The graph of a function g is shown below.
Use the graph of the function to find its average rate of change from x=-2 to x=4.
Simplify your answer as much as possible.
1-10

width = 7

length = 10

Step-by-step explanation:

solve for the one letter that gets talked about the most

which is w or width

width = w

length = 3 + w

2 inch border means

width = w + 2

length = 3 + w + 2

area = length times width

area = ( 3 + w + 2 ) times (w + 2 )

108 = ( 3 + w + 2 ) times (w + 2 )

108 = ( w + 5 ) times (w + 2 )

( w + 5 ) times (w + 2 ) = 108

w^2 + 7w +10 = 108

w^2 + 7w - 98 = 0

going to make w = x

x^2+7x-98=0

(x-7)(x+14)

x = 7

x = -14

w=7

w= -14

cant have a negative measurement so w=7 is used

width = w

length = 3 + w

width = 7

length = 3 + 7 = 10

Answer:

160

Step-by-step explanation:

22+18=40, and this was 25% of the cars.

So, 40(4)=160 cars were sold that week.

The number of cars Captain's Autos sold in total that week is 160.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Number of used car on monday= 22

Number of cars on tuesday= 18

Now,

Let's call the total number of cars sold during the week "x".

We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:

22 + 18 = 0.25x

Simplifying, we get:

40 = 0.25x

Dividing both sides by 0.25, we get:

x = 160

Therefore, by the unitary method the answer will be 160.

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Without using general formula we will solve it in bit lengthy manner

For first half

Time=Distance/Speed

For second half

Time

So

Average speed

Option C

The answer is 412.3 km/h.

The formula to find average velocity is :

[tex]\boxed {V_{avg} = \frac{d_{1}+d_{2}}{t_{1}+t_{2}}}[/tex]

Let's find t₁ and t₂.

Now, let's substitute in the formula to get the answer.

Answer:

13

Step-by-step explanation:

3x + 7

x = 2

3 × 2 + 7 = 6 + 7 = 13

Hi there.

3x+7

x=2 :

3(2)+7

6+7

13

That's it.

The value of ∠B is 60 degrees

The given parameters are

2∠A = 3∠B = 6∠C

Let the angles in a triangle ABC be ∠A, ∠B and ∠C.

The sum of these angles in the triangle ABC is

∠A + ∠B + ∠C = 180

Multiply the above equation by 2

2 * (∠A + ∠B + ∠C) = 2 * 180

Evaluate the product

2∠A + 2∠B + 2∠C = 360

Recall that 2∠A = 3∠B.

Substitute the above in the equation 2∠A + 2∠B + 2∠C = 360

3∠B + 2∠B + 2∠C = 360

This gives

5∠B + 2∠C = 360

Multiply the above equation by 3

3 * (5∠B + 2∠C) = 3 * 360

Evaluate the product

15∠B + 6∠C = 1080

Recall that 3∠B = 6∠C.

Substitute the above in the equation

So, we have:

15∠B + 3∠B = 1080

Evaluate the like terms

18∠B = 1080

Divide both sides by 18

∠B = 60

Hence, the value of ∠B is 60 degrees

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Answer:

a=170

Step-by-step explanation:

(a+10)=180[because being a straight line]

or, a+10=180

or,a=180-10

a=170

Therefore,a=170

Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

It states that, for a normally distributed random variable:

Considering the mean of 110 and the standard deviation of 15, we have that:

These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

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The probabilities of the given events are:

A. P(even) = P(A) = 7/15

B. P(multiple) = P(B) = 3/15

C. P(prime) = 6/15

D. P(B|A) = 3/7

Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.

P(E) = n(E)/n(S)

The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

So, n(S) = 15

A. The selected number is even:

Consider the event as A.

The set of even numbers in the given sample is {2,4,6,8,10,12,14}

So, n(A) = 7

Then, the required probability is

P(A) = n(A)/n(S)

       = 7/15

B. The selected number is a multiple of 4:

Consider the event as B.

