A softball team is participating in a tournament where the team will spend three nights at a hotel. Each hotel offers a 50%
discount for the third night. The coach wants to keep the total cost for each player at $225 with an absolute deviation of at
most $25. Write an absolute value of inequality. Use x for the variable.
Hotel Price per night
Hotel A
$80
Hotel B
$105
Hotel C
$75
Hotel D $90
12.5x2251>25

Answer:

[tex]y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]y=-4x-5[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.

The slope of the given equation is -4.

Therefore, the slope of the perpendicular line is ¹/₄.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point (-2, 3) into the point-slope formula to create the equation of the perpendicular line.

[tex]\implies y-3=\dfrac{1}{4}(x-(-2))[/tex]

[tex]\implies y-3=\dfrac{1}{4}(x+2)[/tex]

[tex]\implies y-3=\dfrac{1}{4}x+\dfrac{1}{2}[/tex]

[tex]\implies y=\dfrac{1}{4}x+\dfrac{7}{2}[/tex]

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:

[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:

(-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).

Step-by-step explanation:

A circle with a center of (-1,2) and a radius

of

[tex]2 \sqrt{2} [/tex]

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:

500,000 can be written in expanded form in two different ways:

500,000 = 500,000

500,000 = 5 x 100,000 + 0 x 10,000 + 0 x 1,000 + 0 x 100 + 0 x 10 + 0 x 1

In both cases, the expanded form shows the value of each digit in the number. The first way simply lists the number itself, while the second way breaks down the number into its component parts and shows the value of each digit in relation to the place value it holds in the number.

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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From the given parameters, the area of the triangle is 288m².

How to calculate the area of a triangle?

A triangle is a polygon with three angles, three vertices and three sides whose sum of angles is 180⁰

Let the vertices of the triangle be labelled ABC

/AB/=16m

/BC/=45m

<ABC=127⁰

The given information formed an obtuse angled triangle.

Area of the triangle (A) = [tex]\frac{1}{2}[/tex]ACsinB

Substituting the various values in the formula we have;

A=[tex]\frac{1}{2} *16*45*sin127^{0}[/tex]

simplifying the equation to get;

A=8*45*0.7986

A=287.5088

A=288m²

Therefore, the area of the triangle to the nearest whole number is 288m²

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Answer:

See below

Step-by-step explanation:

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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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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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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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 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]

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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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:

Answer:

30$ per ft^2

Step-by-step explanation:

6.4x-2.1x=129

4.3x=129

x=30

:]

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

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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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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a) The coordinates of the midpoints P and Q are given as follows:

b) The two segments are parallel because they have the same slope.

The midpoints between two points is given by the mean of the coordinates of these two points.

Hence the midpoint P of AB has the coordinates given as follows:

The midpoint Q of AC has the coordinates given as follows:

Parallel segments are segments that have the same slope, that is, the same result of the division of the change in y by the change of x of two points in the segment.

The slopes of PQ and BC are given as follows:

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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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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 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 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:

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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Answer: y=-7

Step-by-step explanation:

Answer: y=-7

Step-by-step explanation:

Answer:

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

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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