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Oduvanchick [21]
2 years ago
11

A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Creat

e and graph the solution set of the equation for the gallons of water, y, remaining in the barrel in terms of the number of minutes elapsed, x.

Mathematics
2 answers:
emmainna [20.7K]2 years ago
7 0

Answer:

y=-0.10x+60

Step-by-step explanation:

Let

y -----> gallons of water remaining in the barrel

x-----> number of minutes elapsed

we know that

Water leaks out of the barrel at a rate of 1 gallon every 10 minutes

so

1/10=0.10\frac{gal}{min}

The linear equation that represent this situation is  

y=-0.10x+60

The graph in the attached figure

Bad White [126]2 years ago
5 0

Answer:

So you t   start with 60 because that is how many gallons Jim has. Then you can count by tens until you get to 100. it takes 10 tens to get to 100 which means that for each 10 mins 1 gallon is lost. so the number of gallons lost in 100 mins is 10. so the point would read (100, 50) for every hundred mins, 10 gallons of water are lost. nUntil you hit zero because  cannot have negative amounts of water. Even s helps!

Step-by-step explanation:

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Oishi and Schimmack (2010) report that people who move from home to home frequently as children tend to have lower than average
user100 [1]

Answer:

The well-being for frequent movers is significantly different from well-being in the general population. ( Alternate Hypothesis accepted )

cohen's d = -0.91 , ( Large Effect )

Step-by-step explanation:

Given:-

- A sample of size n = 12

- The population mean u_p = 40

- The sample was taken as:

                     38, 37, 41, 35, 42, 40, 33, 33, 36, 38, 32, 39

Find:-

On the basis of this sample, is well-being for frequent movers significantly different from well-being in the general population? Use a two-tailed test with α = 0.05.

Solution:-

- State the hypothesis for sample mean u_s is same as population mean u_p.

                    Null Hypothesis: u_s = 40

                    Alternate Hypothesis: u_s ≠ 40

- The rejection criteria for the Null hypothesis can be modeled by T-value ( n < 30 ) with significance level α = 0.05.

                    DOF = n - 1 = 12 - 1 = 11

                    Significance level α = 0.05

                    t_α/2 = t_0.025 = +/- 2.201

- For the statistic value we have to compute sample mean u_s given by:

             u_s = Σ xi / n

             u_s = (38 + 37 + 41 + 35 + 42 + 40 + 33 + 33 + 36 + 38 + 32 + 39) / 12

             u_s = 37

- For the statistic value we need population standard deviation S_p given by:

            S_p = S_s / √n

Where, S_s : Sample standard deviation.

            S_s^2 = Σ (xi - u_s)^2 / (n-1)

            =[ 2*(38-37)^2 +  (37-37)^2 + (41-37)^2 + (35-37)^2 + (42-37)^2 + (40-37)^2 + 2*(33-37)^2 + (36-37)^2 + (32-37)^2 + (39-37)^2 ] / ( 11 )

            S_s^2 = [ 2 + 0 + 16 + 4 + 25 + 9 + 32 + 1 + 25 + 4 ] / 11

            S_s^2 = 10.73

            S_s = 3.28

The population standard deviation ( S_p ) is:

            S_p = 3.28 / √12

            S_p = 0.95

- The T-statistics value is computed as follows:

            t = ( u_s - u_p ) / S_p

            t = ( 37 - 40 ) / 0.95 = -3.16

- Compare the T-statistics (t) with rejection criteria (t_α/2).

            -3.16 < -2.201

            t < t_α/2 ...... Reject Null Hypothesis.

- The well-being for frequent movers is significantly different from well-being in the general population. ( Alternate Hypothesis accepted )

- The cohen's d is calculated as follows:

         cohen's d = ( u_s - u_p ) / S_s

         cohen's d = ( 37 - 40 ) / 3.28 = -0.91 ,     ( Large Effect )    

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2 years ago
"Our customer retention rate has decreased 10% from last quarter's goal of 250 consumers retained. We need to increase our curre
Lorico [155]
1. multiply 250 by 10% (250 * .1= 25)
2. Then subtract 25 from 250 (250 -25= 225)
2. Then multiply 225 by 16% (225 * .16 = 36)
3. Add 225 + 36 = 261. 
4. 261 is your final answer
6 0
2 years ago
A boy had 20 cents. He bought x pencils for 3 cents each. If y equals the number of pennies left, write an equation showing the
Vesna [10]

Hey there!!

The total number of cents - 20

Cost for each pencil - 3 cents

Number of pencils bought - ' x '

y = number of pennies left

What is the domain ?

Show how y is dependent on x ..

Let's get this into an equation :

... The total cost for x pencils bought = 3x

... Number of pennies left = 20 - 3x

... y = number of pennies left

... y = 20 - 3x

Notice : If the x value changes, the y value changes too

... If x = 1 , then , y = 17; If x = 2 , then , y = 14

Hence, we could say y is dependent upon x

Domain = ?

... Remember - The total number of pennies = 20 ; hence, the total cost cannot go above 20 cents.

Hence, we will have to work with inequalities

The equation  :

... 20 ≥ 3x

Divide 3 on both sides

20 / 3 ≥ x

x ≥ 6.667

Let's take this as 6

Hence , the domain will be :

D : { 1 , 2 , 3 , 4 , 5 , 6 }

Hope my answer helps!

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1 year ago
Which statements about the figure are true? Select two options.
harina [27]

<u>Complete Question</u>

The circle is inscribed in triangle PRT. A circle is inscribed in triangle P R T. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T. The length of R S is 5, the length of P U is 8, and the length of U T is 6. Which statements about the figure are true?

Answer:

(B)TU ≅ TS

(D)The length of line segment PR is 13 units.

Step-by-step explanation:

The diagram of the question is drawn for more understanding,

The theorem applied to this problem is that of tangents. All tangents drawn to a circle from the same point are equal.

Therefore:

|PQ|=|PU|=8 Units

|ST|=|UT| =6 Units

|RS|=|RQ|=5 Units

(b)From the above, TU ≅ TS

(d)Line Segment |PR|=|PQ|+|QR|=8+5=`13 Units

6 0
2 years ago
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Write the decimal 1,072.039 in words
Rina8888 [55]
One thousand seventy two point thirty nine thousandths.

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2 years ago
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