Evaluating Expressions with Exponents

What is the value of the expression 3^3+6 x 3 ?

The radical part for both given expressions are √6 and √2

A radical expression is an expression containing a square root.

Given are two expressions, 3√54 and 3√128, we need to find the radical parts for bot,

1) 3√54=

= 3x√9x6

= 3x3√6

= 9√6

2) 3√128 =

= 3√2x2x2x2x2x2x2

= 3x2x2x2√2

= 24√2

The radical parts are the number under square roots.

Hence, The radical part for both given expressions are √6 and √2

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Answer:

-25

Step-by-step explanation:

[tex]-5^2=-25[/tex]

Answer:

1st and 3rd pictures are not functions. 2nd one is a function.

Step-by-step explanation:

Perform the Vertical Line Test by drawing a line in the functions. If they touch the function twice, they are not a functions. However, if the line touches once, it's a function.

The slope of the line shown in this graph is equal to: B. 1/2.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the graph, we have the following points on the line:

Substituting the given points into the formula, we have;

Slope, m = (-2 - (-4))/(2 - (-2))

Slope, m = (-2 + 4)/(2 + 2)

Slope, m = 2/4

Slope, m = 1/2

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Answer:

Step-by-step explanation:

I plotted this graph on Desmos**

When I plotted the line I got (3,-2) as the point where they intercept.

1st Equation Y=3x-11:
x: 0, 1, 2

y: -11, -8, -5

2nd Equation Y=-2x+4:

x: 0, 1, 2

y: 4, 2, 0

(Hopefully these points are right I went along with the graph I plotted, if wrong, I'm sorry.)

The statement that is true about the proportional relationship of the graph is;

C: Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

We are told that the equation c equals one fourth times s. This is expressed as;

c = ¹/₄s

Where;

c is the number bags of cements

s is the number of bags of sands required to make concrete.

We can see that the number of bags of cements is directly proportional to the number of bags of sands required to make concrete.

In this question, the number of bags of sand is the independent variable while the number of bags of cement is the dependent variable.

From the graph attached, we see that the number of bags of sand is on the y-axis, while the number of bags of cement is on the x-axis.

Hence, the correct statement is option (C) Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

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D'après ce que je sais. La pyramide du Louvre (Pyramide du Louvre) est une grande structure de verre et de métal conçue par l'architecte sino-américain I. M. Pei. La pyramide se trouve dans la cour principale (Cour Napoléon) du Palais du Louvre à Paris, entourée de trois pyramides plus petites. La grande pyramide sert d'entrée principale au musée du Louvre. Achevé en 1988 dans le cadre du projet plus large du Grand Louvre, il est devenu un point de repère de la ville de Paris.

Answer:

The ratio is 8:3

Step-by-step explanation:

18 salt shakers and 48 pepper shakers.

Ratio of pepper shakers to salt shakers

48 : 18

Divide each side by 6

48/6 : 18/6

8 : 3

The ratio is 8:3

Answer:a=17

Step-by-step explanation:

3(4a-8)=180

4a-8=60

4(a-2)=60

a-2=15

a=17

Hope this help!!!!

The number of cones that can be made with 5 pounds of ice is calculated to be 30

From the given information, we have the following parameters that can be employed in our computation:

3 snow cones = 0.5 pounds of ice

For 5 pounds of ice, we have the following representations;

(cones, 5)

Using the above information as a guide, we have the following:

Cones : Pounds of ice = Ratio

Substituting the known values in the above equation as follows;

Cones : 5 = 3 : 0.5

Now multiplying the second ratio by 10

So. we have

Cones : 5 = 30 : 5

By comparison, we determine the number of cones as follows;

Cones = 30

Hence, the number of cones is calculated to be 30

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Answer: WIth the discount: $3.56, you do not have enough money, and are $0.56 short.

Step-by-step explanation:

Find 20% of 4.45

(4.45*0.2)= 0.89

Subtract the 20% from 4.45.

4.45-0.89=3.56

$3.56 is more than the $3 you have.

Subtract the $3 you have from the discounted price.

3.56-3.00=0.56

you are $0.56 short.

Yes, your answer is correct.

First Guess:

I believe that it would be correct

Final Answer:

Your answer is correct

Step-by-step explanation:

How to calculate the average:

     In order to find the average, you need to add a group of numbers and then divide by how many numbers there is.

