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3 years ago

Order each set of numbers from least to greatest.

Mathematics

1 answer:

madam [21]3 years ago

6 0

Answer:

1. -18,-7,-4,3,16

2. -39,-24,-12,20,24

3. -64,-57,-32,0,9

4. -24,-14,-8,-3,-1

Step-by-step explanation:

Negative numbers are always least.

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n an amusement park, the bumper cars are sometimes becoming disabled and in need of repair. The repairman can fix the disabled b

grigory [225]

Answer:

1 hour 20 minutes

Step-by-step explanation:

Time to fix car ( repair time ) = 20 minutes

Breakdown rate ( λ ) = 2 car per hour

<u>first step : determine service the service rate ( μ )</u>

= 60 minutes / 20 minutes

= 3 cars per hour

<u>next : determine the average waiting time for a disabled car </u>

= 1 / (μ - λ)

= 1 / service rate - breakdown rate

= 1 / ( 3 - 2 )

= 1 / 1 = 1 hour

Finally Total time for a disabled car to be fixed

= repair time + average waiting time

= 20 minutes + 60 minutes

= 1 hour 20 minutes

6 0

3 years ago

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

5 0

3 years ago

Phil's age is 7 years more than 1/5 times than Peter's age . Also , 4 times Phil's age is 2 years less than twice Peter's age. I

OverLord2011 [107]

Answer:

x=25

Step-by-step explanation:

we know that "x" is Peter's age

assume that "y" is Phil's age

In the sentence "Phil's age is 7 years more than 1/5 times than Peter's age" are two things: "Phil's age": y and "1/5 times Peter's age": 1/5 x

create equation with these two things

y = 1/5 x

including "7 years more"

many people make a lot of errors with it, they dont know: y+7 = 1/5 x or y=1/5 x + 7 ?

in order to avoid mistakes

read the sentence and point, which: y or 1/5 x is greater and smaller

"Phil's age is 7 years more than ..."

so y is greater, and 1/5 x smaller

y = 1/5 x

greater = smaller

we must add 7 to smaller number to make an equality

greater = smaller + 7

y = 1/5 x + 7

Second sentence:

"4 times Phil's age is 2 years less than twice Peter's age."

Two things: "4 times Phil's age": 4y and "twice Peter's age": 2x

4y = 2x

read the sentence once again

"4 times Phil's age is 2 years less than (...)" , so 4y - smaller, 2x - greater

4y = 2x

smaller = greater

including "2 years less" we add 2 to a smaller number

smaller + 2 = greater

4y + 2 = 2x

Substitute y=1/5 x + 7 to the equation 4y+2 = 2x

$4(\frac15x+7)+2=2x\\ \frac45x+28+2=2x\\ 30=2x-\frac45x\\ 30=1\frac15x\\ \frac65x=30\ \ \ |\cdot 5\\ 6x=150 \ \ \ \ |:6\\ \boxed{x=25}$

3 0

3 years ago

You start your working career when you are 24 years oldEach month, you deposit $144 into a pension planYou continue making depos

maxonik [38]

Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

<h3>What is the monthly payment formula?</h3>

It is given by:

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

In which:

A is the monthly payment.

P is the total amount.

r is the interest rate.

n is the number of payments.

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

$144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}$

$P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}$

P = $26,731.23.

More can be learned about the monthly payment formula at brainly.com/question/26476748

#SPJ1

7 0

2 years ago

I will give Brainlyest!!! Key features of graphing the parabola: y=x^2+12x+32 A. AxisofSymmetry: x = − b/2a B. Vertex: C. Zero

slamgirl [31]

Answer:

Axis of Symmetry: -6

Vertex: (-6, -4)

x- int: (-4, 0) (-8, 0)

y-int: (0, 32)

opens up

3 0

3 years ago