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The area bounded by the graphs of y = x² + 17 and y = 0 over the interval -3 ≤ x ≤ 3 is 120 square units.

To find the area bounded by the two graphs, we need to calculate the definite integral of the difference between the upper function (y = x² + 17) and the lower function (y = 0) over the given interval.

Integrating the difference of the two functions, we have:

∫[from -3 to 3] (x² + 17 - 0) dx

Simplifying, the integral becomes:

∫[from -3 to 3] (x² + 17) dx

To evaluate this integral, we can use the power rule of integration. Integrating x² gives us (1/3)x³, and integrating the constant term 17 gives us 17x.

Applying the limits of integration, the integral becomes:

[(1/3)x³ + 17x] from -3 to 3

Evaluating the expression at the upper limit (x = 3) and subtracting the expression at the lower limit (x = -3), we get:

[(1/3)(3)³ + 17(3)] - [(1/3)(-3)³ + 17(-3)]

Simplifying further:

[(1/3)(27) + 51] - [(1/3)(-27) - 51]

= [9 + 51] - [-9 - 51]

= 60 + 60

= 120

Therefore, the area bounded by the two graphs is 120 square units.

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Answer:

+

Step-by-step explanation:

\(-8-(-3)=-8+3\)

Answer:

On the y-axis line

Step-by-step explanation:

Given the location (a,b) of the point P on the coordinated plane.

If a=0

Then the location of P on the x-axis is at x=0

Since b is not equal to zero, b could be positive or negative.

Therefore, the point P could be located on the positive y-axis or the negative y-axis,

It must be exactly on the line.

Answer:

y=-3/2x-8

Step-by-step explanation:

Answer:

(0,0), or A

Step-by-step explanation:

Given the function { x - 3, y - 1 }:

\((3 -3, 1-1)=(0,0)\)

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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If he puts away 10% of his $32,000 salary every year, The total of his 401(k) be in 10 years is: a. $67,266.16.

First step

Contribution=(10% ×$32,000)+ 50% from employer

Contribution=$3,200+ ($3,200×50%)

Contribution=$3,200+$1,600

Contribution=$4,800

Second step

Future value= 4800 (1 + 0.073)^10 – 1/ 0.073

Future value= 4800 (1 .073)^10 – 1/ 0.073

Future value= 4800 (2.0230062274104 – 1) / 0.073

Future value= 4800 (1.0230062274104) / 0.073

Future value=$4,910.42989157/0.073

Future value=$67,226.16

Therefore the total of his 401(k) be in 10 years is: a. $67,266.16.

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Answer:a. $67,266.16.

Step-by-step explanation:edge

Solving the equations for the total number of adults and children and respective ticket costs, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.

It is given to us that -

A total of 19 people attended the movie theater which was a mix of adults and children

Each adult ticket was $9

Each child’s ticket was $5.50.

Total cost for the party was $150

We have to find out the number of adults and children that attended the movie theater.

Let us assume that the number of adults and children that attended the movie theater be \(x\) and \(y\) respectively.

Since, a total of 19 people attended the movie theater including both adults and children, we can say that -

\(x+y=19\) ------ (1)

It is also given that each adult ticket was $9 and each child’s ticket was $5.50. So,

For \(x\) adults, the ticket price = \(9x\), and

For \(y\) children, the ticket price = \(5.5y\)

It is given that the total cost for the party was $150

\(= > 9x+5.5y=150\) ------- (2)

From equation (1), we have

\(x+y=19\\= > y =19-x\) ------ (3)

Substituting this value of \(y\) in equation (2),

\(= > 9x+5.5y=150\\= > 9x+5.5(19-x)=150\\= > 9x +104.5-5.5x=150\\= > 3.5x=45.5\\= > x=13\)------ (4)

Substituting this value of \(x\) from equation (4) in equation (3), we get

\(y=19-x\\= > y=19-13\\= > y=6\)

Thus, solving the equations, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

24 square units

Step-by-step explanation:

6×4=24

Answer:

24 square units

Step-by-step explanation:

An independent basic service set (IBSS) does not consist of any access points.

In an IBSS, devices such as laptops or smartphones connect with each other on a peer-to-peer basis, forming a temporary network. This type of network can be useful in situations where there is no existing infrastructure or when devices need to communicate with each other directly.

Since an IBSS does not involve any access points, it is not limited by the number of access points. Instead, the number of devices that can be part of an IBSS depends on the capabilities of the devices themselves and the network protocols being used.

To summarize, an IBSS does not consist of any access points. Instead, it is a network configuration where wireless devices communicate directly with each other. The number of devices that can be part of an IBSS depends on the capabilities of the devices and the network protocols being used.

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Answer:

46$ in total

y=2r+20

If Isabella goes on 13 rides, she would have to pay a total of $46. If she rides 'r' times, the total cost would be expressed by the mathematical equation 20 + 2r.

This question relates to a linear relationship involving a fixed cost and a variable cost. In Isabella's case, the fixed cost is the admission fee, which is $20. The variable cost is the rides, where each ride costs $2.

