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3 years ago

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A quality assurance specialist makes $22 an hour for the first 40 hours she works during a week and $29 an hour for each hour wo

rked over 40 hours. Which piecewise equation models her total weekly pay y in dollars as it relates to the number of hours x that she has worked during the week?

1 answer:

Elenna [48]3 years ago

3 0

Answer:

This is the answer on APEX. Hope it helps!!

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Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression.

vitfil [10]

Answer:

(A) $e^2$

(b) $e^{-3}$

(c) $e^2$

(d) $e^3$

Step-by-step explanation:

We have given expression and we have to simplify the expression using exponent property

(A) $(\frac{1}{e})^{-2}$

So $(\frac{1}{e})^{-2}=\frac{1}{e^{-2}}=e^2$

(b) $(\frac{e^5}{e^2})^{-1}$

So $(\frac{e^5}{e^2})^{-1}=(e^{3})^{-1}=e^{-3}$

(c) $\frac{e^5}{e^3}$

So $\frac{e^5}{e^3}=e^2$

(d) $\frac{1}{e^{-3}}=e^3$

7 0

3 years ago

Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both in case

olga nikolaevna [1]

Answer:

(a) The probability that both Dave and Mike will show up is 0.25.

(b) The probability that at least one of them will show up is 0.75.

(c) The probability that neither Dave nor Mike will show up is 0.25.

Step-by-step explanation:

Denote the events as follows:

<em>D</em> = Dave will show up.

<em>M</em> = Mike will show up.

Given:

$P(D^{c})=0.55\\P(M^{c})=0.45$

It is provided that the events of Dave of Mike showing up are independent of each other.

(a)

Compute the probability that both Dave and Mike will show up as follows:

$P(D\cap M)=P(D)\times P (M)\\=[1-P(D^{c})]\times [1-P(M^{c})]\\=[1-0.55]\times[1-0.45]\\=0.2475\\\approx0.25$

Thus, the probability that both Dave and Mike will show up is 0.25.

(b)

Compute the probability that at least one of them will show up as follows:

P (At least one of them will show up) = 1 - P (Neither will show up)

$=1-P(D^{c}\cup M^{c})\\=P(D\cup M)\\=P(D)+P(M)-P(D\cap M)\\=[1-P(D^{c})]+[1-P(M^{c})]-P(D\cap M)\\=[1-0.55]+[1-0.45]-0.25\\=0.75$

Thus, the probability that at least one of them will show up is 0.75.

(c)

Compute the probability that neither Dave nor Mike will show up as follows:

$P(D^{c}\cup M^{c})=1-P(D\cup M)\\=1-P(D)-P(M)+P(D\cap M)\\=1-[1-P(D^{c})]-[1-P(M^{c})]+P(D\cap M)\\=1-[1-0.55]-[1-0.45]+0.25\\=0.25$

Thus, the probability that neither Dave nor Mike will show up is 0.25.

6 0

3 years ago

Read 2 more answers

What is the answer to 6(c+5)

Anna [14]

Answer:

6c+30

Step-by-step explanation:

Distribute it!

3 0

2 years ago

Find (fºg)(1)<br> f(x) = x² - 1<br> g(x) = √x <br> A.0<br> B.1<br> C.4 √2<br> D. √8

Savatey [412]

Given:

The function are

$f(x)=x^2-1$

$g(x)=\sqrt{x}$

To find:

The value of $(f\circ g)(1)$ .

Solution:

We have,

$f(x)=x^2-1$

$g(x)=\sqrt{x}$

We need to find the value of $(f\circ g)(1)$ .

$(f\circ g)(1)=f(g(1))$ $[\because (f\circ g)(x)=f(g(x))]$

$(f\circ g)(1)=f(\sqrt{1})$ $[\because g(x)=\sqrt{x}]$

$(f\circ g)(1)=f(1)$

$(f\circ g)(1)=(1)^2-1$ $[\because f(x)=x^2-1]$

$(f\circ g)(1)=1-1$

$(f\circ g)(1)=0$

The value of $(f\circ g)(1)$ is 0.

Therefore, the correct option is A.

4 0

2 years ago

What is the approximate volume of a cone with a radius of 15 cm and a height of 4 cm? Round your answer to the nearest hundredth

vichka [17]

Answer:

Volume of a cone $=942.86cm^3$

Step-by-step explanation:

Given that the radius of a cone is 15cm and its height is 4cm

That is r=15cm and h=4cm

To find the volume of a cone :

volume of a cone $=\frac{\pi r^2h}{3}$ cubic units

Now substitute the values in the formula we get

volume of a cone $=\frac{(\frac{22}{7}) (15)^2(4)}{3}$

$=\frac{(\frac{22}{7}) (225)(4)}{3}$

$=\frac{19800}{21}$

$=942.857$

Now round to nearest hundredth

$=942.86$

Therefore Volume of a cone $=942.86cm^3$

6 0

3 years ago