The graph below shows the relationship between the number of pages printed (x) at a print shop and the total price (y), in dollars. Print Shop Prices Based on the graph, what is the unit price at the print shop?
Answers
We can find the unit price at the print shop by taking one point of the line and dividing its y-coordinate (price) by its x-coordinate (the number of pages printed).
For example, we can see that the line goes through the point (2,1), then we can take that point to calculate the price per page as mentioned, like this:
unit price = Total price/number of pages = 1$/2 = 0.5$
Then, the answer is 0.5$ per page (option D)
Related Questions
writing inequalities four more than three times a number, is greater than twenty two
Answers
Let the number be y,
From the question, the equation can be written thus;
[tex]3y+4>22[/tex]The next step is to subtract 4 from both sides;
[tex]\begin{gathered} 3y>22-4 \\ 3y>18 \end{gathered}[/tex]We'll then have to divide both sides by 3;
[tex]\begin{gathered} \frac{3y}{3}>\frac{18}{3} \\ y>6 \end{gathered}[/tex]the table below shows Luke's golf score each week he participated in a golf tournament used to line of best fit to estimate Lux score for week 12
Answers
To estimate the score of Luke for week 12, we need to determine first the equation for the line of best fit.
To get the equation, here are the steps:
1. Solve for the average value of the x-coordinates and y-coordinates.
Our x-coordinates will be the number of week while the y-coordinates will be the score in each week.
Average for the x-coordinates is:
[tex]\text{average (x)}=\frac{1+2+3+4+5+6}{6}=\frac{21}{6}=3.5[/tex]Average for the y-coordinate is:
[tex]\text{average(y)}=\frac{95+92+89+88+86+84}{6}=\frac{534}{6}=89[/tex]2. Subtract each x and y coordinates to its corresponding averages.
3. Multiply the difference of x and its average to the difference of y and its average. (5th column)
4. Square the difference of x and its average. (6th column)
5. Solve for the slope of the equation. The formula is:
[tex]m=\frac{\sum ^{}_{}(x-ave_x)(y-ave_y)}{\sum ^{}_{}(x-ave_x)^2\text{ }}[/tex][tex]\begin{gathered} m=\frac{-15-4.5+0-0.5-4.5-12.5}{6.25+2.25+0.25+0.25+2.25+6.25} \\ m=-\frac{37}{17.5} \\ m=-2.11429 \end{gathered}[/tex]The slope of the line is m = -2.11429.
6. Solve for the y-intercept. The formula is:
[tex]b=ave_y-m(ave_x)[/tex]Since we already have ave y = 89, ave x = 3.5, and m = -2.11429, let's plug them in to the formula above.
[tex]\begin{gathered} b=89-(-2.11429)(3.5) \\ b=89+7.4 \\ b=96.4 \end{gathered}[/tex]The y-intercept is 96.4.
Hence, the equation of the line of best fit is y = -2.11429x + 96.4.
To estimate the score of Luke for week 12, plug in x = 12 in the equation above and solve for y.
[tex]\begin{gathered} y=-2.11429x+96.4 \\ y=-2.11429(12)+96.4 \\ y=-25.37148+96.4 \\ y=71.02852 \\ y\approx71 \end{gathered}[/tex]Therefore, the score of Luke for week 12 is estimatedly to be 71.
you spin the spinner twice what is the probability of landing on a number less than eight and then landing on a 6
Answers
The probability of 2 consecutive events is the product of the probabilities of the single events.
The probability (P) of a single event A is:
[tex]P(A)=\frac{number\text{ }of\text{ }favorable\text{ }outcomes}{t=number\text{ }of\text{ total }outcomes}[/tex]So, let's find the probability of the first event:
Event: Landing on a number less than 6.
Number of Favorable outcomes: 2 (Landing on 6 or 7).
Total outcomes: 3 (Landing on 6, 7, or 8).