      (((For example: 2, 3, 3, 5, 7, 10 -- That equals 30. Then to find the average, you need to divide (30) by how many numbers there is (6). 30/6=5. The average of this is 5)))

This set of numbers is 63, 53, 20, 10. The current average is 36.5.

Adding 9 to that number makes it equal 155. To find the average, we now have to divide 155 by 5(because thats how many numbers there is.

155/5=31

(Please give brainliest I worked hard)

Answer:

(-1,5), (0,4), and (-6,7)

Step-by-step explanation:

One may enter each point in both equations and solve matematically to find which points satisfy both equations.  But with access to a free, and easy, online graphing utility, it is more illuminating to plot both inequalites to identify the region containing mutual points (faster, also).  The attached plot illustrates the result.  Each inequality adds a shaded area showing the points satisfying the equation.  The color is darkest where the solution areas overlap, as seen in the upper left of the graph.  All points in this area satify both inequalities.  They are:

(-1,5)

(0,4), and

(-6,7)

Of the remaining three, only (2,-3) satifies neither equation.

Answer:

(-1,5), (0,4), and (-6,7)

Step-by-step explanation:

Option (d) is correct. Heteroscedasticity of residuals in regression suggests that there is a non constant variation in the error.

Heteroscedasticity means unequal scatter. In regression analysis, we talk about heteroscedasticity in the context of the residuals or error term. Heteroscedasticity is a systematic change in the spread of the residuals over the range of measured values. Heteroscedasticity is a problem because ordinary least squares regression assumes that all residuals are drawn from a population that has a constant variance that is heteroscedasticity. the residuals should have a constant variance. Heteroscedasticity is also called as heteroskedasticity. It occurs more often in datasets that have a large range between the largest and smallest observed values. This explains Heteroscedasticity.

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The center line, LCL, and UCL for the p chart that would be used for this processing step are 89%, 88.3%, and 89.7%, respectively.

The center line of a p chart is the average yield of good chips during a processing step, and is calculated as follows:

Centerline = average yield of good chips = 89%

The lower control limit (LCL) and upper control limit (UCL) for a p chart are calculated using the following equations:

LCL = average yield of good chips - 3 × standard deviation

UCL = average yield of good chips + 3 × standard deviation

To calculate the standard deviation, we need to know the number of chips per wafer (156 in this case). The standard deviation is calculated using the equation:

standard deviation = √(p × (1 - p) / n)

where p is the average yield of good chips (89% in this case), (1 - p) is the average yield of defective chips (11% in this case), and n is the number of chips per wafer (156 in this case).

Plugging the values for p, (1 - p), and n into the equation gives us:

standard deviation = √(0.89 × 0.11 / 156) = 0.0256

Substituting the standard deviation into the equations for the LCL and UCL gives us:

LCL = 89% - 3 × 0.0256 = 88.3%

UCL = 89% + 3 × 0.0256 = 89.7%

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7=x

I hope i read the question right, but use this to help you!

Answer:

A

Step-by-step explanation:

Answer:

40.2°

Step-by-step explanation:

The prime factorization of 168 is (d) 2³ × 3 × 7

From the question, we have the following expression that can be used in our computation:

Number = 168

Express 168 as the products of numbers

So, we have the following representation

168 = 2 × 2 × 2 × 3 × 7

Express as exponents

168 = 2³ × 3 × 7

Hence, the prime factorization is 2³ × 3 × 7

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[tex]\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{w}{4}~~ = ~~\cfrac{2}{~~1 \frac{2 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{2}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{\frac{2}{1}}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}=\cfrac{2}{1}\cdot \cfrac{3}{5} \\\\\\ \cfrac{w}{4}=\cfrac{6}{5}\implies 5w=24\implies w=\cfrac{24}{5}\implies {\Large \begin{array}{llll} w=4\frac{4}{5} \end{array}}[/tex]

Answer:

177 - 51i

Step-by-step explanation:

[tex](-5+ i)(12- i)(-3).[/tex]

[tex](-5+ i)(12- i)[/tex]

[tex]-5X12-5(-i)[/tex]+[tex](-i)X12+(i)[/tex][tex](-i)[/tex]

[tex]-60+5i+12i-1i^{2}[/tex]

[tex]-60+5i+12i-1(-1)[/tex]

[tex]-59+17i\\(-59+17i)(-3)\\177-51i[/tex]

Hope it helps u:)

Answer:

[tex]177 - 51i[/tex]

Step-by-step explanation:

Given expression:

