what is 12 plus 12 and take away 67 and then add 24

The compositions are:

f * f(x) = x⁴ - 2x²

g * g(x) = 81/64x

To find the composition f * f, we start by substituting f(x) into f(x) wherever we see x:

f * f (x) = f(f(x)) = f(x² - 1) = (x² - 1)² - 1

Expanding the expression, we get:

f * f (x) = x⁴ - 2x² + 1 - 1 = x⁴ - 2x²

So, f * f(x) = x⁴ - 2x².

To find the composition g * g, we substitute g(x) into g(x) wherever we see x:

g * g (x) = g(g(x)) = g(9/8x) = 9/8(9/8x) = 81/64x

So, g * g(x) = 81/64x.

Therefore, the compositions are:

f * f(x) = x⁴ - 2x²

g * g(x) = 81/64x

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The text format of the question is:

Suppose that the functions f and g are defined as follows.

f(x) = x² - 1

g(x) = 9/8x, x ≠

Find the compositions f * f and g * g

Simplify your answers as much as possible.

(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain)

Answer:

We can use a numerical method such as the Newton-Raphson method or the bisection method to approximate the positive zero of the function f(x) = 2x - 16x³ - 3x² - 8x - 2.

Let's use the Newton-Raphson method to approximate the positive zero of f(x). We start by choosing an initial guess x_0, and then compute successive approximations using the formula:

x_(n+1) = x_n - f(x_n) / f'(x_n)

where f'(x) is the derivative of f(x). We continue this process until we get an approximation that is accurate enough for our needs.

Let's choose an initial guess of x_0 = 1.5. Then we have:

f(x) = 2x - 16x³ - 3x² - 8x - 2

f'(x) = 2 - 48x² - 6x - 8

Using these expressions, we can compute successive approximations as follows:

x_1 = x_0 - f(x_0) / f'(x_0) = 1.5 - (-23.375) / (-73) ≈ 1.320

x_2 = x_1 - f(x_1) / f'(x_1) = 1.320 - (-12.608) / (-50.673) ≈ 1.141

x_3 = x_2 - f(x_2) / f'(x_2) = 1.141 - (-5.364) / (-35.883) ≈ 1.067

x_4 = x_3 - f(x_3) / f'(x_3) = 1.067 - (-1.949) / (-31.120) ≈ 1.042

x_5 = x_4 - f(x_4) / f'(x_4) = 1.042 - (-0.361) / (-30.251) ≈ 1.029

x_6 = x_5 - f(x_5) / f'(x_5) = 1.029 - (-0.012) / (-30.055) ≈ 1.028

So the positive zero of f(x) is approximately 1.028, rounded to two decimal places.

The length or of the segment AD or  distance from point A to point D is 16.6 ft.

Given that Mr. Rose is remodeling his house by adding a room to one side

In order to determine the length of the boards he needs for the roof of the room, he must calculate the distance from point A to point D

We have to find the distance of AD

Sin 25 = 7/x

x is the distance of AD

x=7/sin 25

x=16.6 ft

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Bank B would be the best option since it offers a higher interest rate than Bank A and does not have any fees.

To compare different bank accounts, we need to know the interest rates offered by each bank. Let's assume that we have three local banks, each with a different interest rate: Bank A offers 2% interest, Bank B offers 2.5% interest, and Bank C offers 3% interest.

Using the formula for simple interest, we can calculate the amount of interest earned on the initial deposit of $2000 over four years for each bank:

Bank A: 2% interest per year

After four years, the interest earned is:

$2000 x 2% x 4 = $160

Bank B: 2.5% interest per year

After four years, the interest earned is:

$2000 x 2.5% x 4 = $200

Bank C: 3% interest per year

After four years, the interest earned is:

$2000 x 3% x 4 = $240

So, Bank C offers the highest interest rate and would earn the most interest over the four-year period. However, we also need to consider any fees associated with each account. Let's assume that Bank A and Bank B have no fees, but Bank C charges a $50 annual fee.

Bank A: Total amount after four years = $2000 + $160 = $2160

Bank B: Total amount after four years = $2000 + $200 = $2200

Bank C: Total amount after four years = $2000 + $240 - $50 x 4 = $1960

Even though Bank C offers the highest interest rate, the annual fee significantly reduces the total amount earned over four years. Therefore, Bank B would be the best option since it offers a higher interest rate than Bank A and does not have any fees.

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The regular price of the running shoes is $80.

Let's denote the regular price of the running shoes as P. We know that during the sale, the price is reduced by 20%, which means the sales price is 80% (100% - 20%) of the regular price.

