Write a polynomial f (x) that satisfies the given conditions.
Polynomial of lowest degree with zeros of -4 (multiplicity 3), 3 (multiplicity 1), and with f (0) =960.
f (x)=

greater than 1. If its less than, it will be decreasing.

Given:

Depreciation rate = 75% per year.

Let's find the value of the car in 2 years.

Given:

Cost = $16,500

Depreciation rate = 75%

From the equation we have:

Present value, a = 16500

x is the number of years = 2

Thus, we have:

Therefore, the value of the car in 2 years is $1,031

ANSWER:

$1,031

Answer:

Step-by-step explanation:

it is y

Answer: Y=0x +5

Step-by-step explanation

its going up by 0 so 0x and you start at 5 so plus 5

The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is given by adding the two other ones, we will get:

862x^2 + 93x + 24,621

Here we have two polynomials:

Both of these are in gigawatts, so are in the same units, which means that we can directly add the two polynomials to get a polynomial for the total electricity.

-17x^2 + 165x + 14,481 + 879x^2 - 72x + 10,140

Now we group like terms:

(-17x^2 + 879x^2) + (165x - 72x) + (14,481 + 10,140)

862x^2 + 93x + 24,621

This polynomial represents the total electricity generated during 2002-2007

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For function f(x) = (x − 1)³ and g(x) = 1-6x ,value of following function is:

a. (f ∘ g)(x)=-216x³

b. (g ∘ f)(x)=-6x³+18x²-18x+7

c. f(f(x))=(x³ -3x² +3x -2)³

d. f²(x)=(x-1)⁶

As given,

Given function :

f(x)=(x − 1)³

g(x)=1-6x

The value of following functions are:

a.(f ∘ g)(x)

=f(g(x))

=f(1-6x)

=(1-6x -1)³

=(-6x)³

=-216x³

b.  (g ∘ f)(x)

= g(f(x))

=g(x − 1)³

=1 -6(x − 1)³

=1 -6(x³ -3x² +3x -1)

=-6x³+18x² -18x+7

c. f(f(x))

=f(x-1)³

=((x-1)³ -1)³

=(x³ -3x² +3x -1-1)³

=(x³ -3x² +3x -2)³

d. f²(x)= (f · f)(x)

=f(x) × f(x)

=(x-1)³ × (x -1)³

=(x -1)⁶

Therefore, for function f(x) = (x − 1)³ and g(x) = 1-6x ,the value of following function is:

a. (f ∘ g)(x)=-216x³

b. (g ∘ f)(x)=-6x³+18x²-18x+7

c. f(f(x))=(x³ -3x² +3x -2)³

d. f²(x)=(x-1)⁶

The complete question is:

For function f(x) = (x − 1)³ and g(x) = 1-6x find the value of the following.

a. (f ∘ g)(x)

b. (g ∘ f)(x)

c. f(f(x))

d. f²(x)= (f · f)(x)

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Well, here is the answer . . .

£12 = 13.73€

we have the equation

Solve for x

Step 1

squared both sides

The answer is x=5

The the minimum and maximum possible measures of 31 centimeters is {30.5. 31.5}

To find it, one need to add the biggest possible inaccuracy to each measurement, then multiply to get the biggest volume you can. Also Subtract the largest potential mistake from each measurement, then multiply, to to know the smallest volume that can be produced.

Note that the smallest value in the data set is the minimum. The highest value in the data collection is called the maximum.

Since only one data set is given, the  possible measures can only be around it hence the largest and the smallest value close to it.

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Based on the equation, the value of x in 8x^2 + 9 = 313 is 6.2

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

8x^2 + 9 = 313

Subtract 9 from both sides of the quadratic equation

So, we have

8x^2 + 9 - 9 = 313 - 9

Evaluate the difference in the above equation

So, we have

8x^2 = 304

Divide both sides of the quadratic equation by 8

So, we have

8x^2/8 = 304/8

Evaluate the quotient in the above equation

So, we have

x^2 = 38

Take the square root of both sides

x = 6.2

Hence, the value of x in the quadratic equation given as 8x^2 + 9 = 313 is 6.2

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The probability of getting 12 p events is 0.0139

The expected value, or mean, of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of successes (p), or n x p.

The binomial distribution formula is calculated as:

[tex]P(x:n,p) = ^nC_x * p^x*(1-p)^ {n-x}[/tex]

where:

n is the number of trials (occurrences)

X is the number of successful trials

p is probability of success in a single trial

is the combination of n and x. A combination is the number of ways to choose a sample of x elements from a set of n distinct objects where order does not matter and replacements are not allowed.

