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QveST [7]
3 years ago
12

2x+3y = 15 x-3y=3 Solve

Mathematics
1 answer:
Arada [10]3 years ago
6 0
By process of elimination. 3y and -3y get eliminated. Giving you

3x=18

Divide by 3 on each side

Giving you x=6

Plugging it into equation 2 you get

(6)-3y=3

Taking out the parenthesis you have

6-3y=3

Subtract by 6 on each side giving you

-3y=-3

Divide by -3 on each side giving you

y=1

So the answer for this equation is x=6 and y=1 or the ordered pair (6,1)
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A box of candy hearts contains 52 hearts, of which 19 are white, 10 are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orang
laiz [17]

<u>Answer-</u>

a. Probability that  three of the candies are white = 0.29

b. Probability that three are white, 2 are tan, 1 is pink, 1 is yellow, and 2 are green = 0.006

<u>Solution-</u>

There are 19 white candies, out off which we have to choose 3.

The number of ways we can do the same process =

\binom{19}{3} = \frac{19!}{3!16!} = 969

As we have to draw total of 9 candies, after 3 white candies we left with 9-3 = 6, candies. And those 6 candies have to be selected from 52-19 = 33 candies, (as we are drawing candies other than white, so it is subtracted)

And this process can be done in,

\binom{33}{6} = \frac{33!}{6!27!} =1107568

So total number of selection = (969)×(1107568) = 1073233392

Drawing 9 candies out of 52 candies,

\binom{52}{9} = \frac{52!}{9!43!} = 3679075400

∴P(3 white candies) = \frac{1073233392}{3679075400} =0.29



Total number of ways of selecting 3 whites, 2 are tans, 1 is pink, 1 is yellow, and 2 are greens is,

\binom{19}{3} \binom{10}{2} \binom{7}{1} \binom{5}{1} \binom{6}{2}

=(\frac{19!}{3!16!}) (\frac{10!}{2!8!}) (\frac{7!}{1!6}) (\frac{5!}{1!4!}) (\frac{6!}{2!4!})

=(969)(45)(7)(5)(15)=22892625

Total number of selection = 3 whites + 2 are tans + 1 is pink + 1 is yellow + 2 greens = 9 candies out of 52 candies is,

\binom{52}{9}=\frac{52!}{9!43!} =3679075400

∴ P( 3 whites, 2 are tans, 1 is pink, 1 is yellow, 2 greens) =

\frac{22892625}{3679075400} = 0.006


6 0
3 years ago
Which expression is equivalent to 1/3 divided by 1/6
leonid [27]

Answer:

The answer is A

Step-by-step explanation:

cross mutliply

1×6=6

1×3=3

divide the answers

result: 2

I hope this helps

5 0
2 years ago
Suppose y varies directly as x, and y=14 when x=4. What is the value of y when x=9
Katena32 [7]

Given :-

  • y varies directly as x, and y=14 when x=4.

To Find :-

  • the value of y when x=9 .

Solution :-

<u>A</u><u>c</u><u>c</u><u>o</u><u>r</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>o</u><u> </u><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>,</u>

  • y = kx ( k is constant )

<u>When</u><u> </u><u>y</u><u> </u><u>=</u><u> </u><u>1</u><u>4</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>4</u><u> </u><u>,</u>

  • 14 = k(4)
  • k = 14/4
  • k = 7/2

<u>W</u><u>h</u><u>e</u><u>n</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>9</u><u> </u><u>,</u>

  • y = 7/2*9
  • y = 63/2
  • y = 31.5
8 0
3 years ago
Find the diameter of a circle with a circumference of 443 feet. Use 3.14 for pi.
marishachu [46]

Answer:

\huge\boxed{\sf d = 141\ feet}

Step-by-step explanation:

<u>Given Data:</u>

Circumference = C = 443 ft

<u>Required:</u>

Diameter = d = ?

<u>Formula:</u>

d = C / π

<u>Solution:</u>

d = 443 / 3.14

d = 141.0 feet

d = 141 feet

\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
3 0
2 years ago
Read 2 more answers
A restaurant is offering a dinner special that includes one starter and one entree. The choices are listed below. Starter: bread
artcher [175]

Answer:

There are 15 combinations.

Step-by-step explanation:

A restaurant is offering a dinner special that includes one starter and one entree.

Starter: bread-sticks, soup, salad

Entree: beef, fish, chicken, shrimp, pork

So, we have 3 starters and 5 entrees.

To know the possible dinner special combinations we will simply multiply the two.

3\times5=15

Therefore, there are 15 combinations.

8 0
3 years ago
Read 2 more answers
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