19-42 evaluate the integral.
23. [tex]\int_{0}^{2}(2 x-3)\left(4 x^{2}+1\right) d x[/tex]

Answer: The sample of the survey was 3000 teenagers
               The population of the survey was teenagers across the state

Step-by-step explanation:

"3000 randomly selected teenagers"

"3000 randomly selected teenagers across the state"

Answer:

the andswer there is D

Step-by-step explanation:

just think of it as a cylinder and a square

put both circular parts together and you have a cylinder with the diameter of 12 and a height of 7 and find the volume of that which is πr²h so π 6² 7

then the volume of your rectangular prism is the length times width times height so 12 by 12 by 7

The equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

The line of best fit;
y = mx + c

m = 16.89

c = 134.95

y = 16.89x + 134.95

Plug x = 2010 - 2002 = 8

y = 16.89(8) + 134.95

y = $2700.07

Thus, the equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

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Answer:

15.9

Step-by-step explanation:

x^2 + 6^2 = 17^2

x squared + 36 = 289

                  -36     -36

x squared = 253

[tex]\sqrt{x}[/tex] = [tex]\sqrt{x}[/tex]253

x = 15.9

Answer:

18.0

Step-by-step explanation:

17^2+6^2= 289 + 36=325

The square root of 325 is 18.02 and when you round 18.02 to the nearest tenth it would give you an answer of 18.0.

Answer:

y=6.4

Step-by-step explanation:

The solution is in the image

The system of equations are solved and the value of y = 32/5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x + y = 1   be equation (1)

2x - 3y = -30   be equation (2)

Multiply equation (1) by 2 , we get

2x + 2y = 2   be equation (3)

Subtracting equation (2) from equation (3) , we get

5y = 32

Divide by 5 on both sides , we get

y = 32/5

Hence , the equation is solved and y = 32/5

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Step-by-step explanation:

1 km² = 1km×1km = 1000m × 1000m = 1000000 m²

5 km² = 5000000 m²

so, he has to pay 5000000p as tax.

The amount of tax the farmer must pay is 50000 Rupees.

A compulsory contribution the government has levied on people's income is called the tax , It is of various types and the money accumulated from that is used for the development of the nation.

It is given that the farmer has an area of 5 km²

The farmer must pay 1p tax for each m² of land he owns.

5km² = 5 * (1000)² m²

Area = 5 *10⁶ m²

The amount of tax the farmer needs to pay is

= 1* 5* 10⁶

= 5000000 p

100p = 1 rupees

= 50000 Rupees

Therefore the amount of tax the farmer must pay is 50000 Rupees.

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Answer:

b) g(x) = x + 7

it may seem like its x - 7, but it's actually x + 7 since it shifts up the graph 7 units.

Answer: (0, –5)

Step-by-step explanation:

Don’t worry the other person is right

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

[tex]\text{From the question...}\\9x^2 + 4y \div z\\x = \frac{2}{3}\\y = 3\\z = 6\\\\\text{Substitute in values}\\9(\frac{2}{3})^2 + 4(3) \div (6)\\\\\text{Following the rules of BODMAS or PEMDAS}\\9(\frac{4}{9}) + 12 \div 6\\4 + 2\\6[/tex]

Answer:

15 u³

Step-by-step explanation:

Volume = width × length × height

Given:

⇒ Volume = 2u × 2 ¹/₂ u × 3u

                 = 15 u³

[tex]\underline{\tt{❖ \: Given \: \: ❖}}[/tex]

given figure

[tex] \green{\rule{15pt}{ 15pt}} \: \: \: \green{\rule{15pt}{15pt}} \: \: \: \green{\rule{7.5pt}{15pt}} \\ \: \: \: \: \: \: \green{\rule{15pt}{ 15pt}} \: \: \: \green{\rule{15pt}{15pt}} \: \: \: \green{\rule{7.5pt}{15pt}} \sf \: 2u \\ \green{\rule{15pt}{ 15pt}} \: \: \: \green{\rule{15pt}{15pt}} \: \: \: \green{\rule{7.5pt}{15pt}} \\ \sf \: 2 \dfrac{1}{2}u[/tex]

[tex]\underline{\tt{❖ \: To \: find \: ❖}} [/tex]

[tex]\underline{\tt{❖ \: Using \: formula \: ❖}} [/tex]

[tex]\underline{\tt{❖ \: Solution \: ❖}} [/tex]

we have,

[tex]\sf \: volume = width \times length \times height[/tex]

[tex]\sf \: volume = 2u \times 2 \dfrac{1}{2}u \times 3u[/tex]

[tex]\sf \: volume = 2u \times \dfrac{5}{2}u \times 3u[/tex]

[tex]\sf \: volume = \cancel2u \times \dfrac{5}{ \cancel2}u \times 3u[/tex]

[tex]\sf \: volume = u \times 5u \times 3u[/tex]

[tex]\sf \: volume = 15u {}^{3} [/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer:

  B = 43°

  a = 11.0

  b = 10.2

Step-by-step explanation:

The relationship between side lengths and trig functions in a right triangle is summarized in the mnemonic SOH CAH TOA. It tells you, for example, ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

__

Applied to this triangle, the unknown sides can be found from ...

  sin(47°) = a/15

  a = 15·sin(47°) ≈ 11.0

and

  cos(47°) = b/15

  b = 15·cos(47°) ≈ 10.2

__

The second acute angle in a right triangle is the complement of the first:

  B = 90° -47° = 43°

To draw a 50 degree angle with a protactor, proceed as follows :

Remember that 50 degree angle cannot be constructed using compass.

