number of puzzles would be A(2) = 27 + 2 = 29, and so on.

In summary, the function A(d) = 27 + d represents a linear relationship where the number of puzzles increases by one each day.

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The probability of the normal distribution is  0.8961

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

P(-1.26 < z)

This can be expressed as

P(z > -1.26)

This means that area is to the right of z and is calculated by calculating the probability that the z-score is greater than -1.26

In other words, this is represented as

Probability = P(z > -1.26)

This can then be calculated using a statistical calculator or a table of z-scores,

Using a statistical calculator, we have the area to be

Probability = 0.89617

When this value is approximated, we have

Probability = 0.8961

Hence, the probability is 0.8961

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Question

For a standard normal distribution, find the following.

Express the probability as a decimal rounded to 4 decimal places.

P(-1.26 < z)

a. The simplified expression is determined as -4

b.  The missing expression is determined as - ¹/₂.

c. The simplified expression is determined as - ⁸³⁷/₁₀₄, and - ⁴⁹/₂₅.

The addition operations, subtraction operations and division operation is simplified as follows;

a. The given expression and its simplification;

- 1 + ( - 2) - (-3) - 4

= - 1 - 2 + 3 - 4

= -4

b. The given expression and its simplification;

-3 - ¹/₂ = - 3 + ?

-3 + 3 - ¹/₂ = ?

- ¹/₂ = ?

c. The given expression and its simplification;

1 ¹/₈ (- 7 ²/₁₃)

= ⁹/₈ x - ⁹³/₁₃

= - ⁸³⁷/₁₀₄

-3 ⁴/₁₅ ÷ (- 1 ²/₃)

= - ⁴⁹/₁₅  ÷  ( - ⁵/₃)

= - ⁴⁹/₁₅  × - ³/₅

= - ⁴⁹/₂₅

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i. The equation shows that dy/dx is -8/x² + 2 and d²y/dx² is -2

ii. The curve has a local maximum at the point (-2, y) and the curve has a local minimum at the point (2, y).

(i) Finding dy/dx:

Given: y = 8/x + 2x

To find dy/dx, we'll differentiate each term with respect to x:

Differentiating 8/x with respect to x:

(d/dx)(8/x) = -8/x²

Differentiating 2x with respect to x:

(d/dx)(2x) = 2

Therefore, dy/dx = -8/x² + 2.

(ii) Finding d²y/dx²:

In order to find the second derivative, we'll differentiate dy/dx with respect to x:

Differentiating -8/x² with respect to x:

(d/dx)(-8/x²) = 16/x³

Differentiating 2 with respect to x:

(d/dx)(2) = 0

Therefore, d²y/dx² = 16/x³.

To find the coordinates of the stationary points, we need to solve the equation dy/dx = 0:

-8/x² + 2 = 0

Rearranging the equation, we have:

-8/x² = -2

-8 = -2x²

Dividing both sides by -2:

4 = x²

Taking the square root of both sides:

x = ±√4

Therefore, the stationary points occur at x = -2 and x = 2.

In order to determine the nature of each stationary point, we'll analyze the second derivative.

When x = -2:

d²y/dx² = 16/(-2)³ = 16/(-8) = -2

Since the second derivative is negative at x = -2, the nature of the stationary point is a local maximum.

When x = 2:

d²y/dx² = 16/(2)³ = 16/8 = 2

Since the second derivative is positive at x = 2, the nature of the stationary point is a local minimum.

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The expression "x + x + 10 + 2x - 16" is one that represents the sum of the total scores of  all three players: Erick, Mia, and Isabelle.

The expression can be broken down as:

Therefore, if one can simplify the expression, one can be able get the sum of the scores of all three players who are Erick, Mia, and Isabelle.

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Answer:

The inverse of the statement "A number that has exactly two distinct factors is prime" is:

"If a number does not have exactly two distinct factors, then the number is not prime."

Therefore, the correct option is:

O If a number does not have exactly two distinct factors, then the number is not prime.

Step-by-step explanation:

The inverse of the statement "A number that has exactly two distinct factors is prime" is:

"If a number does not have exactly two distinct factors, then the number is not prime."

Therefore, the correct option is:

O If a number does not have exactly two distinct factors, then the number is not prime.

Answer:

16π

Step-by-step explanation:

Circumference = π X D (D = diameter = 2 X radius)

= π (2 X 8)

= 16π

a) The coefficient of y² is -3x.

b) The constant value of the expression is -4.

c) There are four terms in the expression: 9y, -3xy², -4, and x.

a) In the expression 9y − 3xy² − 4 + x, the coefficient of y² is the numerical value that multiplies y². In this case, the coefficient is -3x. It indicates that the term -3xy² has a variable part of y² and a coefficient of -3x.

b) The constant value of the expression refers to the term that does not have any variables attached to it. In this case, it is -4. The constant term remains the same regardless of the values of the variables. It does not depend on y or x.

c) The expression has four terms. A term is a group of variables and constants separated by addition or subtraction. In this case, the four terms are 9y, -3xy², -4, and x. Each term represents a separate component of the expression and can be individually simplified or manipulated.