The set of multiples of 4 in the given sample is {4,8,12}

So, n(B) = 3

Then, the required probability is

P(B) = n(B)/n(S)

       = 3/15

C. The selected number is prime:

Consider the event as C.

The set of prime numbers in the given sample is {2,3,5,7,11,13}

So, n(C) = 6

Then, the required probability is

P(C) = n(C)/n(S)

       = 6/15

D. calculate P(B|A):

Since events B and A are dependent events of the same sample,

n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is

P(B|A) = n(A∩B)/n(A)

⇒ P(B|A) = 3/7

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Answer:

1436.76

Step-by-step explanation:

Answer:

538.57 m³

Step-by-step explanation:

The formula to find the volume of a sphere is:

V = 4 π r³

Given that,

diameter ⇒ 7 m

∴ radius = d / 2

  radius ( r ) = 7 / 2 = 3.5 m

Let us find the volume now.

V = 4 π r³

V = 4 π × ( 3.5 )³

V = 4 π × ( 3.5 )³

V = 4 π × 42.875

V = 4 π × 42.88

V = 12.56 ×  42.88

V = 538.57 m³

The type of bias which is most likely to be present in the survey results is undercoverage bias because adults with older children are more likely to be included in the sample.

This is a diligent inquiry or examination to seek or revise facts, principles, theories,or applications. It is used to make an extensive investigation or search for truth in an experiment.

Bias

In statistics, bias is the difference between the expectation of the sample estimator and the true population value, which reduces the representativeness of the estimator by systematically distorting it

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Take HJ = x, GH = y and GJ = z

put the value of x from equation 1 in equation 2

[tex]{ \qquad❖ \: \sf \:z = (y + 2) + y - 17} [/tex]

[tex]{ \qquad❖ \: \sf \:z = 2y - 15} [/tex]

now, put the value of x and z in equation 3

[tex]{ \qquad❖ \: \sf \:y + 2 + y + 2y - 15 = 73} [/tex]

[tex]{ \qquad❖ \: \sf \:4y - 13 = 73} [/tex]

[tex]{ \qquad❖ \: \sf \:4y = 86} [/tex]

[tex]{ \qquad❖ \: \sf \:y = 21.5 \: \: in} [/tex]

Now, we need to find HJ (x)

[tex]{ \qquad❖ \: \sf \:x = y + 2} [/tex]

[tex]{ \qquad❖ \: \sf \:x = 21.5 + 2} [/tex]

[tex]{ \qquad❖ \: \sf \:x = 23.5 \: \: in} [/tex]

[tex]{ \qquad \large \sf {Conclusion} :} [/tex]

I'm tentatively changing my answer to say this kind of relies on practical knowledge of how stores tend to operate. If 20 coupons are given out, the store has sold all 500 shirts, arguably at a loss to the retailer. They have to have more shirts in stock to be sold at full price because, well, that's how they make money. It's more likely that such a store would carry more than just 500 shirts at the start of each day, so A is (probably) wrong.

The transformation of the function is illustrated below

Parent function is: f(x) = 2x - 6

Transformations are:

shifts f(x) 4 units down

f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10

stretches f(x) by a factor of 4 away from the x-axis

f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24

shifts f(x) 4 units right

f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14

compresses f(x) by a factor of toward the y-axis (must be 4)

f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6

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The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m

According to the statement

we have given that the Triangular prism of size 0.75 m, 1m and length of 2m.

And we have to find the by which size of advertisement board need to fill the longest side of the shape.

A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

So, for this purpose,

we know that the longest side of triangular prism is 2m and we have to cover it with the advertising board.

Obviously the length of the advertising board is of 2m to cover the longest side of the shape.

So, The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m

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Answer:

Option 3: -2

Step-by-step explanation:

The slope of the graph is negative, and the only option with a negative term for the slope is -2.

So the slope of the graph is -2.