Given that the sales price is $64, we can set up the equation:

0.8P = $64

To find the regular price P, we divide both sides of the equation by 0.8:

P = $64 / 0.8

P = $80

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A relationship between two definitions can be seen through the idea of magnitude or distance.

Finding an absolute value of a number requires us to inspect the difference between that figure and zero on a number line; this amount is always positive regardless of whether the initial number was negative or positive. To illustrate, the absolute value of -5 is 5 since there is only five units separating it from zero.

The absolute value primarily entails a totality- recognizing the entirety of someone's peculiarity independent of their direction. It serves as a method of measuring the scope or size of a number without any external parameters or assessment.

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Answer: The first choice.

Step-by-step explanation:

As you can see in the diagram, the line passes through the points[tex](x, y) = (4, -4)[/tex] and [tex](x, y) = (-4, 8)[/tex] . Thus, the slope of the line is [tex]\frac{8-(-4)}{-4-(4)} = \frac{12}{-8} = -\frac{3}{2}.[/tex] Thus, the correct answer is the first choice, as that line has a slope of [tex]-\frac64=-\frac32.[/tex]

Step-by-step explanation:

Steve spends 20% of £200 = 0.2 * £200 = £40 on his football magazine subscription.

The remaining amount he spends on football stickers, sweets, and fizzy drinks in the ratio of 5:2:1, which means that for every 5 parts he spends on football stickers, he spends 2 parts on sweets and 1 part on fizzy drinks.

So, let's call the amount he spends on football stickers "5x". Then, the amount he spends on sweets is "2x" and the amount he spends on fizzy drinks is "x".

The total amount he spends on these items is:

5x + 2x + x = 8x

We know that he has £200 - £40 = £160 left after paying for his magazine subscription. So, we can set up an equation:

8x = £160

Solving for x, we get:

x = £20

Therefore, Steve spends:

5x = 5 * £20 = £100

on football stickers.

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Answer:

5 : 2 : 1 = 100 : 40 : 20

Step-by-step explanation:

10% = 20 (200÷10=20)

20% = 40 (double both sides)

take away £40 from £200 = £160

£160 is left over after buying the magazine subscription

______________________________

add the radio all together = 5:2:1 = 8

divide 8 by 160 = £20

That now means 1 = 20

5 : 2 : 1

we already found 1, now to find 2 and 5

you times 2

1 = 20

2 = 40

and then do the same for 5

1 = 20

5 = 100

To know this is right, 100 + 40 + 20 = 160 the original number for the money left over.

The estimated actual temperature (x) when the temperature adjusted for wind chill (y) is -35 degrees Fahrenheit =

approximately -6.92 degrees Fahrenheit.

To estimate the actual temperature (x) when the temperature adjusted for wind chill (y) is given as -35 degrees Fahrenheit using the formula y = -26 + 1.3x, we can substitute y with -35 and solve for x.

-35 = -26 + 1.3x

Adding 26 to both sides to isolate the x term:

-35 + 26 = 1.3x

-9 = 1.3x

Dividing both sides by 1.3 to solve for x:

x = -9 / 1.3

x ≈ -6.92

Thus, the estimated actual temperature (x) when the temperature adjusted for wind chill (y) is -35 degrees Fahrenheit would be approximately -6.92 degrees Fahrenheit.

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The estimated actual temperature is -6.92 degrees Fahrenheit.

We can use the given formula to solve for x when y is known. Rearranging the formula, we get:

x = (y + 26) / 1.3

Substituting y = -35 into this formula, we get:

x = (-35 + 26) / 1.3

x = -6.92 (rounded to two decimal places)

Therefore, the estimated actual temperature is -6.92 degrees Fahrenheit.

The term actual temperature typically refers to the true or measured temperature of an object, substance, or environment. It is the temperature that is currently present in a given location or situation, as opposed to a predicted or estimated temperature. The actual temperature can be measured using a thermometer or other temperature sensing device.

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Answer:

the value of x is 7

Step-by-step explanation:

First, find the half of the perimeter that is 36 divided by 2 which is 18

Next, write like this

18= l+w( length = width)

which means you have to get the sum of 18

so try sums of 18 randomly like

17 + 1

11 + 7

16+2 etc

but the thing is the value of x must be the same it must not be different so

11 + 7 will be suitable because

11 = 7 + 4

7 = 2 x 7 - 7 = 7

and to find the area which is l x b

11 x 7= 77sq. cm

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Answer:

x=7

Step-by-step explanation:

7+4=11(2)=22

2(7)-7= 14-7= 7(2)=14

22+14=36

The model predicts that the population of the inner-city area will be 107,079 people in 7 years

The number of inhabitants in a given region is characterized as the quantity of individuals normally living around there, estimated on 1 January in a given year.

