What steps should be taken to calculate the volume of the right triangular prism? Select three options.

A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters.

A. Use the formula A = one-half b h to find the area of the base.
B. Use the formula A = b h to find the area of the base.
C. The area of the base, A, is One-half (7) (8) = 28 meters squared.
D. The area of the base, A, is One-half (8) (14) = 56 meters squared.
E. The volume of the prism, V is (56) (7) = 392 meters cubed.

if there are 4 numbers that average to 60, when mutiplied they must come up to: 60*4= 240

100+30+45= 175

240-175= 65

PROOF:

100+30+45+65= 240

240÷ 4

= 60

Answer:

x=65

Step-by-step explanation:

Mean= sum of terms

number of terms

60=30+45+x+100

4

240=175+x

x=240-175

=65

To determine who came closer to their grade's state record for the triple jump, calculate the difference between each jumper's distance and their grade's record. Alex jumped 39.85 feet, which is 2.4 feet away from the eighth-grade record. Eric jumped 37 feet and 1 1/4 inches, which is 1 foot 1 3/4 inches away from the seventh-grade record. Alex was closer to their grade's state record for the triple jump.

To determine who came closer to their grade's state record for the triple jump, we need to calculate the difference between each jumper's distance and their grade's record.

Alex jumped 39.85 feet, which is 2.4 feet (42.25 - 39.85) away from the eighth-grade record.

Eric jumped 37 feet and 1 1/4 inches, which is 1 foot 1 3/4 inches (39 - 37 - 1 1/4) away from the seventh-grade record.

Therefore, Alex was closer to their grade's state record for the triple jump.

Final answer:

Alex, an eighth grader, was closer to his grade's state record for the triple jump than Eric, a seventh grader.

Explanation:

To determine who came closer to their grade's state record for the triple jump, we need to compare the distances jumped by Alex and Eric to their grade's respective records. Alex jumped 39.85 feet, which is 2.4 feet less than the eighth-grade record of 42.25 feet. Eric jumped 37 feet and 1 1/4 inches, which is 1.75 feet less than the seventh-grade record of 39 feet 3 inches.

By comparing the differences, we can see that Alex was closer to his grade's record by 2.4 feet, while Eric was closer to his grade's record by 1.75 feet. Therefore, Alex was closer to his grade's state record for the triple jump than Eric.

Answer: 30%

Step-by-step explanation:

Ive had this before the answer is 30%

Answer:

y = 2x-1

Step-by-step explanation:

The y intercept is -1

The slope is rise over run

Up 2 / right1

The slope is 2/1 = 2

The slope intercept form of the equation is

y = mx +b where m is the slope and b is the y intercept

y = 2x-1

Answer:

12.56

Step-by-step explanation:

Radius = 8/2 = 4

Arc length = pi × r

= 3.14 × 4

= 12.56

Answer:

Volume of a cone: V = (1/3)πr2h.Step-by-step explanation:

Answer:

28.26

Step-by-step explanation:

volume = 1/3 * pi * r^2 * h

Answer: $10240

Step-by-step explanation: 10 x 2^10 = 10240

_______________________________________________

Answer:

Total expenses: $245.00

Total revenue: $479.00

Total profit $234.00

Step-by-step explanation:

Just did it and got it correct

Answer:

-25%

Step-by-step explanation:

I hope that helps

Answer:

Mr. Flores has mismatched socks in his drawer. He has 5 white, 12 black and 1 gray sock. Destiny selected two socks from the drawer. What is the probability that both socks are black?

Step-by-step explanation:

i need help dont judge me

Answer:

they use 212 gallons

Step-by-step explanation:

(68.9/32.5)*100

the division by 32.5 is to determine the amount of water one percent would be, so multiplying it by 100 will give you the total amount

Final answer:

To find the total daily water usage of a family using 68.9 gallons per day for drinking, which is 32.5% of their total usage, you divide the amount of water for drinking by 0.325. The calculation shows the family uses about 212 gallons of water per day.

Explanation:

The question asks us to calculate the total daily water usage of a family if they use 68.9 gallons per day for drinking, which represents 32.5% of their total daily use. To find the total water use, we divide the amount of water used for drinking by the percentage that represents drinking water.

Step-by-step Calculation:

Convert the percentage to a decimal by dividing 32.5 by 100, giving us 0.325.

Divide the gallons used for drinking by this decimal: 68.9 gallons / 0.325 = 212 gallons (rounded to the nearest whole gallon).

Therefore, the family uses approximately 212 gallons of water every day for all purposes.

Answer:

Style A sold 15 pairs while Style B sold 13 pairs

Step-by-step explanation:

Let the number of Style A pairs be A.

Let the number of Style B pairs be B.

The store sold 28 pairs of cross-trainer shoes for a total of $2,220 and Style A sold for $70 per pair while Style B sold for $90 per pair.

