Find the volume of the triangular prism.

Answer:

56.25 cm

Step-by-step explanation:

your teacher wrote the approach already : the law of sines.

in our example we have

sin(28)/27 = sin(102)/c

c×sin(28)/27 = sin(102)

c×sin(28) = 27×sin(102)

c = 27×sin(102)/sin(28) = 27×0.98/0.47 = 56.25 cm

Answer:

68

Step-by-step explanation:

Let The first number = X

& the Second one = X + 16

Sum of these two numbers = 120

X + X + 16 = 120

2X = 120 - 16

2X = 104

X = 52

So , the first number = 52

& Second one = 52 + 16 = 68

Answer:

The numbers are 52 and 68.

Step-by-step explanation:

Let x be the first number and y be the second. The question tells us that:

1) x = y + 16

2) (x + y) / 2 = 60

2 equations, 2 unknowns. Solve the system. Plug equation 1 into equation 2:

(y + 16 + y) / 2 = 60

2y + 16 = 120

y + 8 = 60

y = 52

Now plug the value of y back into either original equation. I'll use the first:

x = 52 + 16

x = 68

Answer:

The lemonade costs 1.4.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the cost of a cookie.

y is the cost of a lemonade.

Total cost for cookie and lemonade is 1.80.

This means that [tex]x + y = 1.8[/tex].

As we want y, we have that [tex]x = 1.8 - y[/tex]

Lemonade costs 1.00 more than the cookie?

This means that:

[tex]y = x + 1[/tex]

So

[tex]y = 1.8 - y + 1[/tex]

[tex]2y = 2.8[/tex]

[tex]y = \frac{2.8}{2}[/tex]

[tex]y = 1.4[/tex]

The lemonade costs 1.4.

Answer:

6,079.42

Step-by-step explanation:

FV   =   P (1  +  r / n)^Yn

P is the starting principal, r is the annual interest rate, Y is the number of years invested, and n is the number of compounding periods per year. FV is the future value, meaning the amount the principal grows to after Y years.

Answer:

I think it would be 42. If its wrong I'm sorry

Answer:

The mean absolute deviation is: 7.44

Step-by-step explanation:

Given

[tex]Scores: 98, 78, 84, 75, 91[/tex]

Required

The mean absolute deviation

First, calculate the mean

[tex]\bar x = \frac{\sum x}{n}[/tex]

[tex]\bar x = \frac{98+78+84+75+91}{5}[/tex]

[tex]\bar x = \frac{426}{5}[/tex]

[tex]\bar x = 85.2[/tex]

The mean absolute deviation (M) is:

[tex]M = \frac{1}{n}\sum|x - \bar x|[/tex]

So, we have:

[tex]M = \frac{1}{5}(|98 - 85.2|+|78 - 85.2|+|84 - 85.2|+|75 - 85.2|+|91 - 85.2|)[/tex]

[tex]M = \frac{1}{5}(|12.8|+|-7.2|+|-1.2|+|-10.2|+|5.8|)[/tex]

Remove absolute brackets

[tex]M = \frac{1}{5}(12.8+7.2+1.2+10.2+5.8)[/tex]

[tex]M = \frac{1}{5}*37.2[/tex]

[tex]M = 7.44[/tex]

Answer:

4

Step-by-step explanation:

First, the numbers should be in ascending or descending order . Since, 4 numbers are in ascending order we don't have to do that .

Second, find the "middlest" of them . If there were total of odd numbers it would have been easier but, here is total of even number(4) and mean of 2 middlest number would be its median: (4+4)/2=4 .

Answer:

B. $1650

Step-by-step explanation:

the middle share = 3/(2+3+5) × $5500

= 3/10 × $5500 = $1650

Answer:

D

Step-by-step explanation:

[tex]\sqrt{17} = 4.123[/tex]

So we can see that 4.123 lie between 4 and 5

Therefore, option (D) is correct

Answer:

44.8 cm

Step-by-step explanation:

Given

See attachment for shapes

[tex]P_A= 56cm[/tex]

Required

The perimeter of B

Let the length of a side of the square that makes up A be, l.

