Solve the equation by using square roots. 2 x 2 − 9 = 11

Which expression represents this word phrase? eight less than the quotient of x and 3 x−83 8−x3 x3−8 3x−8

lozanna [386]

Quotient is basically the answer produced when dividing two numbers.

For example, the quotient of 6 and 3 is 2 because when I divide 6 by 3, I get 2.

Eight less than the quotient of x and 3 = $\frac{x}{3} - 8$

3 0

3 years ago

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Each statement describes a transformation of the graph of y = lnx. Which statement correctly describes the graph of y = ln(x - 7

vodomira [7]

Hello!

The parent function, y = ln(x), has a vertical and horizontal translation.

y = ln(x - h) + k | In this equation, h is the vertical shift, and k is the horizontal shift.

If ln(x - k), then the graph is translated right k units.

If ln(x + k), then the graph is translated left k units.

If ln(x) + h, then the graph is translated up h units.

If ln(x) - h, then the graph is translated down h units.

Therefore, the graph of y = ln(x - 7) + 3 is translated 3 units up and 7 units to the right, which is choice D.

7 0

3 years ago

////////////// 3x^2-4-x=0

Lelechka [254]

Answer:= -1

Step-by-step explanation:

7 0

2 years ago

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In a candy mix there are 4 green bars for every 3 red bars.how many red bars are there if there are 200 green bars

Viktor [21]

150 red bars, since 200 divided by 4 equals 50, then 3 x 50 would give u 150 red bars

7 0

2 years ago

The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5. C

Bingel [31]

Answer:

The required 97.5% confidence interval is

$\text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\\text {CI} = 15.5 \pm 2.8412\cdot \frac{0.31}{\sqrt{8} } \\\\\text {CI} = 15.5 \pm 2.8412\cdot 0.1096\\\\\text {CI} = 15.5 \pm 0.311\\\\\text {CI} = 15.5 - 0.311, \: 15.5 + 0.311\\\\\text {CI} = (15.19, \: 15.81)\\\\$

Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces

.

Step-by-step explanation:

The amounts (in ounces) of juice in eight randomly selected juice bottles are:

15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5

Let us first compute the mean and standard deviation of the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be

$\bar{x} = 15.5$

=STDEV(number1, number2,....)

The standard deviation is found to be

$s = 0.31$

The confidence interval for the mean amount of juice in all such bottles is given by

$$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\$

Where $\bar{x}$ is the sample mean, n is the samplesize, s is the sample standard deviation and $t_{\alpha/2}$ is the t-score corresponding to a 97.5% confidence level.

The t-score corresponding to a 97.5% confidence level is

Significance level = α = 1 - 0.975 = 0.025/2 = 0.0125

Degree of freedom = n - 1 = 8 - 1 = 7

From the t-table at α = 0.0125 and DoF = 7

t-score = 2.8412

So the required 97.5% confidence interval is

$\text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\\text {CI} = 15.5 \pm 2.8412\cdot \frac{0.31}{\sqrt{8} } \\\\\text {CI} = 15.5 \pm 2.8412\cdot 0.1096\\\\\text {CI} = 15.5 \pm 0.311\\\\\text {CI} = 15.5 - 0.311, \: 15.5 + 0.311\\\\\text {CI} = (15.19, \: 15.81)\\\\$

Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces.

5 0

3 years ago