. An equation is shown below. 2x = 60 Which of these situations could the equation represent?

you earn $420 per week. You pay social security taxes of 7.65% federal taxes of 22%, and state taxes of 5.95%. What is your take

Marysya12 [62]

First you need to solve for how much you lose for each individual tax, so 420x.0765 will give you how much money you lose to social security tax, then do the same for the other types and add them together, the value will give you the amount you have lost, so taking the total (420) minus the amount lost you will have the amount that you can "take home" So 420-((420x.0765)+(420x.22)+(420x.0595)) = amount still in your pocket

8 0

2 years ago

A box of cereal states that there are 75 calories in a

grandymaker [24]

Answer:

The unit rate is 100 calories per cup

and 300 calories in the three cups of cereal

Step-by-step explanation:

4 0

2 years ago

Write your answer in simplest radical form

liubo4ka [24]

Answer:

x = 2 yd

Step-by-step explanation:

Angles of 45 degreees = two congruent legs

for the Pythagorean theorem

2x^2 = 8

x^2 = 4

x = 2

5 0

2 years ago

Read 2 more answers

One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analyst

grandymaker [24]

Answer:

(a) P (X = 0) = 0.0498.

(b) P (X > 5) = 0.084.

(c) P (X = 3) = 0.09.

(d) P (X ≤ 1) = 0.5578

Step-by-step explanation:

Let X = number of telephone calls.

The average number of calls per minute is, λ = 3.0.

The random variable X follows a Poisson distribution with parameter λ = 3.0.

The probability mass function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,3...$

(a)

Compute the probability of X = 0 as follows:

$P(X=0)=\frac{e^{-3}3^{0}}{0!}=\frac{0.0498\times1}{1}=0.0498$

Thus, the probability that there will be no calls during a one-minute interval is 0.0498.

(b)

If the operator is unable to handle the calls in any given minute, then this implies that the operator receives more than 5 calls in a minute.

Compute the probability of X > 5 as follows:

P (X > 5) = 1 - P (X ≤ 5)

$=1-\sum\limits^{5}_{x=0} { \frac{e^{-3}3^{x}}{x!}} \,\\=1-(0.0498+0.1494+0.2240+0.2240+0.1680+0.1008)\\=1-0.9160\\=0.084$

Thus, the probability that the operator will be unable to handle the calls in any one-minute period is 0.084.

(c)

The average number of calls in two minutes is, 2 × 3 = 6.

Compute the value of X = 3 as follows:

$P(X=3)=\frac{e^{-6}6^{3}}{3!}=\frac{0.0025\times216}{6}=0.09$

Thus, the probability that exactly three calls will arrive in a two-minute interval is 0.09.

(d)

The average number of calls in 30 seconds is, 3 ÷ 2 = 1.5.

Compute the probability of X ≤ 1 as follows:

P (X ≤ 1 ) = P (X = 0) + P (X = 1)

$=\frac{e^{-1.5}1.5^{0}}{0!}+\frac{e^{-1.5}1.5^{1}}{1!}\\=0.2231+0.3347\\=0.5578$

Thus, the probability that one or fewer calls will arrive in a 30-second interval is 0.5578.

5 0

2 years ago

The larger of two numbers is 7 times the smaller number. Three times the larger number is 7 more than 4 times the smaller number

Juliette [100K]

Let the smaller number be x.

Given, the larger number is 7 times the smaller number.

So, the larger number = 7x.

Given, 3 times the larger number is 7 more than 4 times the smaller number.

So we can write the equation as,

$3(7x) = 4(x)+7$

$3(7x) = 4x+7$

$21x = 4x+7$

Now we have to move 4x to the left side by subtracting 4x from both sides.

$21x-4x = 4x-4x+7$

$21x-4x = 7$

$17x = 7$

To get x, we will divide both sides by 17. We will get,

$\frac{17x}{17} = \frac{7}{17}$

$x = \frac{7}{17}$

So the smaller number = $\frac{7}{17}$

The larger number = $7(\frac{7}{17} )$ = $\frac{49}{17}$

So we have got the required numbers.

Smaller number = $\frac{7}{17}$ and larger number = $\frac{49}{17}$ .

4 0

2 years ago