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Reika [66]
3 years ago
13

Help. Solving Multi Step Ratio Problems!

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
6 0

Answer:

Part 1) 30\ coupons

Part 2) 12\ sandwiches

Part 3) 60\ push-ups

Part 4) 96\ minutes

Part 5) \$95

Part 6) 1\frac{7}{8}\ cups\ of\ pretzel

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

so

Using proportion

Find out the number of salads you could buy to get $10 in coupons

\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

so

\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does  15 push-ups

so

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

1\ h=60\ min

\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

so

For every mug that Janet sells, she earns 2($5)=$10

using proportion

\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70

step 3

Adds the amount earned by Aly plus the amount earned by Janet

25+70=\$95

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel

Convert to mixed number

\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel

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The random variable X is exponentially distributed, where X represents the waiting time to be seated at a restaurant during the
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Answer:

The probability that the wait time is greater than 14 minutes  is 0.4786.

Step-by-step explanation:

The random variable <em>X</em> is defined as the waiting time to be seated at a restaurant during the evening.

The average waiting time is, <em>β</em> = 19 minutes.

The random variable <em>X</em> follows an Exponential distribution with parameter \lambda=\frac{1}{\beta}=\frac{1}{19}.

The probability distribution function of <em>X</em> is:

f(x)=\lambda e^{-\lambda x};\ x=0,1,2,3...

Compute the value of the event (<em>X</em> > 14) as follows:

P(X>14)=\int\limits^{\infty}_{14} {\lambda e^{-\lambda x}} \, dx=\lambda \int\limits^{\infty}_{14} {e^{-\lambda x}} \, dx\\=\lambda |\frac{e^{-\lambda x}}{-\lambda}|^{\infty}_{14}=e^{-\frac{1}{19} \times14}-0\\=0.4786

Thus, the probability that the wait time is greater than 14 minutes  is 0.4786.

7 0
3 years ago
Find the f^-1(x) and it’s domain
borishaifa [10]

Answer:

f^{-1}(x) = (x + 8)^2

x \ge -8

Step-by-step explanation:

Given

f(x) = \sqrt x - 8

Solving (a): f^{-1}(x)

We have:

f(x) = \sqrt x - 8

Express f(x) as y

y = \sqrt x - 8

Swap x and y

x = \sqrt y - 8

Add 8 to both\ sides

x + 8 = \sqrt y - 8 + 8

x + 8 = \sqrt y

Square both sides

(x + 8)^2 = y

Rewrite as:

y = (x + 8)^2

Express y as: f^{-1}(x)

f^{-1}(x) = (x + 8)^2

To determine the domain, we have:

The original function is f(x) = \sqrt x - 8

The range of this is: f(x) \ge -8

The domain of the inverse function is the range of the original function.

<em>Hence, the domain is:</em>

x \ge -8

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3 years ago
The sketch shows the distance three runners travel during a race. Describe what occurs at times A,B,C and D. In what order do th
goldfiish [28.3K]

Answer:

Notice that the distance is in the y-axis, and the time in the x-axis.

First, let's see what happens in the four points:

A) You can see that in point A, the steepness of the line increases, this means that the speed of the runner increases in that point.

B) In this point, the runner that increased his/her speed in point A crosses the graph of another runner, this means that they are at the same distance to the end and at the same time.

C) In this point again two runners are at the same distance and the same time, and we also can see that the runer that increased his/her speed at point A, now has reached the end of the race (because his line stops increasing, wich means that he/she already finished the race)

D) The las runner finishes the race at point D.

Then the first runner that finishes the race is the one with the shorter graph (shorter graph means that he ran for less time than the others, wich means that he/she finished first)

The last runner is the one that finished at point D,

The middle one finishes right after the point C.

6 0
3 years ago
LCM of 16, 28, and 56
Sindrei [870]

Answer:

2

Step-by-step explanation:

2x8=16, 2x14=28, and 2x28=56

6 0
3 years ago
Please help this is due in 30 minutes!
topjm [15]

Answer:

a is 31 b is 38 x is 133. Y is 47

Step-by-step explanation:

A is 31 because the other side is 31. we know the sides are the same because of the markings. B is 38 because the other side is 38 we know that because of the markings which mean its the same. X is 133 Y should be 47 because ALL ANGLES IN A QUADRILATERAL IS EQUAL TO 360. 133+133=266 360-266 is 94. 94 is for both angles so we need to divide by 2 the answer for Y is 47

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3 years ago
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