The required answers are calculated by using the simple interest formula:

a. She needs to deposit $793.65 in the account each month

b. The total money she put into an account for a year is $285,714.29

c. The total interest she earns is $514,285.71

The formula for the simple interest is

A = P(1 + RT)

Where,

A - amount after T years

P - principal amount

R - the rate of interest

T - time (years)

It is given that,

A = 8,00,000

T = 30 years

R = 6% = 0.06

So,

a. Finding the amount needs to deposit in the account each month:

We have A = P(1 + RT)

⇒ P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

Thus, the amount needs to deposit in the account for each month

= P/T×12

= 285,714.29/30×12

= $793.65

b. Finding the total money that she put into account:

That is nothing but,

P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

c. FInding the total interest:

We have I = A - P

⇒ I = 8,00,000 - 285,714.29

∴ I = $514,285.71

Therefore, a. $793.65, b. $285,714.29, and c. $514,285.71

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Answer:

15 $1 bills

10 $5 bills

10 $10 bills

Step-by-step explanation:

Let x = number of $1 bills

"There are five fewer $5-bills than $1-bills."

The number of $5 bills is x - 5

"There are half as many $10-bills as $5-bills."

The number of $10 bills is (x - 5)/2.

A $1 bill is worth $1.

x $1 bills are worth x × 1 = x dollars

A $5 bill is worth $5.

x - 5 $5 are worth 5(x - 5) dollars.

A $10 bill is worth $10.

(x - 5)/2 $10 bills are worth 10(x - 5)/2 = 5(x - 5) dollars.

Now we add the value of each type of bills and set it equal to $115.

x + 5(x - 5) + 5(x - 5) = 115

x + 10(x - 5) = 115

x + 10x - 50 = 115

11x = 165

x = 15

There are 15 $1 bills.

$5 bills: x - 5 = 10 - 5 = 10

There are 10 $5 bills

$10 bills: (x - 5)/2 = (15 - 5)/2 = 5

There are 5 $10 bills

Answer: 15 $1 bills; 10 $5 bills; 10 $10 bills

Check:

First, we check the total value of the bills.

15 $1 bills are worth $15

10 $5 bills are worth $50

10 $10 bills are worth $50

$15 + $50 + $50 = $115

The total does add up to $115.

Now we check the numbers of bills of each denomination.

The number of $1 is 15.

The number of $5 is 5 fewer that 15, so it is 10.

The number of $10 bills is half the number of $5 bills, so it is 5.

All the given information checks out in the answer. The answer is correct.

Find where the two curves meet.

[tex]x^3 - x^2 + x + 8 = 5x^2 - 7x + 8 \\\\ \implies x^3 - 6x^2 + 8x = 0 \\\\ \implies x (x-2) (x - 4)= 0 \implies x=0, x=2, x=4[/tex]

The area between the curves is

[tex]\displaystyle \int_0^4 \left|\left(x^3-x^2+x+8\right) - \left(5x^2 - 7x + 8\right)\right| \, dx = \int_0^4 \left|x(x-2)(x-4)\right| \, dx[/tex]

When [tex]x[/tex] is between 0 and 2, [tex]x(x-2)(x-4)[/tex] is positive; when [tex]x[/tex] is between 2 and 4, [tex]x(x-2)(x-4)[/tex] is negative. So we split the integral at [tex]x=2[/tex] to get

[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_2^4 x(x-2)(x-4)\,dx[/tex]

In the second integral, substitute [tex]y=x-2[/tex] to get

[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_0^2 (y+2)y(y-2)\,dy[/tex]

[tex]\displaystyle \int_0^2 x(x-2) \bigg((x-4) - (x+2)\bigg) \, dx[/tex]

[tex]\displaystyle -6 \int_0^2 x(x-2) \, dx[/tex]

[tex]\displaystyle 6 \int_0^2 \left(2x - x^2\right) \, dx[/tex]

[tex]\displaystyle 6 \left(x^2 - \frac13x^3\right)\bigg|_0^2 = \boxed{8}[/tex]

Answer:

120 four digit numbers can be created from the gives.

