The first thing we have to identify in our problem are the variables
[tex]\begin{gathered} x\to\text{time} \\ y\to\text{CPI} \end{gathered}[/tex]Now we see the points (x,y) that gives us the problem
[tex]\begin{gathered} 2011\to(11,202.9) \\ 2016\to(16,233.2) \end{gathered}[/tex]Since behavior can be modeled by a straight line, we use the general equation of the straight line
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Taking this into account and with the 2 points that they give us, we proceed to calculate the equation of the line starting with the slope:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{233.2-202.9}{16-11} \\ m=\frac{30.3}{5} \\ m=6.06 \end{gathered}[/tex][tex]\begin{gathered} y=6.06x+b \\ 202.9=6.06(11)+b \\ b=202.9-66.66 \\ b=136.24 \end{gathered}[/tex]The equation that models the behavior of the CPI is
[tex]y=6.06x+136.24[/tex]Now we calculate the CPI values for the years 2013 and 2014
[tex]\begin{gathered} 2013\to x=13 \\ y=6.06(13)+136.24 \\ y=78.78+136.24 \\ y=215.02 \end{gathered}[/tex][tex]\begin{gathered} 2014\to x=14 \\ y=6.06(14)+136.24 \\ y=84.84+136.24 \\ y=221.08 \end{gathered}[/tex]3.50 divide by 24.50
Answer:
1/7 or 0.143
Step-by-step explanation:
i hope this helps
Which ratio table shows equlvalent ratios? O First Quantity 63 Second Quantity 8 5 o First Quantity Second Quantity 15 4 22 First Quantity Second Quantity 6 3 First Quantity 2.1 Second Quantity 4 2
we are asked to determine which ratios are equivalent. For ratios to be equivalent the quotient of the ratios must be the same. For the ratios:
[tex]\frac{2}{4},\frac{1}{2}[/tex]If we take 2/4 and divide the numerator and denominator by 2 we get:
[tex]\frac{\frac{2}{2}}{\frac{4}{2}}=\frac{1}{2}[/tex]Since we got the same fraction that means that the ratios are equivalent.
keisha is an avid reader. One day she read for 8 hours. She read a total of 600 pages during that time. How many pages did keisha read per minute?
To find the number of page she read per minute
First let's chenge the 8 hours to minute
8 hours = 8 x 60 = 480 min
Since she read 600 pages
Number of pages read per min = 600/ 480
=1.25 pages
Match the following. Match the items in the left column to the items in the right column.1. divisor2. decimal fraction3. algorithm4. fraction5.quotient6. reminder7. doidonsa. the result of dividing two numbersb. the number being dividedc. a set of rules to be followed tosolve a problemd. the number of equal parts a number is being divided intoe. a fraction in which the denominator is 10 or a power of 10f. the amount left over after Chivisiong. a number that expresses the portiona whole
We can match as follows:
1. divisor ----> d. the number of equal parts a number is being divided into
2. decimal fraction ----> e. a fraction in which the denominator is 10 or a power of 10
3. algorithm ----> c. a set of rules to be followed to solve a problem
4. fraction ----> g. a number that expresses the portion
5. quotient ----> a. the result of dividing two numbers
6. reminder ----> f. the amount left over after Division
The vertices of a figure are A(1, -1), B(5, -6), and C(1, - 6). Rotate the figure 90° counterclockwise about the origin. Find the coordinates of the image. Polygon
A'(1,1)
B' (6,5)
C' (6,1)
Explanation
Step 1
Let
A(1,-1)
B(5,-6)
C(1,-6)
Step 2
find the image (A'B'C')
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Hence
[tex]\begin{gathered} A\mleft(1,-1\mright)\rightarrow A^{\prime}(1,1) \\ B(5,-6)\rightarrow B^{\prime}(6,5) \\ C(1,-6)\rightarrow C^{\prime}(6,1) \end{gathered}[/tex]so, the coordinates of the image are
A'(1,1)
B' (6,5)
C' (6,1)
I hope this helps you
Which of the binomials below is a factor of this trinomial?x^2 - 13x + 42A. x + 84B. x - 7C. x^2 +12D. x + 7
Given the following trinomial:
[tex]x^2-13x+42[/tex]To factor the trinomial, we need two numbers the product of them = 42
And the sum of them = -13
Two of the numbers of factors of 42 = -6, and -7
So, the factor of the trinomial will be as follows:
[tex]x^2-13x+42=(x-6)(x-7)[/tex]So, the answer will be option B. x - 7
The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the 12 total articles submitted, 5 were editorials. If he liked all the articles equally, and randomly selected 5 articles to go on the front cover, what is the probability that exactly 3 of the chosen articles are editorials? Write your answer as a decimal rounded to four decimal places.