So, we have given that N = 15, P = 0.50 , and x = 12

So,

[tex]^{15}C_1_2 * (0.50)^{12}*(1-0.50)^ {15-12}\\^{15}C_1_2 * 0.50^{12}*(0.50)^ {3}\\[/tex]

=0.0139

Therefore, the probability of getting exactly 12 P events is 0.0139

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Answer:

Side = 10 units

Step-by-step explanation:

Original square area = s x s =s^2    

       now change the sides  and this equals 6s^2

3s  *  ( s+10)  = 6 s^2

                         3s^2 -30s = 0

                              s ( 3s-30) = 0      so s = 0   or  10

(3x+5)-([tex]x^{2} - 3[/tex])=9

[tex]x^{2}[/tex]-3x-8=-9

[tex]x^{2}[/tex]-3x=-1

[tex]x^{2}[/tex]-3x+1=0

Considering the z-test formula, it is found that:

a) Increasing the difference between the sample mean and the original population mean increases the test statistic.

b) Increasing the population standard deviation decreases the test statistic.

c) Increasing the sample size increases the test statistic.

Considering a z-test, the formula for the test statistic is given by the following rule:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which the parameters are defined as follows:

In item a, increasing the difference between the sample mean and the original population mean is increasing the numerator [tex]\overline{x} - \mu[/tex], meaning that the test statistic z will be increased.

In item b, increasing the population standard deviation [tex]\sigma[/tex] means that the denominator of the formula will be increasing, hence the test statistic will be decreased.

In item c, increasing the sample size n means that the denominator will be decreased, as the denominator is a fraction which is inverse proportional to the sample size, hence the test statistic z will be increased.

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Answer: 6.67

Step-by-step explanation: first you divide 4 and 3 to then get 1.3 and times that by 5

Solve for (f - g)(x)

Yes, there is enough information to prove m||n.

By using the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem we can prove that line m is parallel to line n.

In the given figure,

Let the given angles formed by transversal r, adjacent to line m be angle 1, and to line n be angle 2.

Now, the vertically opposite angle to angle 1 will be equal to it as they both are congruent.

The vertically opposite angle equal to angle 1 would be corresponding to angle 2 and corresponding angles formed by a transversal are equal and congruent.

Moreover, angle 1 and angle 2 are alternate exterior angles and by Alternate Exterior Angles Theorem, they are congruent.

Hence, it is proved by the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem that line m is parallel to line n (m||n).

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Answer:

m=-4/3

Explanation:

Given the points: (13,-4) and (1, 12)

To determine the slope of the line that joins the point, use the formula below;

Substitute the given points:

The slope is -4/3.

The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be 5/11.

It should be noted that probability simply means the likelihood that a particular event will happen.

In this case, there are there are 5 Democrats and 6 Republicans and rour of these people will be randomly chosen for early release.

The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be:

Number of Democrats = 5

Number of Republicans = 6

Total number = 5 + 6 = 11

This will be illustrated through the combination formula:

= (5C2 × 6C2) / 11C4

= (10 × 15) / 330

= 150/330

= 5/11

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The expression equivalent to [-40 + (-20) + (-60)] is [−20 + (−40) + (−60)]

As per the question statement, we are provided with a linear expression of [-40 + (-20) + (-60)], and four options.

We are supposed to determine the one expression from the given options, that is equivalent to the question mentioned expression of [-40 + (-20) + (-60)].

To solve this question, we will first calculate the value of the question mentioned equation, and then, calculate and compare the values of individual expressions provided in the options, to obtain our desired answer.

Therefore, [-40 + (-20) + (-60)] = [-40 - 20 -60]

or, [-40 + (-20) + (-60)] = -( 40 + 20 + 60)

or, [-40 + (-20) + (-60)] = -120.

Now, coming to the first option, expression [−40 − (20 − 60)] equates to

[-40 - (-40)] = (-40 + 40) = (40 - 40) = 0,

And [0 ≠ (-120),

Hence, [−40 − (20 − 60)] is not the equivalent expression to

[-40 + (-20) + (-60)].

Now, coming to the second option, expression [-(40 − 20) + (-60)] equates to [-(20) + (-60)] = (-20 - 60) = -(20 + 60) = (-80),

But again, [(-80) ≠ (-120)],

Hence, [-(40 − 20) + (-60)]  is not the equivalent expression to

[-40 + (-20) + (-60)].

Coming to the third option, expression [40 + 20 + 60] equates to (120)

But again, [120 ≠ (-120)],

Hence, [40 + 20 + 60] is not the equivalent expression to

[-40 + (-20) + (-60)].

Finally, Coming to the last option, expression [−20 + (−40) + (−60)] equates to (-20 - 40 - 60) = -(20 + 40 + 60) = (-120).

And [(-120) = (-120)],

Hence, [−20 + (−40) + (−60)]  is the required equivalent expression to

[-40 + (-20) + (-60)].