So, we have:

[tex]P_A = 10 * l[/tex] --- because A is formed by 10 sides of l

[tex]56 = 10 * l[/tex]

[tex]l =\frac{56}{10}[/tex]

[tex]l =5.6[/tex]

The perimeter of B is:

[tex]p_B = 8*l[/tex] --- because B is formed by 8 sides of l

[tex]p_B = 8*5.6[/tex]

[tex]p_B = 44.8[/tex]

Answer:

1/4 of the cost

Step-by-step explanation:

Lisa, Taryn, and Catherine go to a store to buy party supplies. The store has a sale on the supplies they want for 3/4 the original price. The girls agree to each pay 1/3 of the cost. What fraction of the original price did each girl pay?

Discounted price = 3/4 the original price

Each girl agreed = 1/3 of the cost

Amount each girl paid = 3/4 * 1/3

= (3 * 1) / (4 * 3)

= 3 / 12

= 1/4 of the cost

Amount each girl paid = 1/4 of the cost

Step-by-step explanation:

Let running speed = x.

So, cycling speed = 2x.

Total distance traveled = 20 + 25 = 45km

Time taken running = 20/x

Time taken cycling = 25/2c

Total time taken = 5 hours

So, 5 = 20/x + 25/2x

Solving this equation for x gives:

10x = 65. Thus x = 6.5

Since cycling speed = 2x, cycling speed = (6.5)(2)

So cycling speed is 13 km/h.

Hope it helps.

(27-9) x 3 / 9 + 18 = 42

Follow order of operations: parentheses first:

18 x 3 / 9 + 18 = 42

Next is multiplication and division in order from left to right:

18 x 3 = 54

54/9 = 6

Now you have 6 + 18 = 24

24 does not equal 42 so Phillipa is not correct.

The answer is C. She is not correct. The correct answer is 24

Answer:

answer=she is not correct

Step-by-step explanation:

(27-9)*3÷9+18

18*3÷9+18

18*1/3+18

18/3+13

6+13

19

use BODMAS rule (Bracket Of Division Multiplication Addition And Subtraction)

Answer:

15

15

10

Step-by-step explanation:

3/8 x £40 = £15 for Sarah

3/8 x £40 = £15 for Fiona

2/8 x£40 = £10 for david

Answer:

Sarah gets [tex]\frac{3}{8}[/tex] × 40 = £15

Fiona gets [tex]\frac{3}{8}[/tex] × 40 = £15

David gets [tex]\frac{2}{8}[/tex] × 40 = £10

Step-by-step explanation:

If £40 is shared between three person in the ratio of 3:3:2 then calculate the amount each person gets.

To find the amount each person gets we are goin to change the ratios of each person into fractions.

To turn to fraction add all portions in the ratio:

3 + 3 + 2 = 8 (this will be the denominator for all proportions.)

Therefore Sarah gets [tex]\frac{3}{8}[/tex], Fiona gets [tex]\frac{3}{8}[/tex] and David gets [tex]\frac{2}{8}[/tex].

Sarah gets [tex]\frac{3}{8}[/tex] × 40 = £15

Fiona gets [tex]\frac{3}{8}[/tex] × 40 = £15

David gets [tex]\frac{2}{8}[/tex] × 40 = £10

Answer:

Solution given:

[tex]8\frac{7}{12}-3\frac{1}{3}=\frac{8*12+7}{12}-\frac{3*3+1}{3}[/tex]

=[tex]\frac{103}{12}-\frac{10}{3}[/tex]

taking lcm

=[tex] \frac{103-10*4}{12}=\frac{63}{12}=\frac{21}{4}=5\frac{1}{4}[/tex]

Answer:

5 1/4

Step-by-step explanation:

8 7/12 - 3 1/3

We need to get a common denominator of 12

8 7/12 - 3 1/3 *4/4

8 7/12 - 3 4/12

5 3/12

Simplifying the fraction

5 1/4

Answer:

below

Step-by-step explanation:

that is the procedure above

Because the graph is starting high and going down, your answer is c- exponential decay

Answer:

This is exponential decay.

