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Y_Kistochka [10]

3 years ago

7

McKenna and Lara work for their uncle Eddie who repairs skateboards and bicycles. Uncle Eddie is leaving for a vacation to the A

mazon. He asks the girls to order 54 new wheels for 21 skateboards and bicycles in his repair shop. How many bicycles and how many skateboards are in uncle Eddies shop?

1 answer:

natali 33 [55]3 years ago

8 0

Let x be a number of skateboards and y be the number of bicycles in Eddie's repair shop.

Eddie asks the girls to order 54 new wheels for 21 skateboards and bicycles, then

x+y=21.

One scateboard has 4 wheels, then x scateboards have 4x wheels, one bicycle has 2 wheels, then y bicycles have 2y wheels. In total there should be ordered 54 wheels, so

4x+2y=54.

Solve the system of equations:

$\left\{\begin{array}{l}x+y=21\\4x+2y=54.\end{array}\right.$

From the first equation $x=21-y.$ Substitute it into the second equation:

$4(21-y)+2y=54,\\ \\84-4y+2y=54,\\ \\-2y=54-84,\\ \\-2y=-30,\\ \\2y=30,\\ \\y=15.$

Then

$x=21-15=6.$

Answer: 6 scateboards and 15 bicycles.

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At Tech Express, 40% of the customers purchases small coffee and 60% purchases medium. Of those customers purchasing small coffe

Dvinal [7]

Answer and explanation:

Given : At Tech Express, 40% of the customers purchases small coffee and 60% purchases medium. Of those customers purchasing small coffee, 30% prefer decaf. Of those purchasing medium coffee, 50% prefer decaf.

Let $A_1$ customer purchase small coffee.

i.e. $P(A_1)=40\%=0.4$

$A_2$ customer purchase medium coffee.

i.e. $P(A_2)=60\%=0.6$

Let B be the customer purchase prefer decaf.

So, $P(B|A_1)=30\%=0.3$

$P(B|A_2)=50\%=0.5$

(a) What is the probability that the next customer will request medium and decaf coffee?

i.e. $P(A_2\cap B)=P(A_2)\times P(B|A_2)$

$P(A_2\cap B)=0.6\times 0.5$

$P(A_2\cap B)=0.3$

(b) What is the probability that the next customer prefers decaf?

i.e. $P(B)=P(A_1\cap B)+P(A_2\cap B)$

$P(B)=P(A_1)\times P(B|A_1)+P(A_2)\times P(B|A_2)$

$P(B)=0.4\times 0.3+0.6\times 0.5$

$P(B)=0.12+0.3$

$P(B)=0.42$

(c) If the next customer prefers decaf, what is the probability that small is requested?

i.e. $P(A_1|B)=\frac{P(A_1\cap B)}{P(B)}$

$P(A_1|B)=\frac{0.12}{0.42}$

$P(A_1|B)=0.28$

3 0

3 years ago

Original amount 90$ new amount 84.50 what's the percent of change?

diamong [38]

Percent change=100 times change/original

change=original-new
change=90-84.50=5.5

percent change=100 times 5.5/90
percent change=550/90
percent change=6.11111
percent change=6.1%

7 0

3 years ago

25 points. Math question

klio [65]

Answer:

-8

Step-by-step explanation:

I believe it is -8

first you 2(-2) - 4

then you -4 -4= -8

Hope that was helpful.

6 0

4 years ago

Average after 8 test is 91%. if he gets a 78% on his 9th test what will be the new acerage

Vika [28.1K]

All you need to do is add te averages together then divide them by 2. 91%+78%=169% 169%÷2=84.5% So the new test average is 84.5%

6 0

3 years ago

Approximately 5% of workers in the US use public transportation to get to work. You randomly select 25 workers and ask if they u

trasher [3.6K]

Answer:

0.2305 = 23.05% probability that exactly 2 workers say yes.

Step-by-step explanation:

For each worker, there are only two possible outcomes. Either they say yes, or they say no. The probability of a worker saying yes is independent of any other worker, which 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.

5% of workers in the US use public transportation to get to work.

This means that $p = 0.05$

You randomly select 25 workers

This means that $n = 25$

Find the probability that exactly 2 workers say yes.

This is P(X = 2). So

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

$P(X = 2) = C_{25,2}.(0.05)^{2}.(0.95)^{23} = 0.2305$

0.2305 = 23.05% probability that exactly 2 workers say yes.

4 0

3 years ago