i dont know how to answer part b, but you need part a to answer it so that's at the top
Answers
GIVEN:
We are told that the original price of a sofa is $500 and rthen it has been reduced by 20%, leaving the new price at $400.
The company cant sell the sofa after 3 weeks so they reduce the price to $320.
Required;
To find the percentage decrease.
Step-by-step solution;
At the point of reducing the price further, the original price has now been put at $400 and the new price has been set at $320. We take note that in terms of percentage, the original price is 100% while the new price will be represented by x (that is, yet unknown).
With this information we can set up an equation based on the ratio of the two prices as compared to the two percentages.
This means;
[tex]\begin{gathered} Original\text{ }price=400(100\%) \\ \\ New\text{ }price=320(x\%) \end{gathered}[/tex]Therefore;
[tex]\frac{400}{320}=\frac{100}{x}[/tex]Now we cross multiply;
[tex]\begin{gathered} x=\frac{100\times320}{400} \\ \\ x=\frac{320}{4} \\ \\ x=80 \end{gathered}[/tex]The new price is now given as 80% which simply means 20% was deducted from the original price. In other words, there was a 20% price reduction.
ANSWER:
There was a 20% decrease.
Related Questions
find the mean, median and mode of the following distribution:3, 5, 3, 4, 6, 8, 7, 9, 15
Answers
Given:
[tex]3,5,3,4,6,8,7,9,15[/tex][tex]\begin{gathered} \text{Mean}=\frac{3+5+3+4+6+8+7+9+15}{9} \\ \text{Mean}=\frac{60}{9} \\ \text{Mean}=6.6667 \end{gathered}[/tex]Ascending order : 3,3,4,5,6,7,8,9,15
Median : 5th term is the median
[tex]\text{Median}=6[/tex][tex]\text{Mode}=3[/tex]George runs hurdles he clears the hurdles 90% of the time which of the following statements applyGeorge clears the hurdles 9/9George clears the 9/100George clears the hurdles 90 /100George clears the hurdles 90/1000
Answers
90% = 90/100
answer is the third one
Karlo has $7,300 saved for a down payment towards the $26,700 car he wants to buy. He needs to have adown payment of at least 40% in order to get the lowest interest rate. How much more money would he need tosave?
Answers
The Solution:
Given:
The cost of car Karlo wants to buy is $26,700.
Karlo has saved = $7,300
We are required to find how much Karlo need to save more for the car.
Step 1:
Down payment of 40% of the total cost of the car is:
[tex]Down\text{ payment amount}=\frac{40}{100}\times26700=40\times267=\text{\$}10680[/tex]Step 2:
Subtract $10680 from $26700.
[tex]Amount\text{ to save more }=26700-10680=\text{\$}16,020[/tex]Therefore, the correct answer is $16,020.
the table shows how many gummies a candy-maker can make in a certain number of hours
15 =1,500
25= 2,500
50= 5,000
what is the constant of proportionality? show your equation, work, and correct lables.
Answers
The constant of proportionality will be 100.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The table shows how many gummies a candy-maker can make in a certain number of hours;
15 =1,500
25= 2,500
50= 5,000
Now,
We know that;
Th expression is,
⇒ y = kx
Where, K is constant of proportionality.
Here, By the first condition;
k = 1500/15
k = 100
By the second condition;
k = 2500/25
k = 100
By the third condition,
k = 5000/50
k = 100
Thus, The constant of proportionality will be 100.
