Why do we need to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number?

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 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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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: 39 mm

Step-by-step explanation:

1 cm = 10 mm

3.9 cm = 39 mm

I just need to take 3.9 times 10 and you will get 39 mm

Answer:

$41.00

Step-by-step explanation:

To determine the total price of the phone including taxes, we need to first calculate the amount of sales tax by multiplying the price of the phone by the sales tax rate:

Sales tax = Price of phone * Sales tax rate

Sales tax = $39 * 5%

Sales tax = $1.95

Next, we can calculate the total price of the phone including taxes by adding the amount of sales tax to the price of the phone:

Total price including taxes = Price of phone + Sales tax

Total price including taxes = $39 + $1.95

Total price including taxes = $40.95

Rounded to the nearest cent, the total price of the phone including taxes is $41.00.

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 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:

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:

(-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:

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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y= x² - 4 is the function symmetric about the point (0,3).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We need to find the  function's graph is symmetric about the point (0,3)

You want a parabola with a vertex at the point (0,3) so that is symmetrical on each side of that point.

Using the point (0,3),

The equation for a parabola in vertex form and then simplify:

Vertex = (h,k)

Vertex = (0,3)

y = (x - h)² + k

= (x - 0)² +3

y= x² - 4

Hence, y= x² - 4 is the function symmetric about the point (0,3).

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The variables (x, y) have the solution (1, -3) in the system of linear inequality

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In the question given

y ≥ -x + 2 ...eq(i)

y > -5x - 2 ...eq(ii)

Plotting this on a graphing calculator to find the point of intersection which will determine the solution of the graph;

The solutions to the variables (x, y) in the linear inequalities are (1 , -3)

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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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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:

A

Step-by-step explanation:

Answer:

40.2°

Step-by-step explanation:

Based on the correlation coefficient from the technology data given, the data has a strong negative association.

The correlation coefficient is defined as a statistical measure of the strength of a linear relationship that exists between two variables.

The possible range of values for correlation coefficient is from -1.0 to 1.0. This tells us that the values cannot be more than 1.0 nor be less than -1.0.

Thus, a correlation coefficient of -1.0 shows a perfect negative correlation, while a correlation coefficient of 1.0 shows a perfect positive correlation.

We are given a correlation coefficient of r = -0.9478.

Now, the closer the negative correlation is to -1 indicates a strong negative correlation while the farther it is from -1 indicates a weak negative correlation.

Thus, we can conclude that in this case where the  negative correlation is closer to -1 than farther, it can be said to be a strong negative correlation.

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7=x

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

Answer: The two expressions that represent the perimeter of the rectangular pool include the following:

A. x + 3x + 1 + x + 3x + 1

E. 8x + 2

How to calculate the perimeter of a rectangle?

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + x)

Where:

P represents the perimeter of a rectangle.

L represents the length of a rectangle.

x represents the width of a rectangle.

Since the length is 1 more than 3 times the​ width, we have;

Length, L = 3x + 1

Therefore, the two expressions for the perimeter of this rectangle is given by:

P = 2(3x + 1 + x) = x + 3x + 1 + x + 3x + 1

P = 2(4x + 1) = 8x + 2

Next, we would determine the total cost as follows;

P = 8x + 2

P = 8(20) + 2

P = 162 feet.

Total cost = 1.86 × 162

Total cost = $301.32

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Complete Question:

A hotel manager is adding a tile border around the​ hotel's rectangular pool. Let x represent the width of the​ pool, in feet. The length is 1 more than 3 times the​ width, as shown. Find two expressions that represent the perimeter of the pool. Use the expressions to describe two ways to find the perimeter. The length of each tile is 1 foot. If the width of the pool is 20 ​feet, and each tile costs ​$1.86​, what would be the total cost of the tile for the​ border?

A. x + 3x + 1 + x + 3x + 1

B. x + 3x + 1

C. 2x + 3x + 1

D. 8x + 1

E. 8x + 2

F. 4x + 1

Step-by-step explanation:

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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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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The train does not always go the same distance each minute.

Predicted amount of time to travel 30 kilometers is equal to 47.52 minutes.

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the time (in minutes) would be plotted on the x-axis of the scatter plot while the distance (km) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the distance (km) and time (in minutes), a linear equation for the line of best fit is given by:

y = 1.40x + 5.52

Next, we would determine the predicted amount of time to travel 30 kilometers:

y = 1.40(30) + 5.52

y = 42 + 5.52

y = 47.52 minutes.

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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.

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!!!!

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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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:

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 total cost of the skateboard if Loui has to pay a state sale tax of 6. 25% is 72.26.

As per the given data, Loui wants to buy a skateboard that has an original price of 79.91, will be discounted 12 %, and will have a sales tax of 6.25 %.

When performing the calculations, remember to convert percent to decimal form and if needed, round to two decimal places since money must be rounded to the nearest cent.

First, we need to find the amount of the discount and then find the sale price (the price after the discount):

Sale price:

Original price - Amount of discount = 79.91 - 11.9 = 68.01

Now that we have the sale price, we can find the amount of tax and then the total cost:

Amount of tax  = ( sale price) × (sales tax percent)

[tex]$$\begin{aligned}& =\ 68.01 \times \ 0.0625 \\& \approx \ 4.25 \end{aligned}$$[/tex]

Total cost = sale price + amount of tax

= 68.01 +  4.75

= 72.26

Therefore the cost is 72.26.

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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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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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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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