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3 years ago

Rewrite the expression using the GCF and distributive property. (110-44)

Mathematics

1 answer:

Afina-wow [57]3 years ago

3 0

let me divide your question into two parts A and B as;

A.Rewrite the expression using the GCF and distributive property. (110-44)

B.how many 24-foot jump ropes can be made from a rope that is 100 feet long?

Answer:

A.(110-44)=22(5-2)

B. 4 jump ropes of 24 feet length

Step-by-step explanation:

A.Rewrite the expression using the GCF and distributive property. (110-44

Answer:

Find the GCF of 110 and 44 then take that GCF as common factor out of (110-44) then we can get new expression for (110-44) as 22(5-2) i.e.

prime factorization of 110=2x5x11

and 44=2x2x11

GCf is the product of factors that appear in both of the prime factorization which is 2x11=22

thus using GCF (22) as common factor we can rewrite the given expression as

22(5-2) which is distributive law of multiplication over subtraction.

B.how many 24-foot jump ropes can be made from a rope that is 100 feet long?

Answer:

Given

Total length of the rope =100 feet

length of a jump rope =24

solution:

For one jump-rope we need 24 feet

For two jump-ropes we need 48 feet

For three jump-ropes we need 72 feet

For four jump-ropes we need 96 feet

thus from a 100 feet long rope we can make 4 jump-ropes of 24 feet length with 6 feet remaining as extra.

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Check:
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$m_{y4}=1793.61964-\frac{1793.61964\cdot6}{100}\Rightarrow m_{y4}=1686.002462$

For the year previous to that one, he had:

$m_{y3}=1686.002462-\frac{1686.002462\cdot6}{100}\Rightarrow m_{y3}=1584.842314$

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10 months ago

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2 years ago

12.what is the probability that a boy and a girl chosen randsomly will be seniors?

zhenek [66]

$\frac{\textbf{1}}{\textbf{20}}$

Step-by-step explanation:

Probability= $\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

Probability for a randomly chosen girl to be senior= $\frac{\text{number of senior girls}}{\text{total number of girls}}$

Probability for a randomly chosen girl to be senior= $\frac{7}{8+11+9+7}=\frac{7}{35}=\frac{1}{5}$

Probability for a randomly chosen boy to be senior= $\frac{\text{number of senior boys}}{\text{total number of boys}}$

Probability for a randomly chosen girl to be senior= $\frac{9}{10+7+10+9}=\frac{9}{36}=\frac{1}{4}$

For two independent events,

Probability for both event 1 and event 2 to take place= $\text{probability of event 1} \times \text{probability of event 2}$

Since choosing boys and girls is independent,

Probability for both boy an girl chosen to be senior= $\text{probability for boy to be senior}\times\text{probability for girl to be senior}$

Probability for both boy and girl chosen to be senior= $\frac{1}{5} \times \frac{1}{4} = \frac{1}{20}$

So,required probability is $\frac{1}{20}$

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