Step-by-step explanation:

Solution

You are given 5 digits in the givens.

1 3 5 7 9

Therefore

5 * 4 * 3 * 2 is the answer to your question. 4 and 3 and 2 determine that none of the digits can be repeated. That equals 120.

Answer:

x  = 9, y = 13 , z = - 19

Step-by-step explanation:

3y + 4z = - 37 → (1)

2x + 4y - 3z = 127 → (2)

4y = 52 → (3)

divide both sides by 4 in (3)

y = 13

substitute y = 13 into (2) and solve for z

3(13) + 4z = - 37

39 + 4z = - 37 ( subtract 39 from both sides )

4z = - - 76 ( divide both sides by 4 )

z = - 19

substitute y = 13 and z = - 19 into (2) and solve for x

2x + 4(13) - 3(- 19) = 127

2x + 52 + 57 = 127

2x + 109 = 127 ( subtract 109 from both sides )

2x = 18 ( divide both sides by 2 )

x = 9

solution is x = 9, y = 13 , z = - 19

Answer:

600

Step-by-step explanation:

250/1 times 6/ 100 times 40/1

Using translation concepts, the equation for function g is given by:

g(x) = 7x/3 + 1.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

Supposing that we have a function f(x), a horizontal compression by a factor of a is equivalent to finding f(ax).

In this problem, the function is:

f(x) = 7x + 1.

For the horizontal compression by a factor of 1/3, we have that:

g(x) = f(1/3x) = 7x/3 + 1.

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Answer:

-1/3

5

Step-by-step explanation:

We need to complete

y = mx + b

with a slope, m, and with the y-intercept, b.

From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.

We now have y = mx + 5.

Now we need the slope.

We pick two points that are easy to read, (0, 5) and (3, 4).

m = slope = rise/run

To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.

Then we go left horizontally 3 units. The run is -3.

m = slope = rise/run = 1/(-3) = -1/3

Now we have the slope, so we can finish.

y = -1/3 x + 5

Answer:

-1/3

5

Answer:

1,920 watts per circuit

Step-by-step explanation:

To find the load for 1 circuit (per circuit) we can divide 28,800 watts by 15 circuits

28800/15 = 1,920 watts per circuit

[tex]x[/tex] and [tex]3x+5[/tex] are being multiplied to form the expression, and are not being added or subtracted.

Here, x and (3x+5) are given in the form of multiplication, instead of being separated by addition or subtraction. This is why x and (3x+5) are factors of the expression x(3x + 5)² and not terms of the expression.

What are terms and factors in an expression?

Terms of an expression can be a variable, a signed number, or a constant multiplied by one or more variables. On the other hand, the factors are the items that have been multiplied by another items. Any integer, variable, phrase, or lengthier expression can be a factor.

For instance, the expression 2x(y - 5) has three components: 2, x, and (y-3). These three components are its factors, since when multiplied, they produce the same expression. The factors may or may not be comprised of more than one terms.

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The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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if any number or variable is outside a parenthesis it will go to all the number rin the parenthesis.

in this case -y is outside the parenthesis so it will got to both the sides :

-y(-6y-3) = -6y x y - 3 x y

= -6y² -3y//

The expression, the  fifth term of the binomial expansion is y^4

Binomial expansion is a means of expanding expressions into terms

Given the expression (x+y)^4, according to the theorem, as the power of x is decreasing, the power of y will be increasing up till the power of the expression.

Expand (x+y)^4

(x+y)^4 = x^4y^0 + x^3y^1 + x^2y^2 + xy^3 + x^0y^4

Include the coefficients according to the Pascal triangle to have:

(x+y)^4 = x^4y^0 + 4x^3y^1 + 6x^2y^2 + 4xy^3 + x^0y^4

(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

From the expression, the  fifth term of the binomial expansion is y^4

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