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3 years ago

Find the value of x.A. 4B. 5C. 6D. 9

Mathematics

1 answer:

lubasha [3.4K]3 years ago

7 0

Answer:

C. 6

Step-by-step explanation:

You can try the answers to see which satisfies the Pythagorean theorem:

A. 4² +7² = 16+49 ≠ 117

B. 5² +8² = 25 +64 ≠ 117

C. 6² +9² = 36 +81 = 117 . . . . this (C) is the correct choice

and, for completeness, ...

D. 9² +12² = 81 +144 ≠ 117

_____

<em>Working out</em>

You can also actually work the problem. The Pythagorean theorem tells you ...

x² + (x+3)² = (√117)²

2x² +6x +9 = 117

2x² +6x = 108 . . . . subtract 9

x² +3x = 54 . . . . . . divide by 2

x(x +3) = 54 . . . . . . factor

Now, you can compare to your memorized times tables, where you find 6×9 = 54, so you know that x=6.

In case times tables are a challenge, you can continue to complete the square:

x² +3x +1.5² = 54 +1.5²

(x +1.5)² = 56.25 = 7.5² . . . . write as squares

x = 7.5 -1.5 = 6 . . . . . . . . . . . square root, subtract 1.5

The value of x is 6.

_____

The other solution to the quadratic equation is x=-9, but negative segment lengths make no sense. We acknowledge, then ignore, that extraneous solution.

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A bag contains 5 2/5kg of sand. The bag has a hole in it. Every 10 minutes, 1 2/3kg of sand escapes from the bag. After 20 minut

fenix001 [56]

Quantify of sand in a bag =

$= \: 5 \frac{2}{5} \ \:$

$= \frac{(5 \times 5 +2) }{5}$

$= \frac{27}{5} \: kg$

Quantity of sand that escapes in every 10 minutes :-

$= 1 \frac{2}{3} kg$

Quantity of sand that will escape in 20 minutes :-

$= 1 \frac{2}{3} \times 2$

$= \frac{(3 \times 1 + 2)}{3} \times 2$

$= \frac{5}{3} \times 2$

$= \frac{10}{3}$

Quantity of sand that will remain in the sand bag :-

$= \frac{27}{5} - \frac{10}{3}$

$= \frac{(27 \times 3)}{15} - \frac{(10 \times 5)}{15}$

$= \frac{81}{15} - \frac{50}{15}$

$= \frac{31}{15}$

$= 2 \frac{1}{5} \: kg$

$therefore \: , \: 2 \frac{1}{5} \: kg \: sand \: is \: left \: in \: the \: bag \: .$

3 0

3 years ago

Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights

user100 [1]

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that $\mu = 85, \sigma = 8$