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2 years ago

(x+y)(x+6y) pls help me solve question pls and pls also give explanation if possible

Mathematics

1 answer:

steposvetlana [31]2 years ago

7 0

Step-by-step explanation:

$= (x + y)(x + 6y)$

$= x \times x + x \times 6y + y \times x + y \times 6y$

$= {x}^{2} + 6xy + xy + 6 {y}^{2}$

$= {x}^{2} + 7xy + 6 {y}^{2}$

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A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchase

Alona [7]

Answer:

The customer can conclude that the company's claim is correct

Step-by-step explanation:

The percentage of lids that has a free yogurt coupon = 20%

The number of cups a loyal customer purchases = 85 yogurt cups

The number of cups that contained a coupon = 12 (14.1%)

The confidence interval performed = 99% confidence interval for the proportion of yogurt cups containing coupon codes

The interval obtained = (0.044, 0.238)

Therefore, the range of proportion within which the true proportion exists is 0.044 < $\hat p$ < 0.238

The range of percentage within which the true percentage exist is therefore;

0.044 × 100 = 4.4% < $\hat p$ × 100 < 0.238 × 100 = 23.8%

Given that the possible true percentage of lids that has a coupon is between 4.4% and 23.8% at 99% confidence level, the customer can conclude that only 12 of his yogurt cup contained coupon by chance and that the company's claim is correct.

4 0

3 years ago

4x=2 solve for X<br><img src="https://tex.z-dn.net/?f=4x%20%3D%202%20solve%20for%20x" id="TexFormula1" title="4x = 2 solve for x

Bogdan [553]

X=1/2 hope this helps <3

3 0

3 years ago

Read 2 more answers

Julia knows that 65×4,903=318,695. Use this understanding to help Julia solve 6.5×4903

slamgirl [31]

Answer:

31869.5

Step-by-step explanation:

7 0

2 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 tree casts a shadow 8 feet long. A 6-foot Man cast a shadow 4 feet long. The triangle formed by the tree and its shadow is sim

Elden [556K]

Answer:

12 feet

Step-by-step explanation:

Draw a diagram (see picture below). The tree and its shadow is one triangle, the man and its shadow is another triangle. We assume both are right triangles because people and trees stand vertical.

Create a proportion to solve. Put the missing value in a numerator.

Tree height / Tree shadow = Man height / Man shadow

$\frac{x}{8} =\frac{6}{4}$

Solve using cross multiplication. Multiply x by 4. Multiply 6 by 8.

4x = 48 Divide both sides by 4 to isolate x.

x = 12 Height of tree

The tree is 12 feet tall.

4 0

3 years ago