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2 years ago

Solve the equation (x-3)^3-( x - 1 )^3 + 7x^2 = 7(3x - 4 )

Mathematics

1 answer:

Yakvenalex [24]2 years ago

8 0

Answer:

x= -1 or x = -2

Step-by-step explanation:

Your equation:

(x−3)^3−(x−1)^3+7x^2=7(3x−4)

Step 1: Simplify both sides of the equation.

x^2+24x−26=21x−28

Step 2: Subtract 21x-28 from both sides.

x^2+24x−26−(21x−28)=21x−28−(21x−28)

x^2+3x+2=0

Step 3: Factor left side of equation.

(x+1)(x+2)=0

Step 4: Set factors equal to zero.

x+1=0 or x+2=0

which equals to x=−1 or x=−2

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A chemist examines 15 geological samples for potassium chloride concentration. The mean potassium chloride concentration for the

Lelu [443]

Answer:

95% Confidence interval: (0.375,0.377)

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = 0.376 cc/cubic meter

Sample size, n = 15

Alpha, α = 0.05

Sample standard deviation, s = 0.0012

Degree of freedom =

$=n-1\\=15-1\\=14$

95% Confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at degree of freedom 14 and}~\alpha_{0.05} = \pm 2.145$

$0.376 \pm 2.145(\dfrac{0.0012}{\sqrt{15}} )\\\\ = 0.376 \pm 0.0006\\\\ = (0.3754,0.3766)\approx (0.375,0.377)$

(0.375,0.377) is the required 95% confidence interval for the population mean potassium chloride concentration.

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2 years ago

Which of the following statements about the sampling distribution of the sample mean, x-bar, is not true? A. The sampling distri

Elenna [48]

Answer: E. All of the above statements are true

Step-by-step explanation:

The mean of sampling distribution of the mean is simply the population mean from which scores were being sampled. This implies that when population has a mean μ, it follows that mean of sampling distribution of mean will also be μ.

It should also be noted that the distribution's shape is symmetric and normal and there are no outliers from its overall pattern.

The statements about the sampling distribution of the sample mean, x-bar that are true include:

• The sampling distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough.

• The sampling distribution is normal regardless of the sample size, as long as the population distribution is normal. • The sampling distribution's mean is the same as the population mean.

• The sampling distribution's standard deviation is smaller than the population standard deviation.

Therefore, option E is the correct answer as all the options are true.

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2 years ago

The ratio of M & M’s to raisins in a bag of trail mix is 3:5. If there are 36 M & M’s, how many raisins are there?

Iteru [2.4K]

The correct answer is 60 raisins. To get this answer you will write a proportion of M & Ms to raisins and create and equivalent ratio using the number 36.

After you have the proportion set up, you will use cross products to solve for the number of raisins.

You can also use equivalent ratios to find the number of raisins.

Both of these strategies are shown in the attached picture.