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3 years ago

A sum of money is divided among Khairul, Michael and Ethan in the ratio

Mathematics

1 answer:

Leto [7]3 years ago

3 0

Answer:

$360

Step-by-step explanation:

The intial ratio of the sum shared between Khairul, Michael and Ethan is 6 : 4 : 5.

This would be 6x : 4x : 5x

Khairul gives $30 to Michael and $15.

The ratio is. Now;

(6x - 45) : (4x + 30) : (5x + 15)

We are told this is equal to the ratio 7:6:7

Thus;

((6x - 45) + (4x + 30))/(5x + 15) = (7 + 6)/7

(10x - 15)/(5x + 15) = 13/7

Factorize the left hand side;

5(2x - 3)/5(x + 3) = 13/7

5 will cancel out to get;

(2x - 3)/(x + 3) = 13/7

Cross multiply to get;

7(2x - 3) = 13(x + 3)

14x - 21 = 13x + 39

14x - 13x = 39 + 21

x = 60

Amount Khairul had initially was denoted as 6x.

Thus,6x = 5 × 60 = $360

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Alecsey [184]

Answer:

b. 2/15

c. 7/15

Step-by-step explanation:

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X 0 1 2 3 4 5 6 7

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3 years ago

Let's say you have 6 lbs of apples for $12.96. What is the unit price? (Meaning, what is the cost of 1 pound of apples?)

lara [203]

Answer:

$2.16 per pound

Step-by-step explanation:

First, you would need to divide the price by the amount

$12.96 / 6 lbs = $2.16 per pound

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3 years ago

A country is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30

kondaur [170]

Answer:

We conclude that speed is greater than 30 miles per hour.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 30 miles per hour

Sample mean, $\bar{x}$ = 35 miles per hour

Sample size, n = 15

Alpha, α = 0.01

Sample standard deviation, s = 4.7 miles per hour

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 30\text{ miles per hour}\\H_A: \mu > 30\text{ miles per hour}$

We use one-tailed(right) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{35 - 30}{\frac{4.7}{\sqrt{15}} } = 4.120$

Now, $t_{critical} \text{ at 0.01 level of significance, 14 degree of freedom } = 2.624$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis and conclude that speed is greater than 30 miles per hour.

We calculate the p-value.

P-value = 0.00052

Since p value is lower than the significance level, we reject the null hypothesis and accept the alternate hypothesis. We conclude that speed is greater than 30 miles per hour.

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3 years ago

Factor the expression completely. 2-12x

Nikitich [7]

Answer:

2(1 - 6x)

Step-by-step explanation:

2-12x

Common factor: 2

Factored equation:

2(1 - 6x)

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melomori [17]

Step-by-step explanation:

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