Answer:

The length is 7.3m

Step-by-step explanation:

The end of the ladder touches the top of the tree when kept at 2.8m away from the tree.

The Tree is 4.5m tall

The length of the ladder will be: 2.8+4.5 = 7.3

Answer: B

Step-by-step explanation: hope this helps

Answer:

He was enlightened

Step-by-step explanation:

There was a list of things he did to become Buddha

Lives like a prince
Is depressed by the suffering he sees outside the palace
Is impressed by how contented a holy man is
Decides to give up a life of pleasures and comforts
Wanders across India looking for the end of suffering
Sits down under a tree and meditates for several weeks
Gains enlightenment

Answer:

9 sides

Step-by-step explanation:

Formula for finding interior angles of all polygons : 180 ( n - 2) / n = A

(n being the amount of sides it has)

This information is important so you can plug in the numbers that you already know

We know that the interior angle measures to 140 degrees

180 (n - 2) / n = 140

multiply both sides by "n"

(n - 2) x 180 = 140n

Distribute 180 to what's inside the parenthesis

180n - 360 = 140n

Subtract 140n and add 360 to each side (which just moves 360 to the other side of the "="

40n = 360

Divide 40 by both sides

n = 9

hope this helps :)

Answer:

  17.3 cm³

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

  V = 1/3Bh

where B is the area of the base, and h is the height.

__

The volume of a square pyramid with base area 5.5 cm² and height 6.4 cm is ...

  V = 1/3(5.5 cm²)(6.4 cm) ≈ 17.333... cm³

The volume of the pyramid is about 17.3 cm³.

Answer:

the answer is 11 because there are so many no. repeating so in this case we count total no of terms and say it n if terms are odd then mode

Step-by-step explanation:

mode = n+1÷2

Answer:

y = x+8

Step-by-step explanation:

You find the difference between the value of y and value of x which is 8 so no matter what x is you always add 8 to get the y value. :)

Answer:

y = x + 8

Step-by-step explanation:

Find the difference between each x and y-value :

Let's take the pair (18, 26)

Answer: 54 degrees

Step-by-step explanation:

Since AZ is tangent to circle V, it forms a 90 degree angle with the circle. If you compare XW with AZ, you can see they are perpendicular to each other. Angle W has already been found, and it's 36 degrees.

So if you subtract 90 by 36, it gives you YWZ, 54 degrees.

Answer:

10, 20, 15

Step-by-step explanation:

10 is the lowest so that leaves the mean and range well the range is the highest value minus the lowest and the range is 10 so 20-10=10

so we now have 10 and 20 so then what number divided by three as in three darts equals 15 I go down the list and I get 45/3 and it equals 15

Answer:

Step-by-step explanation:

sum of first six  terms of given G.P.=1+2+4+8+16+32=63

let d be c.d. of A.P.

first six terms are 1,1+d,1+2d,1+3d,1+4d,1+5d

1+1+d+1+2d+1+3d+1+4d+1+5d=63

6+15d=63

15d=63-6=57

divide by 3

5d=19

d=19/5=3.8

fifth term=1+4d=1+3.8*4=1+15.2=16.2

Answer:

x = 60

Step-by-step explanation:

Discussion

You have 3600 boxes and 60 trucks

The formula you want is

Total Boxes = Number of trucks * number of boxes per truck.

Givens

Total boxes = 3600

Total trucks = 60

Solution

3600 = 60 * x                    Divide by 60

3600/60 = 60x/60

x = 60

0.35x=73.85, comgining moving terms

divide both sides by 0.35

x=211 quarters, which is $52.75 ANSWER

x+5=216 dimes, which is $21.60 ANSWER

That total is $74.35

Answer:

the answer is 210 quarters and 215 dimes

Step-by-step explanation:

B) y = 53.8x + 1149.8

C) Total Sales increase from one week to the next by $53.8.

Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

D) The restaurant's sales for the Monday of the 15th week is expected to be $1956.8

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

B) As by scatter plot,

The total sales for week 4 is given as 1,365 while that of week 9 is 1,634.

