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Vladimir [108]
3 years ago
15

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 22 h using both

hoses. They also know that Bob's hose, used alone, takes 50% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?
Mathematics
1 answer:
FrozenT [24]3 years ago
4 0

Answer:

correct answer: Bob's hose required alone 33 hours and Jim's hose required alone 66 hours

Step-by-step explanation:

Given:

Bob's hose time = 50% of Jim's hose time ⇒

⇒ Jim's hose time = 2 · Bob's hose time

Let be x  Bob's hose time and  2x Jim's hose time

The following equation will solve the problem:

1/x + 1/ 2x = 1/22  

The common denominator for both fractions is 2x, so we will multiply the first fraction by the number 2 and get:

2/2x + 1/2x = 1/22 ⇒ 3/2x = 1/22 ⇒ x = 3 · 22 / 2 ⇒ x = 3 · 11 = 33 hours

Bob's hose time x = 33 hours and

Jim's hose time 2x = 66 hours

God is with you!!!

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PLEASE HELP!!<br>What is the measure of angle x? ​
lesya692 [45]

Answer:

54

Step-by-step explanation:

90 +36 = 126

There is 180 degrees in a triangle.

180 - 126 = 54

7 0
3 years ago
Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. I
xxTIMURxx [149]

Answer:

t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971    

p_v =2*P(t_{(1699)}>1.971)=0.049  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.

Step-by-step explanation:

Data given and notation  

\bar X=669 represent the sample mean

s=732 represent the sample standard deviation

n=1700 sample size  

\mu_o =68 represent the value that we want to test

\alpha=0. represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is different from 634, the system of hypothesis would be:  

Null hypothesis:\mu = 634  

Alternative hypothesis:\mu \neq 634  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=1700-1=1699  

Since is a two sided test the p value would be:  

p_v =2*P(t_{(1699)}>1.971)=0.049  

Conclusion  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.

3 0
3 years ago
Proportional relationships, please answer all of the parts! Thank you!
Natalka [10]

Answer:

a. No (see below)

b. (see below)

c. Johnny

d. Johnny = $12.50 / hour      Doug = $9.16... / hour

e. Doug: extend the table to show how much he gets paid for 1 hour of work (the unit rate)

Johnny: already on the graph

Step-by-step explanation:

a. No. This is because a proportional relationship would have a certain ratio between payment and the amount of time spent working, which would not change. However, if Doug's neighbour pays him $55 for 6 hours, it's likely that this is not a proportional relationship, or we would be able to divide $55 by the 6 hours Doug spent working.

b. Even though above I said that it's probably not a proportional relationship, if it were, we would have to divide everything equally. I'm guessing the table should look like this:

                            Doug

       Time (hr)                      Earnings ($)

          4                                  $36.66...

          5                                  $45.8333...

          6                                  $55

          7                                  $64.4666....

          8                                  $73.333...

To work out how much Doug would get for working 4 hours:

4/6 x $55 = 2/3 x $55 = $36.66... (so definitely not a proportional relationship)

To work out how much Doug would get for working 5 hours:

5/6 x $55 = $45.8333.... (more evidence that this is not a proportional relationship)

To work out how much Doug would get for working 7 hours (we already got 6 hours):

7/6 x $55 = $64.4666...

To work out how much Doug would get for working 8 hours:

8/6 x $55 = $73.33... (we could double the 4 hour payment, but this is probably more accurate)

c. Johnny is getting paid more. If we look at how much Doug gets for 6 hours, it's $55. If we look out at how much Johnny gets for 6 hours, it's $75. (If we do the same with the other amounts of time, it's the same.

4 hours: D = $36.67 vs J = $50

5 hours: D = $45.83 VS J = $60

etc...

d. Johnny gets $75 per 6 hours --> 75/6 = $12.50 per hour

Doug gets $55 per 6 hours --> 55/6 = $9.1666... per hour

e. Carry on the table for Doug all the way to 1, so you can see the how much Doug gets paid for 1 hour of work (i.e. the minimum).

The unit rate is already on the graph for Johnny.

HOPE THIS HELPED :)

P.S. Mate cld you please give me Brainliest? That table took so much dam work

7 0
3 years ago
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antoniya [11.8K]
3/2 and 9/10. Look at the denominators. 2 times what number equals 10. That number would be 5. So if you multiply the first fractions denominator by 5 you get 10. Do the same to the top. you get a new fracrion which is 15/10. Add normally. 15/10 + 9/10 = 24/10. In lowest terms it is 2 2/5 (2 wholes and 2 out of 5)
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Vadim26 [7]

Answer:

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Step-by-step explanation:

The initial number n gets additional 4 students making the new total number of students to be 32. Therefore, this situation can be represented as

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Therefore, the initial number was 28 and the equation is n+4=32

Since no choices were provided, the equation that can be modified is n+4=32

8 0
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