A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?

The solution for the given equation is, θ = 270°.

What is solving an equation?

Finding an equation's solutions, or the values that satisfy the condition stated by the equation, is known as solving an equation in mathematics. Solutions typically consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

Consider, the given inequality

sinθ = -1

The general solution for sinθ = -1 is

θ = 270° + 360°n

But the condition is,  0° ≤ θ ≤ 360°

Hence, the solution for the given equation is, θ = 270°.

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Answer:

The dividend in the synthetic division below is x+2:

     4 | -6 -5 4 -7

     -   --------------

     -   -1 -1 1 -5

     0 | -5 -4 3 -2

     -   --------------

     2 | x+2

In synthetic division, the numbers in the top row represent the coefficients of the polynomial being divided, and the number in the bottom row represents the value of the dividend. In this case, the dividend is x+2 because it is the only number in the bottom row that is not a result of the division operation

Answer:

Step-by-step explanation:

exponential

The mean and the standard deviation of the distributions are

The distribution is given as:

A uniform continuous model

The mean and the standard deviation of this type of model are

Mean = (a + b)/2

Standard deviation = (b−a)/√12

Using the above formulas, we have

a. U(0, 15)

Mean = (0 + 15)/2 = 7.5

Standard deviation = (15−0)/√12 = 4.3301

b. U(90, 230)

Mean = (90 + 230)/2 = 160

Standard deviation = (230 − 90)/√12 = 40.4145

c. U(4, 92)

Mean = (4 + 92)/2 = 48

Standard deviation = (92 - 4)/√12 = 25.4034

Hence, the standard deviation of U(4, 92) is  25.4034

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Linear regression is a system of plotted points which shows a relationship between two given variables. The required linear equation is: y = 4x.

A graph is a plotted coordinate on a Cartesian plane which shows the relationship between two variables. A system of plotted points in relations to variables that shows a linear relationship is termed linear regression.

In a linear regression, the plotted points can be described by an equation:

y = bx + c

where: y is the dependent variable

            x is the independent variable

            b is the slope of the graph

            c is the intercept

Therefore, considering the given question;

the slope of the graph = [tex]\frac{change in y}{change in x}[/tex]

                = [tex]\frac{12 - 4}{3 - 1}[/tex]

                = [tex]\frac{8}{2}[/tex]

slope of the graph = 4

While there is no intercept, thus intercept is zero.

Therefore, the required equation that shows the relationship between liters of water and number of minutes is:

                       y = 4x

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Answer:

The function f(x) = |x - 3| can be used to determine how far a number x is away from the number 3 on the number line. To find the function value for a given x, we first need to subtract 3 from x and then take the absolute value of the result. For example, if x = 5, then the function value would be f(5) = |5 - 3| = |2| = 2.

The domain of the function is the set of all possible values of x that we can plug into the function to get a real number result. In this case, the function will work for any real number value of x, so the domain of the function is the set of all real numbers, which can be written as:

Domain: (-∞, ∞)

In other words, the function f(x) = |x - 3| can be used to determine how far any real number x is away from the number 3 on the number line.

The degrees of freedom is [tex]12N[/tex]

What is degrees of freedom?

Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.

[tex]\text { Least Common Multiplier of } N, 12: 12 N[/tex]

Find Least Common Multiplier of [tex]$N, 12$[/tex]

Lowest Common Multiplier [tex](LCM)[/tex]

The LCM of [tex]$a, b$[/tex] is the smallest multiplier that is divisible by both [tex]$a$[/tex] and[tex]$b$[/tex]

Factor 12

[tex]$2^2 \cdot 3$[/tex]

Multiply each factor with the highest power:

[tex]12 \mathrm{~N}[/tex]

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The average rate of change in Greenville's population for this six-year period is 35 person per year

What's the math rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.

Given that:

Greenville population = 4,870

Greenville population after 6 years = 5,080

Difference of population = 5080 - 4870 = 210

Average rate = Population / Years = 210/6 = 35 person per year

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Answer:

Could you give a little more context. I can help.

