Kevin said that if you triple his age the result will be 1 less than his mother age Graph

The calculated values of the sum of interior angles of the shapes are 1080 degrees and 360 degrees

The formula of the sum of interior angles of a polygon is

Sum = (n − 2) * 180

For the octagon, we have

n = 8

This means that

Sum of angles = (8 − 2) * 180

Evaluate

Sum of angles = 1080

For the square, we have

n = 4

This means that

Sum of angles = (4 − 2) * 180

Evaluate

Sum of angles = 360

Hence, the sum of interior angles of the shapes are 1080 degrees and 360 degrees

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Answer:

45w + 180 = 900

45w = 720

w = 16 weeks

The finance charge for Sandra Lazzaro, using the average daily balance method, is $13.63.

The average daily balance is one of the methods for computing the finance charges (interest and other fees).

The average daily balance method uses the balance owed at the end of each day of the billing period, and not the balance owed at the end of the week, month, or year.

Billing period for the credit card = 31 days

Unpaid credit card balance = $750

Payment made three days before month-end = $600

Finance charge rate per month = 2.2%

Method = Average daily balance

Day        Description    Amount    Average Balance

1 - 28     Balance           $750       $21,000 ($750 x 28 days)

29 - 31   Payment        -$600       $-1,800 ($600 x 3 days)

31           Total                              $19,200

Average daily balance = $619.35 ($19,200 ÷ 31)

Finance charge = $13.63 ($619.35 x 2.2%)

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Answer:

Each of these functions is a transformation of the parent function f(x) = |x|. The transformations include shifting the graph up or down, stretching or compressing the graph vertically, reflecting the graph across the x-axis, and shifting the graph left or right. The vertex of each graph is located at a different point.

Step-by-step explanation:

- The function f(x) = |x| - 3 is a transformation of the parent function f(x) = |x|. The "-3" at the end of the function shifts the graph 3 units down. This means that the vertex, or lowest point, of the graph is at (0, -3) instead of (0, 0).

- The function f(x) = -|x - 4| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-4" inside the absolute value function shifts the graph 4 units to the right. This means that the vertex of the graph is at (4, 0) instead of (0, 0).

- The function f(x) = (1/3)|x| is a transformation of the parent function f(x) = |x|. The "1/3" in front of the absolute value function stretches the graph vertically by a factor of 1/3. This means that the graph is narrower and closer to the x-axis than the parent function. However, because the absolute value function is symmetrical, the graph is still centered at (0, 0).

- The function f(x) = -2|x - 1| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-1" inside the absolute value function shifts the graph 1 unit to the right. The "2" in front of the absolute value function stretches the graph vertically by a factor of 2. This means that the graph is narrower and closer to the x-axis than the parent function, and it is also reflected across the x-axis. The vertex of the graph is at (1, 0).

The value of missing side lengths are,

m = 4/√3

h = 2 / √3

We have to given that;

A triangle is shown in figure.

Now, We can formulate;

sin 60° = 2 / m

√3/2 = 2 / m

m = 4/√3

cos 60° = h / m

1/2 = h / (4/√3)

1/2 = √3h / 4

2 = √3h

h = 2 / √3

Thus, The value of missing side lengths are,

m = 4/√3

h = 2 / √3

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There were 64 players at the start of the tournament.

To determine the number of players at the start of the tournament

We need to work backwards from the final round to the first round.

In the final round, there will be only two players remaining since the winner of that match will be declared the overall champion.

In the penultimate (fifth) round, there will be four players remaining.

These four players must have come from the previous round, where there were eight players.

Continuing this pattern, in the fourth round, there will be eight players, and in the third round, there will be 16 players.

In the second round, there will be 32 players, and in the first (initial) round, there will be 64 players.

Therefore, there were 64 players at the start of the tournament.

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Answer:

Step-by-step explanation:

Typically you see f(x)=something like you do up in the original equation.

that is your function/graph.

a) f(0)  means plug in 0 for x

   f(0) =  (-0)³-0²-0+13

   f(0) = 13

b)  f(2) =(-2)³-2²-2+13          >simplify the exponenents first

                                               (-2)³ = (-2)(-2)(-2)= -8

    f(2) = -8-4-2+13               >simplify work from left to right

    f(2) = -12-2+13

    f(2) = -14+13

    f(2) = -1

c)  f(-2) = [-(-2)]³-(-2)²-(-2)+13              >multiply - and -  for  (-(-2))³

    f(-2) = (2)³-(-2)²-(-2)+13                  >simplify exponents

    f(-2) = 8-4-(-2)+13          

    f(-2) = 4-(-2)+13

    f(-2) = 6+13

    f(-2) = 18

d)  means add f(1) and f(-1)

f(1) +f(-1) = (-1)³-1²-1+13 +[-(-1)]³-(-1)²-(-1)+13  

f(1) +f(-1) = -1-1-1+13 +[1]³-1-(-1)+13

f(1) +f(-1) = -1-1-1+13 +1-1+1+13            

f(1) +f(-1) = -2-1+13 +1-1+1+13

f(1) +f(-1) = -3 +13 +1-1+1+13

f(1) +f(-1) = 10+1-1+1+13

f(1) +f(-1) = 11 -1+1+13

f(1) +f(-1) = 10 +1 +13

f(1) +f(-1) = 24

The probability of hitting the shaded region is 0.755 or 75.5%.

To find the probability of hitting the shaded region, we need to find the area of the shaded region and divide it by the area of the entire square.

Let's label the side length of the small square as x.

Then, we know that the diagonal of the small square is 7, so we can use the Pythagorean theorem to solve for x:

x^2 + x^2 = 7^2

2x^2 = 49

x^2 = 24.5

So the area of each white square is x^2 = 24.5 square units.

Let's label the side length of the large square as y.

Then, we know that the diagonal of the large square is 20, so we can use the Pythagorean theorem to solve for y:

y^2 + y^2 = 20^2

2y^2 = 400

y^2 = 200

So the area of the large square is y^2 = 200 square units.

Now, we can find the area of the shaded region by subtracting the area of the two white squares from the area of the large square:

Area of shaded region = Area of large square - 2 * Area of white square

= 200 - 2(24.5)

= 151

Therefore, the probability of hitting the shaded region is:

Probability = Area of shaded region / Area of entire square

Probability = 151 / 200

Probability = 0.755 or 75.5% (rounded to one decimal place)

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The value of x it the nearest tenth of degree is 25.6°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/ hyp

cos( tetha) = adj/ hyp

tan( tetha) = opp/ adj

Here, the hypotenuse is 92 and adjascent to the to the angle x is 63

therefore to calculate x we use cosine function

cos x = 83/92

cos x = 0.902

x = cos^-1( 0.902)

x = 25.6° ( nearest tenth)

therefore the value of x is 25.6°

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Answer:

6

Step-by-step explanation:

bc

The car will be worth half its original value after 4 years

A graph for straight-line depreciation for a car is given.

a

The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.

Step 3/7

The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are

(0, maximum car value) and (maximum lifespan,0)

Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600

The intercepts are (0, 25, 600) and (8,0)

Determine the slope of the equation.

Two points determine a line, so only two points are needed to determine the slope of a line.

Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)

Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)

Use the slope ratio as shown below;

The slope of the depreciation equation is.

-3200

The general form for the equation of a straight line is:

y = mx + b

Where m represents the slope of the line and b represents the y-intercept.

The slope is -3,200 and the -intercept is 25,600 as obtained.

Therefore, the straight line depreciation equation is:

y = -3,200x + 25,600

Therefore, the value of the car after 4 years is $12,800

b.

Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.

Therefore, the value of the car after 5 years is $9,600

c.

The half value of the car is half of $25,600 which is $12,800

The car will be worth half its original value after 4 years

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a) The probability that a randomly selected student is taking a Math class or an English class is 0.82.

b) The probability that a randomly selected student is taking neither a math class nor an English class is 0.18.

Probability refers to the chance or likelihood that an expected success, event, or outcome occurs from many possible successes, events, or outcomes.

Probability is represented as a fractional value using decimals, fractions, or percentages.

The percentage of students taking a math class =79%

The percentage of students taking an English class = 70%

The percentage of students taking both classes = 67%

Let the event that a student is taking a math class = m

Let the event that a student is taking an English class = e

The probability of m is p(m) = 0.79

The probability of e is p(e) = 0.70

The probability of m and e is p(m and e) = 0.67

The probability that a randomly selected student is taking a math class or an English class = 0.82 (0.79 + 0.70 - 0.67)

The probability that a randomly selected student is taking neither a math class nor an English class = 0.18 (1 - 0.82)

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Answer:

Step-by-step explanation:

You are looking for the tangent ratio, which is opposite side over adjacent side.  Using the tangent ratio of an angle of 37°.

tan37° = x/89

.75355405 = x/89

.75355405 · 89 = x/89 · 89/1

67.06 = x

rounded to 67.1

Answer:

67.1? that's what I got lol

As indicated by the question, the company's prices have been declining. As a result, a sharp increase is not anticipated, nor is a significant change in the following 30 days.

a public market where business stock and its derivatives can be traded at a set price on a regulated exchange. This means that there is little chance of a big shift in the stock price during the next 30 days.

Look at the query to comprehend the printing company's pricing pattern. The price of this printing company's shares has decreased, according tothe inquiry. It has fallen steadily over time.

Investors shouldn't anticipate a sudden increase in the price of this company's shares because the question doesn't indicate one. However, 30 days is a relatively small period of time to indicate any movement in the stock's price.

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The margin of error is E = 0.67.

We can use the formula:

E = z* (σ / sqrt(n))

Where

In this case, we are given that C = 0.95, σ = 3.4, and n = 100. We can use a standard normal distribution table to find the z-score that corresponds to a 95% confidence level, which is approximately 1.96.

Substituting the values:

E = 1.96 * (3.4 / sqrt(100))

E = 1.96 * 0.34

E = 0.6664

Rounding to two decimal places, the margin of error is approximately 0.67.

Therefore, the margin of error is E = 0.67.

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From Table 2, we can see that Georgia's income tax rate is 7%.

To find the amount of state income taxes Anthony will owe, we can multiply his income by the tax rate:

State income tax = (Anthony's income) x (Georgia's tax rate)

State income tax = $65,750 x 0.07

State income tax = $4,602.50

Therefore, Anthony will owe $4,602.50 in state income taxes. To find out how much money he will have left after he pays these taxes, we can subtract the tax amount from his income:

Money left after paying state income taxes = Anthony's income - State income tax

Money left after paying state income taxes = $65,750 - $4,602.50

Money left after paying state income taxes = $61,147.50

Therefore, Anthony will have $61,147.50 left after he pays state income taxes.

Answer:

Step-by-step explanation:

We are given a figure, consisting of a right triangle with a circle cut out of it.

To Calculate : area of the shaded region below,

First Let's find the Area of the right triangle:

Area(triangle) = 1/2 × Base × Height

= 1/2 × 56 × 56

= 1/2 × 3136

= 3136/2

= 1568 m².

Now, We are diameter of the circle = 20 m

Radius of the circle = 20/2 = 10 m

Acc. to question we have to use 3.14 as an

approximation for pi.

Area (circle) = 3.14 × 10 × 10

Area (circle) = 3.14 × 100

Area (circle) = 314 m²

Area of shaded region = Area of triangle - Area of circle =

= 1568 m² - 314 m²

= 1.254 square meters

Therefore, The approximate area of the shaded region is 1.254 square meters.

Option (a) is the required answer

Answer:

5)

The inverse of the function f(x) = x^7 can be found by following these steps:

Step 1: Replace f(x) with y. The equation becomes y = x^7.

Step 2: Interchange x and y in the equation, so it becomes x = y^7.

Step 3: Solve the equation for y by taking the seventh root of both sides. This yields y = x^(1/7).

Therefore, the inverse function of f(x) = x^7 is g(x) = x^(1/7), which maps any given value of x to its seventh root.

It's important to note that the domain and range of the inverse function are the opposite of those of the original function. The domain of the inverse function is all real numbers, while the range is only positive real numbers. The domain of the original function is all real numbers, while the range is also all real numbers.

6)

To find the inverse of the function f(x) = (-2/5)x^3, we can follow these steps:

Step 1: Replace f(x) with y. The equation becomes y = (-2/5)x^3.

Step 2: Solve the equation for x in terms of y.

Multiply both sides by -5/2:

(-5/2) y = x^3

Take the cube root of both sides:

x = [(-5/2) y]^(1/3)

Step 3: Replace x with f^-1(y) to obtain the inverse function.

f^-1(y) = [(-5/2) y]^(1/3)

Therefore, the inverse function of f(x) = (-2/5)x^3 is f^-1(y) = [(-5/2) y]^(1/3).

It is important to note that the domain and range of the inverse function are the opposite of those of the original function. The domain of the inverse function is all real numbers, while the range is also all real numbers. The domain of the original function is all real numbers, while the range is only negative real numbers if x is negative and only positive real numbers if x is positive.

The required maximum area of the rectangle is 17.5m

The perimeter of a rectangle is = 70m.

We have to find The maximum area of rectangle .

A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four.

Maximum area of rectangle is = 70 / 4

                                                   = 17.5

The required value of maximum area of the rectangle is 17.5m.

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the perimeter of a rectangle is 70m. What are the dimensions that will produce the maximum area of such a rectangle

Using multiplication operation, the amount of pension that Edith will receive after 4 years of service and using the vesting percentage and the pension multiplier is $49,725.

The pension amount is the product of the multiplication of the average salary, the vesting percentage and the pension multiplier factor.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Edith's average salary = $65,000

The number of years of service = 4 years

Pension Multiplier = 2%

Pension multiplier factor = 1.02 (100% + 2%)

Vesting percentage = 75%

Pension to be received = $49,725 ($65,000 x 75% x 1.02)

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Answer: 34.9

Step-by-step explanation: 100 - 65.1

Answer:

4x - 1 > 15

4x > 16

x > 4

The solution set is all numbers greater than 4.

Step-by-step explanation:

You would need a calculator in the degree function I believe, but basically for Number 1,

you would set it up in calculator as Sin ^-1 (6/9) or write it down as Sin(X)=(6/9)

2. would be Cos(45)= (X/4) meaning you'd do Cos(45) times 4.

3. is basically Tan(60) =(x/4) so it's basically Tan(60) times 4.

make sure your calculator is in degree mode ? Sorry, I don't remember if you need to be in radiant or degree mode. I can comment or make an edit when I remember.

The value of amount of R4 670,00 is due to be paid back after​ 1.47 years.

We have to given that;

A discounted loan of R4 670,00 at a simple discount rate of 14% per year is offered to Mr. Mothapo.

And, The actual amount of money that Mr. Mothapo receives is R3 852,75.

Now, Let n be the loan period.

Hence, We get;

4670,00 = 385275 (1 + 0.14)ⁿ

1.212121 = (1.14)ⁿ

n log 1.14 = log 1.2121

n = 1.47

Thus, The value of amount of R4 670,00 is due to be paid back after​ 1.47 years.

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Answer:

B

Step-by-step explanation:

This is a linear function.

:D

If local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52, In terms of price per soda, the supermarket pack is the better value.

To determine which is the better value between the supermarket pack of 12 sodas for $3.48 and the discount warehouse 36-can case for $11.52, we need to calculate the price per soda for each option.

For the supermarket pack, the price per soda can be found by dividing the total cost by the number of sodas in the pack:

Price per soda = $3.48 / 12 = $0.29

For the discount warehouse case, the price per soda can be found by dividing the total cost by the number of sodas in the case:

Price per soda = $11.52 / 36 = $0.32

From these calculations, we can see that the price per soda is lower for the supermarket pack at $0.29 compared to $0.32 for the discount warehouse case. Therefore, in terms of price per soda, the supermarket pack is the better value.

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Company B needs approximately 55 applicants to apply in order to meet their hiring target of 30 new employees, taking into account the percentages of applicants who do not meet the requirements or pass the various stages of the hiring process.

Let's start with the total number of applicants needed to meet the hiring target of 30 new employees. We can call this number "x". We'll work backwards from there to find the number of applicants that need to apply in order to get 30 new employees.

We know that 5% of the remaining applicants fail the background investigation, which means that 95% pass. We also know that 23% of the remaining applicants do not show up for the interview, which means that 77% do show up.

Similarly, 12% of the remaining applicants do not pass the pre-screening assessment, which means that 88% do pass. Finally, 10% of all applicants do not meet the basic business requirements for the job, which means that 90% do meet the requirements.

Putting all of this information into the following equation;

0.9x × 0.88 × 0.77 × 0.95 = 30

Simplifying and solving for x, we get;

x = 30 / (0.9 × 0.88 × 0.77 × 0.95)

x ≈ 55.24

Therefore, Company B needs approximately 55 applicants.

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If line A is parallel to line B then the value of x is 18.

Given that a line A is parallel to line B

We have to find the value of x

3x+7x=180

Combine the like terms

10x=180

Divide both sides by 10

value x=18

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Answer:

x = 4√3

y = 8√3

Step-by-step explanation:

The interior angles of the given right triangle are 30°, 60° and 90°.

Therefore, the triangle is a special 30-60-90 triangle.

In a 30-60-90 triangle, the measures of its sides are in the ratio 1 : √3 : 2.  

Therefore, the formula for the ratio of the sides is b : b√3 : 2b where:

From inspection of the given triangle, the side opposite the 60° angle is 12 units in length. Therefore:

[tex]b\sqrt{3} = 12[/tex]

Solve the equation for b:

[tex]\begin{aligned}b&=\dfrac{12}{\sqrt{3}}\\\\b&=\dfrac{12 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}\\\\b&=\dfrac{12\sqrt{3}}{3}\\\\b&=4\sqrt{3}\end{aligned}[/tex]

"x" is the side opposite the 30° angle. Therefore:

[tex]\begin{aligned}x& = b\\x& = 4\sqrt{3}\end{aligned}[/tex]

"y" is the side opposite the right angle. Therefore:

[tex]\begin{aligned}y&=2b\\y&=2 \cdot 4\sqrt{3}\\y&=8 \sqrt{3}\end{aligned}[/tex]

Therefore, the values of x and y are:

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