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3 years ago

Find the average rate of change for the given function on the given interval.

Mathematics

2 answers:

adoni [48]3 years ago

7 0

The average rate of change is (f(3)-f(0))/3=(7-0)/3=7/3.

shutvik [7]3 years ago

3 0

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\
f(x)=2^x-1 \qquad 
\begin{cases}
x_1=0\\
x_2=3
\end{cases}\implies \cfrac{f(3)-f(0)}{3-0}
\\\\\\
\cfrac{[2^3-1]~~-~~[2^0-1]}{3}\implies \cfrac{[8-1]~~-~~[1-1]}{3}
\\\\\\
\cfrac{7-0}{3}\implies \cfrac{7}{3}$

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What are the steps to solve for x?<br><br> x+ax=b

melisa1 [442]

Answer:

$\displaystyle x = \frac{b}{1 + a}$

General Formulas and Concepts:

<u>Algebra I</u>

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Terms/Coefficients

Factoring

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

<em /> $\displaystyle x + ax = b$

<u>Step 2: Solve for </u><u><em>x</em></u>

Factor: $\displaystyle x(1 + a) = b$
[Division Property of Equality] Divide 1 + a on both sides: $\displaystyle x = \frac{b}{1 + a}$

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3 years ago

2(4x + 1) - 3 = ax + b

White raven [17]

Answer:

Step-by-step explanation:

a=8-1/x-b/x

b=8x-1-ax

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3 years ago

Which is the graph of g(x) = ⌈x + 3⌉? On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The

Furkat [3]

Answer:

see the attachment

Step-by-step explanation:

The ceiling of numbers between -1 and 0 (not including -1) will be 0. Adding 3 to that moves the segment up to y = 3. Hence, the last graph is the appropriate one.

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3 years ago

Read 2 more answers

Three fair coins are flipped. What is the probability that at least 2 of them come up heads?

exis [7]

Answer:

<h3>The probability that atleast 2 of them come up heads is 0.5</h3><h3>∴ P(A)=0.5</h3>

Step-by-step explanation:

Given that three fair coins are flipped.

<h3>To find the probability that at least 2 of them come up heads:</h3>

Sample space for the given event is

$S={\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}\}$

Let A be the events of getting atleast 2 Heads and is given by

A = {HHH, HHT, HTH, THH}

Probability of Getting atleast 2 Heads in 3 Coin Tosses is

$P(A)=\frac{n(A)}{n(S)}$

$P(A)=\frac{4}{8}$

$=0.5$

<h3>∴ P(A)=0.5</h3><h3>∴ the probability that atleast 2 of them come up heads is 0.5</h3>

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3 years ago

The adrenaline concentrations of all sparrows in a county are normally distributed with a mean of 0.3 gram and a standard deviat

Lorico [155]

Answer:

77.45% of the sparrows, taken 10 at a time, have mean concentration between 0.28 and 0.33 gram.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

The adrenaline concentrations of all sparrows in a county are normally distributed with a mean of 0.3 gram and a standard deviation of 0.02 gram. This means that $\mu = 0.3, \sigma = 0.02$ .