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3 years ago

Let x and y be two positive numbers whose sum is 175 and (x+3)(y+4) is a maximum

Mathematics

1 answer:

Vaselesa [24]3 years ago

4 0

Answer:

Step-by-step explanation:

x+y = 175

y = 175 - x

f(x) = (x+3)(y+4)

= x(175-x) + 3(175-x) + 4x + 12

= 175x - x² + 525 - 3x + 4x + 12

= -x² +176x + 537

f'(x) = -2x + 176

maximum when x = 88

y = 175-x = 87

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Bernardo drives to work at an average speed of 50 miles per hour and returns along the same route at an average speed of 25 mile

-BARSIC- [3]

Bernardo travels the same distance at 25mph as he does at 50mph. However, since 25mph is only half of 50 mph, he must travel twice as long at 25mph. If you call the time he traveled 50mph "t", then

t+2t=3 
3t=3 
t=1 

This means he traveled 1 hour at 50mph. In this time, he traveled 50 miles. He traveled the same distance at 25mph, so his total distance was 

50miles+50miles=100miles 

so the round trip was 100 miles.

6 0

3 years ago

Please help!!!!!!!!!!!

adelina 88 [10]

Answer:

9/4 *(x-2)

Step-by-step explanation:

Replace xa and y in the given function then solve for y

8 0

3 years ago

What is the value of x?

scoray [572]

Answer:

x = 54.6 m

Step-by-step explanation:

Δ MAB and Δ MNP are similar, then corresponding sides are in proportion, that is

$\frac{MA}{MN}$ = $\frac{MB}{MP}$ , substitute values

$\frac{80.5-35}{80.5}$ = $\frac{x}{96.6}$

$\frac{45.5}{80.5}$ = $\frac{x}{96.6}$ ( cross- multiply )

80.5x = 4395.3 ( divide both sides by 80.5 )

x = 54.6

8 0

3 years ago

Read 2 more answers

PLZ HELP AND HURRY!!!!

yuradex [85]

Answer: x=30, Good Luck!

Step-by-step explanation:

45/27 = 1.6666666...

1.66666...(18) = 30

8 0

2 years ago

In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a s

Oksi-84 [34.3K]

Answer:

a) $\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

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

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

c) $P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

$P(Z\geq2.070)=1-P(Z$

Step-by-step explanation:

Let X the random variable the represent the scores for the test analyzed. We know that:

$\mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4$

And we select a sample size of 64.

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".

Part a

For this case the mean and standard error for the sample mean would be given by:

$\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

Part b

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

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

Part c

For this case we want this probability:

$P(\bar X \geq 285)$

And we can use the z score defined as:

$z=\frac{\bar x -\mu}{\sigma_{\bar x}}$

And using this we got:

$P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

And using a calculator, excel or the normal standard table we have that:

$P(Z\geq2.070)=1-P(Z$

8 0

3 years ago