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Answer:

−20+(−40)+(−60)

Step-by-step explanation:

they add up to the same thing and the order doesn't matter I think.

Answer:

7⁻²=[tex]\frac{1}{49}[/tex]

3⁻⁴ [tex]=\frac{1}{81}[/tex]

9⁰=1

11⁻¹=[tex]\frac{1}{11}[/tex]

The most appropriate choice for speed will be given by-

Speed of plane in still air = 610 miles/hour

Speed of wind = 20 miles/hour

What is speed?

Distance travelled by a body in unit time is called speed.

Let the speed of plane in still air be x miles/hour

Speed of wind be y miles/hour

A plane traveled 3465 miles with the wind in 5.5 hours

So,

x + y = [tex]\frac{3465}{5.5}[/tex]

x + y = 630.......(1)

The plane travelled 3245 miles against the wind in the same amount of time

so,

x - y = [tex]\frac{3245}{5.5}[/tex]

x - y = 590.......(2)

Adding (1) and (2),

2x = 1220

x = [tex]\frac{1220}{2}[/tex]

x = 610 miles/hour

Putting the value of x in (1),

610 + y = 630

y = 630 - 610

y = 20 miles/hour

Speed of plane in still air = 610 miles/hour

Speed of wind = 20 miles/hour

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Answer:

349.42499999998

Step-by-step explanation:

$232.95 divided by 22 hours of work = amount per hour = 10.588636363636

If you get paid 10.588636363636 per hour then multiply this by 33 hours to get the answer of : $349 and 42499999998 cents

Given

Answer:

B. If I don't eat pizza after midnight, then I won't have a stomach ache.

From the graph, we can determine that the function f(x) is quadratic. The function f(x) is defined as:

The graph of (a) 1/2 f(x):

This implies that f(x) is compressed vertically by a factor of 1/2.

Using the points:

(-4, 8) , (-2, 2), (0,0), (2,2), (4, 8)

The graph of the function using a graphing calculator is shown below:

The graph of (b) 2 f(x)

This implies that the original function was stretched vertically by a factor of 2

Using the points:

(-4, 32), (-2, 8), (0,0), (2,8), (4,32)

The graph using a graphing calculator is shown below:

The domain:

This is a set of allowable x-values

Using interval notation:

The range:

This is a set of allowable y-values:

Using interval notation:

We are given the quadratic function c(p) = p^2 - 28p + 250 and we need to rewrite this in such a way that the minimum value is easy to find.

Remember that the vertex

where (h, k) is the vertex or the minimum point.

We use completing the squares method to do this. We divide the second term, -28p, by 2p, then square it.

We add 196 to p^2 - 28p to make it equal to (p - 14)^2, but since it will change the value of the equation, we need to subtract the same value from 250 so that the net effect is zero.

The equation is c(p) = (p - 14)^2 + 54.

Answer:

lets denote x as 6

so,

(x-2)÷2

(6-2)÷2

4÷2

2(proved)

If Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.

Given data  or information :

Product  = ( – 25. 31 ) (9. 61)

Now let estimate the product by first  approximating the product to the nearest tenth.

Approximation :

So,

-25.31 = - 25 ( Approximately )

9.61 =10 ( Approximately )

Hence , her estimate can be calculated as :

Estimate :

Estimate =  (-25) (10)

Estimate =-250

Therefore based on the information or data  given if  Seema  tend to make used of  compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.

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The length of each side of the octagon would be 8.23 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

We are aware that one side of the square is 20 inches long and that one side is made up of the length of the octagon added. We also know that two sides of a right triangle have smaller angles inside that are 45 degrees, making those two sides equal to one another. Therefore, we add the two sides of the right angle triangle to the side of the octagon, which equals 20 inches, to determine the value of x, which is designated as the side of the octagon.

Since a side of the square is 20 inches

Here, y is the two equal sides of the right-angle triangle

So y + x + y = 20

Using Pythagoras's theorem for the right angle triangle

y² + y² = x²

2y² = x²

y² = (x²)/2

y = x /√2

So substitute the value of y = x /√2 in the equation

x /√2 + x + x /√2 = 20

2x /√2 + x = 20

2x /√2 + x√2 /√2 = 20

x[2/√2 + √2 /√2] = 20

x[(2 + √2) /√2] = 20

x(2 + √2) = 20√2

x = 20√2/(2 + √2)

x = 28.2843/3.4142 = 8.2343

Round to the nearest hundredth of an inch

x = 8.23

Therefore, the length of each side of the octagon would be 8.23 inches.

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We use the following formula for integration:

We have the following integral:

Separate into two integrals:

Calculate the first integral. Take the coefficient out of the integral:

Apply the integration formula:

Calculate the second integral. Take the coefficient out of the integral:

Express the radical as a fractional exponent:

Apply the integration formula:

The total integral is: