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PtichkaEL [24]
1 year ago
9

State the domain of 1b, then determine the equation of any vertical asymptotes and/or coordinates of any holes in the graph of t

he function.

Mathematics
1 answer:
Katena32 [7]1 year ago
6 0

We have

f(x)=\frac{2x^2+x}{x^2-5x+6}

First we will factorize the function

f(x)=\frac{x(2x+1)}{\mleft(x-2\mright)(x-3)}

The domain is

\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)

In this case, we have two vertical asymptotes

x-2=0

x=2

x-3=0

x=3

ANSWER

The domain is

\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)

The vertical asymtotes

x-2=0

x=2

x-3=0

x=3

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Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorab
Katyanochek1 [597]

Answer:

(a) Customer will not purchase the light bulbs at significance level of 0.05

(b) Customer will purchase the light bulbs at significance level of 0.01 .

Step-by-step explanation:

We are given that Light bulbs of a certain type are advertised as having an average lifetime of 750 hours. A random sample of 50 bulbs was selected,  and the following information obtained:

Average lifetime = 738.44 hours and a standard deviation of lifetimes = 38.2 hours.

Let Null hypothesis, H_0 : \mu = 750 {means that the true average lifetime is same as what is advertised}

Alternate Hypothesis, H_1 : \mu < 750 {means that the true average lifetime is smaller than what is advertised}

Now, the test statistics is given by;

       T.S. = \frac{Xbar-\mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, X bar = sample mean = 738.44 hours

               s  = sample standard deviation = 38.2 hours

               n = sample size = 50

So, test statistics = \frac{738.44-750}{\frac{38.2}{\sqrt{50} } } ~ t_4_9

                            = -2.14

(a) Now, at 5% significance level, t table gives critical value of -1.6768 at 49 degree of freedom. Since our test statistics is less than the critical value of t, so which means our test statistics will lie in the rejection region and we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is smaller than what is advertised and so consumer will not purchase the light bulbs.

(b) Now, at 1% significance level, t table gives critical value of -2.405 at 49 degree of freedom. Since our test statistics is higher than the critical value of t, so which means our test statistics will not lie in the rejection region and we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is same as what it has been advertised and so consumer will purchase the light bulbs.

6 0
3 years ago
Li needs 15 pieces of string each 1/2 of an inch long. she cut a 6 inch piece of string into pieces that are 1/2 of an inch long
Paraphin [41]
3 more hope this helps
4 0
3 years ago
Which expression is equivalent to
lutik1710 [3]

Answer:

\frac{\sqrt[4]{3x^2} }{2y}

Step-by-step explanation:

We can simplify the expression under the root first.

Remember to use  \frac{a^x}{a^y}=a^{x-y}

Thus, we have:

\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}} \\=\sqrt[4]{\frac{3x^{2}}{16y^{4}}}

We know 4th root can be written as "to the power 1/4th". Then we can use the property  (ab)^{x}=a^x b^x

<em>So we have:</em>

<em>\sqrt[4]{\frac{3x^{2}}{16y^{4}}} \\=(\frac{3x^{2}}{16y^{4}})^{\frac{1}{4}}\\=\frac{3^{\frac{1}{4}}x^{\frac{1}{2}}}{2y}\\=\frac{\sqrt[4]{3x^2} }{2y}</em>

<em />

<em>Option D is right.</em>

8 0
4 years ago
Help me please ......
oksano4ka [1.4K]
-4 = x - 7
-4 + 7 = x
3 = x

Therefore x = 3
4 0
3 years ago
10(7k+9p+3) I don’t understand
Llana [10]

Answer:

4=0

Step-by-step explanation:

Simplifying

(-9p + 7) + -1(-9p + 3) = 0

Reorder the terms:

(7 + -9p) + -1(-9p + 3) = 0

Remove parenthesis around (7 + -9p)

7 + -9p + -1(-9p + 3) = 0

Reorder the terms:

7 + -9p + -1(3 + -9p) = 0

7 + -9p + (3 * -1 + -9p * -1) = 0

7 + -9p + (-3 + 9p) = 0

Reorder the terms:

7 + -3 + -9p + 9p = 0

Combine like terms: 7 + -3 = 4

4 + -9p + 9p = 0

Combine like terms: -9p + 9p = 0

4 + 0 = 0

4 = 0

Solving

4 = 0

8 0
3 years ago
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