[tex](-5+i)(12-i)(-3)[/tex]

Use the FOIL method to multiply the first two parentheses:

[tex]\implies \left(-5 \cdot 12 -5 \cdot -i +i \cdot 12 + i \cdot -i\right)(-3)[/tex]

[tex]\implies \left(-60 +5i +12i -i^2\right)(-3)[/tex]

[tex]\implies \left(-60 +17i -i^2\right)(-3)[/tex]

Multiply:

[tex]\implies -60 \cdot -3 +17i \cdot -3 -i^2 \cdot -3[/tex]

[tex]\implies 180-51i+3i^2[/tex]

Apply the imaginary number rule:  i² = -1

[tex]\implies 180-51i+3(-1)[/tex]

Simplify:

[tex]\implies 180-51i-3[/tex]

[tex]\implies 177-51i[/tex]

The correct answer is (C) Prediction values are meaningful only for X-values in (or close to the range of the original data.

A regression line is a statistical model that is used to make predictions about the value of a dependent variable (Y) based on the value of an independent variable (X). The regression line is based on a sample of data, and it is typically used to make predictions about the population from which the sample was drawn.

The validity of the predictions made using a regression line depends on the assumptions that were used to create the model. One of these assumptions is that the relationship between X and Y is linear, which means that the predictions are only meaningful for X-values that are within (or close to) the range of the original data. If the X-value is outside this range, the prediction may not be accurate because the model may not accurately represent the underlying relationship between X and Y.

Therefore, to provide meaningful predictions for Y, the values of X should be within (or close to) the range of the original data.

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The new expression is written as a single logarithm with a coefficient of 1 is [tex]\log\left(\frac{125u^3v^6}{w^9}\right)[/tex] .

A mathematical formula known as a logarithm determines how many times the base, or initial number, must be multiplied by itself in order to arrive at the desired result. This indicates that the exponent to which b is raised to obtain a number x is the logarithm of x to the base b.

The property of the logarithm used to calculate the given expression is

[tex]\log a^b=b\log a[/tex]

Then, the new expression is written as,

[tex]\begin{aligned}3\log \left(\frac{5 uv^2}{w^3}\right)&=\log\left(\frac{5 uv^2}{w^3}\right)^3\\&=\log\left(\frac{125u^3v^6}{w^9}\right)\end{aligned}[/tex]

In the above expression, the coefficient is 1. Therefore, the required answer is found to be [tex]\log\left(\frac{125u^3v^6}{w^9}\right)[/tex].

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The team won 24 games out of the 32 they played.

A ratio is an ordered pair of numbers a and b, written a / b in which b does no longer equal 0. A proportion is an equation wherein two ratios are set the same for every other. In arithmetic, a ratio suggests how commonly one wide variety contains every other. as instance, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 to 6 (this is, eight:6, that is equivalent to the ratio four: three).

The share system is used to depict if two ratios or fractions are the same. we are able to locate the lacking fee by using dividing the given values. the share components can be given as a: b::c : d = a/b = c/d, where a and d are the extreme phrases and b and c, are the suggested phrases.

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The exact length of the curve is [tex]\frac{1}{216}[145^{\frac{3}{2} } -1][/tex].

The given equation is [tex]$y=1+8 x^{\frac{3}{2}}$[/tex].

The point is [tex]$$0 \leq x \leq 1$.[/tex]

Arc length: To find the arc length of the function y=f(x), use the power rule. After that use the integration.

Let  f(x)  be a smooth function over the interval [a,b] . Then the arc length of the portion of the graph of  f(x)  from the point (a, f(a))  to the point (b, f(b))  is given by

The formula of the arc length is: [tex]$=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2}$[/tex]

Differentiate this equation

[tex]$$\begin{aligned}& y^{\prime}=8 \frac{\mathrm{d}\left(x^{\frac{3}{2}}\right)}{\mathrm{d} x} \\& =8 \frac{3}{2} x^{\frac{1}{2}} \\& =12 \sqrt{x}\end{aligned}$$[/tex]

Now, find the arc-length.

[tex]$$\begin{aligned}& \text { Arc-length }=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2} \\& =\int_0^1 \sqrt{1+144 x}\end{aligned}$$[/tex]

Use the substitution method.

