Find domains of the following expressions.
sqrt(2-3x)+sqrt(5-x)

Step-by-step explanation:

Bob's points per game are

5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15

Calculating Median:

As the median is the middle number in a sorted list of numbers when there is an odd number of terms.

As the the total number of terms = 37

Therefore, the median is the center term which is 10.

5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15

Calculating Range:

As the given data

5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15

The range is the difference between the highest and lowest values in the data set.

The lowest value is 5

The highest value is 15

The range = 15 - 5 = 10

Calculating the interquartile range (IQR)

The interquartile range is the difference between the third and first quartiles.

So, the bottom half is

5   7   7   7   8   8   8   8   8   9   9   9   9   9   10   10   10   10  

The median of these numbers is 8.5

So, the upper half is

10   11   11   11   11   11   12   12   12   12   13   13   13   14   14   14   15   15  

The median of these numbers is 12

As

The third quartile is 12

The first quartile is 8.5

Therefore,

The interquartile range = 12 - 8.5 = 3.5

Finding Mode

As the given data

5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15

The mode of a set of data is the value in the set that occurs most often.

So, It is bimodal.

Therefore, the mode is 10.

Finding Mean

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

[tex]Mean=Sum\:of\:terms\:\div Number\:of\:terms[/tex]

[tex]Sum\:of\:terms\:=\:385[/tex]

[tex]Number\:of\:terms\:=\:37[/tex]

[tex]Mean\:=\:\frac{385}{37}=10.4[/tex]

Determining whether the data is symmetrical or non-symmetrical

The data is non-symmetric, they do not have about the same shape on either side of the middle. In other words, if you fold the histogram in half, it does not look about the same on both sides. Please check the histogram attached below.

Calculating Mean Absolute Deviation

The mean deviation is a measure of dispersion, A measure of by how much the values in the data set are likely to differ from their mean.

As the given data

5, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15

Population size = 37

[tex]Mean=10.4[/tex]

Mean Absolute Deviation (MAD): 2.0

Keywords: mode, median, mean, non-symmetrical data, range, Interquartile Range (IQR)

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Answer: yes

Step-by-step explanation: the expressions are equivalent because they both simplify to 11x^2 +3y

Yes, the expressions  [tex]8x^2 + 3(x^2 + y) and 7x^2 + 7y + 4x^2-4y[/tex]-  are equivalent.

To see the equivalence, we can simplify both expressions.

Start with the first expression: [tex]8x^2 + 3(x^2 + y)[/tex].

Distribute the 3 inside the parentheses: [tex]8x^2 + 3x^2 + 3y[/tex].

Now, combine like terms: [tex]11x^2 + 3y[/tex].

Now, let's simplify the second expression: [tex]7x^2 + 7y + 4x^2 - 4y[/tex].

Combine like terms: [tex]7x^2 + 4x^2 + 7y - 4y[/tex], which also results in [tex]11x^2 + 3y[/tex].

Both expressions simplify to the same form, [tex]11x^2 + 3y[/tex], which demonstrates their equivalence.

The coefficients and variables are the same in both expressions, just arranged differently, but they yield the same result when simplified.

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Answer:

e=-2

Step-by-step explanation:

9e-7=7e-11

9e-7e-7=-11

2e-7=-11

2e=-11+7

2e=-4

e=-4/2

e=-2

Answer:

e=2

Step-by-step explanation:

9m = 6.48

Divide both sides by 9:

m = 0.72

19m = 13.68

Divide both sides by 19:

m = 0.72

So a one minute call costs 72 cents. We can now set up an equation like this:

c = 0.72m

Answer:

He have 15 action games and 24 sports games.

Step-by-step explanation:

Given:

Ryan has a mix of action and sports games for a total of 39 video games his action collection is three more than half his sports collection.

Now, to find the number of action games and sports games.

Let the sports games be [tex]x.[/tex]

As, given his action collection is three more than half his sports collection.

Thus, the action games = [tex]3+\frac{x}{2}[/tex] .

Total number of video games = 39.

So, we set an equation to get the number of action games and sports games:

[tex]x+(3+\frac{x}{2})=39[/tex]

[tex]x+3+\frac{x}{2} =39[/tex]

Subtracting both sides by 3 we get:

[tex]x+\frac{x}{2} =36[/tex]

[tex]\frac{2x+x}{2}=36[/tex]

[tex]\frac{3x}{2} =36[/tex]

Multiplying both sides by 2 we get:

[tex]3x=72[/tex]

Dividing both sides by 3 we get:

[tex]x=24.[/tex]

The sports games he have = 24.

Now, to get the action games we substitute the value of [tex]x[/tex]:

[tex]3+\frac{x}{2}[/tex]

= [tex]3+\frac{24}{2}[/tex]

= [tex]3+12[/tex]

= [tex]15.[/tex]

The action games he have = 15.

Therefore, he have 15 action games and 24 sports games.

The problem involves a basic algebraic system of equations. By defining variables, setting up the equations based on the problem statement, and solving the system, it is found that Ryan has 24 sports games and 15 action games.

This is a problem related to the field of algebra in mathematics. To find the answer, we first need to assign variables: let's denote the number of sports games as 's' and the number of action games as 'a'.

From the problem, we know that the total number of sports and action games is 39, which can be written in algebra as: a + s = 39.

Also, the problem states that the number of action games is three more than half of the number of sports games. That means, a = s/2 + 3.

Now we need to solve this system of equations. Substituting the second equation into the first (replacing 'a' in the equation 'a + s = 39' with 's/2 + 3'), we get s/2 + 3 + s = 39. Solving this equation for 's', we find that Ryan has 24 sports games.

Substitute s = 24 into the first equation we got 'a + 24 = 39' . Solving this for 'a', we find that Ryan has 15 action games.

Therefore, Ryan has 24 sports games and 15 action games.

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-18 < 5x - 3        Isolate/get x by itself, first add 3 to both sides of the equation

-18 + 3 < 5x - 3 + 3

-15 < 5x      Divide 5 on both sides

-3 < x         Your answer is A

You flip the sign [</>] if you multiply or divide a negative number to both sides of the equation.

Answer:the answer is 40

Step-by-step explanation:

Because you do 5 times x

Answer:-9

Step-by-step explanation:5x+3-48 you do 3-48 you get -45 then you divide 5x by -45 and you get the final answer of -9.

Area = Square - Circle

Area of Square = 10² = 100 m²

Area of Circle = π(5²) = 25π m²

Area of Shaded Region = 100 - 25π = 21.5 m² approx.

answer: second choice

Answer:

x = -4

Step-by-step explanation:

solving simultaneously

Therefore the cost of a bag of chips is $0.75

therefore the cost of a cheeseburger is $3.

Step-by-step explanation:

i) let the cost of a cheesburger be x.

ii) let the cost of a bag of chips be y

iii) therefore it is given that x + y = 3.75

iv) it is also given that 2x + 3y = 8.25

v) multiplying the equation in iii) by 2 we get 2x + 2y = 7.50

vi) subtracting the equation in v) from the equation in iv) we get y = $0.75

vii) Therefore the cost of a bag of chips is $0.75

viii) Substituting the value of y found in vii) into iii) we get x = 3.

ix) therefore the cost of a cheeseburger is $3.

Answer:

The straight line distance between the school and the candy store is 5.

Step-by-step explanation:

Use Pythagorean theorem

a²+b²=c²

3²+4²=c²

9+16=c²

25=c²

5=c

The straight line distance between the school and the candy store will be 5 miles.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

After school, Isaac skateboards directly from school to an ice cream parlor and then from the ice cream parlor to a candy store.

The ice cream parlor is 3 miles south of the school and the candy store is 4 miles east of the ice cream parlor.

