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2 years ago

9

A number is chosen uniformly at random from among the positive integers less than $10^8$. Given that the sum of the digits of th

e number is 9, what is the probability that the number is prime

1 answer:

Reil [10]2 years ago

3 0

Answer:

If the sum of the digits of a number is divisible by 9, then that number is divisible by 9. An..... sorry if this does not help :(

Step-by-step explanation:

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Write a formula for function f in terms of function g.

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$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

so hmm if you notice, your f(x) there, looks just like g(x), but is "shifted horizontally" by about 9 units to the right

that simply means, based on that template above, that C/B = -9, and we can simply make B = 1 and C = -9, and we get C/B = -9/1 which is -9

thus $\bf \begin{array}{llcll}
f(x)=g(&1x&-9)\\
&\uparrow &\uparrow \\
&B&C
\end{array}\iff f(x)=g(x-9)$

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Answer:

i think it is c

Step-by-step explanation:

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A store sells flower arrangements at a cost of $28 each. Which statements are true regarding the price of the arrangements? Chec

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Let's check each case to determine the solution to the problem.

we know that

The cost of each flower arrangements is $\$28$

Statements

<u>case A)</u> If the price is marked down by $10$ percent, the new price will be $\$25.20$

we know that

If the price is marked down by $10$ percent

then

the new price will be

$10\%= \frac{10}{100} =0.10$

$(1-0.10)*\$28=0.90*\$28 \\= \$25.20$

$\$25.20=\$25.20$

therefore

The statement case A) is True

<u>case B)</u> If the price is marked down by $25$ percent, the new price will be $\$21$

we know that

If the price is marked down by $25$ percent

then

the new price will be

$25\%= \frac{25}{100} =0.25$

$(1-0.25)*\$28=0.75*\$28 \\= \$21$

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therefore

The statement case B) is True

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we know that

If the price is marked down by $50$ percent

then

the new price will be

$50\%= \frac{50}{100} =0.50$

$(1-0.50)*\$28=0.50*\$28 \\= \$14$

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therefore

The statement case C) is False

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we know that

If the price is marked down by $35$ percent

then

the new price will be

$35\%= \frac{35}{100} =0.35$

$(1-0.35)*\$28=0.65*\$28 \\= \$18.20$

$\$18.20=\$18.20$

therefore

The statement case D) is True

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we know that

If the price is marked down by $40$ percent

then

the new price will be

$40\%= \frac{40}{100} =0.40$

$(1-0.40)*\$28=0.60*\$28 \\= \$16.80$

$\$16.80 \neq \$29.80$

therefore

The statement case E) is False

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