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3 years ago

5. A store sells bags of pecans for $3.00, bags of walnuts for $3.50, and bags of almonds for $4.00. One day, 15

Mathematics

1 answer:

kondaur [170]3 years ago

5 0

Answer:

x = 4

y = 6

z = 5

Step-by-step explanation:

Let

bags of pecans = x

bags of walnuts = y

bags of almonds = z

x + y + z = 15

3x + 3.5y + 4z = 53

Two more bags of walnuts were sold than pecans.

Walnuts = x + 2

x + y + z = 15

3x + 3.5y + 4z = 53

x + x + 2 + z = 15

3x + 3.5(x+2) + 4z = 53

2x + z = 15 - 2

3x + 3.5x + 7 + 4z = 53

2x + z = 13 (1)

6.5x + 4z = 46 (2)

Multiply (1) by 4

8x + 4z = 52 (3)

6.5x + 4z = 46 (2)

Subtract (2) from (3)

8x - 6.5x = 52 - 46

1.5x = 6

Divide both sides by 1.5

x = 4 bags

y = x + 2

= 4 + 2

= 6

y = 6 bags

Substitute the value of x into (1)

2x + z = 13 (1)

2(4) + z = 13

8 + z = 13

z = 13 - 8

= 5

z = 5 bags

Check:

x + y + z = 15

4 + 6 + 5 = 15

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Three less than two times a number is 55. What’s the number ?

Musya8 [376]

Let n be a number

2n - 3 = 55

Add 3 to both sides

2n + (-3 + 3) = 55 + 3

2n = 58

Divide 2 to both sides

2n/2 = 58/2

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Hope this helped!

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4 0

3 years ago

Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 12 young adul

ddd [48]

Answer:

a) 0.194 = 19.4% probability that more than 7 preferred McDonald's

b) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

c) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they prefer McDonalds, or they prefer burger king. The probability of an adult prefering McDonalds is independent from other adults. So we use the binomial probability distribution 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.

50% of all young adults prefer McDonald's to Burger King when asked to state a preference.

This means that $p = 0.5$

12 young adults were randomly selected

This means that $n = 12$

(a) What is the probability that more than 7 preferred McDonald's?

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

In which

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

$P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.121$

$P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.054$

$P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.016$

$P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.003$

$P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.000$

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.121 + 0.054 + 0.016 + 0.003 + 0.000 = 0.194$

0.194 = 19.4% probability that more than 7 preferred McDonald's

(b) What is the probability that between 3 and 7 (inclusive) preferred McDonald's?

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)$

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

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.054$

$P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.121$

$P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.193$

$P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.226$

$P(X = 7) = C_{12,7}.(0.5)^{7}.(0.5)^{5} = 0.193$

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.054 + 0.121 + 0.193 + 0.226 + 0.193 = 0.787$

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

(c) What is the probability that between 3 and 7 (inclusive) preferred Burger King?

Since $p = 1-p = 0.5$ , this is the same as b) above.

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

7 0

3 years ago

The temperature in Fond cu Lax, Wisconsin, is 48 degrees. The temperature in Houston, Texas, is 80 degrees. What is the differen

DochEvi [55]

Answer:

Step-by-step explanation:

Temperature in Fond cu Lax=48*

Temperature in Houston=80*

Temperature difference=80-48=32*

3 0

3 years ago

It takes Leon 17 hours to seal his driveway working by himself. If Michael helps Leon, they can seal the driveway in 2 hours. Ho

Norma-Jean [14]

Answer:

It takes Michael 1 hour, 14 minutes and 7 seconds to seal the driveway close

Step-by-step explanation:

Leon do the work in 17 hours that means the rate of his work is $\frac{1}{17} work/hr$ , so he do $\frac{2}{17}$ of the work in two hours, therefore Michael do the other $\frac{15}{17}$ of the work, thus Michael rate will be $\frac{15}{17} \div\frac{1}{2} =\frac{30}{17} work/hour$ .

So it takes Michael $1h+\frac{4}{17}h$ to complete the work, or $\frac{4h}{17} \times \frac{60min}{1hour} =14\frac{2}{17} min\\\\\frac{2}{17} min \times \frac{60 secs}{1min}=7secs$

$1h \ 14 min \ 7secs$

8 0

3 years ago

9.12cm 10.36cm 11.34cm 12.61cm

Vinvika [58]

Tan80 = QR / RS
QR = 5.67 (2)
QR = 11.34

answer

11.34cm

8 0

3 years ago