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For the first week of July, Sam Martinez worked 55 hours. Sam earns$8.60 an hour. His employer pays overtime for all hours worked in excess of 40 hours per week and pays
1.5 times the hourly rate for overtime hours. Calculate the following for the first week of July (round your responses to the nearest cent if necessary):
1) Regular Pay Amount;
2)Overtime Pay
3)Gross Pay
Answers
The regular pay amount for the first week of July is $344
The overtime pay amount for the first week of July is $193.50
The gross pay amount for the first week of July is $537.50
How to find the earnings of sam?Total hours Sam worked = 55 hoursTotal regular hours = 40 hoursOvertime hours = Total hours Sam worked - Total regular hours
= 55 - 40
= 15 hours
Amount Sam earn per hour for regular hours = $8.60
Total regular pay amount = Total regular hours × Amount Sam earn per hour for regular hours
= 40 × $8.60
= $344
Amount Sam earn per hour for overtime hours = $8.60 × 1.5
= $12.90 per overtime hour
Total overtime pay amount = Overtime hours × Amount Sam earn per hour for overtime
= 15 × $12.90
= $193.50
Total gross pay = Total regular pay amount + Total overtime pay amount
= $344 + $193.50
= $537.50
In conclusion, the regular, overtime and gross pay of Sam for the first week of July is $344, $193.50 and $537.50 respectively.
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Use the diagram below to answer the next 4 questions that follow. Lines L1 1 pointand L2 are parallel. Point N is the midpoint of segment GH. If the measureof IHM is 125°, what is the measure of ZIHU? *M3N687
Answers
180 - 125 = 55
angle IHJ = 55
IHM + IHJ = 180
Since IHM = 125
Jake drives Go-Karts at an average speed of 2.75 laps per minute. If the relationship between the number of laps completed and numberof minutes varies directly, how long would it take him to complete 41.25 laps?O A. 0.07 minutesOB. 15 minutesO C. 38.5 minutesO D. 113 minutes
Answers
Since the number of minutes and number of laps completed varies directly, therefore if 2.75 laps correspond to 1 min then:
[tex]\frac{2.75\text{laps}}{1\min}=\frac{41.25\text{laps}}{x\min }\text{.}[/tex]Solving for x we get:
[tex]x\min =\frac{41.25}{2.75}1\min =15\min \text{.}[/tex]Answer: Option B.
The Fancy Marble Company makes one type of spherical marble with a radius of 2 cm. The maximum error in measurement is 0.1 cm for the radius. Which of the following is closest to the minimum .volume of one of these marbles? A 7.95 cm B. 8.79 cm C. 28.72 cm D. 38.77 cm
Answers
hello
to solve this question, we need to find the volume of a sphere
the formula is given as
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ r=2\pm0.1 \\ \pi=3.14 \end{gathered}[/tex]the minimum volume of the sphere is would be as a result in reduction of the radius of the sphere
[tex]\begin{gathered} R=r-0.1 \\ R=2.0-0.1 \\ R=1.9\operatorname{cm} \end{gathered}[/tex]we can use this radius to calculate the volume of the sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi R^3 \\ v=\frac{4}{3}\times3.14\times1.9^3 \\ v=28.716\cong28.72\operatorname{cm}^3 \end{gathered}[/tex]from the calculations above, the minimum volume of the sphere is 28.72cm^3 which corresponds to option C
The triangle has the sides AB = 4cm BC = 6cm AC = 8cmCalculate the triangles Area
Answers
Given: A triangle ABC with sides AB=4cm, BC=6cm and AC=8cm
Required: To find out the area of the given triangle.
Explanation: Area of the triangle by Heron's formula is given by,
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]where, a,b,c are the sides of triangle and s is the semi-perimeter given by,
[tex]s=\frac{(a+b+c)}{2}[/tex]Now, let a=4, b=6 and c=8. Hence the semi perimeter s is-
[tex]s=\frac{4+6+8}{2}[/tex][tex]s=9\text{ cm}[/tex]Now, putting these values of s, a, b, and c in Heron's formula we get,
[tex]A=\sqrt{9(9-4)(9-6)(9-8)}[/tex][tex]A=\sqrt{9\times5\times3\times1}[/tex][tex]A=3\sqrt{15}\text{ }cm^2[/tex][tex]A=11.61\text{ }cm^2[/tex]Final Answer: Area of triangle is 11.61 sq cm.