Then,
[tex]P(A)=\frac{2}{3}[/tex]Now, let's find the probability of the second outcome:
Number of Favorable outcomes: 1 (Landing on 6 ).
Total outcomes: 3 (Landing on 6, 7, or 8).
[tex]P(B)=\frac{1}{3}[/tex]Then, the probability of landing on a number less than eight and then landing on a 6 is:
[tex]\begin{gathered} P=P(A)*P(B) \\ P=\frac{2}{3}*\frac{1}{3} \\ P=\frac{2}{9} \end{gathered}[/tex]Answer: 2/9.
M − 58 = 22M = need help
Answers
The given equation is
M - 58 = 22
Adding 58 to both sides, it becomes
M - 58 + 58 = 22 + 58
M = 80
The figure shows lines r, n, and p intersecting to form angles numbered 1, 2, 3, 4, 5, and 6. All three lines lie in the same plane. Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line p? Select all that apply.
Answers
For the lines to be perpendicular the angle between them must be 90 degree.
So for the line r perpendicular to line r means that angle between these two line is of 90 degrees.
The angle between line r and line p are,
[tex]\angle6[/tex][tex]\angle1+\angle2[/tex][tex]\angle5+\angle4[/tex][tex]\angle3[/tex]So all these are of 90 degrees as these are angle between two perpendicular line.
So
[tex]\begin{gathered} \angle6=90^{\circ} \\ \angle1+\angle2=90^{\circ} \\ \angle3=90^{\circ} \end{gathered}[/tex]Since angle 3 and angle 6 are equal to 90 degrees.
[tex]\angle3=\angle6[/tex]So opton B, C, and E are correct.
4. A region has 1,158,000 people within a 7.5-mile radius from the region's center. Find the population density ofthe region. (2pts)
Answers
The first step to solve this problem is to find the area of the region. You do it by using the formula for the area of a circle:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=7.5^2\cdot\pi \\ A=176.7 \end{gathered}[/tex]The area of the region is 176.7 square miles.
Now, divide the population by the area of the region:
[tex]D=\frac{1158000}{176.7}=6553.5[/tex]The population density of the region is 6,553.5 people/square mile
Hello, please help me find arc AC in this circle for geometry
Answers
Given that
[tex]\begin{gathered} \text{arcAB}=\text{arcDC} \\ \text{Thus,} \\ AB+BC+DC+DA=360^0(sum\text{ of angles of a circumference)} \end{gathered}[/tex]Given that
[tex]\begin{gathered} arcDA=2BC \\ 104^0+104^0+2BC+BC=360^0_{} \\ 3BC=360^0-208^0 \\ BC=\frac{152^0}{3}=50.7^0 \\ \text{Hence} \\ AC=50.7^0+104=154.7^0\approx155^0 \end{gathered}[/tex]Use the function values for f and g shown in the table below to evaluate the following expression.
Answers
1) We can do it in parts. So, let's check the table for g(2).
We can tell that at x=2 g(2) yields 6
[tex]f(g(2))=f(6)[/tex]2) Now, for the last part of this composition, we can resort to the table again and tell that:
[tex]\begin{gathered} f(6)=2 \\ \\ Thus\:f(g(2))=2 \end{gathered}[/tex]Thus, this is the answer.
find the volume, show work and use 3.14 for pie round to the nearest hundredth
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given parameters
[tex]r=3.h=9,\pi=3.14[/tex]STEP 2: Write the formula for calculating the volume
[tex]Volume\text{ of a cone}=\pi r^2\frac{h}{3}[/tex]STEP 3: Find the volume of the cone
[tex]\begin{gathered} Volume=\pi r^2\frac{h}{3} \\ By\text{ substitution,} \\ Volume=3.14\times3^2\times\frac{9}{3} \\ Volume=3.14\times9\times3=84.78 \end{gathered}[/tex]Hence, the volume of the given cone is 84.78
Which of the binomials is a factor of this trinomial?
