Translate the following sentence into an equation: "The product of 3 and x increased by 7 equals 25 ."

The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.

What is the central angle?

A central angle is an angle with endpoints and located on a circle's circumference and a vertex located at the circle's center. A central angle in a circle determines an arc.

To determine the measure of the central angle in radians, we can use the formula:

radians = degrees * (π / 180)

So, for the central angle of 120°:

radians = 120 * (π / 180) = 2 * π / 3

The measure of the central angle in radians is approximately 2 * π / 3 radians.

To find the arc length of RS, we can use the formula:

arc length = (central angle / 360) * circumference

The circumference of the circle is given by 2 * π * r, where r is the radius:

circumference = 2 * π * 4 = 8 * π

So the arc length is:

arc length = (120 / 360) * (8 * π) = 4 * π / 3

The arc length of RS is approximately 4 * π / 3 inches.

To find the area of sector RFS, we can use the formula:

area = (central angle / 360) * π * r²

So the area of sector RFS is:

area = (120 / 360) * π * (4)² = 8 * π

Therefore, The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.

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Answer:

Arch length = 8pi/3

Area of sector = 16pi/3

Central angle in radians = 2pi/3

Step-by-step explanation: see picture-

Tammy received 19 phone calls on the first evening, 13 phone calls on the second evening, and 76 phone calls on the third evening.

Let's use algebra to solve the problem.

Let x be the number of phone calls Tammy received on the first evening.

According to the problem, she received 6 fewer calls on the second evening than on the first evening. This means that the number of phone calls she received on the second evening is x - 6.

The problem also states that she received 4 times as many calls on the third evening as she did on the first evening. This means that the number of phone calls she received on the third evening is 4x.

We know that Tammy received a total of 108 phone calls over the three evenings. We can use this information to set up an equation:

x + (x - 6) + 4x = 108

Simplifying the equation:

6x - 6 = 108

Adding 6 to both sides:

6x = 114

Dividing both sides by 6:

x = 19

Therefore, Tammy received 19 phone calls on the first evening, 13 phone calls (19 - 6) on the second evening, and 76 phone calls (4 x 19) on the third evening.

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Complete question is:

Over the last three evenings, Tammy received a total of 108 phone calls at the call center. The second evening, she received 6 fewer calls than the first evening. The third evening, she received 4 times as many calls as the first evening. How many phone calls did she receive each evening?

The correct statements regarding the average rate of change of the function are given as follows:

The average rate of change of a function is given by the change in the output divided by the change in the input.

From x = 1 to x = 3, we have that:

Hence the rate is given as follows:

6/2 = 3.

From x = 2 to x = 4, we have that:

Hence the rate is given as follows:

12/2 = 6.

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[tex]40(x )+6( 1.5x) = 612.5[/tex]

So C.

B:

49x=612.5

x=12.5$

The temperature change for Monday is -30 degrees Fahrenheit,

The completed table is: Monday: -30, Tuesday: +7, Wednesday: +12, Thursday: +2, Friday: -6, to make the total change from Monday to Saturday equal to -15 degrees Fahrenheit.

To complete the table, we need to find the temperature change for Monday that makes the total change from Monday to Saturday equal to -15 degrees Fahrenheit.

Let x be the temperature change for Monday. Then, we can set up the equation:

x + 7 + 12 + 2 - 6 = -15

Simplifying and solving for x, we get:

x = -30

Therefore,

The temperature change for Monday is -30 degrees Fahrenheit, and the completed table is:

Monday: -30

Tuesday: +7

Wednesday: +12

Thursday: +2

Friday: -6

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Answer:

Nick is 6

Andrea is 18

Step-by-step explanation:

Sounds like a system of equations

Letting...

a = Andrea

n = Nick

Since she's 3 times the age, the first equation will be

a = 3n

Since in 10 years, Andrea will be 12 years older than Nick, we can write

a = n + 12

Since we have two a = ,we can set them equal to each other

3n = n + 12

Subtracting n

3n - n = 12

Now combining the n's (n is the same as 1n)

2n = 12

And last but not least, we can divide by 2

n = 6... so Nick is 6 right now.

Going back to our first equation of a = 3n, if we plug 6 in

a = 6(3) = 18.

Making Andrea 18 right now

The number of chips sold is 10

The number of candy bars sold is 23

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

The price of each candy bar = $1.50.

The price of each bag of chips = $1.25.

Number of chips = x

Number of candy bar = x + 13

Yesterday Melanie made $33.25.

So,

x + x + 13 = 33.25

Solve for x.

x + x + 13 = 33.25

2x + 13 = 33.25

2x = 33.25 - 13

2x = 20.25

x = 10.125

x = 10

Now,

Number of chips = 10

Number of candy bar = 10 + 13 = 23

Thus,

Number of chips sold = 10

Number of candy bar sold = 23

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Answer:

the smallest number is 1079

Step-by-step explanation:

Let the numbers be x and y

The probability that the last red ball was the 8th ball out is 3/10

Number of red  balls = 3 red balls

Number of black balls = 7 black balls

Then you randomly draw the balls out one by one without replacement.

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The equation will be

Probability = Number of favorable outcomes / Total number of outcomes

Total number of outcomes = 3 + 7

= 10

Substitute the values in the equation

The probability that the last red ball was the 8th ball out = 3/10

Therefore, the probability is 3/10

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The value of the areas are;

1. 24 cm²

2. 304cm²

3. 28. 36cm²

4. 5cm²

5. 189cm²

The formula for calculating the area of a triangle is expressed as;

Area = 1/2bh

Substitute the values

Area = 1/2 × 4 × 12

Multiply

Area = 24 cm²

For the area of a parallelogram

Area = ab, length of its sides

Substitute the values

Area = 304cm²

For the area of a rectangle

Area = lw, length and width

Area = 28. 36cm²

For the area of a pentagon

Area = 1/2 base × height

Area = 1/2 × 2.5 × 4

Area = 5cm²

For the area of a trapezium

Area = 1/2 (a + b)h

Area = 1/2 (18+24)9

Area = 189cm²

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Answer:

Step-by-step explanation:

is A

The probability that the next component brought in for repair is a compact disc player given that it is already known to be an audio component is 0.83 or 83%.

Probability is a fundamental concept in mathematics, statistics, and various fields of science. It is used to measure the likelihood of an event occurring

In the given scenario, we are told that a certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player. We are also given that P(A) = 0.6 and P(B) = 0.5.

The probability of B given A, denoted by P(B|A), represents the probability that event B will occur given that event A has already occurred. In other words, it tells us how likely it is that the next component brought in for repair is a compact disc player given that it is already known to be an audio component.

To calculate P(B|A), we use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

Here, P(A and B) denotes the probability that both events A and B occur. We know that event B is contained in event A, so it follows that P(A and B) = P(B). Therefore:

P(B|A) = P(B) / P(A)

Substituting the given values, we have:

P(B|A) = 0.5 / 0.6

P(B|A) = 5/6 or 0.83 (rounded to two decimal places)

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Complete Question:

A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A).  Suppose that P(A) = .6and P(B) = .5. What is P(B|A) ?

The required, Rich's monthly mortgage payment will be $1,246.91.

A mortgage payment is the amount of money that a borrower pays to a lender in order to repay a home loan.

Here,
The amount that Rich is financing with the mortgage is the difference between the total cost of the home and the down payment:

Amount financed = $244,800 - 0.15($244,800) = $208,080

To calculate the monthly mortgage payment, we can use the formula for the present value of an annuity,
[tex]PMT = (PV * r) / (1 - (1 + r)^{-n}[/tex]

First, we need to calculate the monthly interest rate. Since the annual interest rate is 5.25%, the monthly interest rate is:

r = 0.0525 / 12 = 0.004375

Next, we need to calculate the total number of payments. Since Rich is taking out a 25-year loan, he will be making 25 x 12 = 300 monthly payments.

Now we can plug these values into the formula and solve for PMT:

PMT = ($208,080 × 0.004375) / (1 - (1 + 0.004375)^(-300))

= $1,246.91

Therefore, Rich's monthly mortgage payment will be $1,246.91.

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The required ordered pair represents the center of the new circle after the transformation is (-x,y). Option A is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them.

Here,
If a circle is reflected across the y-axis, its center, which was originally located at (x, y), will move to a new location that is the same distance from the y-axis but on the opposite side. Since the y-coordinate does not change during a reflection across the y-axis, the y-coordinate of the new center will remain the same as the original, which is y.

