The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function.
Explanation:The subject of this question is Mathematics. The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function:
p(x) = x + 5 = d(x) + 5 = (500 - 2x) + 5 = 505 - 2x
So the price can be represented by the equation p(x) = 505 - 2x.
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The account balance on April 1st is $102.33. On April 15th a payment of $25.00 is made. On April 25th a purchase of $11.27 is made. What is the finance charge if the annual rate is 22%? What is the new account balance?
Answer:
Finance Charge = $1.42
New Account Balance = $90.02
Step-by-step explanation:
APR (Annual Percentage Rate) = 22%
Periodic Rate = 1.83% (APR/12)
Beginning Balance = $102.33
Payment made on 15th day = $25.00
Purchase made on 25th day = $11.27
Finance Charge = (Beginning Balance - Payment made on 15th day) x Periodic Rate
Finance Charge = ($102.33 - $25.00) x 0.0183
Finance Charge = $77.33 x 0.0183
Finance Charge = $1.42
New Account Balance = Beginning Balance - Payment made on 15th day + Purchase made on 25th day + Finance Charge
New Account Balance = $102.33 - $25.00 + $11.27 + $1.42
New Account Balance = $90.02
The finance charge is approximately $1.67, and the new account balance after accounting for the payment and purchase is $90.27.
We start with the account balance on April 1st, which is $102.33. On April 15th, a payment of $25.00 is made, and on April 25th, a purchase of $11.27 is made.
1: Calculate the Average Daily Balance
From April 1st to April 14th (14 days): $102.33From April 15th to April 24th (10 days): $102.33 - $25.00 = $77.33From April 25th to April 30th (6 days): $77.33 + $11.27 = $88.60Average Daily Balance = ( (14 * 102.33) + (10 * 77.33) + (6 * 88.60) ) / 30 = $91.22
2: Calculate the Finance Charge
Given the annual interest rate of 22%, we first find the monthly rate: 22% / 12 = 1.833%.
Then we calculate the finance charge:
Finance Charge = Average Daily Balance * Monthly Rate
Finance Charge = $91.22 * 0.01833 ≈ $1.67
3: Calculate New Account Balance
New Balance = Previous Balance - Payment + Purchase + Finance Charge
New Balance = $102.33 - $25.00 + $11.27 + $1.67 = $90.27
The new account balance is $90.27.
The general equation for a circle is a(x2+y2)+bx+cy+d=0. There is exactly one circle passing through the points (1,2),(3,−1), and (0,0). Find an equation for this circle.
Answer:
Step-by-step explanation:
let the eq. of circle be a(x²+y²)+bx+cy+d=0
x²+y²+b/a x+c/a y+d/a=0
if it passes through (0,0)
0²+0²+b/a*0+c/a*0+d/a=0
so d=0
Hence x²+y²+b/a x+c/a y=0
if it passes through (1,2) and (3,-1)
1²+2²+b/a×1+c/a×2=0
5+b/a+2c/a=0 ...(1)
and 3²+(-1)²+b/a*3+c/a*(-1)=0
10+3b/a-c/a=0 ...(2)
(1)+2(2) gives
5+b/a+2 c/a+20+6 b/a -2 c/a=0
7 b/a+25=0
b/a=-25/7
from (1)
5-25/7+2 c/a=0
2 c/a+10/7=0
2 c/a=-10/7
c/a=-5/7
so eq. of circle is x²+y²-25/7 x-5/7 y=0
7(x²+y²)-25 x-5 y=0
In the diagram below triangle abc ~ triangle dec . What is the value of x
Answer:
the answer is D
Step-by-step explanation
the ratio of the triangles is 3:1 (you find that out because 21:7 is simplified to 3:1.
when you plug in 6 as x then you get 18:6 which simplifies to 3:1 also
In a study commuting patterns of people in a large metropolitan area, respondents were asked to report the time they took to travel to their work on a specific day of the week. What is the individual?a. travel timeb. a personc. day of the weekd. city in which they lived
Answer:
b. a person
Step-by-step explanation:
The conducted study demonstrates the commuting patterns of people. Here, the information is collected from a person about amount of time consumes in travel to their work on a certain day of the week. Thus, here the individual is "a person" because the information is collected from a person about their time travel.
Figure FGHJ is shown below.
Figure F G H J has 4 sides. Sides F J and G H are congruent and parallel, and sides G F and H J are congruent and parallel. Angles G and J are 130 degrees.
Which names accurately describe figure FGHJ? Select two options.
parallelogram
quadrilateral
rectangle
rhombus
trapezoid
Answer:
parallelogramquadrilateralStep-by-step explanation:
The figure has 4 sides, so is a quadrilateral. Opposite sides are parallel, so the figure is a parallelogram.
Angles are not 90°, so the figure is not a rectangle. Sides are not all the same length, so the figure is not a rhombus. Because the figure has two pairs of parallel sides (not just one pair), it is not a trapezoid.
Answer:
a and b on edge
Step-by-step explanation:
Paisley was organizing her shoe collection. She counted 24 pairs of sandals. This represents 32% of the total number of shoes she owns. How many shoes does Paisley own?
Answer:
The number of shoes Paisley own is 75.
Step-by-step explanation:
Given:
Paisley was organizing her shoe collection.
She counted 24 pairs of sandals.
This represents 32% of the total number of shoes she owns.
Now, to find the number of shoes Paisley own.
Let the number of shoes Paisley own be [tex]x.[/tex]
According to question:
32% of [tex]x[/tex] = 24.
[tex]\frac{32}{100} \times x=24[/tex]
[tex]0.32x=24[/tex]
Dividing both sides by 0.32 we get:
[tex]x=75.[/tex]
Therefore, the number of shoes Paisley own is 75.
Answer:
The total number of shoes Paisley owns = 75
Step-by-step explanation:
Given:
24 pairs of sandals represent 32% of the shoes Paisley owns.
To find the total number of shoes Paisley owns.
Solution:
Let the total number of pairs of shoes be = [tex]x[/tex]
Thus, number of sandals can be represented as:
⇒ 32% of [tex]x[/tex]
⇒ [tex]0.32\times x[/tex]
⇒ [tex]0.32x[/tex]
Number of sandals = 24
So, we can write the equation as:
⇒ [tex]0.32x=24[/tex]
Solving for [tex]x[/tex]
Dividing both sides by 0.32.
⇒ [tex]\frac{0.32x}{0.32}=\frac{24}{0.32}[/tex]
⇒ [tex]x=75[/tex]
Thus, the total number of shoes Paisley owns = 75
find the area of a triangle with a base of 18 in. and a height of 6 in. Use the formula for area of a triangle
Area =
[tex] \frac{1}{2} 6h[/tex]
Answer:
The area is 54
Step-by-step explanation:
6x18 = 108
108 x 1/2 = 54
Answer:
area 51
Step-by-stareaep explanation:
Let x be a positive number such that the distance between x and -3.8 on a number line is exactly two times the distance between x and 1.7. What is the value of x? Express your answer as a decimal to the nearest tenth.
Answer:
0.4
Step-by-step explanation:
Equation is
x-(-3.8)=2(x-1.7)
solving for x,
x+3.8=2x-3.4
x=0.4
Final answer:
The value of x is found by setting up an equation based on the distances provided and considering two separate cases for the absolute value. After solving the equation, the positive value of x is determined to be 7.2.
Explanation:
To solve for the value of x in this problem, we need to set up an equation based on the information given about the distances on a number line. The distance between x and -3.8 is twice the distance between x and 1.7. This translates to the following equation:
|x - (-3.8)| = 2|x - 1.7|
We then solve this equation step-by-step:
First, simplify the equation:Therefore, the value of x to the nearest tenth is 7.2.
Manuel's grade on a science quiz was 80%. He got 20 problems correct on the quiz. How many problems were on the science quiz?
Answer:
There were 25 problems on the science quiz
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Grade Manuel got on the science quiz = 80% or 80/100
Number of correct answers = 20
2. How many problems were on the science quiz?
Let's use the Rule of Three Simple, this way:
Problems on the science quiz Percentage
20 80
x 100
x * 80 = 20 * 100
80x = 2,000
x = 2,000/80
x = 25
There were 25 problems on the science quiz
Answer:
25
Step-by-step explanation:
20 x 100/80 = 25
or 20/80 = x/100
A pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. Is the perimeter of the pentagon greater than 26 centimeters?(1) The area of the circle is 16π square centimeters.
(2) The length of each diagonal of the pentagon is less than 8 centimeters.
Answer:
Step-by-step explanation:
Check the attachment for solution
Mrs. Pender shows her students 2 sticks measuring 6 inches and 2 sticks measuring 8 inches. She asks the students to arrange the sticks to make a two-dimensional figure with the greatest possible area. The ways in which Anna and Reggie organize the sticks are shown. Which statement comparing the areas of the figures is true? The areas are the same because . Reggie’s shape has greater area because . Reggie’s shape has greater area because . Anna’s shape has greater area because .