This is a problem of binomial probability. We have two possible outcomes:
• the article selected is an editorial,
,• the article selected is not an editorial.
The probability of success (select an article that is an editorial) is:
[tex]p=\frac{5}{12}[/tex]Because we have 12 total articles submitted, and 5 of them were editorials.
To calculate the probability that selecting 5 random articles, getting as a result that exactly 3 of the chosen articles are editorials, we use the binomial probability formula:
[tex]P(n,x)=C(n,x)\cdot p^x\cdot(1-p)^{n-x}[/tex]Where:
• n = the number of trials = the number of articles selected randomly = 5,
,• x = the number of success = the number of editorials that we expect = 3,
,• p = the probability of getting an editorial = 5/12,
,• C(n,x) = n! / (x! (n-x)!).
Replacing the data in the formula above, we get:
[tex]P(n=5,x=3)=\frac{5!}{3!\cdot(5-3)!}\cdot(\frac{5}{12})^3\cdot(1-\frac{5}{12})^{5-3}\cong0.24615=0.2462[/tex]Answer
Rounded to four decimal places, the probability that exactly 3 of the chosen articles are editorials is 0.2462.
A store is having a " 15 % off sale on perfume . You have a coupon for 50 % off any perfume . What is the final price , in dollars , of a $ 30 bottle of perfume ? If necessary round your answer to the nearest cent .
ANSWER
$12.75
EXPLANATION
The store is selling the perfumes at 15% off the original price, so if a bottle of perfume costs $30, then they are selling it at,
[tex]30\cdot\frac{100-15}{100}=30\cdot\frac{85}{100}=30\cdot0.85=25.50[/tex]But you also have a coupon for 50% off, so you get to buy the perfume at half that price,
[tex]25.50\cdot\frac{50}{100}=25.50\cdot0.5=12.75[/tex]Hence, the final price of the perfume is $12.75.
jonathans science class places weights on a scale during an experiment. each weight weighs 0.2 kilograms. if the class puts 16 weights on the scale at the same time, what will the scale read?
Given the scale reading:
Each weight weighs 0.2 kilograms
If the class put 16 weights on the scale
Then the scale reading will be
[tex]\begin{gathered} 1\text{ weight -}\longrightarrow\text{ 0.2 kg} \\ 16\text{ weight -}\longrightarrow\text{ x} \\ x=16\times0.2 \\ x=3.2\operatorname{kg} \end{gathered}[/tex]Hence the scale reading will be 3.2kg
The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (-5.3, 1). The finishing point will be at(1, -5.3). Quadranto Quadrant P Quadrant Quadrants Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points) Part B: A checkpoint will be at (5.3, 1). In at least two sentences, describe the difference between the coordinates of the starting point and the checkpoint, and explain how the points are d. (4 points)
The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (-5.3, 1). The finishing point will be at(1, -5.3). Quadranto Quadrant P Quadrant Quadrants Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points) Part B: A checkpoint will be at (5.3, 1). In at least two sentences, describe the difference between the coordinates of the starting point and the checkpoint, and explain how the points are d. (4 points)
Part A
we have
starting point of the race is (-5.3, 1)
the x-coordinate is negative and the y coordinate is ;positive
that means-------> is located on quadrant Q
finishing point is (5,3, 1)
x-coordinate is postive and y coordinate is positive
that means -----> is located on Quadrant P
Answer:
Step-by-step explanation:
part A
A If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
we have
y=x+2
y=-2x+8
Solve the system of equations
equate both equations
x+2=-2x+8
x+2x=8-2
3x=6
x=2
Find the value of y
y=(2)+2
y=4
the solution is (2,4)
that means
(2,4) is a common point , that satisfy both equations
Compute the percent of profit or loss on shares of stock purchased at8.625 and sold at 10.75.