Then the straight line distance between the school and the candy store will be

[tex]\rightarrow \sqrt{4^2 + 3^2}\\\\\rightarrow \sqrt{16 + 9}\\\\\rightarrow \sqrt{25}\\\\\rightarrow 5[/tex]

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The slope-intercept form of the equation of the line with a slope of -2/5 that passes through (15, -9/2) is y = -2/5x + 3/2.

To write the slope-intercept form of the equation of a line, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is -2/5. To find the y-intercept, we substitute the coordinates of the point (15, -9/2) into the equation. Thus, we have:

y = -2/5x + b

-9/2 = -2/5(15) + b

-9/2 = -6 + b

b = -9/2 + 6 = 3/2

Therefore, the equation of the line with a slope of -2/5 that passes through (15, -9/2) is y = -2/5x + 3/2.

Final answer:

The equation of the line with a slope of -2/5 that passes through (15, -9/2) in slope-intercept form is y = (-2/5)x + 3.

Explanation:

The student is asking for the slope-intercept form of an equation of a line with a given slope and a point through which it passes. The slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept. Given that the slope (m) is -2/5 and the line passes through the point (15, -9/2), we can substitute the slope and the point's coordinates into the slope-intercept formula to find b. Doing so, we get -9/2 = (-2/5)(15) + b. Solving for b, we find that the intercept is 3. Finally, the equation of the line in slope-intercept form is y = (-2/5)x + 3.

The Pentagon has five sides, each measuring 921 feet. To find the walking distance around its exterior, multiply the length of one side by five. The total distance is 4605 feet.

The student is asking about the walking distance around the exterior of the Pentagon, a five-sided building. Given that each side of the Pentagon measures 921 feet, we would calculate the perimeter for the distance by multiplying the length of one side by the number of sides.

To find the walking distance around the Pentagon we perform this calculation:

Perimeter of Pentagon = Side Length  × Number of Sides

Perimeter of Pentagon = 921 feet× 5

Perimeter of Pentagon = 4605 feet

Therefore, the walking distance around the Pentagon is 4605 feet.

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> number of adult tickets

y ----> number of children tickets

we know that

Jane sold 100 tickets for her school auction

so

[tex]x+y=100[/tex] ----> equation A

Jane collected a total of $944

[tex]12x+8y=944[/tex] ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (36,64)

see the attached figure

therefore

The number of adult tickets sold was 36 and the number of children tickets sold was 64

Answer:

Step-by-step explanation:

i don't know I am a forth grader

Answer:

5 2/3........................

Answer:

-4

Step-by-step explanation:

y-3=-4(x-5)

y=-4x+20+3

y=-4x+23

y=mx+b where m=slope and b=y-intercept

Answer:

The side length of the original square was 6 inches

Step-by-step explanation:

we know that

The area of a square is

[tex]A=b^2[/tex]

where

b is the length side of the square

Let

x ---> the length of the original square

The area of the original square is

[tex]A=x^{2}\ in^2[/tex]

The length of the smaller square is

[tex]b=(x-3)\ in[/tex]

The area of the smaller square is

[tex]A=(x-3)^2\ in^2[/tex]

The area of the smaller square is 1/4 the area of the original square

so

[tex](x-3)^2=\frac{1}{4} x^{2}[/tex]

solve for x

[tex]x^2-6x+9=\frac{1}{4} x^{2}[/tex]

Multiply by 4 both sides

[tex]4x^2-24x+36=x^{2}[/tex]

[tex]4x^2-x^2-24x+36=0\\3x^2-24x+36=0[/tex]

Solve the quadratic equation by graphing

using a graphing tool

x=2, x=6

see the attached figure

The solution is x=6 in

Remember that the solution must be greater than 3 inches (because Stacey cuts  3 inches off of the length of the square and 3 inches off of the width)

therefore

The side length of the original square was 6 inches

Answer:

Step-by-step explanation:

7 purple to 4 red = x purple to 32 red

7 / 4 = x / 32....cross multiply because this is a proportion

(4)(x) = (7)(32)

4x = 224

x = 224/4

x = 56 purple <==

Final answer:

To find the number of purple marbles in a bag that has 32 red marbles, given the ratio of 7 purple marbles for every 4 red marbles, simply divide 32 by 4 to find the number of sets and multiply by 7. The bag will contain 56 purple marbles.