Answers
2 STEP:STEP 1 of 2: Reduce the rational expression to its lowest terms.
Answers
ANSWER:
[tex]\begin{gathered} \frac{3y-3}{1-y}=-3 \\ y\ne1 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
Step 1 of 2:
We have the following expression
[tex]\frac{3y-3}{1-y}[/tex]We factor in order to reduce to the lowest terms, like that:
[tex]\frac{3\cdot(y-1)}{1-y}=\frac{3\cdot(y-1)}{-1\cdot(y-1)}=\frac{3}{-1}=-3[/tex]Step 2 of 2:
In this case the only restriction is when the denominator is equal to 0, therefore we set the denominator equal to 0 and solve for y
[tex]\begin{gathered} 1-y=0 \\ -y=-1 \\ y=1 \end{gathered}[/tex]Therefore y can't take the value of 1
What is the equation of the flower garden represented on the blueprint?
Answers
Given: a rectangleis given .
Find : equation of flower garden represents the blue point.
Explanation:
the center of the circle is
[tex](\frac{10+0}{2},\frac{40+0}{2})=(5,20)[/tex]and the radius of the circle is 60 feet.
so the equation of the folwer garden will be .
[tex](x-5)^2+(y-20)^2=60^2[/tex]Hello can you please explain to me how you do this
Answers
1) 2x = x + 3 x = 3 Check: 6 = 6
2) 3x = x + 4 x = 2 Check: 6 = 6
3) x + 4 = 2x + 3 x = 1 Check: 5 = 5
4) 4x = 2x + 6 x = 3 Check: 12 = 12
Explanations:2) 3x = x + 4
Collect like terms
3x - x = 4
2x = 4
Divide both sides by 2
2x/2 = 4/2
x = 2
Check: 3(2) = 2 + 4
6 = 6
3) x + 4 = 2x + 3
Collect like terms
2x - x = 4 - 3
x = 1
Check: 1 + 4 = 2(1) + 3
5 = 5
4) 4x = 2x + 6
Collect like terms
4x - 2x = 6
2x = 6
2x/2 = 6/2
x = 3
Check: 4(3) = 2(3) + 6
12 = 6 + 6
12 = 12
the slope of the line is ???the y-intercept of the line is ???the linear function is ???
Answers
Given:
The rate of fluid = 300 ml
After 2 hours fluid = 1400 ml
Required:
Find the slope, y-intercept of the line, and linear function.
Explanation:
The rate of the fluid = 300 ml
So the slope m = -300
The fluid after 2 hours = 1400
So the value of y = 1400
and the value of x = 2S
Now the linear equation becomes:
[tex]\begin{gathered} y=mx+b \\ 1400=-300(2)+b \\ 1400=-600+b \\ b=1400+600 \\ b=2000 \end{gathered}[/tex]Substitute the value of m and m in equation y=mx+b.
[tex]y=-300x+2000[/tex]
Final Answer:
Slope Sm = -300
yinear equation 1400=2m+b
Y- intercept =2000
y=-300x+2000
Can you help me on #3 Please show work so I can follow it
Answers
Given:
The decimal form of 1/3 is a repeating decimal.
[tex]\frac{1}{3}=0.3333\ldots[/tex]All the multiple of 1/3 is not repeating decimals.
Example: 3 time 1/3.
[tex]\begin{gathered} \text{Let, x=}\frac{1}{3} \\ 3x=3\times\frac{1}{3}=1 \end{gathered}[/tex]So, 3 time 1/3 is not the repreating decimal.
5(z+1) = 3(z+2) + 11Solve for Z
Answers
This equation an eqaution with brackets with a simple variable z
We will first of all expand the brackets by multiplying through
The question states that,
[tex]\begin{gathered} 5(z+1)=3(z+2)+11 \\ By\text{ expanding the brackets we will have,} \\ 5z+5=3z+6+11 \\ 5z+5=3z+17 \\ By\text{ collecting like terms we will have} \\ \end{gathered}[/tex][tex]\begin{gathered} 5z-3z=17-5 \\ 2z=12 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Hence,
The value of x = 6.
