What is the distance between (-3,1) and (5,1)

A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plate

yulyashka [42]

Answer:

25

Step-by-step explanation:

From the given information;

Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.

= 1000x

Thus, the required number of hours it will take can be computed as:

$\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}$

cost per hour = 125

If each plate costs $20 to make, then the total number of plate will equal to 40x

∴

The total cost can be computed as:

$C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)$

$C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)$

At C'(x) = 0

$\dfrac{12500}{x^2} = 20$

$\dfrac{12500}{20} = x^2$

$x^2= 625$

$x = \sqrt{625}$

x = 25

$C'' (x) = -12500 \times \dfrac{-2}{x^3} +0$

$C'' (x) = \dfrac{25000}{x^3}$

where; x = 25

$C'' (x) = \dfrac{25000}{25^3}$

C''(x) = 1.6

Thus, at x = 25, C'' > 0

As such, to minimize the cost, the printer needs to make 25 metal plates.

4 0

3 years ago

Please help me. I'm confused.

Sholpan [36]

Answer:

u is 4 and v is 18

7 0

3 years ago

Read 2 more answers

= Initial Knowledge Check Rewrite the expression by factoring out (y+9). 3y^2 (y + 9) + 7(y+9)

alex41 [277]

Answer:

$3y {}^{2} (y + 9) + 7(y + 9) \\ = (y + 9)(3y { }^{2} + 7)$

6 0

3 years ago

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .