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Zielflug [23.3K]
3 years ago
13

Steve Ballmer, the current CEO of Microsoft, used to be the manager of his college football team. Among his duties, he had to be

sure the players were hydrated. When nearby construction forced a water shut off, Steve went to the Star Market to purchase bottles of water. He needed a total of 80 liters of water. Star Market sold water in two liter bottles and in half liter bottles. What possible combinations of the small and large bottles might he purchase in order to bring 80 liters to the football team?
a. Write an equation that models the possible combinations of half liter bottles and two liter bottles that would total 80 liters. (Be sure to define the variables.)
b. What is the x-intercept and what does it represent?
c. What is the y-intercept and what does it represent?
Mathematics
1 answer:
lutik1710 [3]3 years ago
7 0

9514 1404 393

Answer:

  a.  x + 4y = 160

  b.  160

  c.  40

Step-by-step explanation:

a. We can define the variables as ...

  x = number of 1/2-liter bottles

  y = number of 2-liter bottles

For the total number of liters to be 80, we require

  1/2x + 2y = 80

We can multiply this by 2 to eliminate the fraction.

  x + 4y = 160

__

b. The x-intercept is 160. It is the number of 1/2-liter bottles required when no 2-liter bottles are used.

__

c. The y-intercept is 40. It is the number of 2-liter bottles required when no 1/2-liter bottles are used.

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A lawyer has an annual income of $240,000. The income tax that doctor has to pay is 6%. What is the amount of income tax in doll
ZanzabumX [31]

Answer:

Step-by-step explanation:

240,000*6=14,400 dollars

the dr has to be taxes 14,400 dollars

4 0
3 years ago
Lifetime of $1 Bills The average lifetime of circulated $1 bills is 18 months. A researcher believes that the average lifetime i
OLEGan [10]
<h2>Answer with explanation:</h2>

Let \mu be the population mean lifetime of circulated $1 bills.

By considering the given information , we have :-

H_0:\mu=18\\\\H_a:\mu\neq18

Since the alternative hypotheses is two tailed so the test is a two tailed test.

We assume that the lifetime of circulated $1 bills is normally distributed.

Given : Sample size :  n=50 , which is greater than 30 .

It means the sample is large so we use z-test.

Sample mean : \overline{x}=18.8

Standard deviation : \sigma=2.8

Test statistic for population mean :-

z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

\Rightarrow\ z=\dfrac{18.8-18}{\dfrac{2.8}{\sqrt{50}}}\approx2.02

The p-value= 2P(z>2.02)=0.0433834

Since the p-value (0.0433834) is greater than the significance level (0.02) , so we do not reject the null hypothesis.

Hence, we conclude that we do not have enough evidence to support the alternative hypothesis that the average lifetime of a circulated $1 bill differs from 18 months.

6 0
3 years ago
(3?2)+(4?1)to the power of 2=10
Advocard [28]
Sol_

( 3 - 2 ) + ( 4 - 1 ) ^ 2

= 1 + 3^2

= 1 + 9

= 10

Answer is " - " .

hope it helped !

Thanks!

3 0
3 years ago
Y = 3/5x + 1, 5y = 3x - 2, 10x - 6y = -4<br> is it perpendicular, parallel, neither
Ber [7]

Answer:

y=\frac{3}{5} x+1 and 5y=3x-2 are parallel.

10x-6y=-4 is neither parallel nor perpendicular.

Step-by-step explanation:

First, you have to simplify each equation in terms of y.

y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4

Your first equation is already in terms of x, so simplify your second equation.

5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}

Now you can simplify your third equation.

10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}

These are your three equations in terms of y:

y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}

Now, all you have to know is how to tell using your slope if a line is parallel or perpendicular to another.

Two parallel lines will have the exact same slope.

Two perpendicular lines will have slopes which are opposite reciprocals. For example, a line with a slope of 2 is perpendicular to a line with a slope of -\frac{1}{2}, as they have opposite signs and are reciprocal (2/1 versus 1/2) to each other.

Your first two equations have the same slope and are therefore parallel.

Your third equation is a reciprocal, but it is not opposite, and is therefore not parallel nor perpendicular.

5 0
2 years ago
Which is a vertical pair of angles?
sleet_krkn [62]

Answer:

B.

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
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