The correct answer is Option C
If the box and whisker plot represents data from 16 shows had ticket sales between 140 and 200 ? Explain
Answers
From the given box plot, which represents data from 16 shows, let's explain the box lot.
Using the box plot, we have the following:
• Maximium data = 100
,• Minimum data = 220
,• First quartile, Q1 = 120
,• Thrid quartile, Q3 = 200
,• Average = 140
Since the average is 140, it means that the average number of tickets sold is 140
The lower quartile(first quartile) is 120.
This median of the lower half of tickets sold is 120.
The upper quartile is 200.
The minimum number of tickets bought from a show is 100.
The maximum number of tickets bought for a show is 220.
ANSWER:
• Maximium data = 100
,• Minimum data = 220
,• First quartile, Q1 = 120
,• Thrid quartile, Q3 = 200
,• Average = 140
I need help will this besin A =a/c or the followingsin A =b/csin A =b/asin A =c/bsin A =c/asin A =a/csin A =a/b
Answers
In a right-angled triangle, the side facing the reference angle is the opposite side, the side facing the right angle is the hypotenuse
Since sinA= opposite/hypotenuse
opposite= a
hypotenuse = c
Thus, sinA= a/c
Find the better buy:A 32-ounce bottle of apple juice for $2.50 or a 48-ounce bottle for $3.84.
Answers
Given:
32-ounce for $2.50 and 48-ounce for $3.84
[tex]\text{Cost of 1-ounce juice in 32-ounce bottle=}\frac{2.50}{32}[/tex][tex]\text{Cost of 1-ounce juice in 32-ounce bottle= \$0.078125}[/tex][tex]\text{Cost of 1-ounce juice in 48-ounce bottle=}\frac{3.84}{48}[/tex][tex]\text{Cost of 1-ounce juice in 48-ounce bottle=\$}0.08[/tex]Juice cost of 32-ounce bottle is less than the juice cost of 48-ounce bottle.
Therefore, Buying 32-ounce bottle is better.
What would make the following equation true? -4+_____=2m+(3m-4)A: -5mB: -4mC: -1mD: 6mE: 5m
Answers
When you open the parenthesis at the right-hand side of the equation
2m + (3m - 4) = 2m + 3m - 4
= 5m - 4
Comparing the left-hand side with the right -hand side
5m is the answer
1. If you are given a rectangle, how many lines of symmetry does it have?
Answers
Answer:
Two lines of symmetry
Explanation:
A line of symmetry is a line that cut a shape into two equal halves.
Given a rectangle, the possible lines of symmetry are shown below.
So, a rectangle can only have two lines of symmetry.
In the graph of an inequality, the region below a dashed horizontal line through the point (4, 1) is shaded. What inequality does the graph represent?
Answers
We are given the following graph of an inequality:
Since we are given that the line is dashed and it is shaded under the line this means that the area represents the values that tare less than y = 1, therefore, the inequality is:
[tex]y<1[/tex]a box with the same dimensions as the a prism in the opening exercise would be used to ship miniature dice whose side length have been cut in half. The dice are 1/2 inches x 1/2 inches x 1/2 inch cubes. how many dice of this size can fit in the box below ?
Answers
Answer:
1920 dice
Explanation:
First we need to find the volume of cuboid
Volume of the cuboid = 6in * 4in * 10in
Volume of the cuboid = 240in^3
Volume of the dice = 1/2 in * 1/2 in * 1/2 in
Volume of the dice = 1/8 in^3
Number of dice that can fit in the box = Volume of box/Volume of dice
Number of dice that can fit in the box = 240/(1/8)
Number of dice that can fit in the box = 240 * 8
Number of dice that can fit in the box = 1920 dice
hence 1920 dice can fit into the box
-2(3n+5)+4(2n+3)Use the Distributive Property towrite an equivalent expression
Answers
Step 1
Given
[tex]-2(3n+5)+4(2n+3)_{}[/tex]Required; to use the distributive property to write an equivalent expression
Step 2
State the distributive property (distributive law)
[tex]\begin{gathered} a(b+c)\text{ = ab + ac} \\ or \\ a(b-c)=ab-ac \\ \text{where a,b and c are real numbers} \end{gathered}[/tex]Step 2
Apply the property to the question at hand.
