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jasenka [17]
3 years ago
12

One number is 8 times another number. The numbers are both positive and have a difference of 70. Find the numbers. Which of the

following equations could be used to solve the problem?
Mathematics
1 answer:
worty [1.4K]3 years ago
4 0
Let, the first (smaller) number = x
Larger number = 8x
Then, 8x - x = 70
7x = 70
x = 70/7
x = 10
& 8(10) = 80

In short, Your Numbers would be, 10 & 80

Hope this helps!
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A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one
TiliK225 [7]

In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are \binom44\binom{48}1=48 possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by \binom{13}1=13. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing \binom41\binom{48}4=778,320 possible hands. Exactly 2 aces are drawn in \binom42\binom{48}3=103,776 hands. And so on. This gives a total of

\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656

possible hands containing at least 1 ace, and hence B occurs with probability

\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412

The product of these probability is approximately 0.000082.

A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. P(A\cap B)=P(A)P(B). This happens if

  • the hand has 4 aces and 1 non-ace, or
  • the hand has a non-ace 4-of-a-kind and 1 ace

The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So A\cap B consists of 96 possible hands, which occurs with probability

\dfrac{96}{\binom{52}5}\approx0.0000369

and so the events A and B are NOT independent.

4 0
3 years ago
5x + 3x - 2 = 22<br><br> Number only please.
sattari [20]

x=3

5x+3x-2=22

8x-2=22

8x=24

x=3

7 0
3 years ago
Read 2 more answers
If the coordinates of point E are (-4, y), what is the value of<br> у?
BlackZzzverrR [31]

Answer:

-8

Step-by-step explanation:

First we need to find the slope of CD.

We know C is (-10, -2)

and we know D is (10,6)

If we use the slope formula, we can see the slope is m=\frac{6-(-2)}{10-(-10)}

m = \frac{8}{20} \\m=\frac{2}{5}

We can see point F is at (6,-4)

We can find the equation of this line by using point slope form, and plugging in F as our point.

y-(-4)=\frac{2}{5}(x-6)\\y=\frac{2}{5}x-\frac{32}{5}

To find where E, we need to find the y value when x = -4

y=\frac{2}{5}(-4)-\frac{32}{5}\\y =-8

8 0
3 years ago
Read 2 more answers
Simplify each expression.
lutik1710 [3]

Answer:

1. 80

2. 18.9

3. 7

4. 146

5. 2

6. 4

Step-by-step explanation:

1. 6+4=10

10×8=80

2. 3.6×4.5= 16.2

16.2+2.7= 18.9

3. 3+2=5

5×2= 10

17-10=7

4. 4×3=12^2

12×12=144

144+2= 146

5. 3+2=5

5×6=30

30÷15=2

6. 5×2= 10

40÷10=4

4 0
3 years ago
What does it mean to divide figures into known shapes
Ede4ka [16]
I think it means to split a shape into common shapes. I.e. splitting a house shape into a triangle and a square
6 0
3 years ago
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