ANSWER:
24.63%
STEP-BY-STEP EXPLANATION:
The first thing is to mention that it is a profit because it was bought at a lower amount than it was sold, therefore
We take 100% as the lowest value, and thus we calculate the profit percentage
[tex]10.75\cdot\frac{100}{8.625}=124.63[/tex]Then the difference between both percentages is the profit percentage
[tex]124.63-100=24.63[/tex]A machinist must follow part drawing with scale 1 to 16. Find the dimensions (in inches) of the finished stock shown in the figure. That is find the lengths A, B, C, and D.
Length of the dimensions of the finished stock shown are as follow:
A = 13/4 inches , B = 3/4 inches , C =5/2 inches , D = 3/16 inches.
As given in the question,
Mechanist must follow part drawing with scale 1 to 16.
Dimensions of the finished stock shown in the figure
A represents the length .
B represents the height
C represents the length
D represents the height
Length of A is
= 3 1/4 inches
= 13 /4 inches
Height of B is
=3/4 inches
Length of C is
= 2 1/2 inches
= 5/2 inches
Height of D is
= 3/16 inches
Therefore, length of the dimensions of the finished stock shown are as follow: A = 13/4 inches ,B = 3/4 inches ,C =5/2 inches , D = 3/16 inches.
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What is the product?(4y − 3)(2y2 + 3y − 5)8y3 + 3y + 158y3 − 23y + 158y3 − 6y2 − 17y + 158y3 + 6y2 − 29y + 15
We need to find the product of :
[tex]\mleft(4y-3\mright)\mleft(2y2+3y-5\mright)[/tex]So, the result as following:
[tex]\begin{gathered} \mleft(4y-3\mright)\mleft(2y^2+3y-5\mright) \\ =4y\cdot(2y^2+3y-5)-3\cdot(2y^2+3y-5) \\ =8y^3+12y^2-20y-(6y^2+9y-15) \\ =8y^3+12y^2-20y-6y^2-9y+15 \\ \\ =8y^3+6y^2-29y+15 \end{gathered}[/tex]So, the answer is the option 4. 8y3 + 6y2 − 29y + 15
please help me solve this no tutor can ahelp me
Solution:
Since the confidence interval width is inversely proportional to n , the answer is the smallest n.
CORRECT OPTION: 36
which of the following lines are parallel, skew, intersection, or none of these.
Parallel lines are lines that have the same direction and there is always the same distance between them
Skew lines are lines that are not on the same plane (they are not coplanar) and also they do not intersect.
Intersecting lines are lines that cross at a point, they can be on the same plane or on different planes.
Let's analyze the parts of this problem.
DE and AB.
These two lines are shown in red and blue in the following diagram:
These are not parallel lines because one line is vertical and the other line is horizontal. They are also not intersecting lines because they do not cross at any point. Lines DE and AB are skew lines because they do not intersect and they are on different planes.
--> DE and AB --> skew
CB and
A chemist needs to mix a 12% acid solution with a 20% acid solution to obtain 160 ounces of a 15% acid solution. How many ounces of each of the acid solutions must be used?
Answer:
100 ounces of 12% solution and 60 ounces of the 20% solution.
Step-by-step explanation:
Let x ounces be the amount of 12% solution, then there will be 160-x ounces of the 20% solution.
So, we have the equation:
0.12x + 0.20(160 - x) = 0.15* 160
0.12x - 0.20x + 32 = 24
-0.08x = -8
x = 100.
So, it is 100 ounces of 12% solution and 60 ounces of the 20% solution.
Choose the correct equation in point slope form for the line through the given points or through the given point with the given slope
Answer:
[tex]y-3=-1(x+2)[/tex]Explanation:
The point-slope form of the equation of a line is generally given as;
[tex]y-y_1=m(x-x_1)[/tex]where m = the slope of the line
y1 = y-coordinate of the one point
x1 = x-coordinate of the one point
Given the slope of the line as m = -1 and the point (-2, 3) where x1 = -2 and y1 = 3, let's go ahead and substitute these given values into the point-slope formula to obtain the required equation as seen below;
[tex]\begin{gathered} y-3=-1\lbrack x-(-2)\rbrack \\ y-3=-1(x+2) \end{gathered}[/tex]Write the expression as a product of two factors. 12s + 10 + 6y
to write the expression as a product between two factors you must identify the common factor between all the terms in tis case the common factow will be 2
[tex]12s+10+6y=2\cdot(6s+5+3y)[/tex]Three ships, A, B, and C, are anchored in the atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879B. m∠A=74.4879; m∠B=17.22942; m∠C=88.28267C. m∠A=17.22942; m∠B=74.4879; m∠C=88.28267D. m∠A=88.28267; m∠B=74.4879; m∠C=17.22942
Question: Three ships, A, B, and C, are anchored in the Atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.