[tex]$$\begin{aligned}& u=1+144 x \\& d x=\frac{1}{144} d u \\& =\frac{1}{144} \int_1^{145} \sqrt{u} d u \\& =\frac{1}{144}\left[\frac{u^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^{145} \\& =\frac{1}{216}\left[145^{\frac{3}{2}}-1\right]\end{aligned}$$[/tex]

Hence, the exact length is [tex]\frac{1}{216}\left[145^{\frac{3}{2}}-1\right][/tex].

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y=x is the equation of line parallel to y=x-8 which passes through (7, 7).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the equation of line parallel to y=x-8 and assing through the point (7, 7).

The slope of parallel lines is same.

So the slope is 1.

Now let us find the equation of the parallel line.

To find this we need to find the y intercept.

7=7+b

b=0

The equation of line is y=x

Hence, the equation of line parallel to y=x-8 and passing through (7, 7) is y=x.

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g sio2 is always 0.4 mg too high regardless of the weight of the sample taken for analysis. The relative error in parts per thousand would be 400.

This is because the relative error is calculated by taking the difference between the actual value and the measured value, and dividing this by the actual value.

In this case, the actual value is 0.4 mg and the measured value is

0.4 mg + (10% x 0.4 mg) = 0.44 mg. Thus the relative error is

(0.44 – 0.4)/0.4 = 0.1/0.4 = 0.25 = 400 parts per thousand.

The relative error in parts per thousand would be 400.

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When the probability distribution of x, where x is the number of times a college graduate changed majors where P(0) = 0.135, P(1) = 0.271, P(2) = 0.271, P(3) = 0.180, P(4) = 0.090, P(5) = 0.036, P(6) = 0.012, P(7) = 0.003 and P(8) = 0.002, the probability that a randomly selected college graduate has changed majors more than two times is 0.323.

Therefore, the answer is 0.323.

The probability that a randomly selected college graduate has changed majors more than two times is obtained by

P( x > 2) = P(3) + P(4) + P(5) + P(6) + P(7) + P(8)

P(x > 2) = 0.180 + 0.090 + 0.036 + 0.012 + 0.003 + 0.002

P(x > 2) = 0.323

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Answer: The ordered pair that represents the location of vertex A after the dilation is (-40, 35).

Step-by-step explanation:

How do we dilate a figure with the origin as the center of dilation?

To dilate a figure with the origin as the center of dilation, we multiply the coordinates of each point by the scale factor. This has the effect of stretching or shrinking the figure, depending on whether the scale factor is greater than or less than 1.

To dilate a figure by a scale factor of 5 with the origin as the center of dilation, we need to multiply the x- and y-coordinates of each point in the figure by 5.

So, to find the coordinates of vertex A after the dilation, we start with the coordinates of vertex A before the dilation, which are (-8, 7).

Then, we multiply the x-coordinate by 5 to get (-8)5 = -40, and we multiply the y-coordinate by 5 to get (7)5 = 35.

Vertex A is located at (-8, 7). If we multiply these coordinates by 5, we get (-40, 35). Therefore, the coordinates of vertex A after the dilation are (-40, 35).

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After the dilation, the ordered pair that depicts where vertex A is located is (-40, 35).

How can we increase a figure so that the origin serves as the dilation center?

We multiply the coordinates of each point by the scale factor to dilate a figure with the origin as the center of dilation. Depending on whether the scale factor is larger than or less than 1, this has the effect of either expanding or shrinking the figure.

The x- and y-coordinates of each point in the figure must be multiplied by 5 in order to dilate it by a scale factor of 5, with the origin serving as the centre of dilation.

Thus, we begin with the coordinates of vertex A before the dilation, which are, in order to obtain the coordinates of vertex A after the dilation (-8, 7).

The x-coordinate is then multiplied by 5 to get (-8)5 =-40, while the y-coordinate is multiplied by 5 to get (7)5 = 35.

Vertex A can be observed at (-8, 7). These coordinates are multiplied by 5 to get (-40, 35). As a consequence, vertex A's coordinates after dilation are (-40, 35).

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Answer:

x = [tex]\frac{36}{5}[/tex]

Step-by-step explanation:

7 + [tex]\frac{x}{3}[/tex] = 2x - 5 ( subtract 7 from both sides )

[tex]\frac{x}{3}[/tex] = 2x - 12 ( multiply through by 3 to clear the fraction )

x = 6x - 36 ( subtract 6x from both sides )

- 5x = - 36 ( divide both sides by - 5 )

x = [tex]\frac{-36}{-5}[/tex] = [tex]\frac{36}{5}[/tex] = 7.2 ( in decimal form )