Answer:

Step-by-step explanation:

This in standard form (Ax + By = C.) In order to make this slope-intercept form, you need to isolate y.

y = -1.5x + 2.75

y=mx + b is slope intercept, where m is the slope and b is the y-intercept.

In this case, -1.5 is the slope and 2.75 is the y-intercept.

Hope this helps!!

The total addition of numbers is, 53975687481.

What is addition of numbers?

The other three fundamental arithmetic operations are subtraction, multiplication, and division. Addition is one of these four operations. The total sum or value obtained by adding two whole numbers is the result of the addition.

For the given addition first add the digits on 1st place.

7 + 7 + 7 + 7 + 2 + 2 + 2 + 1 + 8 + 7 + 1 = 51

Take 1 as it is and add 5 on the 10th place numbers.

Now add 10th  place numbers,

6 + 6 + 8 + 8 + 2 + 3 + 4 + 4 + 6 + 6 + 5 = 58

Take 8 as it is and add 5 to the 100th place numbers.

Now, 9 + 9 + 9 + 1 + 2 + 4 + 4 + 0 + 7 + 4  + 5= 54

Take 4 as it is and add 5 to the 1000th place numbers.

Now, 4 + 4 + 4 + 7 + 6 + 7 + 7 + 0 + 1 + 2 + 5 = 47

Take 7 as it is and add 4 to the next addition.

Now, 9 + 6 + 7 + 4 + 8 + 3 + 1 + 2 + 4 + 4 = 48

Take 8 as it is and add 4 to the next addition.

Now, 8 + 7 + 7 + 9 + 7 +  2 + 2 + 4 = 46

Take 6 as it is and add 4 to the next addition.

Now, 7 + 6 + 6 + 2 + 6 + 1 + 3 + 4 = 35

Take 5 as it is and add 3 to the next addition.

Now, 4 + 9 + 4 + 3 + 4+ 3  = 27

Take 7 as it is and add 2 to the next addition.

Now, 7 + 4 + 2 + 4 + 2= 19

Take 9 as it is and add 1 to the next addition.

Now, 9 + 3 + 1 = 13

Take 3 as it is and add 1 to the next number.

4 + 1 = 5.

Now take the last numbers one by one from step by step.

⇒  53975687481

Hence, the total addition of numbers is, 53975687481.

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Answer:

the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).

Step-by-step explanation:

A point (x,y) falls on a line where the constant of proportionality is k if y is equal to k times x. In other words, the equation for the line is y = kx.

Given this, we can determine which of the given points fall on a line where the constant of proportionality is k by evaluating whether the y-coordinate of each point is equal to k times the x-coordinate.

For example, if k = 2, then the point (6,8) falls on the line y = 2x because 8 is equal to 2 times 6. Similarly, the point (3,2) falls on the line y = 2x because 2 is equal to 2 times 3.

On the other hand, the point (6,4) does not fall on the line y = 2x because 4 is not equal to 2 times 6.

Therefore, the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).

Note that if k is not specified, then any of the given points could potentially fall on a line where the constant of proportionality is k, depending on the value of k.

Answer:

30$ per ft^2

Step-by-step explanation:

6.4x-2.1x=129

4.3x=129

x=30

:]

Answer:

(-8.6)

Step-by-step explanation: If you look at a graph and pinpoint the location of (8,-6) by going up 8 and then going to the left 6. so the point of (8.-6) is in the top left box and if we are reflecting over the x-axis and the y-axis the point will be at the lower right box therefore the answer is (-8.6).

The image of triangle ABC under a dilation whose center is A and scale factor is 4 is as follows.

What is dilation?

Dilation involves changing the size of a shape.

Main body:

Assume point P is the center of origin, then we have the following coordinates of ABC

A= (1,0)

B= (-2,0)

C= (0,2)

The scale factor (k) is given as:

K = 4

So, the dilation rule is represented as:

(x, y) = 4 *(x,y)

Using the above dilation rule, the following coordinates represent the image of triangle ABC

A' =(4,0)

B' =(-8,0)

C' =(0,8)

See attachment for the image of the dilation.