Solution:
Note: In finding the angles of a triangle given its three sides, we will use the Cosine Law.
[tex]\begin{gathered} c^2=a^2+b^2\text{ -2abcosC} \\ or\text{ it can be written as:} \\ \text{Cos(C) = }\frac{a^2+b^2-c^2}{2ab} \end{gathered}[/tex]
In finding angle C, we use the formula given above.
[tex]\begin{gathered} \text{Cos(C) = }\frac{37.674^2+11.164^2-36.318^2}{2\cdot37.674\cdot11.164} \\ \text{Angle C = 74.4879 degrees} \end{gathered}[/tex]Note: Side a is the side opposite Angle A, side b is the side opposite Angle B, and side c is the side opposite Angle C.
Let's find the next angle.
[tex]\begin{gathered} \text{Cos(B) = }\frac{a^2+c^2-b^2}{2ac} \\ \text{Cos(B) = }\frac{37.647^2+36.318^2-11.164^2}{2\cdot37.647\cdot36.318} \\ \text{Angle B = 17.2294}2\text{ degrees} \end{gathered}[/tex]Note: We can still use the cosine law in finding Angle A. But another solution is subtracting the Angles A and B from 180 degrees. The measure of the internal angle of a triangle is always 180 degrees no matter what type of triangle it is.
[tex]\begin{gathered} \text{Angle A = 180-74.4849 -17.22942} \\ \text{Angle A = 88.28 degrees} \end{gathered}[/tex]ANSWER:
A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879
Speeding tickets provide a significant source of revenue for many American cities. For one city in South Florida, the average annual speeding ticket revenue per police officer is $300,000. The standard deviation for these annual speeding ticket revenues is $58,000. If these amounts have a normal distribution, find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue generating officers from the other ninety-five percent.
Explanation
To find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue-generating officers from the other ninety-five percent.
We will need to find
[tex]P\left(x>z\right)=0.05[/tex]Therefore; using a z score calculator, this gives;
[tex]z=1.645[/tex]We can then find the cutoff amount z using the formula below;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}[/tex]Therefore, we will have
[tex]\begin{gathered} 1.645=\frac{x-300000}{58000} \\ \mathrm{Switch\:sides} \\ \frac{x-300000}{58000}=1.645 \\ crossmutiply \\ x-300000=58000\times1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}[/tex]Answer: 395410
A circle has a radius of .10 in. Find
the increase in area when the radius is increased by 2 in. Use
3.14 for
The increase in area of the circle when the radius is increased by 2 is 13.8 in.
How to calculate area of circle?Area of a circle can be described as the region that is been taken by the circle.
The area of the circle can be expressed as A=πr^2
We were told that the radius of the circle is been given as 0.10 in.
Then we can calculate the are of the circle by input the given radius into the formula above as:
A=πr^2
r= radius of the circle
A= area of the circle
A=3.14 (0.10)^2 =0.0314 in.
Then we were told that the radius is increased by 2 in.
Then the area of the circle will now be A=3.14* (2.10)^2 =13.85 in.
Then the the increase in area can be calculated as : (13.85 in. - 0.0314 in.) = 13.8 in.
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Consider the function y = f(x) shown at right, trace each interval where the function behavior is A. Increasing, using a GREEN pencil Identify the interval(s) ___B. Decreasing, using a RED pencil Identify the interval(s) ___ C. Constant, using a YELLOW pencil Identify the interval(s) ___ D. State the Domain of the function ___ E. State the Range of the function ___ F. What thoughts do you have about the intervals stated above? Did you use brackets (closed/included points) or parentheses (open/non-included points)? Why or why not?