Explanation:

Given the ratio of 7 purple marbles to 4 red marbles in a bag sold by Latoya's Marble Company, we can determine the number of purple marbles if a bag has 32 red marbles. To do this, we need to use the ratio to find out how many times the number of red marbles fits into the given amount and then multiply that number by the amount of purple marbles in the ratio.

Step-by-Step Calculation:

Start with the given ratio: 7 purple marbles for every 4 red marbles.

Determine how many sets of 4 red marbles there are in 32 red marbles by dividing 32 by 4, which is 8.

Since there are 7 purple marbles for every set, multiply 7 by the number of sets, which is 8.

The result is 56 purple marbles.

Therefore, a bag with 32 red marbles will contain 56 purple marbles.

Answer:It is greater than 10 because as you add both distances from the image its greater than 10 by a bit, looking at  the angle it gives you a bigger perspective in how far the cue ball is from the pocket

Its basically 8+6 which equals 14 but adding the way the angle is going the distance is shorter than 14 but greater than 10

Answer:

10 inches

Explanation:

correct on edge

Answer: x = 2 , y = 5

Step-by-step explanation:

10x - 2y = 24 ..................... equation 1

6x + 2y = 8 ........................ equation 2

solving the system of linear equation by elimination method , add equation 1 and 2

16x = 32

divide through by 16

x = 2

substitute x = 2 into equation 1 to find the value of y

10(2) - 2y = 2y

20 - 2y = 2y

20 = 4y

y = 5

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=457.17\\ h = 15 \end{cases}\implies 457.17=\cfrac{\pi r^2(15)}{3}\implies 457.17=5\pi r^2 \\\\\\ \cfrac{457.17}{5\pi }=r^2\implies \sqrt{\cfrac{457.17}{5\pi }}=r\implies 5.39 \approx r~\hfill \boxed{\stackrel{diameter = 2r}{2(5.39) = 10.78}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = -cos\:(2x - \frac{\pi}{2}) + 1} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the centre photograph displays the trigonometric graph of [tex]\displaystyle y = -cos\:2x + 1,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [centre photograph] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -cos\:(2x - \frac{\pi}{2}) + 1.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-\pi, 1],[/tex]from there to [tex]\displaystyle [-2\pi, 1],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 1,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

Let's simplify step-by-step.

0.8x+19−0.7x

=0.8x+19+−0.7x

Combine Like Terms:

=0.8x+19+−0.7x

=(0.8x+−0.7x)+(19)

=0.1x+19

Answer:

=0.1x+19

Step-by-step explanation:

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Answer:

ju mmmmmmjjum,,,,i,,,,, enjoy

Step-by-step explanation:

Answer:

its option b: (-2,-1)

Step by step:

y=2x

-2=2(-1)

-2=-2

Infinitely many solutions

Answer:

114, 156

Step-by-step explanation:

Answer: 114,156

Step-by-step explanation:

To add 84,396+29,760 you must add each row.

6+0 = 6

9+6 = 15 (Carry up the one)

3+7 = 10 + 1 = 11 (Carry up the one)

4+9 = 13 + 1 = 14 (Carry up the one)

8+2 = 10 + 1 = 11

So the answer will be 114,156

Answer:

The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.

Step-by-step explanation:

Answer:

I believe the answer to this question is: (-3,1) X=-3, Y=1.

Answer:

12.7 degrees

Step-by-step explanation:

there are 180 degrees in a straight line, and since the angle opposite a is 167.3, we subtract that from 180 and we get 12.7