Zabato is thinking of a number. Three times the sum of the number and ten is the same as eight times the number. What is his number??

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{12 \dfrac{2}{3} \times 3 \dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{12 \dfrac{2}{3} \times 3 \dfrac{1}{4}}[/tex]

[tex]\mathsf{= \dfrac{12\times3 + 2}{3}\times\dfrac{3\times4+1}{4}}[/tex]

[tex]\mathsf{= \dfrac{36 + 2}{3}\times\dfrac{12 + 1}{4}}[/tex]

[tex]\mathsf{= \dfrac{38}{3}\times \dfrac{13}{4}}[/tex]

[tex]\mathsf{= \dfrac{38\times13}{3\times4}}[/tex]

[tex]\mathsf{= \dfrac{494}{12}}[/tex]

[tex]\mathsf{= \dfrac{494\div2}{12\div2}}[/tex]

[tex]\mathsf{= \dfrac{247}{6}}[/tex]

[tex]\mathsf{\approx 41 \dfrac{1}{6}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{41 \dfrac{1}{6}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Convert \ 12\frac{2}{3} \ to \ an \ improper \ fraction. Use \ this \ rule: a \frac{b}{c}=\frac{ac+b}{c}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{12\times3+2}{3}\times3\frac{1}{4} \ \to \ \ Multiply \ 12\times 3 }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{36+2}{3}\times3\frac{1}{4} \ \to \ \ Add \ 36+2 }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{38}{3}\times3\frac{1}{4} }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Convert \ 3\frac{1}{4} \ to \ an \ improper \ fraction. Use \ this \ rule: a \frac{b}{c}=\frac{ac+b}{c}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{38}{3}\times\frac{3\times4+1}{4} \ \ \to \ \ Multiply \ 3\times 4}} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{38}{3}\times\frac{12+1}{4} \ \ \to \ \ Add \ 12+1}} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{38}{3}\times\frac{13}{4}}} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule:\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{38\times13}{3\times4} \ \ \to \ \ Multiply }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Simplify \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{492}{12}=\frac{247}{6}= }} \end{gathered}$}\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{41\frac{1}{6} }} \end{gathered}$}}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Therefore,the \ \bf{\underline{correct \ option}} \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"D"}.} \end{gathered}$}[/tex]

Answer:

83

Step-by-step explanation:

Answer: The point slope form of the equation for this line is given by

[tex]y-8=-(x+3)[/tex]

Step-by-step explanation:

Since we have given that

The slope intercept form of the equation of a line is given by

[tex]y=-x+6-------------------(1)[/tex]

Line passing through a point is given by

(-3,8)

So, from the equation (1), we get that

m = Slope of line = -1

So, Point slope form of the equation of the line is given by

[tex]y-y_0=m(x-x_0)\\\\(y-8)=-1(x+3)\\\\y-8=-(x+3)[/tex]

Hence, the point slope form of the equation for this line is given by

[tex]y-8=-(x+3)[/tex]

Answer:

$1797914.419

Step-by-step explanation:

Given : Revenue in 2000 for a bakery chain totaled $10 billion from 5,562 shops nationwide

To Find:What was the average revenue in 2000 per shop?

Solution:

Revenue in 2000 for a bakery chain totaled $10 billion from 5,562 shops

So, the average revenue in 2000 per shop =[tex]\frac{10000000000}{5562}[/tex]

                                                                         =[tex]1797914.419[/tex]

Hence the average revenue in 2000 per shop was $1797914.419

To find how long it will take for $4,227.29 to grow to $9,000 with a 4.9% interest rate compounded monthly, we use the compound interest formula rearranged to solve for time. The calculation involves using the natural logarithm to find the number of years required for the investment to reach the target amount.

The question pertains to determining how long it will take for a sum of money, specifically $4,227.29 deposited into a savings account with a 4.9% interest rate compounded monthly, to grow to be worth $9,000. We can use the formula for compound interest to solve for the time period required for the investment to reach the desired amount. This formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

To find the time (t), we rearrange the formula: t = [log(A/P)] / [n*log(1 + r/n)]

The calculation will provide the time in years, which can be multiplied by 12 to convert it to months, in case the answer is needed in months.

The expression which shows 12 more than the quotient of 63 and 9 is option A) 12 + (63 ÷ 9).

We have to find the expression which shows 12 more than the quotient of 63 and 9.

For that, first find the quotient of 63 and 9.

Divide 63 by 9.

63/9 = 7

12 more than the quotient of 63 and 9 = 7 + 12 = 19

So the result is 19.

Now, we have to mathematically write the given word sentence.

12 is added to the quotient of 63 and 9.

12 is added to (63 ÷ 9)

12 + (63 ÷ 9)

Thus, A is the correct option.

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Answer:

To find the quotient of 2 fractions, you have to change the division sign too a multiplication sign, and flip the second fraction, and multiply.

An example (the answer to the first question)

1/2 ÷ 1/4 = 1/2 * 4/1 = 2

Hope this explanation helped! If you want the answers to all the questions, please just tell me and I will answer whenever I have some free time! I would also appreciate a Brainliest.

Every number belongs to at least one number set, but might also belong to several other sets, depending on its attributes.

The question is asking you to categorize numbers into different sets based on their attributes. Let's use the sets S, A, and B from Solution 3.1 as an example.

Set S:{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}. This is a set of all positive integers from 1 to 19.

Set A:{2, 4, 6, 8, 10, 12, 14, 16, 18}, is a set of even numbers from the set S.

Set B:{14, 15, 16, 17, 18, 19} is a set that includes certain numbers from set S that satisfy a given condition.

So, every number belongs to at least one set (set S), but may also belong to multiple other sets (like A and B) depending on its attributes.

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The requried, at the beginning of May (the fifth month), the niece will have $162 in her account.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

In the first month, the niece has $1 in her account.

In the second month, she triples that amount to have $3, and Mr. Howard doubles it to $6.

In the third month, she triples $3 to have $9, and Mr. Howard doubles it to $18.

In the fourth month, she triples $9 to have $27, and Mr. Howard doubles it to $54.

So at the beginning of May (the fifth month), the niece will have 54×3 = $162 in her account.

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