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nika2105 [10]
3 years ago
13

A baker, in 70 minutes, iced 40 cupcakes and, in 49 minutes, iced 28 cupcakes. What is the constant of proportionality?

Mathematics
1 answer:
Zinaida [17]3 years ago
8 0

Answer:

\frac{4}{7}

Step-by-step explanation:

The constant of proportionality is the slope of the line joining the two points

(70,40) and (49,28).

Recall the slope formula:

m =  \frac{ y_2 -  y_1 }{ x_2 - x_1}

We substitute the point to get:

m =  \frac{28 - 40}{49 - 70}  =  \frac{ - 12}{ - 21}  =  \frac{4}{7}

<u>Alternatively</u>:

A proportional relation is given by

y = kx

where k is the constant of proportionality.

Using any point, we substitute and solve for k.

40 = 70k

k =  \frac{40}{70} = \frac{4}{7}

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A chemist is mixing two solutions, solution A and solution B Solution A is 15% water and solution Bis 20% water. She already has
slavikrds [6]

Answer:

15 mL of the solution with 20% water will be needed.

Step-by-step explanation:

Use the inverse relationship

10 mL * (18-15)% = x mL * (20-18)%

x = 10 mL * (3/2) = 15 mL

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3 years ago
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Patsy found a top on the clearance rack marked 60% off the original price. If the original price is $48, how much will Patsy sav
Arlecino [84]
If the top is $48 and it is 60% off you will multiply the cost by the decimal form of the sale percentage: 48*0.60= $28.80. This is the amount she will save and I think is the answer you are looking for.

If there is a follow up question asking for the final cost of the top you would find that by subtracting the amount saved from the original cost: 48.00-28.80=$19.20.
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3 years ago
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A real estate agent has 1212 properties that she shows. She feels that there is a 50P% chance of selling any one property during
forsale [732]

Answer:

0.6127 = 61.27% probability of selling no more than 6 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either it is sold, or it is not. The probability of a property being sold is independent of any other property. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

12 properties

This means that n = 12

She feels that there is a 50% chance of selling any one property during a week.

This means that p = 0.5

Compute the probability of selling no more than 6 properties in one week.

This is:

P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002

P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029

P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161

P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537

P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.1208

P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.1934

P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.2256

P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0002 + 0.0029 + 0.0161 + 0.0537 + 0.1208 + 0.1934 + 0.2256 = 0.6127

0.6127 = 61.27% probability of selling no more than 6 properties in one week.

6 0
2 years ago
What is the coefficient of the c-term of the algebraic expression 14 a minus 72 r minus c minus 34 d?
Artemon [7]

Answer:

-1 is the answer so B is the answer

7 0
2 years ago
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A bottle of sugar syrup soda had 3 3/9 grams of sugar in it. If Will drank 2 full bottles and 1/2 of a bottle, how many grams of
notka56 [123]

Will drank 8\frac{1}{3} grams of sugar.

Step-by-step explanation:

Given,

Amount of sugar in one bottle = 3\frac{3}{9}=\frac{30}{9}\ grams

Amount of bottles drank by Will = 2+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}\ bottles

Total sugar drank by Will = Amount of sugar in one bottle * Amount of bottles drank by Will

Total sugar drank by Will = \frac{30}{9}*\frac{5}{2}

Total sugar drank by Will = \frac{150}{18}=\frac{25}{3}

Total sugar drank by Will = 8\frac{1}{3}

Will drank 8\frac{1}{3} grams of sugar.

Keywords: fraction, multiplication

Learn more about multiplication at:

  • brainly.com/question/2115122
  • brainly.com/question/2116906

#LearnwithBrainly

8 0
3 years ago
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