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3 years ago

The town of Passaic had 58,753 people in 1990 and 71,509 people in 2014.

Mathematics

1 answer:

OLEGan [10]3 years ago

7 0

Answer:

21.71% increase

Step-by-step explanation:

increase = Increase ÷ Original Number × 100

12756/58753*100

0.217112318*100

21.71% increase.

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You might be interested in

Consider the computer output below. Fill in the missing information. Round your answers to two decimal places (e.g. 98.76). Test

slamgirl [31]

Answer:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

The 95% confidence interval would be given by (96.625;100.915)

a) $df=n-1= 19-1= 18$

b) $p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

c) The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

Step-by-step explanation:

Previous concepts and data given

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

$\bar X=98.77$ represent the sample mean

$s=4.77$ represent the sample standard deviation

n=19 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if we have significant difference on the mean of 100, the system of hypothesis would be:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we can calculate the Standard error for the mean like this:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$98.77-1.96\frac{4.77}{\sqrt{19}}=96.625$

$98.77+1.96\frac{4.77}{\sqrt{19}}=100.915$

So on this case the 95% confidence interval would be given by (96.625;100.915)

Part a

The degree of freedom are given by:

$df=n-1= 19-1= 18$

Part b

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

Then since is a two sided test the p value would be:

$p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Part c

If the system of hypothesis on this case are:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu > 100$

The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

7 0

3 years ago

How many unknowns does a system of equations have

Salsk061 [2.6K]

A system of equations may have a single unknown to varying multiples of unknowns , as much the number of unknowns increases , that much system of equations are also built up , else , it can't be resolved

6 0

3 years ago

Find the rate of interest when the principal is Rs. 6000, simple interest is Rs. 900 and time is 5 years.

Ainat [17]

Step-by-step explanation:

in the pic. If possible, give brainliest.

5 0

3 years ago

Read 2 more answers

math help asap a train travels 100 km in the same the plane covers 350km. If the speed of the plane is 20 km per less than 4 tim

Svet_ta [14]

R=train speed
p=plaane speed
t=time
d=st

100=tr
350=pt
p=4r-20

ok so 100 times 3.5=350
times 1st equaton by 3.5
350=3.5tr
350=pt
sub
3.5tr=pt
divide both sides by t
3.5r=p
sub p=4r-20
3.5r=4r-20
minus 3.4 from both sides
0=0.5r-20
add 20
20=0.5r
times 2
40=r
sub
p=4r-20
p=4(40)-20
p=160-20
p=140

plane=140kmph
train=40kmph

4 0

3 years ago

Which dimensions can create only one unique triangle?

Wittaler [7]

<h2>Answer:</h2>

<em>Three sides measuring 5 in., 12 in., and 14 in. </em>

<h3 /><h2>Explanation:</h2>

First of all, you need to know some facts about every triangle:

FIRST FACT:

If two sides of a triangle are $a \ and \ b$ , then the third side must be less than $a+b$ . Why? because if its length is exactly $a+b$ , then you can't build up a triangle, but you'll have a line segment. In other words:

$a$

SECOND FACT:

The internal angles of any triangle add up to 180°. So if ∠A, ∠B and ∠C are the internal angles of a triangle, then:

$\angle A +\angle B+ \angle C=180^{\circ}$

__________________________

So let's analyze each case:

<h3>Case 1. Three angles measuring 25 degrees, 65 degrees, and 90 degrees :</h3>

$\angle A=25^{\circ} \\ \\ \angle B=65^{\circ} \\ \\ \angle C=90^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=25^{\circ}+65^{\circ}+90^{\circ}=185^{\circ} \neq 180^{\circ}$

<em>The sum is greater than 180 degrees, so these angles can't form a triangle</em>

<h3>Case 2. Three angles measuring 50 degrees, 50 degrees, and 50 degrees </h3><h3 /><h3> $\angle A=50^{\circ} \\ \\ \angle B=50^{\circ} \\ \\ \angle C=50^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=50^{\circ}+50^{\circ}+50^{\circ}=150^{\circ} \neq 180^{\circ}$ </h3><h3 />

<em>The sum is less than 180 degrees, so these angles can't form a triangle</em>

<h3 /><h3>Case 3. Three sides measuring 5 in., 12 in., and 14 in. </h3><h3 /><h3 /><h3> $a=5 \\ \\ b=12 \\ \\ c=14 \\ \\ \\ 5$ </h3><h3><em></em></h3>

<em>The inequalities are true, so these sides form a triangle. </em>

Case 4: Three sides measuring 4 ft, 8 ft, and 14 ft

$a=4 \\ \\ b=8 \\ \\ c=14 \\ \\ \\ 4$

<em>Since the third inequality is not true, then we can't form a triangle with these sides.</em>

6 0

3 years ago