However, the x-coordinate will be negated, since the reflection across the y-axis involves flipping points to the opposite side of the y-axis. Therefore, the center of the new circle will have the coordinates (-x, y).

So the answer is A) (-x, y).

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4 x 9 is a multiplication problem, which means 4 is being multiplied by 9. This can also be written as 4 x 9 = 36. 4 multiplied by 9 is equal to 36 because 4 is being added to itself 9 times, resulting in 36.

4 x 9 is a multiplication problem which means we are multiplying 4 and 9 together. This can also be written as 4 x 9 = 36. When multiplying two numbers together, you are adding the first number to itself the second number of times. In this case, 4 multiplied by 9 is equal to 36 because we are adding 4 to itself 9 times: 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 36. This can also be written as 4 x 9 = 36, which means that 4 times 9 equals 36.

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Answer:

-1/2-4x/5=1/2-2x

Starting from the left side, we can simplify:

-1/2 - 4x/5 = 1/2 - 2x

Next, we can isolate x by adding 2x to both sides:

-1/2 - 4x/5 + 2x = 1/2 - 2x + 2x

-1/2 + 2x/5 = 1/2

Adding 1/2 to both sides:

0 + 2x/5 = 1

Finally, solving for x:

2x/5 = 1

Multiplying both sides by 5:

2x = 5

Dividing both sides by 2:

x = 5/2

7x² + 9x² = -6x² - 7x

Combining like terms:

16x² = -6x² - 7x

Adding 6x² to both sides:

22x² = -7x

Dividing both sides by -7:

-22x²/-7 = 7x/-7

-22x²/7 = -7x/7

-22x²/7 = -x

Multiplying both sides by -7:

22x² = x

Dividing both sides by 22:

x² = x/22

Since this equation states that x² equals x divided by 22, it has no real solutions for x.

-7x² + 6 = x² - 7x²

Combining like terms:

-8x² + 6 = 0

Adding 8x² to both sides:

-8x² + 8x² + 6 = 0 + 8x²

6 = 8x²

Dividing both sides by 8:

6/8 = 8x²/8

3/4 = x²

Taking the square root of both sides:

sqrt(3/4) = sqrt(x²)

x = +/- sqrt(3/4)

The given functions f(x) = 3x + 6 and g(x) = (x+5)/3 are not inverses of each other, as their compositions of functions are not equal.

When we want to check if two functions are inverses of each other, we need to verify if composing the functions in both orders results in the input variable. In other words, we need to check if (f ∘ g)(x) = x and (g ∘ f)(x) = x, where f and g are the two functions.

For this problem, we have two functions:

f(x) = 3x + 6

g(x) = (x + 5)/3

Let's start by computing (f ∘ g)(x):

(f ∘ g)(x) = f(g(x)) = f((x + 5)/3) = 3((x + 5)/3) + 6

We can simplify this by canceling the 3's:

(f ∘ g)(x) = x + 5 + 6 = x + 11

Now let's compute (g ∘ f)(x):

(g ∘ f)(x) = g(f(x)) = g(3x + 6) = ((3x + 6) + 5)/3

Again, we can simplify this by canceling the 3's:

(g ∘ f)(x) = (3x + 11)/3

We can see that neither (f ∘ g)(x) nor (g ∘ f)(x) is equal to x, so we can conclude that the functions f(x) = 3x + 6 and g(x) = (x + 5)/3 are not inverses of each other.

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Answer:

7.09

Step-by-step explanation:

s = r∅ = 7.09

s = (7 cm)(1.0123) = 7.086

58 deg x π/180 = 1.0123 radians

Answer:

CB ≈ 7.09 cm

Step-by-step explanation:

the length of arc CB is calculated as

AB = circumference of circle × fraction of circle

    = 2πr × [tex]\frac{58}{360}[/tex] ( r is the radius )

   = 2π × 7 × [tex]\frac{29}{180}[/tex]

  = [tex]\frac{14\pi (29)}{180}[/tex]

  ≈ 7.09 cm ( to 2 decimal places )

Here both triangles are congruent by SAS.

What is congruent by SAS?

Side-Angle-Side congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

In the given triangles it's given that,

in both triangles the two sides are similar along with an angle.

So Here both triangles are congruent by SAS.

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Using a trigonometric relation we will see that the measure of angle x is 40°.

