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1 year ago

A whole number from 1 to 15 inclusive is picked at random.

Mathematics

1 answer:

Helen [10]1 year ago

8 0

Answer:

a) 3/7

b) 3/5

Explanation:

The figure attached shows the Venn diagram for the given sets.

a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?

From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.

There are a total of 7 multiples of 24, from 1 to 15.

Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:

b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?

The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.

The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.

Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:

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Jan accidentally ran 7 minutes longer than she was supposed to. Write an expression for the total amount of time Jan ran if she

vovangra [49]

Answer:

m+7

Step-by-step explanation:

If she ran 7 minutes longer and m represents the amount of time she ran, then it would just be addition.

Let's say m=60 minutes. She would've ran for 67 minutes, which is also m+7.

6 0

2 years ago

Algebra. Find the variable in the equation 803 divided by 73=m

weeeeeb [17]

Answer:

The value of variable "m" in the equation 803 divided by 73 = m is equal to 11.

Solution:

Need to find the variable in the given equation 803 divided by 73 = m

That means need to solve below expression to determine value of variable m.

$\frac{803}{73}=m$

So let’s solve left hand side to get the value of m.

For sake of simplicity let’s do factorization of numerator and denominator and remove the common terms in numerator and denominator.

$\begin{array}{l}{803=73 \times 11} \\\\ {73=73 \times 1} \\\\ {=>\frac{803}{73}=\frac{73 \times 11}{73 \times 1}=11}\end{array}$

Hence value of variable m is equal to 11.

8 0

2 years ago

Lyle works at a bakery. He needs to mix 1 cup of brown sugar and 12 cup of granulated sugar to make each tray of 60 cookies. Eac

andriy [413]

Answer:

50 trays

3000 cookies

Step-by-step explanation:

We are given the following in the question:

1 cup of brown sugar and $\frac{1}{2}$ cup of granulated sugar makes a tray of 60 cookies.

Total cups of sugar used(brown and granulated) = 1.5 cups

Number of sugar cups used by Lyle each week = 75

We have to find the number of trays made each week.

$\text{Ratio} = \dfrac{\text{Cups of sugar mixture}}{\text{Number of trays}}\\\\\dfrac{1.5}{1} = \dfrac{75}{\text{Number of trays}}\\\\\Rightarrow \text{Number of trays} = \dfrac{75}{1.5} = 50$

Thus, 50 trays of cookies are made each week.

Total number of cookies made each week =

$=\text{Number of trays}\times \text{Number of cookies in 1 tray}\\=50\times 60\\=3000$

Thus, 3000 cookies are made each week.

8 0

2 years ago

Joanna has a total of 7 rolls of coins worth $23. She has rolls of dimes worth $5 each, and

son4ous [18]

Answer:

3 rolls of dimes and 8 rolls of nickels

hope it helps!!!!!!!!! :]

7 0

1 year ago

A high school wants to sell postage stamps with the school logo on them. The fundraising group have purchased 500 sheets of stam

erma4kov [3.2K]

Answer:

a) Cost

$C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050$

b) Sales income

$S(q)=20q\\\\S(500)=20\cdot 500 = 10,000$

c) Table of values

$\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right]$

d) Attached

e) Breakeven point = 12.5 sheets

f) Profit at 550 sheets = $1,950

Step-by-step explanation:

a) We have a fixed cost for the image, at $50.

We also have a variable cost of $16 a sheet.

The purchased quantity is 500 sheets.

Then, the cost function is:

$C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050$

b) The price for each sheet is $20, so the income from sales are:

$S(q)=20q\\\\S(500)=20\cdot 500 = 10,000$

c) Table of values

$\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right]$

d) Attached

e) The minimum number of sheets the group must sell so they don't lose any money is the breakeven point (BEP) and can be calculated making the income sales equal to the cost:

$S(q)=C(q)\\\\20q=50+16q\\\\(20-16)q=50\\\\4q=50\\\\q=50/4=12.5$

f) This profit can be calculated as the difference between the sales income and the cost:

$P(500)=S(500)-C(500)\\\\P(500)=20\cdot 500-(50+16\cdot 500)=10,000-8,050=1,950$

3 0

2 years ago