i need help with this problem its a two step equation -17= -9- 8m
Answers
Solve the equation 2-(y+9)<-3
Answers
Step 1:
Write the equation
[tex]\begin{gathered} 2\text{ - (y + 9) < -3} \\ 2\text{ - y - 9 < - 3} \\ -y\text{ < - 3 - 2 + 9} \\ \text{ - y < 4} \\ y\text{ > -4} \end{gathered}[/tex]Final answer
y > -4
In set-builder notations the solution set is
{y | y > -4}
In interval notation, the solution set is
[tex]\lbrack-3,\text{ }\infty)[/tex]For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−110)^2+6,050. The maximum capacity of the company is 150 items.Assuming that the company sells all that it produces, what is the profit function?P(x)=What is the domain of P(x)?The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose?
Answers
To solve this question, follow the steps below.
Step 01: Find the profit function P(x).
Given
C(x) = cost of producing x units
R(x) = revenue when producing x units
Then, P(x) is = R(x) - C(x).
Substituting the equations in the formula:
[tex]P(x)=0.5*(x-110)^2+6050-(40x+150)[/tex]Solve the equation, by solving first the quadratic part.
[tex]\begin{gathered} P(x)=-0.5*(x^2-2*110*x+110^2)+6050-40x-150 \\ P(x)=-0.5x^2+110x-6050+6050-40x-150 \\ P(x)=-0.5x^2+110x-40x-150 \end{gathered}[/tex]Then, sum the like-terms.
[tex]P(x)=-0.5x^2+70x-150[/tex]Step 02: Find the domain.
Since the maximum capacity of the company is 150 items. So, x-maximum is 150.
The minimum number of products is 0.
Then, 0 ≤ x ≤ 150.
Domain: 0 ≤ x ≤ 150 or [0, 150].
Step 03: Compare the profit for x = 70 and x = 80.
[tex]\begin{gathered} P(x)=-0.5x^{2}+70x-150 \\ P(70)=-0.5*70^2+70*70-150 \\ P(70)=-2450+4900-150 \\ P(70)=2300 \end{gathered}[/tex][tex]\begin{gathered} P(x)=-0.5x^{2}+70x-150 \\ P(80)=-0.5*80^2+70*80-150 \\ P(80)=2250 \end{gathered}[/tex]Comparing both profits, the profit for x = 70 is greater. So, they should choose x = 70.
In summary:
(a) Profit equation:
[tex]P(x)=-0.5x^{2}+70x-150[/tex](b )Domain:
0 ≤ x ≤ 150 or [0, 150].
(c) Comparing x = 70 and x = 80.
Comparing both, the company should choose x = 70, because the profit is greater.
Paula started reading a book and read 1/12 of the book on the first day. The next day, she read 1/3 of the book. How much does she still need to read the book?
Answers
ANSWER
7/12
EXPLANATION
We have that Paula first read 1/12 of her book. Then she read, 1/3 of the book.
First, we have to find how much of the book she has read.
We do that by adding the amounts she has read.
That is:
[tex]\begin{gathered} \frac{1}{12}+\frac{1}{3} \\ \frac{1+(4\cdot1)}{12}=\frac{1+4}{12} \\ =\frac{5}{12} \end{gathered}[/tex]Now, to find how much she still has to read, we have to subtract the fraction she has read from 1.
That is:
[tex]\begin{gathered} 1-\frac{5}{12} \\ \Rightarrow\text{ }\frac{12}{12}-\frac{5}{12} \\ =\frac{7}{12} \end{gathered}[/tex]Therefore, she still has to read 7/12 of the book.
