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3 years ago

Please help these two questions!!! If you know it! It will mean a lot if you show me how to do it!

Mathematics

1 answer:

Kryger [21]3 years ago

8 0

A ) = $ 0.18/oz = 4.68/26

b) = $0.19/oz = 2.66/14= 0.19

a is a better buy

9) for every 5 babies they need 1 babysitter, so for 40 babies they will need 8 babysitters.

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Is the line for the equation y = −8 horizontal or vertical? What is the slope of this line?

ZanzabumX [31]

Check the picture below.

so, say let's use two points on that line to see what's its slope then.

$\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-8-(-8)}{4-(-6)}\implies \cfrac{-8+8 }{4+6}\implies \cfrac{0}{10}\implies 0$

8 0

4 years ago

There are 50 students in a calculus class. The amount of time needed for the instructor to grade a randomly chosen midterm exam

natta225 [31]

Answer:

14.46% probability that the instructor can finish grading in 4 and a half 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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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 $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of n values from a distribution, the mean is $n\mu$ and the standard deviation is $s = \sqrt{n}\sigma$

In this problem, we have that:

$\mu = 6*50 = 300, s = \sqrt{50}*4 = 28.2843$

What is the probability that the instructor can finish grading in 4 and a half hours

Four and half hours is 4.5*60 = 270.

So this probability is the pvalue of Z when X = 270.

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

By the Central Limit Theorem

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

$Z = \frac{270 - 300}{28.2843}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

14.46% probability that the instructor can finish grading in 4 and a half hours

8 0

3 years ago

A thermometer is taken from an inside room to the outside, where the air temperature is 20° f. after 1 minute the thermometer re

fomenos

The change in the temperature is proportional to the difference in temperatures. Let's call the initial temperature of the room and the thermometer $E_0$ and the current temperature $E(t)$ where $t$ is the elapsed time in minutes. The outside temperature is 20 F.

Newton's Law of Cooling:

$E(t) - 20 = (E_0 - 20) e^{- k t}$

We're given $E(1)=70 \textrm{ and } E(5)=45$

$70-20 = (E_0 - 20) e^{-k}$

$45-20 =(E_0 - 20) e^{-5k}$

Dividing,

$\dfrac{50}{25}=e^{4k}$

$k = \dfrac 1 4 \ln 2$

Now,

$E(t) - 20 = (E_0 - 20) e^{- k t}$

$E_0 = 20 + (E(t) - 20)e^{k t}$

$E_0 = 20 + (E(1) - 20)e^{k}$

$E_0 = 20 + (70 - 20)e^{\ln 2/4}$

$E_0 = 20 + 50 \cdot 2^{1/4} \approx 79.46 \textrm{ degrees F}$

3 0

4 years ago

Simplify 6 - 4[x + 1 - (y + 3)] + 5y.

Sidana [21]

2(x+1-3y)+5y

2x+2-6y+5y

2x+2-y

-y+2x+2

7 0

4 years ago

Antonio's father has a cutting form that can cut a pizza into 12 slices and another form that can cut into 8 slices.

n200080 [17]

A. 5/8
b. 3/8

sorry. I don't have enough time to do C
If you need more help then let me know

3 0

3 years ago