Answer:
its d
Step-by-step explanation:
if im wrong then sorry :(
Answer:
A
100% Correct ANSWER. Pls, give me brainliest. Thank You!
Using a metric line, convert the following metric measurement. (Remember to use the same number of significant figures as in the original measurement.) 505 kL expressed in La. 50,500 Lb. 505,000 Lc. 5,050 Ld. 50.5 L
Answer:
B
Step-by-step explanation:
This question is asking to make a conversion from kilolitres to liters.
There is a total of 1000L in 1kL.
Hence to make the conversion from KL to L , we have to multiply the KL by 1000. Hence, for 505KL, its equivalent measurement in L would be 505 * 1000 = 505,000
Hence, 505kL expressed in L is 505,000
In order to study whether IQ level is related to birth order, data were collected from a sample of 540 students on their birth order (Oldest/In Between/Youngest) and their score on an IQ test.
Which of the following would be a meaningful display of the data from this study?
a. A pie chart
b. A histogram
c. A scatterplot
d. A two-way table
e. Side-by-side boxplots
Answer:
correct answer is e. Side-by-side boxplots
Step-by-step explanation:
given data
IQ test
sample = 540 students
solution
here Side-by-side boxplots that is apply it to the data set with 1 quantitative and 1 categorical variable
Side-by-side boxplots is also very useful in the comparing fundamental information for 2 data set
eg median value and range of value they cover from data
and
Side-by-side boxplots also provide target summary and it analysis the data
so here correct answer is e. Side-by-side boxplots
The relation between the two dataset can be shown by placing the
dataset side-by-side, to give a meaningful display.
Correct response:
The correct option is; e. Side-by-side boxplotsMethod used to make the above selectionThe number of student in the study = 540
The categories of the data = Oldest/In Between/Youngest
The category of the other data collected = Their score on IQ test
Required:
To choose the option that would be a meaningful display of the data
from the study.
Solution:
The number of categories of the order of birth = 3
Therefore, a meaningful display of the order of birth is possible using a boxplot.
The IQ test scores can be categorized as follows;
Maximum test score;75th percentile = Third quartile = Q₃50th percentile = Second quartile = Q₂25th percentile = first quartile = Q₁Minimum test scoreTherefore, the dataset for the order of birth and the dataset for the IQ
test score can be presented side-by-side, thereby providing a
meaningful display.
The correct option is therefore;
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A car drives 40 miles on local roads at 20 mph, and 180 miles on the highway at 60 mph, what is the average speed of the entire trip?
(A) 36 mph
(B) 40 mph
(C) 44 mph
(D) 52 mph
(E) 58 mph
Answer: C) 44 mph
Step-by-step explanation:
We know that [tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]
Given : A car drives 40 miles on local roads at 20 mph.
i.e. Time taken : [tex]t_1=\dfrac{40}{20}=2\ hour[/tex]
Also, it drives 180 miles on the highway at 60 mph.
i.e. Time taken : [tex]t_2=\dfrac{180}{60}=3\ hour[/tex]
We know that the formula for Average speed is given by :-
[tex]A.V.=\dfrac{\text{Total distance}}{\text{Total Time}}[/tex]
So the average speed of the entire trip will be :-
[tex]\dfrac{40+180}{t_1+t_2}\\\\\\=\dfrac{220}{2+3}=\dfrac{220}{5}\\\\=44[/tex]
Hence, the average speed of the entire trip is 44 mph.
Therefore , the correct answer is C) 44 mph.
y varies jointly as x and z z. If y = 6 when x = 3 and z = 9, find y when x = 4 and z = 3.6.
but z is in square root, just the symbol doesn't show.
Answer:
y = (8/5)√10
Step-by-step explanation:
You seem to have ...
[tex]y=kx\sqrt{z}[/tex]
We can find k from the given values ...
[tex]\dfrac{y}{x\sqrt{z}}=k=\dfrac{6}{3\sqrt{9}}=\dfrac{6}{3\cdot 3}=\dfrac{2}{3}[/tex]
Then for the new values, ...
[tex]y=\dfrac{2}{3}\cdot 4\sqrt{3.6}=\dfrac{8\sqrt{90}}{3\cdot 5}=\dfrac{8\sqrt{10}}{5}[/tex]
what is the midpoint of the segment shown below?
