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Helen [10]
3 years ago
8

A farmer is tracking the amount of wheat his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 75 models

the crops in pounds per acre over x years. Find and interpret the average rate of change from year 5 to year 15.
Mathematics
2 answers:
mr_godi [17]3 years ago
6 0

Answer:

Average rate of change: 0

Interpretation: No increment in yield from year 5 to year 15.

Step-by-step explanation:

The function that models the yield is:

f(x)=-x^2+20x+75

f(15)=-(15)^2+20(15)+75=150

f(5)=-(5)^2+20(5)+75=150

The average rate of change  of f(x) from x=a to x=b is given by the formula;

AOC=\frac{f(b)-f(a)}{b-a}

The average rate of change from year 5 to year 15 is:

\frac{f(15)-f(5)}{15-5}

\frac{150-150}{15-5}

\frac{0}{10}=0

Interpretation: There has not been any increment in yield from year 5 to year 15.

lesantik [10]3 years ago
3 0

Answer:

the answer is The crop yield did not change from year 5 to year 15

Step-by-step explanation:

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Home Videos Inc. surveys 450 households and finds that the mean amount spent for renting or buying videos is P135 a month and th
adell [148]

SOLUTION:

Case: Hypothesis testing

Step 1: Null and Alternative hypotheses

\begin{gathered} H_0:\mu=P127.50 \\ H_1:\mu\leq P127.50 \end{gathered}

Step 2: T-test analysis

\begin{gathered} t=\frac{\hat{x}-\mu}{\frac{s}{\sqrt{n}}} \\ t=\frac{135-127.5}{\frac{75.25}{\sqrt{450}}} \\ t=2.144 \end{gathered}

Step 3: t-test with the significance level

\begin{gathered} t_{\alpha}=? \\ \alpha=0.05 \\ From\text{ }tables \\ t_{0.05}=1.654 \end{gathered}

Step 4: Comparing

t>t_{\alpha}

So tail to reject the null hypothesis. There is enough evidence at a 0.05 level of significance to claim that the mean spent is greater than P127.50.

Final answer:

Yes, there is evidence sufficient to conclude that the mean amount spent is greater than P127.50 per month at a 0.05 level of significance.

6 0
1 year ago
Find the slope of the line below using rise/run.<br>​
QveST [7]

Answer:

A, 2/3

Step-by-step explanation:

you rise 2 and run 3

6 0
3 years ago
Read 2 more answers
Please help me! Need answer quick!
aksik [14]

Let h = height of triangle


h^2 + 12^2 = 15^2


h^2 + 144 = 225


h^2 = 225 - 144



h^2 = 81


sqrt{h^2} = sqrt{81}


h = 9 cm


For part B, we need to find surface area because it represents the perimeter of this 3-D figure. The formula needed is SA = B + LA.


1. First find the lateral area.


LA = perimeter of triangle • height


LA = ph


p = 15 + 15 + 24


p = 30 + 24


p = 54 cm


LA = (54)(9)


LA = 486 cm^2


2. We now find the base of each triangle. This is found by finding the area of each triangle and multiplying by 2.


A = (1/2)bh


A = (1/2)(24)(9)


A = 108 cm^2


A = 2•108 cm^2


A = 216 cm^2 = our B in the surface area formula.


SA = B + LA


SA = 216 cm^2 + 486 cm^2


SA = 702 cm^2


The amount of cardboard needed is 702 cm^2.






6 0
3 years ago
A scale model of a rectangular building lot measures 7feet by 5 feet. If the actual house will be built using a scale factor of
Tamiku [17]
Actual area of the rectangular building = 5040 feet²
Step-by-step explanation:
Length of the rectangular building = 7 feet
Width of the rectangular building = 5 feet
Now, The building is made with a scale factor of 12
So, Actual length of the rectangular building = 84 feet
Actual width of the rectangular building = 60 feet
Now, Actual area of the rectangular building = Length × Width
⇒ Actual area of the rectangular building = 84 × 60
⇒ Actual area of the rectangular building = 5040 feet²
5 0
2 years ago
2)
Elenna [48]

Parallel lines are in the same plane, never intersect, and have the same slope.

7 0
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