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Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.

Given that,

Kristin spends thirty percent of her savings on a watch and sixty percent on a dress.

We have to find what portion of her savings is still available.

We know that,

Kristin spends thirty percent of her savings on a watch.

Sixty percent on a dress.

The money she has a 100%  in that if she spend 30% on watch she get 70% then if she spend 60% on dress she will have 10%

Therefore, Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.

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Answer:hope i helped A. 20% B.45%

A= 40,000/40,000/200000=.2 Or 20%b. 90,000/200000=.45

Step-by-step explanation:

Step-by-step explanation:

this is a college question ?

oh, my dear ...

we start at -426 ft.

swimming upwards reduces depth by adding hight.

so,

-426 + 212 = -214 ft

basically the same method is used as if we would subtract 212 from 426.

so, the diver is currently at -214 ft (214 ft below the surface).

Since y<-0.0005x^2+x+20 and y represents the time in minutes needed to make x cell phone parts, the longest it will take the factory to make 600 cell phone parts will be y=-0.0005(600)^2+600+20

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

A number is a solution to an inequality in x if it can be used to replace x with a statement that is true. Therefore, while 8 is not a solution for example 1, 4, it is. The collection of all solutions makes up the solution set for an inequality.

Wealth inequality, treatment and responsibility disparity, political inequality, life inequality, and membership inequality are the five systems or sorts of social inequality.

In mathematics, larger than symbol (>), less than symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols.

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Answer: y=-7

Step-by-step explanation:

Answer: y=-7

Step-by-step explanation:

Answer:

[tex]\boxed{\tt A. \;y = .613x + 4.142}[/tex]

Step-by-step explanation:

Equation: (y-y_1)=y_2-y_1/x_2-x_1 (x-x_1)

Here,

[tex]\tt (x_1,y_1):(-2,2.9)[/tex]

[tex]\tt (x_2,y_2): (-3.5,2)[/tex]

[tex]\tt y-2.9=\cfrac{(2-2.9)}{(-3-5-(-2))} (x-(-2))[/tex]

[tex]\tt y-2.9=\cfrac{-0.9}{-1.5} (x+2)[/tex]

[tex]\tt y-2.9=0.6(x+2)[/tex]

[tex]\tt y-2.9=0.6x+1.2[/tex]

[tex]\tt y=.613x+4.142[/tex]

___________________

Hope this helps you!

Have a nice day!

Answer:

----------------------------

The other half is:

The answer, considering both halves, is:

or

Answer:

[tex]10 \leq t \leq 20[/tex]

Step-by-step explanation:

Given absolute value inequality:

[tex]1000(-2|t-15|+30) \geq 20000[/tex]

Isolate the absolute value on one side of the equation:

[tex]\implies \dfrac{1000-2|t-15|+30)}{1000} \geq \dfrac{20000}{1000}[/tex]

[tex]\implies -2|t-15|+30 \geq 20[/tex]

[tex]\implies -2|t-15|+30-30 \geq 20-30[/tex]

[tex]\implies -2|t-15|\geq -10[/tex]

[tex]\implies \dfrac{-2|t-15|}{-2}\geq \dfrac{-10}{-2}[/tex]

[tex]\implies |t-15|\leq 5[/tex]

[tex]\textsf{Apply absolute rule:\quad {If} $|u| \leq a, \;a > 0$ \;then\; $-a \leq u \leq a$}[/tex]

[tex]\implies -5 \leq t-15\leq 5[/tex]

Solve both equations:

[tex]\begin{aligned}\underline{\sf Equation\;1} && \underline{\sf Equation\;2}\\t-15 &\geq -5 \quad & t-15& \leq 5\\t-15+15& \geq-5+15 &\qquad t-15+15& \leq 5+15\\t&\geq10 & t &\leq20\end{aligned}[/tex]

Merge the overlapping intervals:

[tex]10 \leq t \leq 20[/tex]

Based on the study, the researcher may develop a hypothesis that smoking is associated with an increased risk of depression.