Olga purchases a rectangular mirror (the shaded region) that fits exactly inside a frame. The outer perimeter of the frame measures 60 cm by 80 cm. The width of each side of the frame is 10 cm. What is the area of the mirror?
Answer:
2,400cm^2
Step-by-step explanation:
This is quite an interesting question.
Now, we know the frame measures 60 by 80. We also know that the thickness of the frame is 10cm in length. Hence from the side of the mirror to the other side of the frame is 10cm.
We have the 10cm on each side of the frame. Making a total of 40cm and 20cm each allowance on the length and breadth of the mirror. The length and breadth of the mirror is thus 40cm by 60cm.
The area of a rectangle is L * B
The area of the mirror is 40 * 60 = 2,400cm^2
The fact that the width of each side of the frame is 10 cm means that each side of the mirror is 20 cm smaller than the corresponding side of the frame. Therefore, the mirror measures 40 cm by 60 cm, with an area of 2400.
For the graph above, what is the rate in miles per hour?
Answer:
26 2/3
Step-by-step explanation:
The easiest way to find the answer is to look at the graph value for 1 hour. It is slightly more than 25, but the graph isn't detailed enough to let us read a precise value.
The next best way is to find a grid intersection that the line goes through. We observe that (1.5 hours, 40 miles) is on the plotted line, so the proportion is ...
(40 mi)/(1.5 h) = 26 2/3 mi/h
Determine whether the underlined number describes a population parameter or a sample statistic. Explain your reasoning. Modifying Sixty minus five with underline of the 97 passengers aboard an airship survived an explosion.
Answer:
Step-by-step explanation:
A company wants to decrease their energy use by 13%. If their electric bill is currently $1,800 a month, what will their bill be if they are successful?
Step-by-step explanation:
What happens to principal and interest of the monthly payment on a loan over time?
A. They go up
B. They go down
C the principal goes down and interest goes up
D. The principal goes up and the interest goes down
Answer:
The answer is C because the principal goes down and interest goes up. The part of your payment goes to....
Step-by-step explanation:
Lizette's math test grades are 70, 72, and 68. If she scores 100 on her next test, what will happen to the RANGE of her scores? A) It will double. B) It will stay the same. C) It will increase 6 times. D) It will increase 8 times.
Answer D.It will increase 8 times.
Step-by-step explanation:
Answer: It will increase 8 times
Step-by-step explanation:
Range simply means the smallest number subtracted from the biggest number. Initially, the scores were 70, 72 and 68 then making the range 68-72 = 4. Now a new score is added which is 100 and it is obviously the biggest number now. So we subtract 68 from 100 that is ; 100-68= 32. This new range is 8 times more than the former. That is, 32/4 = 8.
Every day a new frog is born weight grams and grows at a rate of 10 grams/day, maxing out at 100grams in 10 days. On day n, what is the total weight of the frog community?
10n * f where f is the number of frogs in that community.
Step-by-step explanation:
The growth rate is given as 10g /day
For 10 days, the weight in grams will be 10*10 =100 grams
This means that for n days, the weight gained by a new frog will be; n*10 g
=10n grams
Lets assume the frog community has a population of f frogs, then total weight of the frog community will be;
10n * f where f is the number of frogs in that community.
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Bonds from the city of Tavel Gorge worth $1,000 each are selling at 110.611. If Sean wishes to purchase three such bonds, how much can he expect to pay? a. $3,000.00.b. $3,331.83.c. $3,318.33.d. $331.83.
The bonds are being sold at 110.611% of their face value, so each bond costs roughly $1,106.11. Therefore, to purchase three bonds, Sean would need to pay roughly $3,318.33.
Explanation:When the question states that the bonds are 'selling at 110.611', it means that each bond is sold at 110.611% of its face value, which is $1,000. So to find the price of one bond you would multiply $1,000 by 1.10611 (110.611%), which equals roughly $1,106.11. Thus, if Sean wishes to purchase three bonds, you would simply multiply the price of one bond by three: $1,106.11 times 3 equals $3,318.33. So, Sean should expect to pay approximately $3,318.33 if he wants to purchase three bonds from the city of Tavel Gorge.
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Answer:
The bonds are being sold at 110.611% of their face value, so each bond costs roughly $1,106.11. Therefore, to purchase three bonds, Sean would need to pay roughly $3,318.33.
Step-by-step explanation:
A library contains 2000 books. There are 3 times as man non fiction books. Write and solve a systems of equations to determine the number of nonfiction and fiction books.