Step-by-step explanation:

Lets break down the answers:

A: Linear Growth. Well, we can eliminate this because the line is going down, its decay. Also, linear means line, a straight line.

B: Exponential Growth. This might work, but then again, it says *growth* not decay. Exponential is correct because as the values get bigger and bigger, the line curves.

C: Exponential Decay. Yes! This is exactly what we need. Exponential because of the curve... and of the decay.

D: Linear Decay. No, linear, again, is for lines. But now, we have already eliminated it because it says linear.

Answer:

Hence, In this scenario, __Group NoMW____ is the control group and the ___Group MW___ is the experimental group.

Step-by-step explanation:

The control group is the one which is not subjected to any testing situation or condition.

While the experimental group is the one which is subjected to testing condition.

Hence, In this scenario, __Group NoMW____ is the control group and the ___Group MW___ is the experimental group.

Answer:

S = 62.5%

Step-by-step explanation:

Given the following data;

Ratio of J:S = 3:5 = 3 + 5 = 8

To find what percent of team members are seniors;

[tex] S = \frac {5}{8} * 100 [/tex]

[tex] S = \frac {500}{8} [/tex]

S = 62.5%

Additionally, to find what percent of team members are juniors;

J = 100 - S

J = 100 - 62.5

J = 37.5%

Answer:

Step-by-step explanation:

The only way this can be factored is by pulling out the GCF. 2 and x are common to both terms:

[tex]2x(x^2-100)[/tex]

BUT you should also recognize that what's inside the parenthesis is the difference of perfect squares. And that factors to

(x - 10)(x + 10). So the complete factorization is

2x(x - 10)(x + 10)

Answer:

[tex]17 \le t \le 28[/tex]

Step-by-step explanation:

Given

[tex]t = 22\frac{1}{2}[/tex] --- average time

[tex]\triangle t = 5\frac{1}{2}[/tex] --- the variation

Required

The inequality to represent the scenario

To do this, we simply add and subtract the variation from the average time.

i.e.

[tex]t \± \triangle t[/tex]

So, the inequality is:

[tex]22\frac{1}{2} - 5\frac{1}{2} \le t \le 22\frac{1}{2} + 5\frac{1}{2}[/tex]

Solve:

[tex]17 \le t \le 28[/tex]

Answer:

3rd option

Step-by-step explanation:

The zeros ( where the graph crosses the x- axis ) are x = 3 and x = 7

The corresponding factors are then (x - 3) and (x - 7)

The equation is then

f(x) = a(x - 3)(x - 7) ← a is a multiplier

To find a substitute any point on the graph into the equation.

Using (8, 15 ) , then

15 = a(8 - 3)(8 - 7) = a(5)(1) = 5a ( divide both sides by 5 )

3 = a

Thus

f(x) = 3(x - 3)(x - 7)

Answer:

190

Step-by-step explanation:

1+2+3+4......19=210-20

=190

Answer:

I'm probably just really bad at math and got this wrong, but I think the answer is 40 cm. Sorry if this doesn't help, like I said I think I'm just bad at math, which it doesn't really make sense as to why I'm answering a math problem, but anyways there's the (probably wrong) answer.

I really hope that helped :P

Answer:

15units

Step-by-step explanation:

BC is: 5x=5×3=15 units. so,Length of BC=15 units

Answer:

150 degrees

Step-by-step explanation:

8x-10=3x+90

solve for x in calculater

x = 20

Substitute:

3(20)+90 = 150

Answer:

Step-by-step explanation:

8x - 10 = 3x + 90

5x - 10 = 90

5x = 100

x = 20

8(20) - 10 = 160 - 10 = 150