This implies 2 things:

A + B = 28 ________________ (1)

and

(70*A) + (90*B) = 2220

=> 70A + 90B = 2220 ________(2)

We now have two simultaneous equations:

A + B = 28 ________________ (1)

70A + 90B = 2220 __________(2)

From (1):

A = 28 - B ________________ (3)

Put (3) in (2):

70(28 - B) + 90B = 2220

1960 - 70B + 90B = 2220

1960 + 20B = 2220

Collecting like terms:

20B = 2220 - 1960

20B = 260

B = 260 / 20

B = 13

Therefore:

A = 28 - 13 = 15

Style A sold 15 pairs while Style B sold 13 pairs.

Final answer:

By setting up and solving a system of equations, it was determined that the store sold 15 pairs of Style A shoes and 13 pairs of Style B shoes.

Explanation:

To determine how many pairs of Style A and Style B cross-trainer shoes were sold, we can set up a system of linear equations using the information provided: 28 pairs of shoes were sold for a total of $2,220, with Style A shoes selling for $70 per pair and Style B selling for $90 per pair.

Let x represent the number of Style A shoes sold and y represent the number of Style B shoes sold. We can then set up the following equations based on the information provided:

System of Equations

Total cost equation: 70x + 90y = 2220 (since Style A costs $70 and Style B costs $90)

-70(x + y) = -70(28), which simplifies to -70x - 70y = -1960

70x + 90y = 2220

Adding the two equations results in:

20y = 260

Dividing both sides by 20 gives us y = 13.

Now we substitute y back into the first equation to find x:

x + 13 = 28

x = 28 - 13

x = 15.

Therefore, the store sold 15 pairs of Style A shoes and 13 pairs of Style B shoes.

Answer:

The answer is B .

Step-by-step explanation:

You have to use Indices Law,

[tex] {a}^{m} \times {a}^{n} = {a}^{(m + n)} [/tex]

So for this question :

[tex] {6}^{9} \times {6}^{x} = {6}^{2} [/tex]

[tex] {6}^{9 + x} = {6}^{2} [/tex]

[tex]9 + x = 2[/tex]

[tex]x = 2 - 9[/tex]

[tex]x = - 7[/tex]

Answer:

the answer is B

Step-by-step explanation:

Answer: n+22 less than 120 (B)

Step-by-step explanation:

I got it right on edg

The inequality equation is n ≤ 98

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total number of people the room can hold = 120 people

The number of coaches and players = 22

Let the number of people to be invited be n

So , n + 22 should not be more than 120

On simplifying the equation , we get

n + 22 ≤ 120

Subtracting 22 on both sides of the equation , we get

n ≤ 98

Hence , the inequality is n ≤ 98

To learn more about inequality equations click :

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Answer:

[tex]-b\leq a\leq b[/tex]

Step-by-step explanation:

When we have absolute value inequalities, there are specific way to find the solution sets.

If [tex]|a| < b[/tex] then [tex]-b<a<b[/tex]

If [tex]|a| >b[/tex] then [tex]a>b[/tex] or [tex]a<-b[/tex]

These definitions apply for the inequlity signs that involve equivalence.

If [tex]|a| \leq b[/tex] then [tex]-b\leq a\leq b[/tex]

If [tex]|a| \geq b[/tex] then [tex]a\geq b[/tex] or [tex]a\leq -b[/tex]

Therefore, the expression that completes the statement is

[tex]-b\leq a\leq b[/tex]

Answer:

x=7

Step-by-step explanation:

Inscribed Angle =1/2 Intercepted Arc

<T = 1/2 (WRS)

11x+5 = 1/2(10x-6 + 100)

Multiply each side by 2

2(11x+5 )= (10x-6 + 100)

Distribute

22x +10 = 10x+94

Subtract 10x from each side

22x-10x +10 = 10x-10x+94

12x +10 = 94

Subtract 10 from each side

12x = 94-10

12x = 84

Divide each side by 12

12x/12 = 84/12

x = 7

Answer:

82 students

Step-by-step explanation:

The total number of students who attended the dance can be found by subtracting the initial rental cost from the total cost, and then dividing this amount by the cost per student. The number of students who attended the dance was 82.

This problem can be solved with a little bit of algebra. The initial cost of the building was $120, and there was an additional cost of $2.50 for each student who attended. The total cost was $325. Therefore, in order to determine how many students attended the dance, you would first need to subtract the initial cost of the building from the total cost. This leaves us with $325 - $120 = $205.

Next, you would divide this amount by the cost per student. $205 ÷ $2.50 = 82.

Therefore, the number of students who attended the dance was 82.