Answer:
The number of fiction books is 500 and non fiction books is 1500.
Step-by-step explanation:
Given:
Total book library contains = 2000.
There are 3 times as many non fiction books as fiction books.
Now, to determine the number of non fiction books and fiction books.
Let the fiction books be [tex]x.[/tex]
And the non fiction books be [tex]3x.[/tex]
Total books = 2000.
Now, to get the number of non fiction books and fiction books we put an equation:
[tex]3x+x=2000.[/tex]
[tex]4x=2000.[/tex]
Dividing both sides by 4 we get:
[tex]x=500.[/tex]
Fiction books = 500.
Non fiction books = [tex]3x=3\times 500=1500.[/tex]
Therefore, the number of fiction books is 500 and non fiction books is 1500.
To solve for the number of nonfiction and fiction books in the library, set up a system of equations and solve them to find there are 500 fiction books and 1500 nonfiction books.
Explanation:To determine the number of nonfiction and fiction books in the library, we can use a system of equations. Let's denote the number of fiction books as F and the number of nonfiction books as NF. According to the problem, the total number of books in the library is 2000, and there are 3 times as many nonfiction books as there are fiction books.
Our two equations will be:
F + NF = 2000 (Total number of books)
NF = 3F (3 times as many nonfiction books)
To solve these equations:
Substitute the second equation into the first one:
F + 3F = 2000
4F = 2000
Divide both sides by 4 to find F:
F = 2000 / 4
F = 500
There are 500 fiction books. Now we can find the number of nonfiction books by multiplying 500 by 3:
NF = 3 * 500 = 1500
So, the library has 500 fiction books and 1500 nonfiction books.
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Rhombus ABCD, with side length 6, is rolled to form a cylinder of volume 6 by taping side AB to side DC. What is sin(angle ABC)?
Final answer:
To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder.
Explanation:
To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Since the volume of the cylinder is given as 6, we can use the formula V = πr^2h to find the height of the cylinder. Plugging in the values, we get 6 = πr^2h. Since the radius of the cylinder is half the length of side AB, which is 3, we can solve for h to find that h = 4/π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder. Plugging in the values, we get θ = 6π/3 = 2π.
Colorblindness is an X-linked recessive condition. If a woman with normal vision whose father was colorblind has a son with a man with normal vision, what is the probability that he will be colorblind?
Answer: 0.25 or 25%
Step-by-step explanation:Women have two chromosomes XX and men have two also XY.
From the question, it can be seen that colorblindness is an X-linked recessive condition.
Let the X-linked recessive gene be specified as [tex]X^{-}[/tex] and the dominant gene which is not colorblind linked as [tex]X^{+}[/tex].
The question says the woman has a father who is colourblind which means her father possesses the X-linked recessive gene [tex]X^{-}[/tex] which means he has chromosomes [tex]X^{-}Y[/tex] and therefore must have given his daughter the recessive gene
For her husband who has normal vision his chromosomes will be [tex]X^{+} Y[/tex].
So, the probability that their son will be colourblind will be;
Chromosomes [tex]X^{+}[/tex] Y
[tex]X^{+}[/tex] [tex]X^{+} X^{+}[/tex] [tex]X^{+}Y[/tex].
[tex]X^{-}[/tex] [tex]X^{-} X^{+}[/tex]. [tex]X^{-}Y[/tex].
Therefore, the probability that their son will be color blind = ¼ or 0.25 or 25%
A bag of baby carrots and a container of hummus dip contain a total of 650 calories. For a snack, Rosarita ate of the bag of carrots and of the container of hummus. Her snack contained a total of 260 calories. If x represents the total number of calories in the bag of carrots and y represents the total number of calories in the container of hummus, what is one of the equations for this scenario? X+y=650 x+y=260
Answer:
[tex]x + y = 650[/tex]
Step-by-step explanation:
We are given the following in the question:
Total calories in a bag of carrot and a container of hummus dip = 650
Rosarita's snack:
Some of the bag of carrots and some of the container of hummus.
Total calories in Rosarita's snack = 260
Let x represents the total number of calories in the bag of carrots and y represents the total number of calories in the container of hummus.
Then, we can write the following equation to represent total number of calories in both a bag of carrot and a container of hummus dip:
[tex]x + y = 650[/tex]
Since Rosarita did not eat the whole bag of carrot and the whole container of hummus and also x and y are the total calories in whole bag of carrot and container of hummus respectively.