So, if she goes on 13 rides, she will have to pay: $20 (for admission) + ($2 * 13 (rides)) = $20 + $26 = $46.

For r rides, the total cost would be: $20 (for admission) + ($2 * r (rides)). So the total cost for r rides can be expressed in a mathematical equation as: 20 + 2r.

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A bar graph is used to represent categorical data, while a histogram is used to represent continuous data.

The appropriate graph for the frequency distribution of a group of patients in a weight loss program that ranges from 185 to 312 pounds would be a histogram. This is because a histogram is a graphical representation of a frequency distribution. It is used to represent the distribution of a set of continuous data. A histogram is a graph that shows the number of times that each value appears in a set of data by grouping the data into classes of equal size. The number of values that fall within each class is represented by the height of a bar on the graph. The area of each bar is proportional to the frequency of the class.The six age groups will be grouped into classes that have the same size interval. The number of patients that fall within each class interval will be represented on the vertical axis, while the class intervals will be represented on the horizontal axis. The bars of the histogram will be plotted at the midpoints of each class interval. The height of each bar will represent the frequency of the class interval. It is important to note that a histogram is not the same as a bar graph.

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Answer:

Total surface area = 132 square feet

Step-by-step explanation:

Surface area of the triangular prism = Area of the triangular bases + Area of the lateral rectangular sides

Area of the triangular surface = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                                 = \(\frac{1}{2}\times 5\times 4\)

                                                 = 10 square feet

Area of the rectangular side with dimensions 5ft by 7ft,

Area = 5 × 7 = 35 square feet

Area of the rectangular side with dimensions 7ft by 4ft,

Area = 7 × 4 = 28 square feet

Area of the rectangular side with dimensions 7ft by 7ft,

Area = 7 × 7 = 49 square feet

Total surface area = 2(10) + 35 + 28 + 49

                               = 132 square feet

Answer:

brand b

Step-by-step explanation:

quality over quantity

Answer:

120.9

Step-by-step explanation:

I dunno if this is right or wrong but this is what a calculated somehow please tell me if this is wrong or not

Answer:

{(1, 3), (2, 3), (3, 3), (4, 3)}

{(-3, 7), (1, 4), (2, 9), (5, 0)}

{(-2,5), (-1, 2), (0, 1), (1, 2)}

Step-by-step explanation:

those three have different domains

Step-by-step explanation:

the probability of making one shot is 75% or 0.75 or 3/4.

the probability to make 2 shots is then

3/4 × 3/4 = 9/16 = 0.5625

and so on.

the probability to miss 1 shot is then 25% or 0.25 or 1/4.

the probability to make at least 4 out of 5 shots is the sum of the probability to make all 5 shots plus the probability to make 4 shots.

or the probability to miss 0 plus the probability to miss 1 shot.

anyway, we can go with the positive approach. it seems to be the same complexity as the negative approach.

the probability to make all 5 shots is

(3/4)⁵ = 3⁵/4⁵ = 243 / 1024 = 0.237304688...

the probability to e.g make the first 4 shots and miss the 5th is

(3/4)⁴×1/4 = 3⁴/4⁵ = 81 / 1024 = 0.079101563...

how many possibilities do we have to make 4 out of 5 shots ?

there is no repetition, and the sequence inside the "picked" 4 does not matter, so we need combinations :

C(5,4) = 5! / (4! × (5-4)!) = 5

so, the probability to make exactly 4 out 5 shots is

81/1024 × 5 = 405/1024 = 0.395507813...

and the total probability to make at least 4 shots is

243/1024 + 405/1024 = 648/1024 = 81/128 = 0.6328125

to control,

this plus making exactly 3 plus exactly 2 plus exactly 1 plus none must be the probability 1 (as there is no other possible outcome).

making 3 :

(3/4)³×(1/4)² = 3³/4⁵ = 27/1024

C(5,3) = 5×2 = 10

270/1024

making 2 :

3²/4⁵ = 9/1024

C(5,2) = 5×2 = 10

90/1024

making 1 :

3/1024

C(5,1) = 5

15/1024

making 0 :

1/1024

in sum

(270+90+15+1)/1024 = 376/1024

plus the 648/1024 = 1024/1024 = 1

correct.

Answer:

The slope between the points (-2, -1) and (4, 3) is \(\frac{3}{2}\)

Step-by-step explanation:

First, we must know the equation for finding the slope.

\(Slope(m) = \frac{y2-y1}{x2-x1}\)

Next, we plug in the coordinate points.

\(m=\frac{4-(-2)}{3-(-1)}\)

\(m=\frac{6}{4}\)

Finally, we simplify this answer.

\(Slope = \frac{3}{2}\)

Answer:

I think point b but egh

Step-by-step explanation:

im not really for sure...

Answer:

QR, QT

Step-by-step explanation:

A radii is a line from the center of the circle to the circumfrence of the circle.

In this case the radii are QR, QT, and QK because they all start from the center of the circle which is point Q and stop at the circumfrence of the circle.

