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3 years ago

Simplify the following expression (30/45g+20)-(8/9g+7)

Mathematics

2 answers:

Nata [24]3 years ago

6 0

117 - 2g

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olga_2 [115]3 years ago

4 0

$\frac{30}{45}g +20 - \frac{8}{9}g + 7 = \frac{15}{9}g + 27 -\frac{8}{9}g = \frac{7}{9}g+27$

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Which of these is NOT an integer

Tema [17]

Hi there!

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I believe your answer is:

Option A

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Here’s why:

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$\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}$

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$\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}$

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$\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}$

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$\text{Option \textbf{A} does not simplify into an integer.}$

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Hope this helps you. I apologize if it’s incorrect.

7 0

2 years ago

Consider m = y2 - y1/ x2 - x1 . Which x1 and x2-values would determine that the line is vertical? Justify your answer

Y_Kistochka [10]

Answer:

$x_2=x_1$

Step-by-step explanation:

We were given the slope formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

This line is vertical if the denominator is zero.

That is when $x_2-x-1=0$

This implies that;

$x_2=x_1$

Justification;

When $x_2=x_1$ , then, the line passes through;

$(x_1,y_1)$ and $(x_1,y_2)$

The slope now become

$m=\frac{y_2-y_1}{x_1-x_1}=\frac{y_2-y_1}{0}$

The equation of the line is

$y-y_1=\frac{y_2-y_1}{0}(x-x_1)$

This implies that;

$0(y-y_1)=(y_2-y_1)(x-x_1)$

$0=(y_2-y_1)(x-x_1)$

$\frac{0}{y_2-y_1}=(x-x_1)$

$0=(x-x_1)$

$x=x_1$ ... This is the equation of a vertical line.

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2 years ago

Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per student. The Dino D

Marianna [84]

Set it up like a regular equation. I used:
$3x+135 \ \textless \ 6x$

As you can see, however, I inserted the "less than" symbol rather than the equal sign because values greater than a certain value can also equal "x". Solve it like a normal equation and you will arrive at:
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</u> $x \ \textgreater \ 45$

This means that, as long as x is greater than 45, "6x" will be greater than "3x+135". Thus, if you bring 46 students, the Science Center will cost less.

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3 years ago

In a survey of adults who follow more than one sport, 30% listed football as their favorite sport. You survey 15 adults who foll

maxonik [38]

Answer: 0.5

Step-by-step explanation:

Binomial probability formula :-

$P(x)=^nC_x\ p^x(q)^{n-x}$ , where P(x) is the probability of getting success in x trials , n is the total trials and p is the probability of getting success in each trial.

Given : The probability that the adults follow more than one game = 0.30

Then , q= 1-p = 1-0.30=0.70

The number of adults surveyed : n= 15

Let X be represents the adults who follow more than one sport.

Then , the probability that fewer than 4 of them will say that football is their favorite sport,

$P(X\leq4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)\\\\=^{15}C_{0}\ (0.30)^0(0.70)^{15}+^{15}C_{1}\ (0.30)^1(0.70)^{14}+^{15}C_{2}\ (0.30)^2(0.70)^{13}+^{15}C_{3}\ (0.30)^3(0.70)^{12}+^{15}C_{4}\ (0.30)^4(0.70)^{11}\\\\=(0.30)^0(0.70)^{15}+15(0.30)^1(0.70)^{14}+105(0.30)^2(0.70)^{13}+455(0.30)^3(0.70)^{12}+1365(0.30)^4(0.70)^{11}\\\\=0.515491059227\approx0.5$

Hence, the probability rounded to the nearest tenth that fewer than 4 of them will say that football is their favorite sport =0.5

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3 years ago

Todd can run 1/2 a mile in 1/12 of an hour. what is todd’s rate in miles per hour?

stiks02 [169]

If he runs 1/2 a mile in 5 minutes then 60 minutes would be 5x12 and 1/2x12 would be 6 so he can run 6 miles per hour

7 0

3 years ago

Read 2 more answers