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Step-by-step explanation:

solate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x≤193x≤193

Interval Notation:

(−∞,193]

Answer:

9 units from point A to B.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

because if you count the graph you will count nine

Answer:

[tex]x1 = 2 \\ x2 = - \frac{3}{2} [/tex]

Step-by-step explanation:

[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{1 + - \sqrt{ {( - 1)}^{2} - 4(2)( - 6) } }{2(2)} \\ x = \frac{1 + - \sqrt{1 + 48} }{4} \\ x = \frac{1 + - \sqrt{49} }{4} \\ x = \frac{1 + - 7}{4} \\ \\ x1 = \frac{1 + 7}{4} = \frac{8}{4} = 2 \\ x2 = \frac{1 - 7}{4} = - \frac{6 }{4} = - \frac{3}{2} [/tex]

Answer:

x = -1 ± √7

The picture explains the rest...

Answer: The length of rectangle is 15 cm and width is 20 cm

Step-by-step explanation:

As according to question

Let the width of rectangle = x cm

Length of rectangle =(x- 5) cm

Area of rectangle is 300 cm²

As we know Area of rectangle is given by

[tex]Area = length \times breadth \\\\\Rightarrow 300 = (x-5)x\\\\\Rightarrow 300 = x^2-5x\\\\\Rightarrow x^2-5x-300 = 0 \\\\\Rightarrow x^2-20x+15x-300 = 0 \\\\\Rightarrow x(x-20) +15(x-20) =0\\\\\Rightarrow (x-20)(x+15)=0[/tex]

Therefore either (x-20)= 0 or (x+15)=0

i.e. either x= 20 or x = -15

Now width can not be negative

Therefore it cant be -15

Hence the width is 20 cm

Length = x- 5 = 20-5 = 15 cm

Hence the length of rectangle is 15 cm and width is 20 cm

Final answer:

To find the dimensions of a rectangle when given the area, set up an equation using the information and solve for the unknowns.

Explanation:

To find the dimensions of the rectangle, we can set up an equation using the given information. Let's use 'L' to represent the length and 'W' to represent the width. The problem states that the length is 5 centimeters less than the width, so we can write the equation as: L = W - 5.

We also know that the area of a rectangle is found by multiplying the length and width together. In this case, the area is given as 300 square centimeters. So, we can write another equation: L * W = 300.

Now, we can substitute L = W - 5 into the second equation to solve for the width. (W - 5) * W = 300. Simplifying this equation will give us a quadratic equation, which we can solve to find the width. Once we know the width, we can subtract 5 to find the length.

Answer:

I believe the answer is 28. Hope this helps :)

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Answer:

Bradley practice 109500 more  minutes than Jonas over the course of 2 years.

Step-by-step explanation:

Jonas practices guitar 1 hour a day for 2 years.

1 year = 365 days

2 years = [tex]365 \times 2 = 730 days[/tex]

1 hour = 60 minutes

So, Jonas practice for 60 minutes in 1 day

Jonas practice for minutes in 365 days =[tex]365 \times 60 =21900 minutes[/tex]

Bradley practices the guitar 2 hours a day more than Jonas.

So, Bradley practice the guitar for hours per day = 2+1=3 hours

3 hours = 3 \times 60 = 180 minutes

Bardley practice for minutes per day = 180 minutes

Bardley practice for minutes for 730 days = [tex]180 \times 730 =131400 minutes[/tex]

Difference in minutes in 2 years = 131400-21900=109500  minutes

Hence Bradley practice 109500 more  minutes than Jonas over the course of 2 years.

Answer:

1. h = h₀ + u×t - 1/2×g×t²

2. 2.95 s

3. 152.14 ft

4. 3.07 s

Step-by-step explanation:

The given parameters are;

Vertical velocity of the balloon = 95 ft/s

Height from which the balloon is released = 12 feet

The function is h = h₀ + u×t - 1/2×g×t²

Where:

h = Height of the balloon at time t

h₀ = Initial height of the balloon = 12 feet

u = Initial upward velocity of the balloon = 95 ft/s

t = Time duration of motion

g = Acceleration due to gravity = 32.2 ft/s²

2. The time to maximum height is found from;

v = u - g·t

Where:

v = Final velocity = 0 m/s at maximum height

∴ 0 = 95 - 32.2 × t

32.2·t = 95

t = 95/32.2 = 2.95 s

Therefore, the time it will take to reach maximum height = 2.95 s

3. From h = h₀ + u×t - 1/2×g×t², we have;

h = 12 + 95×2.95 - 1/2×32.2×2.95² = 152.14 ft

4. Therefore;

152.14 = 0×t + 1/2 × 32.2 × t²

t² = 152.14/16.1 = 9.45 s

t = √9.45 = 3.07 s

Answer:

The function is: y(t) = 12 + 95*t - 16.085*t²

The time it'll take to reach the maximum height is: 2.95 s

The maximum height is: 152.27 ft

The time it'll take to hit the ground is: 12 s

Step-by-step explanation:

The water ballon is under the constant acceleration of gravity, therefore it's movement can be modelled by the equations that describe constant acceleration movement, as shown below:

y(t) = y(0) + v(0)*t - 0.5*g*t²

The acceleration is negative, because they are contrary to the movement. Applying the data form the problem, we have:

y(t) = 12 + 95*t - 0.5*32.17*t²

y(t) = 12 + 95*t - 16.085*t²

This equation describes a parabolla, therefore the time at which it achieves the maximum height is the "x" coordinate for the vertex, which can be found by using the formula below:

t = (-b)/[2*a]

t = (-95)/[2*(-16.085)] = -95/(-32.17) = 2.95 s

And the maximum height is:

y(2.95) = 12 + 95*2.95 - 16.085*(2.95)² = 152.27 ft

The time it'll take to reach the ground  is:

y(0) = 12 + 95*0 - 16.085*(0)² = 12 s

Answer:

10

Step-by-step explanation:

- x - =+

Answer:

+10

Step-by-step explanation:

because when u multiply by 2 negatives u get a positive

Answer:

It is greater than -24

Step-by-step explanation:

-170 divided by 7 is -24.2857...(repeating)

-170 is from doing -169 - 1

The answer to the question is that 7n - 1 is greater than -24.

To determine the relationship between 7n - 1 and -24, we need to solve the inequality 7n - 1 > -169 and then compare the solution to -24.

First, let's solve the inequality 7n - 1 > -169:

7n - 1 + 1 > -169 + 1

7n > -168

n > -168 / 7

Now, we have the solution to the inequality, which tells us that n must be greater than -24 to satisfy the inequality 7n - 1 > -169.

Since n > -24, it follows that 7n - 1 will also be greater than 7(-24) - 1. Let's calculate 7(-24) - 1:

7(-24) - 1 = -168 - 1 = -169

But we know from the inequality that 7n - 1 is strictly greater than -169. Therefore, 7n - 1 must be greater than -24 as well, because -169 is less than -24.

Hence, 7n - 1 is greater than -24.

Answer:

mean = 19.54

median = 17

mode 16

range 52

Step-by-step explanation:

17, 22, 34, 3, 16, 16, 24, 55, 18, 3, 16, 12, and 18

First put the numbers in order from smallest to largest

3,  3, 12, 16, 16, 16,17,18, 18,22,24, 34, 55

The mean is where you add up all the numbers and divide by the number of numbers

(3+  3+ 12+ 16+ 16+ 16+17+18+ 18+22+24+ 34+ 55)/13

254/13

19.53846154

mean = 19.54

The median is the middle number

Since there are 13 numbers the middle number is 13/2 = 6.5 which rounds to 7

The 7th number is 17

median = 17

Mode is the number that appears most often

16 appears 3 times which is more often than any other number

mode 16

The range is the largest number minus the smallest number

55-3 = 52

range = 52

Answer:

k=10°

Step-by-step explanation:

<ZYX

<ZYM + <ZYX = 180° ( angle on straight line)

115° + <ZYX = 180°

<ZYX = 180° - 115°

<ZYX = 65°

k

<YZX + <ZXY + <ZYX = 180° ( sum of interior angles of a triangle)

(4k + 5)° + (6k + 10)° + 65° = 180°

10k + 80° = 180°

10k = 180° - 80°

10k = 100°

Multiplying both sides by 10

k = 100°

10

k = 10°

Answer:

a

Step-by-step explanation:

yes

Answer:

Step-by-step explanation:

Given the complex numbers in polar cordinates

[2cis 33˚][3cis 22˚]

Generally, if z = rcis[tex]\theta\\[/tex], then z = r(cos[tex]\theta+isin\theta[/tex])

2cis33° = 2(cos33°+isin33°)

3cis22° =  3(cos22°+isin22°)

Taking tthe product of both complex numbers;

[2cis 33˚][3cis 22˚] = [2(cos33°+isin33°)][3(cos22°+isin22°)]

= 6{cos33cos22+icos33sin22+isin33cos22+i²sin33sin22}

since i² = 1

= 6{cos33cos22+icos33sin22+isin33cos22-sin33sin22}

= 6{(cos33cos22-sin33sin22)+i(cos33sin22+sin33cos22)}

Applying the trigonometric identity as shown;

cos(A+B)= cosAcosB-sinAsinB and;

sin(A+B)= sinAcosB + cosAsinB

[2cis 33˚][3cis 22˚] = 6{(cos(33+22)+ i(sin(33+22)}

[2cis 33˚][3cis 22˚] = 6(cos55°+isin55°)

[2cis 33˚][3cis 22˚] = 6cis55°

The product of the complex numbers is 6cis55°

Answer:

Answer: 23.7

Step-by-step explanation: Its correct on Brainly.