An explanation that is put up for a phenomena or a group of facts is called a hypothesis. It is a speculative explanation that needs more testing and improvement because it is supported only by a small body of data. A hypothesis is not a tested theory, but rather a point of departure for more research. A hypothesis is examined in scientific study by testing and observationit. The purpose of hypothesis testing is to evaluate the likelihood that the suggested explanation is accurate and to spot any discrepancies or holes in the available data. The act of testing and improving hypotheses is a crucial component of the scientific method since it ensures that scientific ideas are supported by reliable data.

How to solve?

This hypothesis can then be tested through further research, such as conducting a larger study with more participants, or conducting experiments to evaluate the potential mechanisms by which smoking may affect the development of depression.

The researcher may also use statistical methods to analyze the data collected from the study, in order to determine the significance of the relationship between smoking and depression.

If the hypothesis is supported by the evidence, the researcher may conclude that smoking is a risk factor for depression, and may recommend interventions or preventative measures to reduce the risk of depression among smokers.

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Answer:

See below

Step-by-step explanation:

a) The exponential function that models the population in t years after 2000 is of: P(t) = 14300(1.06)^t.

b) The estimate for the population in 2008 is of: 22792.

Considering it's standard format, the increasing exponential function is defined as follows:

P(t) = P(0)(1 + r)^t.

In which the parameters of the function are defined as follows:

Hence the values of these parameters are given as follows:

P(0) = 14300, r = 0.06.

Thus the function is given by:

P(t) = 14300(1.06)^t.

2008 is eight years after 2000, thus the estimate is P(8), which is obtained as follows:

P(8) = 14300 x (1.06)^8 = 22792.

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Answer:

x=4

Step-by-step explanation:

x=4 because when you have 3x+2=14 Subtract 2 from both sides. Then 3x+2−2=14−23x=12. Divide both sides by 3.3x3=123

The value of x in the figure having 3 angles on a line as shown in the image attached below is 28.

The angle is formed by two rays and a common point.

To calculate the value of x using the diagram attached below:

∠AOC+∠COD+∠BOD = 180° because the sum of all the angles on a line is 180°

On substituting the values from the figure,

∠AOC=3x-7

∠COD=55

∠BOD=x+20

∠AOC+∠COD+∠BOD =3x-7+55+x+20

3x-7+55+x+20=180

4x+68=180

4x=112

x=28

Thus, the value of x is 28 for the figure attached below.

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Yes , we can drag fields from the field list to an area box in the pivot table fields pane in order to create a pivot table. Hence , true.

The four sections of the pivot table

are located at the bottom of the PivotTable Field List window.

The fields will appear in the corresponding region of the worksheet's pivot table layout when you drag them into these locations.

Only the fields included in the PivotTable Field List can be moved in Excel 2007. If you try to drag the Promo field onto the pivot table in the screen photo below, the cursor displays an X. The drag-and-drop function is broken.

You can alter a setting in the pivot table options if you'd like to drag the pivot fields onto the worksheet layout.

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The value of x is 13 and value of x in second question is 28, in the angle of line. The angle between a line's inclination and the x-axis's positive direction is known as the inclination.

From first fig :

26° = 2x °

x = 26 / 2 = 13

Second fig :

134° = 4x + 22

x = 134 - 22 / 4 = 28

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3/2 part of the garden is planted by both the sisters.

A division is a process of splitting a specific amount into equal parts.

Given,

Jane's family divided up their garden so that 2/3 of garden will have vegetables.

Jane and her sister will plant2/3 of the vegetable portion of the garden

2/3 is the vegetable portion

In this vegetable portion 2/3 part is of the vegetable portion of the garden

3/2/2/3

3/2×3/2

6/4

3/2

Hence, 3/2 part of the garden is planted by both the sisters.

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