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Alexxandr [17]
3 years ago
14

John’s age in 5 years time will be the same as Jack’s age is now. In two years, Jack will be twice as old as John. How old are t

hey now?
Mathematics
1 answer:
Elden [556K]3 years ago
8 0
Let's say John's age is x and Jack's age is y

(1) x + 5 = y
(2) y + 2 = 2(x + 2)

Now if we substitute equation (1) into equation (2) we get:

x + 5 + 2 = 2(x + 2)
x + 7 = 2x + 4
x = 3

If x = 3, then from equation (1) we get:
3 + 5 = y
y = 8

Therefor John is 3 years old and Jack is 8 years old
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The  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

<h3>Circle theorem</h3>

The given diagram shows two intersecting lines tangential to a circle at points A and C.

Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.

Mathematically;

<B = 1/2(arcADC - arcAC)

58 = 1/2(238 -x)

Hence the  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

Learn more on circle theorem here: brainly.com/question/26594685

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(3 marks) A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year. The battery live
Ksenya-84 [330]

Answer:

0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years

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.

A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year

This means that \mu = 3, \sigma = 0.5

What is the probability that a given battery will last between 2.3 and 3.6 years?

This is the p-value of Z when X = 3.6 subtracted by the p-value of Z when X = 2.3. So

X = 3.6

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

Z = \frac{3.6 - 3}{0.5}

Z = 1.2

Z = 1.2 has a p-value of 0.8849

X = 2.3

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

Z = \frac{2.3 - 3}{0.5}

Z = -1.4

Z = -1.4 has a p-value of 0.0808

0.8849 - 0.0808 = 0.8041

0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years

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3 years ago
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