Here we can see a right triangle where one of the angles is x, the hypotenuse is 14 units long, and the opposite cathetus to the known angle is 9 units long.

Here we can use the trigonometric relation:

sin(x) = (opposite cathetus)/hypotenuse

Then we can write:

sin(x) = 9/14

Using the inverse sine function we will get:

Asin(sin(x)) = Asin(9/14)

x = Asin(9/14)

x = 40°

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The slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

In the given graph two lines are plotted.

Part A: From the graph, the two equations are intersected at (-1.5, 0) and the solution is (-1.5, 0).

Part B: Slope and y-intercept

Equations of lines from the graph are y=3/4 x+1 and y= -4/3 x-2.

For the equation y=3/4 x+1,

Compare, y=3/4 x+1 with y=mx+c, we get

Slope (m)= 3/4 and the y-intercept (c)=1

For the equation y= -4/3 x-2,

Compare, y= -4/3 x-2 with y=mx+c, we get

Slope (m)= -4/3 and the y-intercept (c)=-2

Therefore, the slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

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Answer:

x=12

Step-by-step explanation:

12 =2 (x - 6)

Solve for x.

Divide each side by 2

12/2 =2/2 (x - 6)

6 = x-6

Add 6 to each side

6+6 = x-6+6

12 = x

Answer:

x = 12

Step-by-step explanation:

Simplify  both sides of the equation

Turn the equation around

Add 12 to both sides

Divide both the sides by 2

The number of solutions of the system of equations is given as follows:

D. Infinitely many solutions.

The system of equations is defined as follows:

The second equation was obtained multiplying the first equation by 3, meaning that the two equations are multiples, and thus the system of equations has an infinity number of solutions and the correct option is given by option D.

The system of equations is defined as follows:

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Answer:

50) i. C 800cm^2

50)ii. B 120cm

Step-by-step explanation:

Use the picture in its given 2-d to mark the unknown measures. Such as, the gray rectangle on top has a bottom that is also 20 and the left side is 15.

The small horizontal jutting out on the left mid-way down is 5cm same as the 5cm just below.

When you mentally "unfold" the shape to its full rectangular shape and size, all the lengths are marked.

Use:

Area=length×width

and,

Perimeter

=L + w + L + w

There are lots of perimeter formulas, for perimeter, you just add up all the sides all the way around the shape.

see image.

There are 4,608 different ways that the class can elect a president, vice president, and secretary.

To find the number of different ways that a class of 18 students can elect a president, vice president, and secretary, we will use the formula for permutations, which is given by -

nPk = n! / (n - k)!

where n is the total number of items and k is the number of items to be selected in a specific order.

In this case, we are given n = 18 students and k = 3 positions.

Thus, the number of different ways to elect a president, vice president, and secretary will be -

18P3 = 18! / (18 - 3)! = 18! / 15! = 18 x 17 x 16 = 4,608

Therefore, there are 4,608 different ways that the class can elect a president, vice president, and secretary.

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Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.

The formula for this problem is: Number of Defects = (total number of items)*(percent of defects)For this problem, we know that the total number of items is 12,500 and the percent of defects can be found by taking the 5 defective items out of the 500 items produced, which is 1%.Plugging these numbers into the formula, we get :Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.

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The table is

x = 0            5         8            10           30.

y = 300       250    220        200         0

The height of the airplane decreases with time. Thus airplane landed in the time interval.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Given equation is y = -10x + 300.

Putting x = 0 in the equation:

y = -10×0 + 300

y = 300

Putting x = 5 in the equation:

y = -10×5 + 300

y = -50 + 300

y = 250

Putting x = 8 in the equation:

y = -10×8 + 300

y = -80 + 300

y = 220

Putting x = 10 in the equation:

y = -10×10 + 300

y = -100 + 300

y = 200

Putting x = 30 in the equation:

y = -10×30 + 300

y = -300 + 300

y = 0

The height of the airplane after 5 minutes is 250 feet.

The height of the airplane after 30 minutes is 0 feet.

The altitude of the airplane decreases with time. The altitude of the airplane decreases with time. The airplane is landing in the time interval.

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Answer: acute

Step-by-step explanation:

   This triangle does not have any right angles (90°), or any angles larger than a right angle, so it is an acute triangle.

Answer:

C.

Step-by-step explanation:

Multiply then divide