What is the mean of 13, 7, 8 and 4

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:

R-1={(2,1),(3,2),(9,3),(5,4)

Step-by-step explanation:

R-1={(2,1),(3,2),(9,3),(5,4) because (- 1) means reverse in relation

The sum of the set of x - values given to us is calculated as; ∑X = -1

We are given;

X1 = 2, X2 = -8, X3 = 4, X4 = -8 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6

1) ∑X = X1 + X2 + X3 + X4

∑X = 2 + (-8) + 4 + 1 = -1

2) ∑Y = Y1 + Y2 + Y3 + Y4

∑Y = 3 + (-8) + 10 + 6

∑Y = -11

3) ∑ X² = X₁² + X₂² + X₃² + X₄²

∑X² = (2)² + (-8)² + (4)² + (1)²

∑X² = 85

4) ∑Y² = Y₁² + Y₂² + Y₃² + Y₄²

∑X² = (-3)² + (-8)² + (10)² + (6)²

∑X² = 209

Complete question is;

Two variables, X and Y assume the values X1 = 2, X2 = -5, X3 = 4, X4 = 1 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6, respectively. Calculate (a) ∑X, (b) ∑ Y, (c) ∑ X² (d) ∑ Y²

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Answer:

The answer is 2970

Step-by-step explanation:

Collectively, all the students can make about 54 books rds per minute (27 * 2)

Therefore in 55 minutes there should be 2970

(54*55) :)

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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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 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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The intercepts of the given equations is as given in the task content is; Choice B; (15,0,0),(0,10,0) ,(0,0,5).

The x-intercept of the given equation can be determined by setting values of y and z to zero.

The y-intercept can be determined by setting x and z to zero.

While the z-intercept can be determined by setting x and y to zero.

Consequently, the X-intercept of the given equations is; 2x +3(0) = 30; x = 15.

Therefore, we have; (15,0,0)

The y-intercept is therefore; 2(0) +3y = 30; 3y = 30; y = 30/3 = 10 and. we have; (0,15,0)

And hence, the z-intercept is; z = 30/6 = 5.

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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

f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.

⇒ f(x) =  a(x - r₁)(x - r₂)(x - r₃)

where a is the leading coefficient

Here in the question it is given that,

By using the formula of polynomial function we get,

⇒ f(x) =  a(x - r₁)(x - r₂)(x - r₃)

⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))

⇒ f(x) = 1(x + 3)(x - 4)(x + 3)

⇒ f(x) = (x + 3)(x² - x - 12)

⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36

⇒ f(x) = x³ + 2x² - 15x - 36

Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.

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The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.

A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.

A 2-digit number is any number between 10 and 99.

According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.

Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.

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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:

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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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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Step-by-step explanation:

Divide, the same as ÷

divide 6 by 3

by is the same as the symbol

6 ÷ 3 = 2

Difference, This is another way of saying take away or minus

the difference of 6 and 3 is

6 - 3 = 3

Product, This is another word for multiply or times

the product of 2 and 3 is

2 × 3 = 6

divide (÷)  the difference of 20 and 6 (20 - 6) by the product of 7 and 2       (7 × 2)

so

(20 - 6) ÷ (7 × 2)

can you do the rest???

1. The best way that we can represent the condo that Claire bought is by option B. [tex]350000(1.05)^{t}[/tex]

To determine the function, we would have to do so by making use of the given equation that we have here.

This is given as

Ct = [tex]A(1+r)^t[/tex]

Where a is the principal

r is the rate of interest and

t is the time

2. we have 70 = 30(1.03)^t

70/30 = (1.03)^t

We have to take the log of the function above in order to find the value of t

t = 28.665

This is approximated to 29

Hence the answer here is option A after 29 weeks.

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Benjamin is correct about the diameter being perpendicular to each other and the points connected around the circle.

The steps involved in inscribing a square in a circle include;

Alicia deductions were;

Draws two diameters and connects the points where the diameters intersect the circle, in order, around the circle

Benjamin's deductions;

The diameters must be perpendicular to each other. Then connect the points, in order, around the circle

Caleb's deduction;

No need to draw the second diameter. A triangle when inscribed in a semicircle is a right triangle, forms semicircles, one in each semicircle. Together the two triangles will make a square.

It can be concluded from their different postulations that Benjamin is correct because the diameter must be perpendicular to each other and the points connected around the circle to form a square.

Thus, Benjamin is correct about the diameter being perpendicular to each other and the points connected around the circle.

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Answer:

m=8

Step-by-step explanation:

-5m=-40

divide both side by -5

-5m=-40

-5=-5 answer is m=8

[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]

Answer:

160 cm × 120 cm

Step-by-step explanation:

this means 1 cm turns into 20 cm.

so, 8 cm × 6 cm becomes

8×20 = 160 cm × 6×20 = 120 cm

The graph is shown in the attached image.

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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Answer:

963 hours

Step-by-step explanation:

I subtracted 20 from the 981

The correct answer for the hours elaine spend attending classes is  [tex]817.5[/tex]  hours.

Given,

The time spent doing homework was 20% less than the time she spent attending class.

Assume the time Elaine spent attending class is "x" hours.

So, the time spent on these activities is 0.2 * x hours.

Now, the total time  spent attending class, doing homework, or  in extracurricular activities is 981 hours.

The equation representing the total time is:

[tex]x + 0.2x = 981[/tex]

solve for "x":

[tex]1.2x = 981[/tex]

[tex]x= \dfrac{981}{1.2}[/tex]

[tex]x= 817.5[/tex]

Elaine spent approximately [tex]817.5[/tex] hours attending class.

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The correct answer is Option 4.

Last box

As it's 7:2

Difference between x and y must increase in big number as x and y increases

Option D is correct in that manner

Let's double check

Step-by-step explanation:

(52900 ÷ 28.7) × 100 = 184320 ( rounded to nearest whole number, since you cannot have half humans)

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