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krek1111 [17]
3 years ago
5

please help me to solve this word problems leading to quadratic equation: A girl is 6 years younger than her brother. the produc

t of their age is 135. find their ages.​
Mathematics
1 answer:
vova2212 [387]3 years ago
5 0

Answer:

Brother is 70.5 and sister is 64.5

Step-by-step explanation:

you will need to set up a simple equation and give out variables.

Girls age = 6-x

Brother's age= x

the you will take those 2 and add them and place them equal to 135:

6-x+x=135

6-2x+6=135+6

The 6 cancels out

2x=141

2x/2=141/2

x=70.5

The brother's age would be 70.5 then and the girl's would be 64.5

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Aaron is 15 centimeters taller than Peter, and five times Aaron's height exceeds two times Peter's height by 525 centimeters. Th
Tatiana [17]
The system of linear equations that relates x and y:
x= 15 + y
5 x = 2 y+ 525
We will solve this system using substitution method:
5(15 + y)=2 y + 525
75 + 5 y = 2 y + 525
5 y - 2 y = 525 - 75
3 y = 450,           y = 450 : 3        y = 150
x = 15 + y           x = 15 + 150     x = 165
Answer: Aaron´s height is 165 cm and Peter´s height is 150 cm.
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3 years ago
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4/5 divided by 1 2/5
scoundrel [369]

Answer:

4/7

Step-by-step explanation:

Multiply the number by The reciprocal of 1 2/5

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Let f(x) = 5x ^ 2 - x + 1 and g(x) = - 3x . Evaluate the composition (fg)(1)
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If m ACB = 48° and <br> m CAB = 47°, is line BC a tangent to circle A?
muminat

Answer: No, because ABC is not a right angle.


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7 0
3 years ago
The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plan
Nataly_w [17]

Answer:

95.64% probability that under 30% of the dogs are emotional support trained

Step-by-step explanation:

For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

\mu = E(X) = np = 100*0.23 = 23

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.23*0.77} = 4.21

What is the probability that under 30% of the dogs are emotional support trained?

30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

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

Z = \frac{30 - 23}{4.1}

Z = 1.71

Z = 1.71 has a pvalue of 0.9564.

So there is a 95.64% probability that under 30% of the dogs are emotional support trained

5 0
3 years ago
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