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2 years ago

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Which number can each term of the equation be multiplied by to eliminate the fractions before solving? m – negative StartFractio

n 3 Over 4 EndFraction m minus StartFraction one-half EndFraction equals 2 StartFraction one-fourth EndFraction m. = 2 + m 2 3 4 5

1 answer:

svetoff [14.1K]2 years ago

7 0

Answer: Each term of the equation can be multiplied by $4$ to eliminate the fractions before solving.

Step-by-step explanation:

Given the following expression:

$-\frac{3}{4}m-\frac{1}{2}=2+\frac{1}{4}m$

You need to simplify before solve it.

Notice that the denominators are different, then you must find the Least Common Denominator (LCD).

Descompose the denominators into their prime factors:

$4=2*2=2^2\\2=2$

Choose $2^2$ , because it has the highest exponent. Then:

$LCD=2^2=4$

Finally you can multiply on both sides by 4 in order to to eliminate the fractions before solving:

$(4)(-\frac{3}{4}m)-(4)(\frac{1}{2})=(4)(2)+(4)(\frac{1}{4}m)\\\\-3m-2=8+m$

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According to a report from a business intelligence company, smartphone owners are using an average of 20 apps per month Assume t

Eddi Din [679]

Answer: 0.547

Step-by-step explanation:

As per given , we have

Population mean = $\mu=20$

Population standard deviation= $\sigma=4$

Sample size : n= 36

We assume that number of apps used per month by smartphone owners is normally distributed.

Let $\overline{x}$ be the sample mean.

Formula : $z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

The probability that the sample mean is between 19.5 and 20.5 :-

$P(19.5$

[using standard normal distribution table for z]

Hence, the required probability = 0.547

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2 years ago

Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?

Lana71 [14]

Answer:

The value of x = - 1 and 2 double root of this function

Step-by-step explanation:

we need to find the value of x which double root of $f(x)=x^{3} -3x-2$

If we replace x with -2 then

$f(-2)=(-2)^{3} -3(-2)-2 = -8+6-2 =-4$

If we replace x with -1 then

$f(-1)=(-1)^{3} -3(-1)-2 = -1+3-2 =0$

If we replace x with 1 then

$f(1)=(1)^{3} -3(1)-2 = 1-3-2 =-4$

If we replace x with 2 then

$f(2)=(2)^{3} -3(2)-2 = 8-6-2 =0$

Hence, the value of x = - 1 and 2 double root of this function

4 0

2 years ago

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27

densk [106]

Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

or

$y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Step-by-step explanation:

Vertex form of equation : $f (x) = a(x - h)^2 + k,$ where (h, k) is the vertex of the parabola.

$y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-\dfrac{13}{2})\\\\=2(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{13}{2})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{1+26}{4})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{27}{4})=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

Hence, the vertex form of the equation is $y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}$

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2 years ago

Read 2 more answers

Twenty-five juniors from a University volunteer to allow their Math GRE test scores to be used in a study. These 25 juniors had

fgiga [73]

Let's start first by writing down the given:
σ = 100
sample mean = 450
sample size = 25

These information, plus the fact that we know that the population is approximately normally distributed, would tell us that we can use the normal distribution curve in analyzing the problem.

A confidence interval of the mean is just a range statistically estimated to contain the population mean. For a 90% confidence interval, we would look at the Z-table and see where 90% of the data falls. We'll notice that it will fall within 1.645 standard deviations of the mean.

Next, we look for the standard error of the mean. This will have a formula
$error= \frac{standard deviation of population}{ \sqrt{N} }$

The standard error would just therefore be equal to
$\frac{100}{ \sqrt{25} }= \frac{100}{5} =20$

Lastly, we just get the product of the standard error and 1.645 and add it to 450 for the maximum value and subtract it to 450 for the minimum value.
$450-20(1.645)=417.1$
$450+20(1.645)=482.9$

ANSWER: 417.1<μ<482.9

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2 years ago

3. Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over the course of

Montano1993 [528]

Answer:

3. Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over the course of

2 hours, 4 times Adrian’s favorite team was ahead by 3 points, and 4 times Adrian’s favorite team was behind

by 4 points. All other times, the two teams were tied.

(a) What is the average score of Adrian’s favorite team relative to its opponent using the observations

Adrian made during the game? Show your work neatly.

(b) Explain what this value means about Adrian’s favorite team’s performance

Step-by-step explanation:

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1 year ago