Answer:
x+y=650
Step-by-step explanation:
its right on edge 8th grade math
Cathy is looking for a job as a bookkeeper. One online job site lists a job in a stereo store that pays 34.6K. Another job, in a clothing store, has a weekly salary of $620. A. Which job is the higher-paying job? B. What is the difference in the weekly salaries of these two jobs? Round to the nearest dollar.
Answer:
A. Stereo Store Job is highest paying Job.
B. The Difference between the weekly salaries of these two jobs is $45.
Step-by-step explanation:
Given:
Annual Pay of job in stereo store = 34.6K
Now K here means (1000).
So we can say that;
Annual Pay of job in stereo store = [tex]\$34.6\times 1000= \$34600[/tex]
Also Given:
Weekly salary of Job at clothing store = $620
We need to find which job is the higher-paying job.
Also We need to find the difference in the weekly salaries of these two jobs
Solution:
First we will find the weekly salary of job in stereo store.
Now we know that there are 52 weeks in a year.
So weekly salary of job in stereo store can be calculated by Annual Pay of job in stereo store divided by total number of weeks.
framing in equation form we get;
weekly salary of job in stereo store = [tex]\frac{34600}{52}=\$665.38[/tex]
Now we see that weekly salary of job in stereo store is greater than Weekly salary of Job at clothing store.
Hence Stereo Store Job is highest paying Job.
Now we need to find the difference in the weekly salaries of these two jobs.
difference in the weekly salaries can be calculated by weekly salary of job in stereo store minus weekly salary of job in clothing store.
framing in equation form we get;
Difference = [tex]\$665.38-\$620 =\$45.38[/tex]
Rounding to nearest dollar we get;
Difference = $45
Hence the Difference between the weekly salaries of these two jobs is $45.
A. The job in the clothing store is the higher-paying job. B. The difference in the weekly salaries of these two jobs is $45.
To determine which job is higher-paying, we need to compare the annual salaries of both jobs and convert them to weekly salaries for a fair comparison, assuming a standard work year of 52 weeks.
A. Comparing the annual salaries:
1. The job at the stereo store pays $34,600 per year. To find the weekly salary, we divide this amount by 52 weeks:
[tex]\[ \frac{34,600}{52} = 665.38 \][/tex]
So, the weekly salary for the job at the stereo store is approximately $665.38.
2. The job at the clothing store pays a weekly salary of $620.
Now, comparing the weekly salaries:
Stereo store: $665.38 per week
Clothing store: $620 per week
The job at the clothing store pays more per week than the job at the stereo store.
B. Calculating the difference in weekly salaries:
To find the difference between the weekly salaries of the two jobs, we subtract the weekly salary of the stereo store job from the weekly salary of the clothing store job:
[tex]\[ 665.38 - 620 = 45.38 \][/tex]
Rounding to the nearest dollar, the difference in the weekly salaries is approximately $45.
However, the question asks for the difference in the weekly salaries of these two jobs, not the difference in the weekly salary of the stereo store job from the clothing store job. Since the clothing store job pays more, we should actually subtract the weekly salary of the clothing store job from the weekly salary of the stereo store job to find the additional amount the clothing store job pays per week:
[tex]\[ 620 - 665.38 = -45.38 \][/tex]
Since we are looking for a positive difference, we take the absolute value:
[tex]\[ |-45.38| = 45.38 \][/tex]
Rounding to the nearest dollar, the difference in the weekly salaries of these two jobs is approximately $45. However, it seems there was a mistake in the initial answer provided for part B. Let's correct this:
The correct calculation for the difference in weekly salaries is:
[tex]\[ 665.38 - 620 = 45.38 \][/tex]
Rounding to the nearest dollar, the difference is $45.
The points (1, r) and (4, -13) lie on a line with slope – 3. Find the missing coordinate r.
The value of missing coordinate "r" is -4
Solution:
Given that,
The points (1, r) and (4, -13) lie on a line with slope – 3
To find: missing coordinate r
The slope of a line is given by formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Where, "m" is the slope of line
Here in this sum,
m = -3
[tex](x_1, y_1) = (1, r)\\\\(x_2, y_2) = (4, -13)[/tex]
Substituting the values in formula,
[tex]-3 = \frac{-13-r}{4-1}\\\\-3=\frac{-13-r}{3}\\\\-9 = -13 - r\\\\r = -13+9\\\\r = -4[/tex]
Thus the value of missing coordinate "r" is -4