You have a function f(x). To identify the increasing interval and decreasing interval of f(x), you consider that an increasing interval is determined by the values of x in which the value of f(x) increases. For the decreasing interval you focus on the values of x in which the values of f(x) decreases.
You can notice in the given graph:
The increasing interval is (-8 , -4) U (3 , 6)
The decreasing interval is (-4 , -2)
The constant interval is (-2 , 3)
The domain of the function is (-8 , 6)
The previous interval is given by the available values of x
The range of the function is (-4 , 8)
The previos interval is given by the values of f(x) for the values of x in the domain.
The following image is a sketch of the graph with the respective intervals.
A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different options are available at this store?
If a gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. The number of different options that are available at this store is 1344.
How to find the different options?Using this formula to determine the number of different options
Number of different options available = Number of shapes of boxes × Number of wrapping paper × Number of different bowl
Let plug in the formula
Number of different options available = 8 × 14 × 12
Number of different options available = 1,344
Therefore we can conclude that 1,344 different options are available.
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For each angle, determine the measure of the arc subtended by the angle's ray in units of 1/10th of the circumference of the given circle.Measurement for the diagram below:
Assuming you want the measure of the arc (in red) shown:
The circumference is divided into 10 equal parts. The red color arc is 1 and a half part.
The circumference is 360 degree and each part is 360/10 = 36 degrees
Thus, 1 and a half part will be:
[tex]1.5\times36=54\degree[/tex]Measure of Arc (in red) is:
54 degrees
how does the common ratio and ratio of the perimeters of FDE to CAB compare
Answer
The common ratio and the ratio of the perimeters of the two triangles are exactly the same (2/3).
Explanation
The common ratio is obtained by expressing corresponding sides as a fraction of each other.
The common ratio for this triangles = (8/12) = (6/9) = (12/18) = (2/3)
Perimeter is expressed as the sum of all the exterior dimensions of a figure.
For the first figure, Perimeter = 8 + 6 + 12 = 26 inches
For the second figure, Perimeter = 12 + 9 + 18 = 39 inches
Ratio of perimeters = (26/39) = (2/3)
Hope this Helps!!!
Write this ratio as a fraction in simplest form without any units.75 minutes to 1 hourYou can use the table below to help convert the units.1 minute = 60 seconds1 hour = 60 minutes-1 day = 24 hours1 week = 7 days0
To get an unitless ratio, both of our quantities have to be in the same units. Let's convert that hour into minutes:
[tex]1h\rightarrow60\min [/tex]Thereby, our ratio would be:
[tex]\frac{75\min }{60\min }\rightarrow\frac{5}{4}[/tex]find the slope and y intercept, then write out the linear equation (y=mx+b) below
Answer:
y = 2x + 3
Step-by-step explanation:
You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.
Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.
The slope is 2. Fill in 2 in place of m in
y = mx + b
y = 2x + b
Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.
y = 2x + 3
eric is giving a presentation about average rainfall in the united states and wants to create a graph that shows how yearly rainfall has changed over the past decade. what type of chart should he use?
To represent the yearly rainfall in a graph, eric should use the Bar Graph
which is commonly used worldwide
Bar Graph:
The graphic representation of data in the form of vertical or horizontal bars or rectangular strips having uniform width is called bar graphs.
A bar graph is used to give the comparison between two or more groups. It comprises of two or more parallel vertical (or horizontal) rectangles.
With bar graphs, we can compare data sets from different groups. The graph depicts groups on one axis and a discrete value on the other. The main purpose is to display the relationship between the two axes.
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Please show formula and explain work in 6th grade format
The surface area of a pyramid is given as:
[tex]SA=\frac{1}{2}pl+B[/tex]where p is the perimeter of the base, l is the slant height and B is the area of the base.
In this case the slant height is 4 in.
Now, since the base is a square which sides that has length 5 in. then the perimeter is:
[tex]p=4\cdot5=20[/tex]The area of the base is the length of the side squared, then we have:
[tex]B=5^2=25[/tex]Once we know the values we plug them in the formula, then we have:
[tex]\begin{gathered} SA=\frac{1}{2}(20)(4)+25 \\ SA=40+25 \\ SA=65 \end{gathered}[/tex]Therefore the surface area is 65 squared inches.