The given model for the number of inhabitants in the rough part of town region is:

P(t) = 108,000 - 0.011t

where t is the number of years from the present and P(t) is the estimated population at time t.

To find the predicted population in 7 years, we can substitute t=7 into the given model and evaluate:

P(7) = 108,000 - 0.011(7)

P(7) = 108,000 - 0.077

P(7) = 107,923

As a result, the model projects that the inner-city area will have a population of 107,079 people in seven years, rounded to the nearest person.

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The woman invested $4,000 at 5% and $3,000 at 12%.

Let x be the amount invested at 5% and y be the amount invested at 12%. Then we have:

x + y = 7,000 (equation 1)

0.05x + 0.12y = 560 (equation 2)

To solve for x and y, we can use substitution method :

From equation 1, we have y = 7,000 - x. Substituting this into equation 2, we get:

0.05x + 0.12(7,000 - x) = 560

Simplifying and solving for x, we get:

0.05x + 840 - 0.12x = 560

-0.07x = -280

x = 4,000

Substituting x = 4,000 into equation 1, we get:

4,000 + y = 7,000

y = 3,000

Therefore, the woman invested $4,000 at 5% and $3,000 at 12%.

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Answer:

The salary of a paramedic can vary depending on several factors such as location, experience, and employer. According to the Bureau of Labor Statistics, the median annual wage for paramedics and EMTs was $36,650 in May 2020.

Assuming a constant annual income of $36,650 over 30 years, the estimated total income for a paramedic would be:

$36,650 x 30 = $1,099,500

However, it is important to note that this is just an estimate and does not take into account potential salary increases, promotions, or changes in the job market.

Answer:

25.12 m (or 25.13 m)

Step-by-step explanation:

Recall the formula for the circumference of a circle:

[tex]2\pi r[/tex]

where r is the radius.

We are given that the radius is 4 m, so let's plug that into our formula:

[tex]2\pi r=\\2\pi *4=\\8\pi[/tex]

[tex]\pi[/tex] is approximately 3.14, so let's multiply 8 m by 3.14. We get:

25.12

So, the circumference is about 25.12 m.

(if you multiply by pi itself using a calculator, the answer is about 25.13 m)

Answer:

To determine the classification of a triangle based on its side lengths, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the shorter sides) is equal to the square of the length of the hypotenuse (the longest side).

For this particular triangle with side lengths 6 cm, 10 cm, and 12 cm, we can apply the Pythagorean theorem to determine whether the triangle is acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is equal to 90 degrees).

Using the Pythagorean theorem, we find:

6^2 + 10^2 = 136

12^2 = 144

Since 136 is less than 144, we know that 6 cm, 10 cm, and 12 cm are the side lengths of a triangle that is obtuse (one angle is greater than 90 degrees), because the longest side (the hypotenuse) is greater than the sum of the squares of the lengths of the other two sides.

Therefore, the correct answer is: obtuse, because 6^2 + 10^2 < 12^2.

The senior math contest ended at 10:40 pm on Sunday

If the senior math contest began at 6:00 am on a Sunday and ended 1000 minutes later, we can add 1000 minutes to the starting time to find the ending time.

To do this, we can first convert the starting time of 6:00 am into minutes. There are 60 minutes in one hour, so 6:00 am is equivalent to:

6 hours × 60 minutes/hour = 360 minutes

Now, we can add 1000 minutes to this starting time:

360 minutes + 1000 minutes = 1360 minutes

Finally, we can convert this total number of minutes back into hours and minutes.

Since there are 60 minutes in one hour, we can divide 1360 minutes by 60 to get:

1360 minutes ÷ 60 = 22 hours and 40 minutes

Therefore, the senior math contest ended at 10:40 pm on the day (Sunday).

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Answer:

Yes it is a parallelogram because opposite sides of this quadrilateral are equal.

Answer:

[tex] \frac{4}{3} \pi {r}^{3} = 1332[/tex]

[tex]r = \sqrt[3]{ \frac{1332}{ \frac{4}{3}\pi } } = 6.8[/tex]

The radius of this sphere is about 6.8 feet

Answer:

Step-by-step explanation

The answer is 72. 2 x 36 equals 72.

Using Integration,  Area of the curve is 16/3 unit² and the maximum height of the curve is 2 unit.

What exactly is integration?