[tex]\begin{gathered} we\text{ will start with the first part : (-2(3n+5))} \\ \text{-2(3n+5) =(-2(3n)) + (-2(5)) } \end{gathered}[/tex][tex]\begin{gathered} \text{Then the second part ; (4(2n+3))} \\ 4(2n+3)=(4(2n))\text{ + (4(3))} \end{gathered}[/tex]Step 3
Write the full equivalent expression
[tex]\lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack[/tex]Hence
[tex]-2(3n+5)+4(2n+3)\text{ = }\lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack[/tex][tex]\begin{gathered} \lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack\text{ = -6n +(-10)+8n+12} \\ \lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack=\text{ }-6n+8n-10+12 \\ \lbrack-2(3n)+(-2(5))\text{ \rbrack+\lbrack}4(2n)+4(3)\rbrack=2n+2 \end{gathered}[/tex]Hence
[tex]-2(3n+5)+4(2n+3)\text{ = 2n+2}[/tex]Answer = 2n+2
Find the area of the rectangle with length 12 1/3 m and width 1 1/3m A. 12 1/9 m2B. 16 1/9 m2C. 13 1/3 m2D. 16 4/9 m2
Answers
We have the following:
the area of a rectangle is the multiplication of the length by the width
[tex]A=L\cdot W[/tex]replacing:
[tex]\begin{gathered} L=12\frac{1}{3}=\frac{37}{3} \\ W=1\frac{1}{3}=\frac{4}{3} \\ A=\frac{37}{3}\cdot\frac{4}{3}=\frac{148}{9} \\ A=16\frac{4}{9} \end{gathered}[/tex]Therefore the answer is D. |6 4/9 m^2
The larger of two numbers is 15 more than three times the smaller number. If the sum of the two numbers is 63, find the larger of the two numbers.
Answers
Information given
The larger of two numbers is 15 more than three times the smaller number. If the sum of the two numbers is 63, find the larger of the two numbers.
Solution
Let x and y the two numbers and let's assume that y is the larger number so we have the following relation:
[tex]y=15+3x[/tex]the sum of th two numbers is :
[tex]x+y=63[/tex]If we replace the first equation into the second one we got:
[tex]x+15+3x=63[/tex]And solving for x we got:
[tex]4x=48[/tex][tex]x=\frac{48}{4}=12[/tex]And the value of y would be:
[tex]y=63-12=51[/tex]
The mean rate for internet from a sample of householdswas $30 per month, with a standard deviation of $2.50 permonth. The data set has bell-shaped distribution.Estimate the percent of internet rates between $27.50 and$35?
Answers
step 1
Find the z-score
For x=$27.50
z=(27.50-30)/2.50
z=-1
For x=35
z=(35-30)/2.50
z=2
using Standard Normal Distribution Tables
between z=0 and z=2 ------> P=0.4772
between z=-1 and z=0 -----> P=0.3413
therefore
P=0.4772+0.3413
P=0.8185
P=81.85%
answer is 81.5%There are 3 red balls,2 blue balls and 5 whiteballs in an urn. A ball is selected and color notedthen replaced. A second ball is selected and it'scolor noted. Find the probability of getting 2blue balls. Also find the probability of getting 1blue ball and 1 white ball. And then find theprobability of getting 1 red ball and 1 blue ball
Answers
Solution:
The probability of an event is expressed as
[tex]pr(\text{event)}=\frac{\text{number of desired outcome}}{number\text{ of possible outcome}}[/tex]Given that 3 red balls,2 blue balls and 5 white balls in an urn, this implies that
[tex]\begin{gathered} \text{Number of red }\Rightarrow\text{N(R)=}3 \\ Number\text{ of blue balls}\Rightarrow N(B)=2 \\ \text{Number of white}\Rightarrow N(W)=5 \\ \text{Total number of balls}\Rightarrow N(Total)=10 \end{gathered}[/tex]A ball is selected and color noted then replaced, a second ball is selected and its color noted.
