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3 years ago

8. If VW = 9x-11 and SU = 16x - 12 find WT

Mathematics

1 answer:

IRISSAK [1]3 years ago

5 0

Answer:

WT = 34

Step-by-step explanation:

The ultimate goal here to pinpoint what x is equivalent to. In a rectangle we know that the diagonals are congruent as well as the fact that they bisect each other. This means cutting in half. Using this knowledge we know VW = 9x - 11 is half of SU = 16x - 12.

Step One: Multiply 9x - 11 by 2.

2(9x - 11) = 18x - 22

Step Two: Set up your equation

18x - 22 = 16x - 12

Step Three: Solve for x

18x - 22 = 16x - 12

2x - 22 = -12

2x = 10

x = 5

Step Four: Substitute to check your work

16(5) - 12 = 68

9(5) - 11 = 34

Again, since the diagonals of a rectangle bisect each other VW = WT.

34 is half of 68 proving our findings.

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The probability that when 11 adults are randomly selected, 3 or fewer are in excellent health is 0.6483.

Step-by-step explanation:

The random variable X can be defined as the number of adults questioned reported that their health was excellent.

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P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)

$=\sum\limits^{3}_{x=0}{{11\choose x}(\frac{3}{11})^{x}(1-\frac{3}{11})^{11-x}}\\=0.02998+0.12385+0.23254+0.26197\\=0.64834\\\approx 0.6483$

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3 years ago

Johnny has $100 in the bank and plans to deposit $15 per day. Sal has $250

ICE Princess25 [194]

Answer:

6 days

Step-by-step explanation:

First we have to write an expression that represents Johnny's and Sal's banking plans.

Johnny: He has an initial value of $100 and that value will increase by $15 every day. So the expression looks like: 15x + 100, where x is the amount of days it's been.

Sal: An initial value of $250 and the value will decrease by $10 everyday. The expression looks like: -10x + 250, where x is the amount of days it's been.

To find how many days they have until they have the same amount of money in the bank, we can set the expressions equal to each other and solve for x:

15x + 100 = -10x + 250

Add 10x to both sides to isolate the x on one side of the equation:

25x + 100 = 250

Subtract 100 from both sides of the equation to isolate 25x:

25x = 150

Divide both sides by 25 to find the value of x:

x = 6

Since x represents the amount of days it's been, x = 6 means that it will take 6 days for their bank accounts to have the same amount of money in them.

Hope this helps :)

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3 years ago