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2 years ago

8

A group of eight grade 11 and five grade 12 students wish to be on the senior prom committee. The committee will consist of thre

e students. What is the probability that only grade 12 students will be elected, assuming that all students have an equal chance of being elected?

1 answer:

BaLLatris [955]2 years ago

7 0

5/13*4/12*3/11=5/143 I believe

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Mark has a 25 ounce drink. He drinks 5 ounces. What percent of the drink does he have left?

valina [46]

Answer: $80\%$

Step-by-step explanation:

This problem can be solved by the <u>Rule of Three</u>, which is a mathematical rule to find out an amount that is with another quantity given in the same relation as other two also known.

In this case, the 25 ounce drink represents the $100 \%$ . So, if Mark drinks 5 ounces, this means he has 20 ounces left and we have to find the percent this represents:

$25 oz$ ------- $100\%$

$20 oz$ -------- $?$

$?=\frac{(20 oz)(100\%)}{25 oz}$

$?=80\%$ This is the percent of the drink Mark has left

4 0

2 years ago

SOLVE PLEASE Sarah must maintain a balance of at least $500 in her checking account to avoid finance charges. If her current bal

dem82 [27]

So since her balance must be at least 500, her ballance cannot reach 500
so 794-500=294
see how many 25's you can fit into 294
we know that 4 25's =100 and 294 is roughly 300
so 4 times 3=12
we minus one of the 25's because 294 is less than 300 so
the innequality is
>means more than
794-25x>500

5 0

2 years ago

Let f(x)=−3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 u

deff fn [24]

<h2>Answer:</h2>

Ques 1)

$g(x)=-12x+48$

Ques 2)

$g(x)=|3x|+4$

<h2>Step-by-step explanation:</h2>

Ques 1)

We know that if a graph is stretched by a factor of a then the transformation if given by:

f(x) → a f(x)

Also, we know that the translation of a function k units to the right or to the left is given by:

f(x) → f(x+k)

where if k>0 then the shift is k units to the left

and if k<0 then the shift is k units to the right.

Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.

This means that the function g(x) is given by:

$g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48$

Ques 2)

We know that the transformation of the type:

f(x) → f(x)+k

is a shift or translation of the function k units up or down depending on k.

If k>0 then the shift is k units up.

and if k<0 then the shift is k units down.

Here, The graph of the function f(x)=|3x| is translated 4 units up.

This means that the transformed function g(x) is given by:

$g(x)=|3x|+4$

4 0

2 years ago

Which equation is the inverse of y = 2x2 – 8?

natita [175]

The inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$

Explanation:

To find the inverse of the equation $y=2x^{2} -8$ , we need to interchange the variables x and y for the variables y and x.

Thus, the equation becomes

$x=2y^{2} -8$

Now, we shall find the value of y.

Now, adding 8 to both sides of the equation, we have,

$x+8=2y^{2}$

Interchanging the sides,

$2y^{2} =x+8$

Dividing by 2 on both sides,

$y^{2} =\frac{x+8}{2}$

Taking square root on both sides,

$y=\pm \sqrt{\frac{x+8}{2}}$

Thus, the inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$

5 0

2 years ago

If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to (StartFraction r Over s EndFraction) (6)?

Airida [17]

Answer:

$\dfrac{r}{s}(6)=\dfrac{3(6)-1}{2(6)+1}$

Step-by-step explanation:

We know that for any two function f(x) and g(x) ,

$\dfrac{f}{g}(x)=\dfrac{f(x)}{g(x)}$

Given functions : $r(x)=3x-1$ and $s(x)=2x+1$

Then, $\dfrac{r}{s}(x)=\dfrac{r(x)}{s(x)}$

$\Rightarrow\ \dfrac{r}{s}(x)=\dfrac{3x-1}{2x+1}$

At x= 6 , we get

$\dfrac{r}{s}(6)=\dfrac{3(6)-1}{2(6)+1}$

The , The expression is equivalent to $\dfrac{r}{s}(6)=\dfrac{3(6)-1}{2(6)+1}$

When we further simplify it , we get $\dfrac{r}{s}(6)=\dfrac{18-1}{12+1}=\dfrac{17}{13}$

5 0

2 years ago