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2 years ago

Of the following sets, which numbers in {1, 2, 3, 4, 5} make the inequality 5x + 2 > 12 true?

Mathematics

2 answers:

NemiM [27]2 years ago

5 0

Answer:

{ 3, 4, 5 }

Step-by-step explanation:

Given inequality,

5x + 2 > 12

By subtracting 2 on both sides,

5x > 12 - 2

5x > 10

Since, $\frac{1}{5}>0$

Thus, after multiplying both sides of inequality by 1/5, the sign of inequality will not change,

That is,

$\frac{5x}{5} > \frac{10}{5}$

$x > 2$

⇒ x ∈ ( 2, ∞ )

Hence, numbers in set { 1, 2, 3, 4, 5} that make the given inequality true are,

{ 3, 4, 5 }

harina [27]2 years ago

4 0

(3,4,5)

Using 1 you get, 7>12
Using 2 you get, 12>12
Using 3 you get, 17>12
Using 4 you get, 20>12
Using 5 you get, 27>12

this is why only 3,4, and 5 work.

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In a random sample of 150 customers of a high-speed Internetprovider, 63 said that their service had been interrupted one ormore

erastovalidia [21]

Answer:

a) The 95% confidence interval would be given by (0.341;0.499)

b) The 99% confidence interval would be given by (0.316;0.524)

c) n=335

d)n=649

Step-by-step explanation:

1) Notation and definitions

$X_{IS}=63$ number of high speed internet users that had been interrupted one or more times in the past month.

$n=150$ random sample taken

$\hat p_{IS}=\frac{63}{150}=0.42$ estimated proportion of high speed internet users that had been interrupted one or more times in the past month.

$p_{IS}$ true population proportion of high speed internet users that had been interrupted one or more times in the past month.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

1) Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.42 - 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.341$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.499$

The 95% confidence interval would be given by (0.341;0.499)

2) Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.42 - 2.58\sqrt{\frac{0.42(1-0.42)}{150}}=0.316$

$0.42 + 2.58\sqrt{\frac{0.42(1-0.42)}{150}}=0.524$

The 99% confidence interval would be given by (0.316;0.524)

3) Part c

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.42(1-0.42)}{(\frac{0.05}{1.96})^2}=374.32$

And rounded up we have that n=335

4) Part d

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.42(1-0.42)}{(\frac{0.05}{2.58})^2}=648.599$

And rounded up we have that n=649

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3 years ago

In Australia, road distance is measured in kilometres.

maks197457 [2]

Answer:

Step-by-step explanation:

5 miles-8km

x miles-120 km

x=120×5÷8

x=75 (miles)

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What is 0.11 as a fraction in simplest form

bazaltina [42]

11 hundredths , or 11/100

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3 years ago

The vertex angle of an isosceles triangle measures 42°. A base angle in the triangle has a measure given by

siniylev [52]

Answer:

the value of x=33

the measure of each base angle = 42 ,69,69

Step-by-step explanation:

Bases od isosceles triangles are congruent,so

2(2x+3)=4x+6 (This is the sum ob both anlgles base)

All angles in a triangle add to 180

4x+6 + 42 = 180

4x = 132

x=33

2(33)+3= 69

69+69+42 = 180

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2 years ago

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Sarah runs a day camp in the summer and needs to buy paper towels and soap for the restrooms. She spends $129 on t cases of pape

Cloud [144]

Let x be the number of cases of paper towels and y be the number of cases of soap. The system of linear equation that would best represent the given is,
x + y = 10
12x + 15y = 129
The values of x and y are 7 and 3.

Sarah both 7 cases of paper towel.

It is not possible for Sarah to buy exactly 20 bottles because first of all the cases contains only 12 bottles and 20 is not divisible by 12.

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