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julia-pushkina [17]
2 years ago
15

Assume that y varies directly with x. If y=−4 when x=2, find y when x=−6. Enter in any fractions using a / (e.g. "1/2" is the sa

me as 1^/2).
Mathematics
1 answer:
Inessa05 [86]2 years ago
8 0

Answer: 12

Step-by-step explanation:

This is a direct proportion and we use the formula:

y = kx

If y = −4 when x=2, we need to find the constant of proportionality. This will be:

y = kx

-4 = 2k

k = -4/2

k = -2

To find y when x=−6 guess this:

y = kx

y = -2 × -6

y = 12

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Suppose that 5 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 5 are not black?
lions [1.4K]
Here's the way I see it:  5 cards are drawn, one by one, without replacement.  Half (or 26) of the original deck are black and half (26) are white.

P(5 are not black) = P(5 are red)

P(5 are not black) = P(first card is red) * P(second card is red) * P(third card is red)*P(fourth card is red)*P(fifth card is red) =

(26/52) * (25/51) * (24/50) * (23/49) * (22/48) = 0.025   (answer)

We start with 52 cards.  We draw one, leaving 51 cards, 25 of which are red.  And so on.
6 0
3 years ago
Bess drew a rectangular prism that is 12 units long, 8 units wide, and 13 units tall. What is the volume of the rectangular pris
Katena32 [7]

Answer:

D. 1,248 cubic units

Step-by-step explanation:

the volume of the rectangular prism = length*width*height = 12*8*13 = 1248 cubic units

5 0
3 years ago
In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays.Find the probability that he did not hit a bounda
Margarita [4]

Answer:

The probability of NOT hitting a boundary is (4/5).

Step-by-step explanation:

Let E: Be the event of hitting a boundary

now, Probability of any event E =  \frac{\textrm{Number of favorable outcomes}}{\textrm{Total number of outcomes}}

Here, number of favorable outcomes = 6

So, P(E)  = \frac{6}{30}  = \frac{1}{5}

⇒Probability of hitting a six is 1/5

Now, P(E)  + P(not E)  = 1

So, P(not hitting a boundary ) = 1  -  P(hitting a boundary)

= 1 - (1/5)  = 4/5

Hence, the probability of NOT hitting a boundary is (4/5).

4 0
3 years ago
True or False The Solutions, Roots, X-intercepts and zeros of a quadratic equation are all the same thing? why
Zepler [3.9K]

Yes, solutions, roots, x-intercepts, and zeros are the same thing.

<h3>What is a quadratic equation?</h3>

The general quadratic equation is given by:

a*x^2 + b*x + c = 0

So the solutions are the values of x such that the above thing is zero.

On another hand, a parabola or a quadratic function is given by:

a*x^2 + b*x + c = y

The roots, zeros, or x-intercepts (these represent the same thing) are given by:

a*x^2 + b*x + c = 0

  • Zero or Root means that when you evaluate the function in that value the outcome is zero.
  • X-intercept means that for that value of x, the function intercepts the x-axis, so the function is equal to zero.

So these are the values of x such that the function becomes equal to zero, so these are exactly the same thing as the solutions of a quadratic equation.

Concluding, yes, solutions, roots, x-intercepts, and zeros are the same thing.

If you want to learn more about quadratic functions, you can read:

brainly.com/question/1214333

8 0
2 years ago
Monica is a lawyer who earns $8,322.65 every month. She spends $830.98 on rent, $210.36 on food, and $120.45 on gas every month.
Step2247 [10]
She would have $7160.86 left over in cash here's why.....
she starts off with $8,322.65 and spends $830.98 on rent $8,322.65-$830.98= $7,491.67 
then spends $210.36 on food and another $120.45 on gas 
$7,491.67-$210.36= $7,281.31 - $120.45= $7,160.86 <---- Left over $
7 0
3 years ago
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