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2 years ago

Determine if 0.515115111511115111115... is rational or irrational and give

1 answer:

7 0

It’s rational, for a number to be rational you have to be able to write it as a fraction and you can write 0.515115111511115111115... as a fraction.

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Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

In-s [12.5K]

Answer:

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis

Step-by-step explanation:

f(x)= $2x^{3}-26x-24$

$2x^{3}-26x-24$ =0

$2x^{3}-26x-24=0\\2x^{3}-2x-24x-24=0\\2x(x^{2} -1)-24(x+1)=0\\2x(x+1)(x-1)-24(x+1)=0\\(x+1)(2x^{2} -2x-24)=0\\=> x+1=0 => x_{1}=-1\\$

$=> 2x^{2} -2x-24=0\\=>2(x^{2} -x-12)=0\\=> x^{2} -x-12=0\\=> x^{2} -4x+3x-12=0\\=> x(x-4)+3(x-4)=0\\=> (x-4)(x+3)=0\\$

$=> x-4=0\\=> x_{2}=4\\=> x+3=0\\=>x_{3}=-3\\$

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis

7 0

2 years ago

Read 2 more answers

Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown. The height is S

Lubov Fominskaja [6]

<h2>Explanation:</h2><h2></h2>

We know that the volume of a prism is defined by:

$V=lwh \\ \\ \\ Where: \\ \\ l:length \\ \\ w:width \\ \\ h:height \\ \\ \\ l=\frac{d-2}{3d-9} \\ \\ w=\frac{4}{d-4} \\ \\ h=\frac{2d-6}{2d-4}$

Substituting values:

$V=\left(\frac{d-2}{3d-9}\right)\left(\frac{4}{d-4}\right)\left(\frac{2d-6}{2d-4}\right) \\ \\ \\ Simplifying: \\ \\ V=\frac{d-2}{3d-9}\cdot \frac{4}{d-4}\cdot \frac{d-3}{d-2} \\ \\ V=\frac{\left(d-2\right)\cdot \:4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)\left(d-2\right)} \\ \\ V=\frac{4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)} \\ \\ V=\frac{4\left(d-3\right)}{3\left(d-3\right)\left(d-4\right)}$

$Finally: \\ \\ \boxed{V=\frac{4}{3\left(d-4\right)}}$

4 0

2 years ago

Read 3 more answers

if the current batch of pills is the first of the day and your goal is to produce a total of 600 what percentage of your goal wi

Zanzabum

Answer:

Step-by-step explanation:

The rest of the question is: There are 75 pills in the batch.

The current batch of pills is the first of the day and our goal is to produce a total of 600.

If there are 75 pills in the batch so percentage of goal completed will be

[(number of pills in the batch)/(Total pills)] * 100

$\frac{75}{600}*100 = 12.5 \%$

≈ 13% to the nearest whole number

7 0

2 years ago

In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed

sleet_krkn [62]

Answer:

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

Step-by-step explanation:

The interpretation of a confidence interval of level x% means that we are x% sure that the interval contains the true mean of the population.

In this problem, we have that:

The population are all the cell phone users.

The 95% confidence interval is (73.1%, 76.9%).

Which of the following is an appropriate interpretation of the 95% confidence interval?

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

3 0

1 year ago

True or false a corollary is a statement that can be easily proved using a theorem

sammy [17]

Answer:

The given statement is true.

Step-by-step explanation:

A corollary is a statement that can be easily proved using a theorem. This statement is true.

A corollary is usually defined as some idea formed from something that is already existing or already been proven.

This is the reason it is not difficult to prove as it has already been proven.

7 0

1 year ago