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tamaranim1 [39]
4 years ago
15

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?

Mathematics
1 answer:
elena55 [62]4 years ago
5 0
<span>6x2 -5x –3 = 0
a = 6 b=-5 and c=-3

x = [-b +-sq root (b² -4ac)] / 2a
x = [--5 +-sq root (25 -4*6*-3)] / 2*6
x = [5 +- sq root (25 +72)] / 12
x = [5 +- sq root (97)] / 12

x1 = [5 + </span><span><span><span>9.8488578018 </span> </span> </span> ] / 12
x1 = <span> <span> <span> 14.8488578018 </span> </span> </span> / 12
x1 = <span> <span> <span> 1.2374048168 </span> </span> </span>

x2 = [5 - <span> <span> <span> 9.8488578018 </span> </span> </span> ] / 12
x2 = <span> <span> <span> -4.8488578018 </span> </span> </span> / 12
x2 = <span> <span> <span> -0.4040714835 </span> </span> </span>


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Cassandra spends 6.75 hours each day at school.<br> Round the amount of time to the nearest hour.
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6.75 round to 7

Step-by-step explanation:

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A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a stand
Art [367]

Answer:

b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

Subtraction of normal Variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. Sample of 35:

This means that:

\mu_G = 15

s_G = \frac{4.2}{\sqrt{35}} = 0.71

The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Sample of 40:

This means that:

\mu_E = 13.4

s_E = \frac{3.7}{\sqrt{40}} = 0.585

Which of the following best describes the sampling distribution of the difference in mean life span of gas ranges and electric ranges?

Shape is approximately normal.

Mean:

\mu = \mu_G - \mu_E = 15 - 13.4 = 1.6

Standard deviation:

s = \sqrt{s_G^2+s_E^2} = \sqrt{0.71^2+0.585^2} = 0.92

So the correct answer is given by option b.

8 0
3 years ago
If function F is defined by f(x) = 3x^2 + 5, what is f(x-4)
shepuryov [24]

Answer:

The function f(x) when x=x-4 is f(x-4)=3x^2-24x+53  or f(x-4)=3x(x-8)+53

Step-by-step explanation:

Given function f is defined by f(x)=3x^2+5

Now to find the function f(x-4):

f(x)=3x^2+5

Put x=x-4 in the above function we get

f(x-4)=3(x-4)^2+5

f(x-4)=3(x^2-2(x)(4)+4^2)+5 (using the formula (a-b)^2=a^2-2ab+b^2)

f(x-4)=3(x^2-8x+16)+5

f(x-4)=3x^2-24x+48+5 (adding the like terms)

f(x-4)=3x^2-24x+53

f(x-4)=3x(x-8)+53

Therefore f(x-4)=3x^2-24x+53  or f(x-4)=3x(x-8)+53

The function f(x) when x=x-4 is f(x-4)=3x^2-24x+53  or f(x-4)=3x(x-8)+53

4 0
3 years ago
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