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Cloud [144]
2 years ago
12

Liam has to fill a hole in the ground that is 24 inches deep. He fills the hole at a rate of 6 inches in 30 minutes. Write a fun

ction that models the depth of the hole in feet over time in hours.
Mathematics
1 answer:
kupik [55]2 years ago
6 0

Answer:

The function that models the depth of the hole in feet over time in hours is h(t) = 24 - 12\cdot t.

Step-by-step explanation:

According to the statement, the variable to be modelled is the depth of the hole, which decreases whereas is filled. Under the assumption that the hole is filled at constant rate, we obtain the following expression:

h(t) = h_{o}-\frac{\Delta h}{\Delta t}\cdot t (1)

Where:

h(t) - Current depth of the hole, measured in inches.

h_{o} - Initial depth of the hole, measured in inches.

\Delta h - Filled level, measured in inches.

\Delta t - Filling time, measured in hours.

t - Time, measured in hours.

If we know that h_{o} = 24\,in, \Delta h = 6\,in and \Delta t = 0.5\,h, then the function that models the depth of the hole is:

h(t) = 24 - 12\cdot t

The function that models the depth of the hole in feet over time in hours is h(t) = 24 - 12\cdot t.

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8x - 3y, using x = 5 and y = 2
jeka57 [31]

Step 1: plug in 5 and 2 for your X and Y

Step 2: multiply 8*X or in this case 8*5 and you will get 40

Step 3: multiply 3*Y or in this case 3*2 and you will get 6

Step 4: subtract 40-6 and you will get 34

5 0
3 years ago
Last year, Lien earned $1,600 more than her husband. Together they earned $51,000. How much did each of them earn?
jok3333 [9.3K]

Answer:

Lien: $26300 Her husband: $24700

Step-by-step explanation:

x+(x+1600)=51000

2x+1600=51000

2x=49400

x=24700

Her husband earned 24700

24700+1600=26300

Lien earned 26300

3 0
2 years ago
Write an equation in slope-intercept form of the line that passes through (-1,4) and (0,2).
ratelena [41]

Answer:

1,3

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
In a random sample of 200 Americans, 51% said they favor building more nuclear power plants. In a random sample of 150 French, 4
Varvara68 [4.7K]

Answer:

Yes, there is enough evidence to say the proportions are the same.

Step-by-step explanation:

Null hypothesis: The proportions are the same.

Alternate hypothesis: The proportions are not the same.

Data given:

p1 = 51% = 0.51

n1 = 200

p2 = 48% = 0.48

n2 = 150

pooled proportion (p) = (n1p1 + n2p2) ÷ (n1 + n2) = (200×0.51 + 150×0.48) ÷ (200 + 150) = 174 ÷ 350 = 0.497

Test statistic (z) = (p1 - p2) ÷ sqrt[p(1-p)(1/n1 + 1/n2) = (0.51 - 0.48) ÷ sqrt[0.497(1-0.497)(1/200 + 1/150)] = 0.03 ÷ 0.054 = 0.556

The test is a two-tailed test. At 0.10 significance level the critical values -1.645 and 1.645

Conclusion:

Fail to reject the null hypothesis because the test statistic 0.556 falls within the region bounded by the critical values.

8 0
2 years ago
Choose the option that correctly completes the statement.
Tresset [83]

The answer is:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

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3 years ago
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