(x²+4x+3)/2(x²-10x+25)

the horizontal asymptote when the numerator and the denominator have the same degree (in this case, both of a degree of 2) is ration of the coefficients of the numerator and denominator. In this case, the coefficient for numerator x² is 1, and the coefficient for the denominator 2x² is 2, so the horizontal asymptote is y=1/2=0.5

the vertical asymptote is the x value. the denominator cannot be zero, if x²-10x+25=0, x would be 5, so the vertical asymptote is x=5

this is just one example. There can be others:
(2x²+5x+2)/[(4x-7)(x-5)] for another example, but this example has a second vertical asymptote 4x-7=0 =>x=7/4

5 0

3 years ago

Olivia is making salad dressing. She has ⅞ cup of olive oil. She needs 1/3 cup for the first recipe and ¼ cup for her second rec

suter [353]

Answer:

yes

Step-by-step explanation:

6 0

3 years ago

A textbook company states that the average time a student needs to take a quiz from its book is 30 minutes with a standard devia

faltersainse [42]

Answer:

We conclude that her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company states.

Step-by-step explanation:

We are given;

Population mean; μ = 30 minutes

Population standard deviation; σ = 3 minutes

Sample size; n = 10

Sample mean; x¯ = 25

Significance level = 5% = 0.05

Let's define the hypotheses;

Null hypothesis; H0: μ = 30

Alternative hypothesis: Ha: μ ≠ 30

Let's find the test statistic;

z = (x¯ - μ)/(σ/√n)

z = (25 - 30)/(3/√10)

z = -5.27

From online p-value from z-score calculator attached using, z = -5.27, significance level = 0.05, two tailed hypothesis, we have;

p < 0.00001

This is less than the significance level, and so we will reject the null hypothesis and conclude that Her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated.

8 0

3 years ago

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