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It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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Answer:

B

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

the endpoints of b₁ are (- 2, - 2) and (8, - 2)

since the y- coordinates are equal then b₁ is the difference of the x- coordinates, that is

b₁ = 8 - (- 2) = 8 + 2 = 10

similarly for b₂ with endpoints (2, 3) and (6, 3) , then

b₂ = 6 - 2 = 4

h = 5 ( perpendicular distance between the bases ) , then

A = [tex]\frac{1}{2}[/tex] × 5 × (10 + 4) = 2.5 × 14 = 35 units²

Answer:

Step-by-step explanation:

You want the area and volume ratios when two figures have a similarity ratio of 2 : 7.

The ratio of areas is the square of the similarity ratio:

  2² : 7² = 4 : 49

The ratio of volumes is the cube of the similarity ratio:

  2³ : 7³ = 8 : 343

__

Additional comment

It can help to think about the units of area and volume. For linear dimensions in inches, area dimensions are in square inches, and volume dimensions are cubic inches. Any ratio of inches will be squared when those inch dimensions are used for area, and will be cubed when volume is computed.

  side length of a square or cube: smaller: 2", larger: 7"

  area of the square: smaller: 2² in², larger: 7² in² or 4 in² and 49 in²

  volume of the cube: smaller: 2³ in³, larger: 7³ in³ or 8 in³ and 343 in³

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The matched form of the expressions are:

(x - 8)² → x² - 16x + 64

(x + 6) (x - 6) → x² - 36

(2x - 5) (2x + 5) → 4x² - 25

(3x + 1)² → 9x² + 6x + 1

(x + 4)² → x² + 8x + 16

Let's go through each expression and expand them:

(x - 8)²:

To expand this expression, we can use the formula (a - b)² = a² - 2ab + b². In this case, a = x and b = 8.

Expanding (x - 8)², we get:

(x - 8)² = x² - 2(x)(8) + 8²

= x² - 16x + 64

(x + 6) (x - 6):

To expand this expression, we can use the distributive property. Multiply each term in the first set of parentheses (x + 6) by each term in the second set of parentheses (x - 6):

(x + 6) (x - 6) = x(x) + x(-6) + 6(x) + 6(-6)

= x² - 6x + 6x - 36

= x² - 36

(2x - 5) (2x + 5):

Again, we use the distributive property to expand the expression:

(2x - 5) (2x + 5) = (2x)(2x) + (2x)(5) + (-5)(2x) + (-5)(5)

= 4x² + 10x - 10x - 25

= 4x² - 25

(3x + 1)²:

To expand this expression, we can use the formula (a + b)² = a² + 2ab + b². In this case, a = 3x and b = 1.

Expanding (3x + 1)², we get:

(3x + 1)² = (3x)² + 2(3x)(1) + 1²

= 9x² + 6x + 1

(x + 4)²:

Using the formula (a + b)² = a² + 2ab + b², where a = x and b = 4:

(x + 4)² = (x)² + 2(x)(4) + 4²

= x² + 8x + 16

These are the expanded forms of the given expressions.

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Answer:

Step-by-step explanation:

To test penalties' effect on a team's wins, analyze the data and calculate the correlation coefficient. Penalties and wins may be correlated, but one does not necessarily cause the other.

Other factors like team skill and strategy may influence penalties and wins.

The new questions using mathematics are

Is there a relationship between the gravity of penalties assessed against a football team (penalty yards) and their total points scored in a season?

Does the number of fouls committed by a basketball team in a season influence their shooting percentage?

By  using the available data, one can conduct a statistical analysis to establish a potential correlation between the total number of penalties a team has accumulated throughout a season and their overall number of wins.

Although there is a correlation between fines and victories, it does not imply that one is the direct cause of the other. It is possible that there are other contributing elements, such as team abilities, tactics, etc.

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The number of gallons of water that you drink in a year is 240.9 gallons.

We have to find the number of gallons of water that you drink in a year.

For that, first wee need to find the amount of water that you drink in a day.

Each person will drink water in a day in different amounts.

We can take an average of 2.5 liters that a man drink in a day.

Then

Amount of water drink in a year = 2.5 × 365

                                                      = 912.5 liters

Now we need to find the amount of water in gallons.

Convert liters in gallons.

1 liter = 0.264 gallons

So,

912.5 liters = 912.5 × 0.264 gallons

                  = 240.9 gallons

Hence the amount is 240.9 gallons.

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Answer:

Below

Step-by-step explanation:

a. rate of drinks = 210/13 milliliters per second

b. 17.02 seconds

Answer:

tina harner scored 733 points

jessica bradley scored 842 points

Step-by-step explanation:

b + h = 1575

h + 109 = b

plug the second equation into the first

h + 109 + h = 1575

2h + 109 = 1575

subtract 109 from both sides to isolate the variable and its coefficinet

2h = 1466

divide both sides by 2 to get h

h = 733