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2 years ago

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John and Amelia have a baby daughter Sonia John is 23 kg heavier than Amelia who is four times as heavy as Sonia their combined

weight is 122. how heavy is each person

1 answer:

3241004551 [841]2 years ago

7 0

x+4x+4x+23

9x+23=122

122-23=99

9\99=11

J=67

A=44

S=11

11+44+67=122 kg

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use the point-slope equation to identify the slope and the coordinates of a point on the line y – 4 = 1/2 (x – 1). the slope of

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Answer:

The slope of the line is $\dfrac{1}{2}$ and a point on the line is $(1, 4)$

Step-by-step explanation:

The general point slope of line passing through $(x_1,y_1)$ and having slope as m.

$y-y_1=m(x-x_1)$

The given equation of the straight line,

$y-4=\dfrac{1}{2}(x-1)$

Comparing this to the general equation we get the point as $(1, 4)$ and slope as $\dfrac{1}{2}$

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2 years ago

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The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.94. T

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Answer:

a) 25

b) 67

c) 97

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

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In which $\sigma$ is the standard deviation of the population and n is the size of the sample. In this problem, $\sigma = 0.25$

(a) The desired margin of error is $0.10.

This is n when M = 0.1. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.1 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.1\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.1}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.1})^{2}$

$n = 24.01$

Rounding up to the nearest whole number, 25.

(b) The desired margin of error is $0.06.

This is n when M = 0.06. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.06 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.06\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.06}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.06})^{2}$

$n = 66.7$

Rounding up, 67

(c) The desired margin of error is $0.05.

This is n when M = 0.05. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.05 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.05\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.05}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.05})^{2}$

$n = 96.04$

Rounding up, 97

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2 years ago

In a room there are a mixture of people and dogs. there are 72 heads, and 200 legs. how many dogs are in the room?

IRINA_888 [86]

There are a total of 9 dogs

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2 years ago

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Answer:

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2 years ago

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For which values of a the system has no solution: x≤5, x≥a

soldi70 [24.7K]

Given:

The system of inequalities is

$x\leq 5$

$x\geq a$

To find:

The values of a for which the system has no solution.

Solution:

We have,

$x\leq 5$ ...(1)

It means the value of x is less than or equal to 5.

$x\geq a$ ...(2)

It means the value of x is greater than or equal to a

Using (1) and (2), we get

$a\leq x\leq 5$

But if a is great than 5, then there is no value of which satisfies this inequality.

Therefore, the system has no solution for a>5.

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2 years ago