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2 years ago

If f(x) = 2x^2 + 1 and g(x) = 3x - 2, what is the value of f(g(-2))?

Mathematics

1 answer:

makkiz [27]2 years ago

6 0

If f(x) = 2x^2 + 1 and g(x) = 3x - 2, what is the value of f(g(-2))?
1) -127
2) -23
3) 25
4) 129

the answer is d

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Consider triangle ABC. The legs have a length of 5 units each. What is the length of the hypotenuse of the triangle?

Korvikt [17]

Answer:

$5\sqrt{2}$ units.

Step-by-step explanation:

We have been given that two legs of triangle ABC measures 5 units each. We are asked to find the length of the hypotenuse.

We will use Pythagoras theorem to solve for the hypotenuse of triangle ABC.

$\text{Hypotenuse}^2=\text{Leg}^2+\text{Leg}^2$

Substituting our given values in above equation we will get,

$\text{Hypotenuse}^2=5^2+5^2$

$\text{Hypotenuse}^2=25+25$

$\text{Hypotenuse}^2=50$

Upon taking square root of both sides of our equation we will get,

$\text{Hypotenuse}=\sqrt{50}$

$\text{Hypotenuse}=\sqrt{25*2}$

$\text{Hypotenuse}=5\sqrt{2}$

Therefore, the length of hypotenuse of triangle ABC is $5\sqrt{2}$ units.

6 0

2 years ago

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The scatter plot below shows the relationship between the diameter (x), in mm, and mass f(x), in grams, of a berry: ordered pair

ivann1987 [24]

For this case the first thing we must observe is that the mass increases 0.4 grams when the diameter increases 1 millimeter.
Therefore, the slope of the line is given by:
m = 0.4
Thus, the function that best suits the table is given by:
f (x) = -4 + 0.4x
For example, for x = 20 we have:
f (20) = -4 + 0.4 (20)
f (20) = -4 + 8
f (20) = 4
The result, matches the table.
Answer:
The function that is best represented by the scatter plot is:
f (x) = -4 + 0.4x

6 0

3 years ago

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Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of

tia_tia [17]

Answer:

Using a formula, the standard error is: 0.052

Using bootstrap, the standard error is: 0.050

Comparison:

The calculated standard error using the formula is greater than the standard error using bootstrap

Step-by-step explanation:

Given

Sample A Sample B

$x_A = 30$ $x_B = 50$

$n_A = 100$ $n_B =250$

Solving (a): Standard error using formula

First, calculate the proportion of A

$p_A = \frac{x_A}{n_A}$

$p_A = \frac{30}{100}$

$p_A = 0.30$

The proportion of B

$p_B = \frac{x_B}{n_B}$

$p_B = \frac{50}{250}$

$p_B = 0.20$

The standard error is:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}$

$SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}$

$SE_{p_A-p_B} = \sqrt{0.00274}$

$SE_{p_A-p_B} = 0.052$

Solving (a): Standard error using bootstrapping.

Following the below steps.

Open Statkey
Under Randomization Hypothesis Tests, select Test for Difference in Proportions
Click on Edit data, enter the appropriate data
Click on ok to generate samples
Click on Generate 1000 samples ---- <em>see attachment for the generated data</em>

From the randomization sample, we have:

Sample A Sample B

$x_A = 23$ $x_B = 57$

$n_A = 100$ $n_B =250$

$p_A = 0.230$ $p_A = 0.228$

So, we have:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}$

$SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}$

$SE_{p_A-p_B} = \sqrt{0.002475064}$

$SE_{p_A-p_B} = 0.050$

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2 years ago

One year, the population of a city was 64,000. Several years later it was 53,120. Find the percent decrease.

ohaa [14]

Answer:

17% i think

Step-by-step explanation:

4 0

1 year ago

What is the domain of the function f(x)=45/(x-23)?

galben [10]

Domain is the set of numbers you can use
usually, domain=all real numbers except those that divide by zero

so find those exceptions
find what numbers make deonenator equal to 0 and exclude them
x-23 is denom
x-23=0
x=23

doman is all real numbers except 23

5 0

3 years ago

Read 2 more answers