The open intervals on which f is concave upward. (enter your answer using interval notation.

ben earned 45 dollars mowing lawns. he worked 3.2 hours on monday and 4.3 hours on tuesday. how much did he earn per hour?

dlinn [17]

Answer:

6 dollars per hour

Step-by-step explanation:

We can set up and solve an equation to answer this question. For this problem, let x stand for the amount he earned per hour. The equation that represents this situation is 3.2x + 4.3x = 45. The first term represents monday and the second represents tuesday. When these add up they should equal 45 because that is the total amount he made. To find his pay per hour, solve for x.

First, combine the like terms

7.5x=45

Next, divide both sides by 7.5

x=6

3 0

1 year ago

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

2 years ago

Nina decided to raise money for a community organization that provides free classes and legal

Over [174]

A percentage is a way to describe a part of a whole. The money that is raised by Nina in the second month is $960.

<h3>What are Percentages?</h3>

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the money raised by Nina in the first month is $800, while the money raised by Nina in the second month is 20% more.

Therefore, the money raised by Nina in the second month is,

Money raised = $800 + 20% of $800

= $800 + 0.20($800)

= $800 + $160

= $960

Hence, the money that is raised by Nina in the second month is $960.

Learn more about Percentages here:

brainly.com/question/6972121

#SPJ1

8 0

1 year ago

Round 3,047 to the nearest hundredth

Aleksandr-060686 [28]

It should be 3,000
------------------------

3 0

2 years ago

-30 + 5a < 16<br> A. a 9.2<br> C.<br> a < 9.2<br> a> -2.8<br> a < -2.8

Goryan [66]

Answer:

-30 + 5a < 16

5a < 46

$a < \frac{46}{5}$

a < 9.2

Hope this help...

4 0

2 years ago