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2 years ago

The expression x2y - 2xy - 24y can be factored by first factoring out a common factor of y.

Mathematics

2 answers:

gladu [14]2 years ago

6 0

Answer:

quadratic

Step-by-step explanation:

Given

x²y - 2xy - 24y ← factor out y from each term

= y(x² - 2x - 24) ← quadratic factor

To factor the quadratic

Consider the factors of the constant term ( - 24) which sum to give the coefficient of the x- term (- 2)

The factors are - 6 and + 4, since

- 6 × 4 = - 24 and - 6 + 4 = - 2, hence

x² - 2x - 24 = (x - 6)(x + 4) and

x²y - 2xy - 24y = y(x - 6)(x + 4) ← in factored form

Otrada [13]2 years ago

6 0

Answer:

trinomial that is not a perfect square

Step-by-step explanation:

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Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60percent of their plants are

DaniilM [7]

Answer:

There are 20 vegetable plants in garden.

Step-by-step explanation:

We are given the following in the question:

Percentage of flowers = 60%

Percentage of vegetable = 40%

Number of plants in garden = 50

Number of vegetables in garden =

$40\% \times \text{Number of plant}\\\\= \dfrac{40}{100}\times 50\\\\= 20$

Number of flowers in garden =

$60\% \times \text{Number of plant}\\\\= \dfrac{60}{100}\times 50\\\\= 30$

Thus, there are 20 vegetable plants in garden.

6 0

2 years ago

The function y=log(x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?

SVEN [57.7K]

Given the function $y=\log x.$

1. Translation to the right 1 unit changes the function $y=\log x$ into the function $y=\log (x-1).$

2. Translation 2 units down changes the function $y=\log (x-1)$ into the function $y=\log (x-1)-2.$

3. Two translations change the funcion $y=\log x$ into the function $y=\log (x-1)-2.$

4. The graph of the final function you can see in attached diagram.

5 0

2 years ago

Read 2 more answers

A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st

maxonik [38]

Answer:

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

$p_v =2*P(z>1.413)=0.158$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance

Step-by-step explanation:

Data given and notation

$\bar X=5.0611$ represent the sample mean

$\sigma=0.2803$ represent the population standard deviation for the sample

$n=42$ sample size

$\mu_o =5$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 5, the system of hypothesis would be:

Null hypothesis: $\mu = 5$

Alternative hypothesis: $\mu \neq 5$

If we analyze the size for the sample is > 30 but and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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".

Calculate the statistic

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

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(z>1.413)=0.158$

Conclusion

8 0

2 years ago

Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form

9966 [12]

The rule of the geometric sequence is $a* r^{n-1}$
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio

Given: the fourth term (a4) = 121.5 and the common ratio = 3 and n = 4

∴ $121.5 = a* 3^{4-1}$
∴ a = 121.5/3³ = 121.5/27 = 4.5

So, The formula for this sequence will be $4.5 * 3^{n-1}$

8 0

2 years ago

Read 2 more answers

A car insurance company suspects that the younger the driver is, the more reckless a driver he/she is. They take a survey and gr

erastovalidia [21]

Answer:

The confidence interval for the difference in proportions is

$-0.028\leq p_1-p_2 \leq 0.096$

No. As the 95% CI include both negative and positive values, no proportion is significantly different from the other to conclude there is a difference between them.

Step-by-step explanation:

We have to construct a confidence interval for the difference of proportions.

The difference in the sample proportions is:

$p_1-p_2=x_1/n_1-x_2/n_2=(183/217)-(322/398)=0.843-0.809\\\\p_1-p_2=0.034$

The estimated standard error is:

$\sigma_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2} } \\\\\sigma_{p_1-p_2}=\sqrt{\frac{0.843*0.157}{217}+\frac{0.809*0.191}{398} } \\\\\sigma_{p_1-p_2}=\sqrt{0.000609912+0.000388239}=\sqrt{0.000998151} \\\\ \sigma_{p_1-p_2}=0.0316$

The z-value for a 95% confidence interval is z=1.96.

Then, the lower and upper bounds are:

$LL=(p_1-p_2)-z*\sigma_p=0.034-1.96*0.0316=0.034-0.062=-0.028\\\\\\UL=(p_1-p_2)+z*\sigma_p=0.034+1.96*0.0316=0.034+0.062=0.096$

The confidence interval for the difference in proportions is

$-0.028\leq p_1-p_2 \leq 0.096$

Can it be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group?

No. It can not be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group, as the confidence interval include both positive and negative values.

This means that we are not confident that the actual difference of proportions is positive or negative. No proportion is significantly different from the other to conclude there is a difference.

8 0

2 years ago