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4 years ago

What is the volume of the following prism

Mathematics

1 answer:

Bond [772]4 years ago

6 0

The volume of a triangular prism is the area of the base multiplied by the height.

<u>Let's first identify our values:</u>

20 cm = height of prism

12 cm = base of triangle

10 cm = height of triangle

First, we need to calculate the area of the triangle. To calculate the area of the triangle, we multiply the base of the triangle by the height of the triangle. In this case, the base is 7 and the height is 5 so 7 × 5 = 35 and then we divide 35 by 2 and we will get a quotient of 17.5.

Finally, we will multiply the area of the triangle which is 17.5 by 12.

17.5 × 12 = 210 $m^{2}$ .

Therefore, the area of the triangular prism is 210 $m^{2}$ .

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A bike and skate shop rents bike for $21 per day and pairs of skates for $20 per day. To remain viable, the shop needs to make a

Leya [2.2K]

Let the number of bike be x and the number of skates be y, then
21x + 20y ≥ 362 . . . (1)
2y = x . . . (2)

Putting (2) into (1), then
21(2y) + 20y ≥ 362
42y + 20y ≥ 362
62y ≥ 362
y ≥ 5.84

The least number of pairs of skates they need to rent each day to make their minimum is 6.

7 0

3 years ago

Jessica has an account with a credit union. Her account earns 2.5% simple interest yearly. Exactly a year and a half ago, she op

elena55 [62]

Answer:

$22.5

Step-by-step explanation:

2.5% = .025

900 divided by 1.5 = 600

600 multiplied by .025 = 15

15 divided by .5 = 7.5

15 + 7.5 = 22.5

4 0

3 years ago

At the theater, tickets for adults cost $4.75

shutvik [7]

X+y= 26 and 4.75x + 2.25y= 83.50

y=26-x( substitute this into second equation for y and solve for x)

4.75x + 2.25(26-x)= 83.50

4.75x + 58.5-2.25x= 83.50

x= 10

Now solve for y by substituting your answer for x

10+ y= 26

y=16

Therefore, 16 tickets were purchased for kids and 10 for adults.

7 0

3 years ago

I can't find area of the triangle

Andreas93 [3]

Answer:

First do the Base multiplied by the Height.

After divide by 2

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 an

kolbaska11 [484]

Answer:

z = 1.28 < a - 200/20

And if we solve for a we got

a = 200 + 1.28 * 20 = 225.6

So the value of height that separates the bottom 90% of data from the top 10% is 225.6.

Step-by-step explanation:

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X ~ N (200,20)

For u = 200 and o = 20

For this case we can use the z score in order to solve this problem, given by this formula:

Z = x-u/o

For this part we want to find a value a, such that we satisfy this condition:

P (X > a) = 0.1 (a)

P (X < a) = 0.9 (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

P ( X < a) = P (X-u/o < a - u/o) = 0.9

P (z < a-u/o) = 0.9

But we know which value of z satisfy the previous equation so then we can do this:

z = 1.28 < a - 200/20

And if we solve for a we got

a = 200 + 1.28 * 20 = 225.6

So the value of height that separates the bottom 90% of data from the top 10% is 225.6.

3 0

2 years ago