Since QK isn't an answer choice the only  answers are ...

QR and QT

Step-by-step explanation:

\(\large\underline{\sf{Solution-}}\)

Let we assume that

Sum invested at the rate of 12 % per annum be Rs x

Sum invested at the rate of 10 % per annum be Rs y

According to statement,

Annual interest earned = Rs 1145

We know,

Interest received on a sum of Rs p invested at the rate of r % per annum for n years is

\(\boxed{\tt{ \: I \: = \: \dfrac{p \times r \times n}{100} \: }}\)

So, we get

\(\rm :\longmapsto\:\dfrac{x \times 12 \times 1}{100} + \dfrac{y \times 10 \times 1}{100} = 1145\)

\(\rm :\longmapsto\:\dfrac{12x }{100} + \dfrac{10y}{100} = 1145\)

\(\rm :\longmapsto\:\boxed{\tt{ 12x + 10y = 114500 }}- - - (1)\)

According to second condition

Sum invested at the rate of 12 % per annum be Rs y

Sum invested at the rate of 10 % per annum be Rs x

According to statement,

Annual interest earned = Rs 1055

So,

\(\rm :\longmapsto\:\dfrac{x \times 10 \times 1}{100} + \dfrac{y \times 12 \times 1}{100} = 1055\)

\(\rm :\longmapsto\:\dfrac{10x }{100} + \dfrac{12y}{100} = 1055\)

\(\rm :\longmapsto\:\boxed{\tt{ 10x + 12y = 105500 }}- - - (2)\)

Now, On adding equation (1) and (2), we get

\(\rm :\longmapsto\:22x + 22y = 220000\)

\(\rm :\longmapsto\:22(x + y) = 220000\)

\(\rm :\longmapsto\:\boxed{\tt{ x + y= 10000}} - - - - (3)\)

On Subtracting equation (2) from equation (1), we get

\(\rm :\longmapsto\:2x - 2y = 9000\)

\(\rm :\longmapsto\:2(x - y) = 9000\)

\(\rm :\longmapsto \:\boxed{\tt{ x - y = 4500}} - - - - (4)\)

On adding equation (3) and (4), we get

\(\rm :\longmapsto\:2x = 14500\)

\(\bf\implies \:x = 7250\)

On substituting the value of x in equation (3), we get

\(\rm :\longmapsto\:7250 + y = 10000\)

\(\rm :\longmapsto\:y = 10000 - 7250\)

\(\bf\implies \:y = 2750\)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

So,

Sum invested at the rate of 12 % per annum be Rs 7250

Sum invested at the rate of 10 % per annum be Rs 2750

Polygons are shapes that have the following:

-sides are all straight

-no overlapping

-shape is always closed

Hope this helps :)

Surface area of a square prism: 2(a^2) + (4a) h

Where:

a = side lenght=7km

h = heigth =5 km

Replacing:

SA = 2 (7)^2 + (4*7)5

SA = 2*49 +28*5

SA = 238 km2

Step-by-step explanation:

\(\large\underline{\sf{Solution-}}\)

Given that,

A car covers the distance between two cities in 6 hours.

A van covers the same distance in 5.5 hours.

The speed of the van is 4 km per hour faster than the speed of car.

Let assume that

Speed of the car be x km per hour

So,

Speed of van is x + 4 km per hour.

Let further assume that

Distance between two cities be y km.

We know, Distance covered = Speed × Time.

➢ Now, Distance (y) covered by car at the speed of x km per hour in 6 hours is

\(\rm :\longmapsto\:\boxed{\tt{ y = 6x}} - - - - (1)\)

➢ Also, Distance (y) covered by van at the speed of x + 4 km per hour in 5.5 hours is

\(\rm :\longmapsto\:\boxed{\tt{ y = 5.5(x + 4)}} - - - - (2)\)

So, from equation (1) and (2), we have

\(\rm :\longmapsto\:6x = 5.5(x + 4)\)

\(\rm :\longmapsto\:6x = 5.5x + 22\)

\(\rm :\longmapsto\:6x - 5.5x = 22\)

\(\rm :\longmapsto\:0.5x = 22\)

\(\rm :\longmapsto\:\dfrac{5}{10} \times x = 22\)

\(\rm :\longmapsto\:\dfrac{1}{2} \times x = 22\)

\(\bf\implies \:x = 44\)

On substituting the value of x, in equation (1), we have

\(\rm :\longmapsto\:y = 6 \times 44\)

\(\bf\implies \:y = 264\)

So,

\(\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Distance \: between \: cities = 264 \: km} \\ \\ &\sf{Speed \: of \: car \: = \: 44 \: km \: per \: hour}\\ \\ &\sf{Speed \: of \: van \: = \: 48 \: km \: per \: hour} \end{cases}\end{gathered}\end{gathered}\)

Answer:

4x3=3x4

Step-by-step explanation:

Answer:

2 or C

Explanation:

X intercept is where the line passes through the x-axis at, in this case it is (2,0)