A) Probability of getting 2 blue balls.
[tex]\begin{gathered} Pr(B\text{ and B)= Pr(B)}\times Pr(B) \\ \Rightarrow Pr(B_{})=\frac{N(B)\text{ }}{N(\text{Total)}}=\frac{2}{10}=\frac{1}{5} \\ \text{thus,} \\ Pr(B\text{ and B)=}\frac{1}{5}\times\frac{1}{5} \\ \therefore Pr(B\text{ and B)}=\frac{1}{25} \end{gathered}[/tex]The probability of picking 2 blue balls is
[tex]\frac{1}{25}[/tex]B) Probability of getting 1 blue ball and 1 white ball.
[tex]\begin{gathered} Pr(1\text{ blue and 1 white ball)=Pr(B and W) or Pr(W and B)} \\ \Rightarrow Pr(B)=\frac{N(B)}{N(\text{Total)}}=\frac{2}{10}=\frac{1}{5} \\ \Rightarrow Pr(W)=\frac{N(W)}{N(\text{Total)}}=\frac{5}{10}=\frac{1}{2} \\ \text{Thus, we have} \\ Pr(1\text{ blue and 1 white ball)=Pr(B and W) or Pr(W and B)} \\ =(\frac{1}{5}\times\frac{1}{2})+(\frac{1}{2}\times\frac{1}{5}) \\ =\frac{1}{10}+\frac{1}{10}=\frac{2}{10} \\ \Rightarrow Pr(1\text{ blue and 1 white ball)}=\frac{1}{5} \end{gathered}[/tex]The probability of getting 1 blue ball and 1 white ball is
[tex]\frac{1}{5}[/tex]C) Probability of getting 1 red ball and 1 blue ball
[tex]\begin{gathered} Pr(1\text{ red ball and 1 blue ball) = Pr(R and B) or Pr(B and R)} \\ \Rightarrow Pr(B)=\frac{1}{5} \\ \Rightarrow Pr(R)=\frac{N(R)}{N(\text{Total)}}=\frac{3}{10} \\ Pr(1\text{ red ball and 1 blue ball) = Pr(R and B) or Pr(B and R)} \\ =(\frac{3}{10}\times\frac{1}{5})+(\frac{1}{5}\times\frac{3}{10}) \\ =\frac{3}{50}+\frac{3}{50}=\frac{6}{50} \\ \Rightarrow Pr(1\text{ red ball and 1 blue ball) }=\frac{3}{25} \end{gathered}[/tex]The probability of getting 1 red ball and 1 blue ball is
[tex]\frac{3}{25}[/tex]Write the equation that represents this statement 23 more than z is 76.________________What is the value of z in the equation above?_______________
Answers
First statement
z + 23 = 76 (First answer)
Isolating z, we have,
z = 76 - 23 Transposing 23 to the other side of the equation
z= 53
The value of z in the equation is 53
Write the equation of the line that passes through the points (4,8) and (-9,5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
The equation of a line in point-slope form is:
y - y1 = m(x - x1)
The slope m of a line is given by the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]In this case, we are given the points (4,8) and (-9,5), then we get:
[tex]m=\frac{5-8}{-9-4}=\frac{-3}{-13}=\frac{3}{13}[/tex]By replacing the value of m into the point-slope equation, we get:
[tex]y-y1=\frac{3}{13}(x-x1)[/tex]By replacing 4 for x1 and 8 for y1, we get:
[tex]y-8=\frac{3}{13}(x-4)[/tex]