Find the given equation of the line through (8,-7) which is perpendicular to the line y= x/2-9
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
By comapring the given equation,
slope, m = 1/2
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Thus,
slope of line passing through (8, - 7) = - 2/1 = - 2
We would find the y intercept of the line passing through (8, - 7) by substituting x = 8, y = - 7 and m = - 2 into the slope intercept equation. We have
- 7 = - 2 * 8 + c
- 7 = - 16 + c
c = - 7 + 16 = 9
The equation of the line is
y = - 2x + 9
Find the next 3 terms of the arithmetic sequence 5, 9, 13, 17
Answers
You have the following arithmetic sequence:
5, 9, 13, 17
due to the it is an arithmetic sequence, difference between consecutive numbers is constant.
In fact, when you calculate the difference between consecutive numbers you have:
9 - 5 = 4
13 - 9 = 4
17 - 13 = 4
To determine the next three terms it is necessary to sum 4 (the previous result) to each previous term, just as follow:
17 + 4 = 21
21 + 4 = 25
25 + 4 = 29
Hence, 21, 25 and 29 are the next three terms
The table below shows data for a class's mid-term and final exams:
Mid-TermFinal
96 100
95 85
92 85
90 83
87 83
86 82
82 81
81 78
80 78
78 78
73 75
Which data set has the smallest IQR? (1 point)
Group of answer choices
They have the same IQR
Mid-term exams
Final exams
There is not enough information
Answers
The interquartile range is a measure of where the “middle fifty” is in a data set, where the bulk of the values lies.
The interquartile range formula is the first quartile subtracted from the third quartile:
[tex]IQR=Q_3-Q_1[/tex]IQR of the Mid-Term
Step 1: Arrange the numbers in order
[tex]73,78,80,81,82,86,87,90,92,95,96[/tex]Step 2: Find the median
[tex]Median\Rightarrow86[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=80[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=92[/tex]Step 4: Calculate the IQR
[tex]IQR=92-80=12[/tex]IQR of the Final
Step 1: Arrange the numbers in order
[tex]75,78,78,78,81,82,83,83,85,85,100[/tex]Step 2: Find the median
[tex]Median\Rightarrow82[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=78[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=85[/tex]Step 4: Calculate the IQR
[tex]IQR=85-78=7[/tex]ANSWER
The data with the smallest IQR is the FINAL.
Mrs. Nolan hired a painter to paint the exterior of her house. It took the painter 3 days to paint her house. The painter agreed to a rate of $23 per hour with a 12-hour unpaid lunch break each day. The table shows when the painter clocked in and out each day.Before taxes, how much money did the painter make
Answers
Given that the painter took three days to paint the exterior of the house in the following timings.
Thursday 7.30 am to 5.15 pm = 9 hours 45 minutes
Friday 7.00 am to 4.40 pm = 9 hours 40 minutes
Saturday 8.30 am to 4.30 pm = 8 hours
Also, it is given that the rate 23 $ per hour, and there is a rest of 1/2 hour lunch break each day.
So total lunch break = 3 x 1/2 hours = 3/2 hours = 1.5 hours = 1 hour 30 minutes
Total working time = 9 hours 45 minutes + 9 hours 40 minutes + 8 hours
= 27 hours 25 minutes
For 1 hour the rate is $ 23
1 hour = $ 23
60 minutes = $ 23
1 minute = $ 23/60
Now we have to subtract the lunchtime from the total time.
Then,
Time for which he was paid = 27 hours 25 minutes - 1 hour 30 minutes
= 25 hours 55 minutes
So,
25 hours = $ 25 x 23 = $ 575
55 minutes = $ 55 x 23/60 = $ 21.08
Hence, the total money he was paid is = $ 575 + $ 21.08 = $ 596.08
Therefore the required answer is $ 596.08
A growing company has been hiring employees at a steady rate of 1 new hire per month. The company started with 2 employees. The growth of the company can be modeled by the function g (2) = 2 + 2, where x represents the number of months, and g(x) represents the number of employees. Evaluate the function over the domain {3,4, 18, 24}.
