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1 year ago

The function y = f(x) is graphed below. What is the average rate of change of the

Mathematics

1 answer:

Serjik [45]1 year ago

3 0

The average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

<h3>What is the average rate of change?</h3>

The average Rate of Change of the function f(x) can be calculated as;

$f(x) = \dfrac{f(b) - f(a)}{b-a}$

Interval -3 ≤ x ≤-1

a = -3, b = -1

f(a) = f(-3) = -20

f(b) = f(-1) = 0

Step 2: Find Average

$f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\\\f(x) = \dfrac{f(-1) - f(-3)}{-1-(-3)}\\\\\\f(x) = \dfrac{0 - (-20)}{2}\\\\f(x) = 10$

Therefore, the average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

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According to this diagram, what is tan 67° ?

Zanzabum

Answer:

B. 12/5

Step-by-step explanation:

tan=opp. leg/adj. leg

tan 67= 12/5

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3 years ago

Read 2 more answers

Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mush

tigry1 [53]

Answer:

Sample Space = {(OSI), (OSH), (OEI), (OEH), (MSI), (MSH), (MEI), (MEH)}

Step-by-step explanation:

Given

Salad Meats Dressings

O = Olives S = Shrimp I = Italian

M = Mushroom E = Egg H = Honey mustard

To determine the sample space, we simply select one from each column.

Take for instance, a combination of Olives, Shrimp and Italian will be represented as: OSI

So, the following sample space exists:

Sample Space = {(OSI), (OSH), (OEI), (OEH), (MSI), (MSH), (MEI), (MEH)}

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3 years ago

A business was valued at £80000 at the start of 2013. In 5 years the value of this business raised to £95000. this is equivalent

dedylja [7]

Answer:

20%

Step-by-step explanation:

Value increased in 5 years = £95000 - £80000 = £5000

Value increase in 1 year =5000/5 = 1000

Increase % = (1000/5000 ) * 100 = (1/5) *100 = 20%

6 0

3 years ago

The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room

Alexandra [31]

Answer:

$\bar x = 260.1615$

$\sigma = 70.69$

The confidence interval of standard deviation is: $53.76$ to $103.25$

Step-by-step explanation:

Given

$n =20$

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}$

$\bar x = \frac{5203.23}{20}$

$\bar x = 260.1615$

$\bar x = 260.16$

Solving (b): The standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

$\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}$ $\sigma = \sqrt{\frac{94938.80}{19}}$

$\sigma = \sqrt{4996.78}$

$\sigma = 70.69$ --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

$c =0.95$

So:

$\alpha = 1 -c$

$\alpha = 1 -0.95$

$\alpha = 0.05$

Calculate the degree of freedom (df)

$df = n -1$

$df = 20 -1$

$df = 19$

Determine the critical value at row $df = 19$ and columns $\frac{\alpha}{2}$ and $1 -\frac{\alpha}{2}$

So, we have:

$X^2_{0.025} = 32.852$ ---- at $\frac{\alpha}{2}$

$X^2_{0.975} = 8.907$ --- at $1 -\frac{\alpha}{2}$

So, the confidence interval of the standard deviation is:

$\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }$ to $\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }$

$70.69 * \sqrt{\frac{20 - 1}{32.852}$ to $70.69 * \sqrt{\frac{20 - 1}{8.907}$

$70.69 * \sqrt{\frac{19}{32.852}$ to $70.69 * \sqrt{\frac{19}{8.907}$

$53.76$ to $103.25$

8 0

2 years ago

Four friends go to an amusement arcade.

galben [10]

Answer:

The rule is:

T(x) = 8x + 20

Explanation:

We are given that:

The rule for the amount that one friend pays is:

C(x) = 2x + 5

Now, we know that:

Each of the four friends will pay the entry fee which is $5 per person

The 4 friends will play the same number of games represented by x

This means that:

We can simply get the rule for the total amount to be paid by the four friends (T(x)) by multiplying the amount paid by each friend by 4

This means that:

T(x) = 4 * C(x)

T(x) = 4(2x + 5)

T(x) = 8x + 20

Hope this helps :)

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3 years ago