Therefore, we shall determine the equation for the line of best fit using the points;

( 4, 1365) and ( 9, 1634)

The first step would be to determine the slope of this line;

slope = (1634 - 1365)/ (9 - 4)

       = 53.8

The equation of the line in slope-intercept form is thus;

Sales = 53.8(Week) + c

We need to determine c, the y-intercept. We can use the point ( 4, 1365);

1365= 53.8(4) + c

c = 1365-215.2

c = 1149.8

The equation of the line of best fit is thus;

y = 53.8x + 1149.8

C) The slope of the equation for the lines of best fit was found to be 53.8.  

    This value is positive which implies

    Total Sales increase from one week to the next by $53.8.

    The slope in regression is defined as the change in y for every unit change in x.

Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

D) The equation  for the line of best fit was found to be;

  y = 53.8x+ 1149.8

where y denotes the total sales and x the corresponding week. We are required to determine y when x is 15;

y = 53.8(15) + 1149.8

y = 1956.8

Therefore, the restaurant's sales for the Monday of the 15th week is expected to be $1956.8.

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Answer:

-2x < 23-7

-2x < 16

-2x÷-2 < 16 ÷ -2

x > -8

Answer:

1: The limit doesn't exist

2:

Step-by-step explanation:

Question 1:

f(x) = x + 10 for when x approaches 8

18 = 8 + 10 which is NOT true x < 8             18 < 8

f(x) = 10 - x for when x approaches 8

2 = 10 - 8 which is NOT true x ≥ 8                2 ≥ 8

Question 2:

f(x) = 5 - x for when x approaches 5

0 = 5 - 5 which is TRUE x < 5           0 < 5

f(x) = 8 for when x approaches 5

which is NOT x = 5                          8 = 5

f(x) = x + 3 for when x approaches 5

8 = 5 + 3 which is TRUE x > 5           8 > 5

Answer:

10 meters.

Step-by-step explanation:

We know the ball travelled a distance of at least 6 meters as that is how far it was dropped.

It rebounded 2/3 of 6 meters, which is 4 meters.

6 meters add 4 meters is 10 meters.

As there is the highest degree 4 there are four zeros .

Using calculator

the roots are(attached)

The graph is also attached

Answer:

a) 4 roots

b) x = 1 and x = -3

[tex]\textsf{c)} \quad x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]

d) see attached

Step-by-step explanation:

Given function:

[tex]f(x)=x^4+3x^3-x-3[/tex]

Part (a)

From inspection of the function, the highest exponent of the polynomial is 4.  Therefore, it is expected that the polynomial will have 4 roots.

Part (b)

To find the rational roots, find values of x where [tex]f(x)=0[/tex]

[tex]f(1)=(1)^4+3(1)^3-1-3=0[/tex]

[tex]f(-3)=(-3)^4+3(-3)^3-(-3)-3=0[/tex]

Therefore, the rational roots are: x = 1 and x = -3

Part (c)

As there are only 2 rational roots, the other 2 roots must be complex roots. To find these, first factor the polynomial using the 2 rational roots found in part (b):

[tex]\implies f(x)=(x-1)(x+3)(x^2+bx+1)[/tex]

[tex]\implies f(x)=(x^2+2x-3)(x^2+bx+1)[/tex]

[tex]\implies f(x)=x^4+bx^3+x^2+2x^3+2bx^2+2x-3x^2-3bx-3[/tex]

[tex]\implies f(x)=x^4+(2+b)x^3+(2b-2)x^2+(2-3b)-3[/tex]

Compare coefficients to find b:

[tex]\implies (2+b)x^3=3x^3[/tex]

[tex]\implies b=1[/tex]

Therefore the fully factored function is:

[tex]\implies f\:\!(x)=(x-1)(x+3)(x^2+x+1)[/tex]

Therefore:

[tex](x^2+x+1)=0[/tex]

To find the complex roots, use the quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\sqrt{-1}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3}i}{2}[/tex]

Therefore, all the roots of the function are:

[tex]x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]

Part (d)

End behaviors:

As the degree of the function is even and the leading coefficient is positive, the end behaviors are:

[tex]\textsf{As } x \rightarrow - \infty, \:\: f(x) \rightarrow + \infty[/tex]

[tex]\textsf{As } x \rightarrow + \infty, \:\: f(x) \rightarrow + \infty[/tex]

y-intercept

Substitute x = 0 into the function:

[tex]f\:\!(0)=(0)^4+3(0)^3-(0)-3=-3[/tex]

Therefore, the y-intercept is (0, -3)

To find the approximate x-coordinates of the turning points (stationary points), differentiate the function, set it to zero, then solve for x:

[tex]f'\:(x)=4x^3+9x^2-1[/tex]

[tex]\implies 4x^3+9x^2-1=0[/tex]

Using a calculator, x ≈ -2.2, x ≈ -0.4, x ≈ 0.3

Therefore the approximate coordinates of the turning points are:

(-2.2, -9.3),  (-0.4, -2.7)  and (0.3, -3.2)

We don't need to plot these points, they merely help us with the approximate shape of the curve.