Answers
The function that represents the number of employees by the number of months is:
[tex]g(x)\text{ = 2+x}[/tex]For x = 3:
[tex]\begin{gathered} g(3)\text{ = 2+3} \\ g(3)\text{ = 5} \end{gathered}[/tex]For x=6:
[tex]\begin{gathered} g(6)=2+6 \\ g(6)\text{ = 8} \end{gathered}[/tex]For 18:
[tex]\begin{gathered} g(18)\text{ = 2+18} \\ g(18)\text{ = 20} \end{gathered}[/tex]For 24:
[tex]\begin{gathered} g(24)=24+2 \\ g(24)=26 \end{gathered}[/tex]The solid shape is made from a hemisphere and a cone.
The radius of the hemisphere is equal to the radius of the base of the cone.
The cone has a height of 10 cm.
The volume of the cone is 270π cm3.
Work out the total volume of the solid shape in cm³
.
Give your answer in terms ofπ .
Answers
The volume of the solid shape is 756 cm³ .
What is the volume of the solid shape?The volume of the solid shape is the sum of the volume of the hemisphere and the cone.
Volume of the solid shape = volume of the hemisphere + volume of the cone
Volume of the cone = 1/3πr²h
270π = 1/3πr² x 10
r² = (270π x 3) / 10π
r² = 81
r = √81
r = 9
Volume of a hemisphere = (2/3) × r³ × π
Volume of a hemisphere = 2/3 x 9³ × π
Volume of a hemisphere = 486π cm³
Volume of the solid shape = 486π cm³ + 270π cm³ = 756 cm³
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WHAT IS THE MEASURE OF
Answers
The measure of the angle ∠XYZ = 76°
What is an angle?Angles are formed when two lines intersect at a point. The measure of the 'opening' between these two rays is called an 'angle'. It is represented by the symbol ∠. Angles are usually measured in degrees and radians
∠XYZ = ∠WXY + ∠XWY( exterior angle of a triangle is equal to the sum of the two interior angle)
substituting their values,
12x - 20 = 3x + 11 + 5x + 1
collecting like terms we have
12x -3x - 5x = 20 + 1 + 11
4x = 32
x = 32/4
x = 8
recall ∠XYZ = 12x - 20
substitute x = 8 into the above equation
∠XYZ = 12(8) - 20
∠XYZ = 96 - 20
∠XYZ = 76°
In conclusion, the value of ∠XYZ = 76°
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John compares the graph of two functions.• The first function was y=3x +4.• The second function fits the values in the table below.22What is the distance between the y-intercepts of the two functions?O A. 5 unitsO B. 6 unitsO C. 4 unitsOD. 3 units
Answers
the y-intercept of a parabola is the y coordinate of the point where does the graph intersect the y-axis.
so from the figure, we can see that the parabola is intersecting the y-axis at (0, -6)
and it is intersecting the x-axis at (3,0)
thus. y-intercept is (0, -6) and x-intercept is (3,0)
that is option D
jacobs school is selling tickets to a fall musical. On the first day of ticket sales the school sold 2 senior citizens tickets and 6 child tickets for a total of $26. The school took in $54 on the second day by selling 12 senior citizen tickets and 2 child tickets. Find the price of senior citizen ticket and the price of a child ticket.
Answers
Let s and c represent the prices of the senior citizen and the child tickets respectively
Then the problem can be modelled as follows:
[tex]\begin{gathered} 2s+6c=26--------------------(1) \\ 12s+2c=54--------------------(2) \\ We\text{ will now solve the simultaneous equation by elimination method} \\ \text{equation (1) }\times6\colon \\ 12s+36c=156---------------------(3) \\ 12s+2c=54-----------------------(2) \\ ---------------------------------------- \\ \text{equation (3) - equation (2):} \\ 34c=102 \\ \Rightarrow c=\frac{102}{34}=3 \\ \text{Substituting the value of c into equation (1), we have:} \\ 2s+6(3)=26 \\ 2s+18=26 \\ \Rightarrow2s=26-18=8 \\ \Rightarrow s=\frac{8}{2}=4 \end{gathered}[/tex]What is mZS? Q 108° P R S m2S = O
Answers
First, we find arc RSP
[tex]\begin{gathered} 108=\frac{1}{2}\cdot RSP \\ \text{RSP}=2\cdot108=216 \end{gathered}[/tex]Arc RSP measures 216°.
