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3 years ago

How do you solve 1/4x4/7=

2 answers:

8 0

If you would like to solve 1/4 * 4/7, you can do this using the following steps:

<span>1/4 * 4/7 = (1 * 4) / (4 * 7) = 4/28 = 1/7
</span>
The correct result would be 1/7.

sergey [27]3 years ago

4 0

Answer:

4/28

1/7

Step-by-step explanation:

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Serhud [2]

Answer: c

Step-by-step explanation:

5 0

3 years ago

(b)Newton has bought 12 dozen copies in Rs 4320. His expenditure to bring the copies

Alexeev081 [22]

Answer:

30%

Step-by-step explanation:

4320 - 288 = 4032

4032/12 =336 per copies

So, he sold them in 5760

5760 - 4032 = 1728

(1728/5760)*100 = 30%

8 0

3 years ago

At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical popul

vampirchik [111]

Answer:

a) Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b) The 95% confidence interval would be given by (910.05;959.95)

c) Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d) $z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

Step-by-step explanation:

a. State the hypotheses.

On this case we want to check the following system of hypothesis:

Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x¯¯¯= 935?

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".

$\bar X=935$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=180$ represent the population standard deviation

n=200 represent the sample size

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=3278.222$

The sample deviation calculated $s=97.054$

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):

$935-1.96\frac{180}{\sqrt{200}}=910.05$

$935+1.96\frac{180}{\sqrt{200}}=959.95$

So on this case the 95% confidence interval would be given by (910.05;959.95)

c. Use the confidence interval to conduct a hypothesis test. Using α= .05, what is your conclusion?

Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d. What is the p-value?

The statistic is given by:

$z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

If we replace we got:

$z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

So then since the p value is less than the significance we can reject the null hypothesis at 5% of significance.

8 0

3 years ago

a hot tub pump circulate 4 cubic feet of water per minute, how many cubic inches of water does it circulate earch minute?

Shtirlitz [24]

$4 {ft }^{3} \times {( \frac{12in}{ft} )}^{3} = 6912 {in}^{3}$

4 0

2 years ago

Evaluate the surface integral. s x ds, s is the part of the plane 18x + 9y + z = 18 that lies in the first octant.

IceJOKER [234]

In the first octant, the given plane forms a triangle with vertices corresponding to the plane's intercepts along each axis.

$(x,0,0)\implies 18x+9\cdot0+0=18\implies x=1$
$(0,y,0)\implies 18\cdot0+9y+0=18\implies y=2$
$(0,0,z)\implies 18\cdot0+9\cdot0+z=18\implies z=18$

Now that we know the vertices of the surface $\mathcal S$ , we can parameterize it by

$\mathbf s(u,v)=\langle(1-u)(1-v),2u(1-v),18v\rangle$

where $0\le u\le1$ and $0\le v\le1$ . The surface element is

$\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|\,\mathrm du\,\mathrm dv=2\sqrt{406}(1-v)\,\mathrm du\,\mathrm dv$

With respect to our parameterization, we have $x(u,v)=(1-u)(1-v)$ , so the surface integral is

$\displaystyle\iint_{\mathcal S}x\,\mathrm dS=2\sqrt{406}\int_{u=0}^{u=1}\int_{v=0}^{v=1}(1-u)(1-v)^2\,\mathrm dv\,\mathrm du=\frac{\sqrt{406}}3$

5 0

3 years ago