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natita [175]
3 years ago
10

Given that f(x) = 2x2 − 96, find x.

Mathematics
2 answers:
Serhud [2]3 years ago
8 0

Answer:

x=\pm 4\sqrt{3}

Step-by-step explanation:

We have been given an equation f(x)=2x^2-96. We are asked to solve for x.

To solve for x, we will equate our function with 0 as:

2x^2-96=0

2x^2-96+96=0+96

2x^2=96

\frac{2x^2}{2}=\frac{96}{2}

x^2=48

Upon taking square root of both sides, we will get;

\sqrt{x^2}=\pm \sqrt{48}

x=\pm \sqrt{48}

Factor out perfect square from square root:

x=\pm \sqrt{16\cdot 3}

x=\pm \sqrt{4^2\cdot 3}

x=\pm 4\sqrt{3}

Therefore, the solution of our given equation is x=\pm 4\sqrt{3}.

NISA [10]3 years ago
3 0
F(x)=2x(2)−96

Step 1: Add -4x to both sides.

xf+ −4x = 4x−96+ −4x

xf −4x= −96

Step 2: Factor out variable x.

x(f−4)= −96

Step 3: Divide both sides by f-4.

x(f−4)/ f−4 = −96/ f−4

x= −96/f−4

Answer:

x= −96/ f−4

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Which value of x makes x-3/4 +2/3= 17/12 a true statement
NeTakaya

Answer:

34/24

Step-by-step explanation:

x-3/4+2/3=17/12

x-17/12=17/12

X=17/12+17/12

X=34/24

5 0
2 years ago
what is the inverse of the conditional statement: If my mom has to work, then I babysit my little sister.
madam [21]
The inverse of the conditional statement can be made by negating both the hypothesis and the conclusion

The inverse of ur conditional statement is : If my mom does not have to work, then I will not babysit my little sister.
3 0
3 years ago
In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1
Serga [27]

Answer:

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

1999:

20 out of 100 in the bottom third, so:

p_1 = \frac{20}{100} = 0.2

s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04

2001:

10 out of 100 in the bottom third, so:

p_2 = \frac{10}{100} = 0.1

s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03

Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:

H_0: p_1 - p_2 = 0

At the alternative hypothesis, we test if the proportion has been reduced, that is, the subtraction of the proportion in 1999 by the proportion in 2001 is positive. So:

H_1: p_1 - p_2 > 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = p_1 - p_2 = 0.2 - 0.1 = 0.1

s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05

Value of the test statistic:

z = \frac{X - \mu}{s}

z = \frac{0.1 - 0}{0.05}

z = 2

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of at least 0.1, which is the p-value of z = 2.

Looking at the z-table, the p-value of z = 2 is 0.9772.

1 - 0.9772 = 0.0228.

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

5 0
2 years ago
Billy has a die. He rolls the die, and if the result is not even, he rolls the die
PIT_PIT [208]

Answer:

1/4 is the answer.

Step-by-step explanation:

If he has a die then it is 6 sided. He has a 1/2 chance the 1st time that he gets a non-even number. The next time he also has a 1/2 chance of getting an even number so it's 1/2 times 1/2 = 1/4.

4 0
2 years ago
Amanda is going to make up some concrete by
lianna [129]

Answer:

Yes, Amanda has enough materials to make the concrete mix.

Step-by-step explanation:

Total units = 1+3+5

                 = 9

9 units = 630kg

1 unit = 630kg ÷ 9

        = 70kg (Less than 80kg of cement, more than enough)

3 units = 3 × 70kg

           = 210kg (Less than 215kg of sand, more than enough sand)

5 units = 5 × 70kg

           = 350kg (Less than 370kg of gravel, more than enough gravel)

4 0
2 years ago
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