Then,
[tex]\begin{gathered} 216+RQP=360 \\ \text{RQP}=360-216=144 \end{gathered}[/tex]Now, we find angle S
[tex]m\angle S=\frac{1}{2}\cdot144=72[/tex]Hence, angle S measures 72°.Label the sides of the right triangle.*2 pointsCaptionless ImageA) Hypotenuse = 8 m, Adjacent = 15 m, Opposite = 17 mB) Hypotenuse = 17 m, Adjacent = 8 m, Opposite = 15 mC) Hypotenuse = 15 m, Adjacent = 17 m, Opposite = 8 mD) Hypotenuse = 17 m, Adjacent = 15 m, Opposite = 8 m
Answers
Given:
There are given that the right angle triangle, UVW.
Where,
[tex]\begin{gathered} UV=8m \\ VW=15m \\ UW=17m \end{gathered}[/tex]Explanation:
According to the concept:
The hypotenuse is defined as the longest side in the right-angle triangle.
The perpendicular side is defined by the perpendicular base angle.
And,
The adjacent side is defined by the leg of the right-angle triangle.
Final answer:
Hence, the correct option is D.
Which of the following is an example of independent events? A. Drawing a king from a standard deck of cards and then drawing an 8 without replacing the kingB. Four people are drawn successively without replacement from a group of 30 to represent the groupC. Spinning a 3 on a spinner and getting a head from a coin tossD. Selecting a head from a bag of 9 different colored breads and then selecting a second bead without putting the first back
Answers
Two events are independent if the fact that one takes palce does not affect the probability of the other. This means that spinning a spinner and tossing a coin are indepent events since the probabilities do not affect each other.
The temperature fell by 3°F every hour during a 6-hour period. What
was the overall change in temperature during the 6-hour period?
PLS HELP THIS IS DUE TMR
Answers
Answer:
it decreased 18°F over 6 hours
Step-by-step explanation:
if it fell 3°F every hour for 6 hours just times it by 6
3x6=18
it decreased 18°F over 6 hours
During 5/8 of the 72 physical education classes, Ethan played games involving running. During how many of this years physical education classes did Ethan have to run?
Answers
Ethan has to run in 45 classes
Here, we want to get the number of games that involved running
Mathematically, what we have to do here is to calculate the number in the fraction
We have this as;
[tex]\frac{5}{8}\text{ of 72 = }\frac{5}{8}\times\text{ 72 = 45}[/tex]Write an equation of a line that passes through the given point and has the given slopethe correct blanks for the value of mand b.2.(-1, 4), slope - 1
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
We would find c by substituting x = - 1, y = 4 and m = - 1 into the slope intercept equation. It becomes
4 = - 1 * - 1 + c
4 = 2 + c
c = 4 - 2 = 2
The equation would be
y = - x + 2
Find the value of the variable that is not given: V=I w h; Given V = 90,1 = 10, h = 3 (Round the answer to 2 decimal places if necessary)
Answers
V= l*w*h
V=90
l=10
h=3
Replace the values in the expression and clear w
V= l*w*h
90=10*w*3
90=30w
w=3
Triangle 1 is a scale drawing of Triangle 2 as shown below. Based on the information shown in these triangles, what is the length of the side x? A. 9 B. 15.75 c. 7
Answers
x = 7
Explanations:Since triangle 1 is a scale drawing of triangle 2, the ratio of corresponding sides will be the same.
Therefore:
[tex]\frac{4}{6}=\text{ }\frac{x}{10.5}[/tex]Cross multiply:
4(10.5) = 6x
42 = 6x
6x = 42
x = 42/6
x = 7