Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function

The percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Given data:

44, 19, 51, 12, 34, 21, 15, 24

fuel efficiency less than 24 mpg is 19, 12, 21, 15

So, the percentage is

=4 / 8 x 100

= 1/2 x 100

= 50%

Hence, the percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.

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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

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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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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(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

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 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.

we have the equation

Solve for x

Step 1

squared both sides

The answer is x=5

olution:

Recall the Fundamental Counting principle; if there are m ways to make a selection and n ways to make a second selection, then there are m x n number of ways in which two selection can be made.

ut of the provided digits, if the number ends with 3

ase 1: Tnumber of one digit numbers.

ut of the digits provided, only one way to fil;l the box that is with one.

Thus, there is one digit odd integer here.

Case 2: The number of two digits.

Out of the digits provided, only one way to fill the last box is with digit 3, and any one of the 4 digits can filled in it as 0 cannot filled in either of the box.

Thus, number of ways are;

Aase 3: The number of three digit numbers.

ut of the digits provided, only one way to flll the last box is with digit 3, and any one of the 5 digits can be filled in second box, and thus any one of the 4 digits can be filled in first box as 0 cannot be fixed in the box.

Thus, number of ways are;

Lastly;

: The numbver of four digit numbers.

he number of ways are;

Thus, the total number of ways to select are;

INAL ANSWER: 125

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:

8

Step-by-step explanation:

To find the time the rocket is in the air, we can find the time when the height is 0 (remember this time is not 0).

[tex]-16t^2+128t=0 \\ \\ t^2-8t=0 \\ \\ t(t-8)=0 \\ \\ t=0,8 \\ \\ t \neq 0 \implies t=8[/tex]

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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Solve for (f - g)(x)

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:

7⁻²=[tex]\frac{1}{49}[/tex]

3⁻⁴ [tex]=\frac{1}{81}[/tex]

9⁰=1

11⁻¹=[tex]\frac{1}{11}[/tex]

Answer:

lets denote x as 6

so,

(x-2)÷2

(6-2)÷2

4÷2

2(proved)

Given

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.

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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Well, here is the answer . . .

£12 = 13.73€

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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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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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:

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

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:

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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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:

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