Integration is a fundamental concept in calculus, which is a branch of mathematics that deals with rates of change and accumulated quantities. Integration is the process of finding the integral of a function, which is the inverse of differentiation.

Now,

For the maximum height that the curve has we have to

put dy/dx=0

d(4x-2x²)/dx=0

4-4x=0

x=4/4

x=1

and when x=1 then y=4*1-2*1²

=4-2

=2

So, the maximum height of the curve is 2 unit.

and for the area

we need to find y.dx for the curve

So,

y.dx=(4x-2x²).dx

=4x+2x²-2x³-2x³/3 for x=0 to x=2

=8+8-16-16/3

=16/3 unit²

Hence, Area of the curve is 16/3 unit².

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a) The mean of the mileage is 90.4 miles per day

b) The median of the mileage is 255.5 miles

Given data ,

Let the data be represented as A

Now , the value of A is

A = { 248 176 379 263 202 }

And , Mean = (248 + 176 + 379 + 263 + 202) / 5 = 452 / 5 = 90.4 miles per day (rounded to one decimal place)

Therefore, the mean of the data is 90.4 miles per day.

To find the median of the data, we need to first put the distances in order from least to greatest:

176, 202, 248, 263, 379

There are 5 data points, so the median is the middle value.

Median = (248 + 263) / 2 = 511 / 2 = 255.5 miles

Hence , the median of the data is 255.5 miles

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The complete question is attached below :

The Swamis family went on a vacation. They recorded the number of miles they drove each day. The mileage is shown in the table. Day 1 2 3 4 5 Distance (mi) 248 176 379 263 202 What is the mean of the data? ____miles What is the median of the data? ______miles

The description describes the solutions to this inequality in all the positive numbers that are greater than ten. The correct option is B.

Relationships between two expressions that aren't equal to one another are known as inequalities. Social justice theories are fundamentally based on the idea of inequality, which is the condition of not being equal, especially in terms of status, rights, and opportunities.

The given equation is 9 > 52.

everything that is positive and bigger than 10

Therefore, the correct option is B. All the positive numbers are greater than ten.

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Answer:

y^2 - 4

Step-by-step explanation:

We are given the statement,'The square of y decreased by the quotient of 28 and 7'. i.e. Subtracting the quotient 28/7 = 4 from y^2 . i.e. y^2 - 4

Hence, the expression which represents the given statement is y^2 - 4 .

The length of the tank should be approximately 150.4 inches in order to hold 450 gallons of water, with a width of 21 inches and a height of 33 inches.

To find the length of the tank, we first need to convert the volume of water from gallons to cubic inches, using the given conversion factor:

1 gallon = 231 cubic inches

Therefore, the volume of water in the tank is:

450 gallons * 231 cubic inches/gallon = 103950 cubic inches

We can then use the formula for the volume of a rectangular prism to find the length of the tank:

Volume = length * width * height

Substituting the given dimensions, and solving for the length, we get:

103950 cubic inches = length * 21 inches * 33 inches

length = 103950 cubic inches / (21 inches * 33 inches)

length ≈ 150.4 inches

Therefore, the length of the tank should be approximately 150.4 inches in order to hold 450 gallons of water, with a width of 21 inches and a height of 33 inches.

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The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is 11400

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

q = 20,000 − 2p

q = 8,500 + 0.5p

The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is when q = q

So, we have

20,000 − 2p = 8,500 + 0.5p

Evaluate the like terms

2.5p = 28500

Divide by 2.5

p = 28500/2.5

Evaluate

p = 11400

Hence, the equilibrium tuition price p is 11400

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The correct option are - A. x²  + (y – 3)²  = 36 and E. x²  + (y + 8)²  = 36 , for the equation of circle.

The standard form equation for just a circle, which is (x - s)² + (y - t)² = r², is used to formulate our equation if we assume a generic centre point like (s,t)and r is the radius of circle.

By simply expanding basic binomial squares in their regular form and merging like words, circles can likewise be presented in expanded form.

Now for the given data:

Put the values in the standard form of the circle:

(x - s)² + (y - t)² = r²,

(x - 0)² + (y - t)² = 6²,

x² + (y - t)² = 36

Where 't' can be any integer.

Thus, the options that satisfy the stated conditions are-

A. x²  + (y – 3)²  = 36 : here t = 3

and E. x²  + (y + 8)²  = 36 ; here t = - 8.

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Correct question:

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis?

Select two options.

A. x²  + (y – 3)²  = 36

B. x²  + (y – 5)²  = 6

C. (x – 4)² + y² = 36

D. (x + 6)² + y² = 144

E. x²  + (y + 8)²  = 36