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2 years ago

Mathieu is finding the x-intercepts of the function f(x) = x2 + 4x + 3. His work is shown below

Mathematics

2 answers:

Alex_Xolod [135]2 years ago

7 0

Answer:

I can't see Mathieu's work but I will show the right steps and maybe you can find where Mathieu went wrong.

f(x)=x^2+4x+3

f(x)=(x+3)(x+1) Since 3*1=3 and 3+1=4

The x-intercepts can be found by setting y to 0 and solving for x

(in other words replace that f(x) thing with 0 and solve for x)

0=(x+3)(x+1)

Now set both factors equal to 0

x+3=0 or x+1=0

x =-3 x=-1

The x-intercepts are at (-3,0) and (-1,0)

Xelga [282]2 years ago

5 0

Answer:

The answer is C

Step-by-step explanation:

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Consider the following function. f(x) = 2/x, a = 1, n = 2, 0.6 ≤ x ≤ 1.4 (a) Approximate f by a Taylor polynomial with degree n

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Answer:

Step-by-step explanation: please go through the attached file for detailed explanation .

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2 years ago

Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Se

Ugo [173]

Answer:

a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 175$

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that $p = 0.467$ . So

$\mu = E(X) = np = 175*0.467 = 81.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6$

This probability, using continuity correction, is $P(X \geq 85 - 0.5) = P(X \geq 84.5)$ , which is 1 subtracted by the pvalue of Z when X = 84.5. So

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

$Z = \frac{84.5 - 81.725}{6.6}$

$Z = 0.42$

$Z = 0.42$ has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is $P(80 - 0.5 \leq X < 90 - 0.5) = P(79.5 \leq X \leq 89.5)$ , which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

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

$Z = \frac{89.5 - 81.725}{6.6}$

$Z = 1.18$

$Z = 1.18$ has a pvalue of 0.8810.

X = 79.5

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

$Z = \frac{79.5 - 81.725}{6.6}$

$Z = -0.34$

$Z = -0.34$ has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that $p = 0.063$

$\mu = E(X) = np = 175*0.063 = 11.025$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141$

This probability, using continuity correction, is $P(X < 12 - 0.5) = P(X < 11.5)$ , which is the pvalue of Z when X = 11.5. So

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

$Z = \frac{11.5 - 11.025}{3.2141}$

$Z = 0.15$

$Z = 0.15$ has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that $p = 0.227$

$\mu = E(X) = np = 175*0.227 = 39.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54$

Using continuity correction, this probability is $P(X \leq 55 + 0.5) = P(X \leq 55.5)$ , which is the pvalue of Z when X = 55.5. So

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

$Z = \frac{55.5 - 39.725}{5.54}$

$Z = 2.85$

$Z = 2.85$ has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

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2 years ago

Think about the commutative property of real number operations as it applies to addition and subtraction of functions how do you

kati45 [8]

The question does not make sense.
The commutative property applies to addition and multiplication, not addition and subtraction.
The commutative property does not apply to subtraction or division because in those operations, the order of the numbers makes a difference, whereas in addition and subtraction the order does not make a difference.

For example:

Addition
5 + 4 = 9
4 + 5 = 9
5 + 4 = 4 + 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to addition.

Multiplication
5 * 4 = 20
4 * 5 = 20
5 * 4 = 4 * 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to multiplication.

Subtraction
5 - 4 = 1
4 - 5 = -1
5 - 4 is not equal to 4 - 5
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to subtraction.

Division
5/4 = 1.25
4/5 = 0.8
1.25 is not equal to 0.8.
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to division.

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Not sure if this is right or not, but I chose 125.11 after I typed in the equation, haven’t used R-value at all. Will comment if correct — APEX

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earnstyle [38]

Hello, there!

5/4 = 1.25

So, we know that the answer is not A or B.

1.25 = 125%

Now, we know that the answer is not D ether.

So, the answer must be C.

I hope I helped!

Let me know if you need anything else!

~ Zoe

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