a. The changes in each four-month period are as follows:
Month and Prices Absolute Relative
Year in Dollars Change Change
Apr-20 1.841 n/a n/a
Aug-20 2.183 $0.342 18.58%
Dec-20 2.195 0.012 0.55%
Apr-21 2.858 0.663 30.21%
Aug-21 3.158 0.300 10.50%
Dec-21 3.307 0.149 4.72%
Apr-22 4.109 0.802 24.25%
b. The change in gas prices has been relatively unstable.
c. Using the inflation calculator, the costs of gas in April 2020 in 2022 dollars terms should be $2.08.
d. The inflation-adjusted cost of gas in April 2020 when compared to April 2022 as absolute and relative changes are as follows:
Absolute change = $2.268 ($4.109 - $1.841)
Relative change = 123.2% ($2.268/$1.841 x 100)
e. The two most drastic rises in gasoline prices in April 2021 and April 2022 can be attributed to spikes in demand relative to supply.
What causes gasoline prices to rise?Gasoline prices rise when there is an increased demand relative to supply.
Increasing prices in gasoline prices can also be attributed to cuts in production and supply by the oil cartel.
What is the difference between Absolute and Relative Changes?An absolute change is a dollar change from one period to another.
A relative change is an absolute change expressed in percentages.
The calculations of absolute change and relative change are demonstrated below.
Data and Calculations:Month and Prices Absolute Relative
Year in Dollars Change Change
Apr-20 1.841 n/a n/a
Aug-20 2.183 $0.342 18.58% ($0.342/$1.841 x 100)
Dec-20 2.195 0.012 0.55% ($0.12/$2.183 x 100)
Apr-21 2.858 0.663 30.21% ($0.663/$2.195 x 100)
Aug-21 3.158 0.300 10.50% ($0.3/$2.858 x 100)
Dec-21 3.307 0.149 4.72% ($0.149/$3.158 x 100)
Apr-22 4.109 0.802 24.25% ($0.802/$3.307 x 100)
Absolute Change for Aug-20 = $0.342 ($2.183 - $1.841)
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WHEN LOIS MARTIN WAS BORN, HER FATHER DEPOSITED $2000 IN A SAVINGS
ACCOUNT IN HER NAME AT A SAVINGS AND LOAN ASSOCIATION (S&L). AT THE TIME,
THE S&L PAID 6% INTEREST COMPOUNDED SEMI-ANNUALLY. AFTER 10 YEARS, THE
S&L CHANGED TO A RATE OF 6% COMPOUNDED QUARTERLY. WHAT WAS THE
VALUE OF THE ACCOUNT AFTER 18 YEARS WHEN THE MONEY WAS WITHDRAWN TO
HELP PAY FOR HER COLLEGE EXPENSES
The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.
How are the future values determined?The future values of the savings account are calculated in two installments.
The first installment is for 10 years when the account earns 6% compounded semiannually.
Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.
Future values can be determined using the future value formula or an online finance calculator, as follows:
Data and Calculations:Investment of $2,000 for 10 years:N (# of periods) = 20 (10 years x 2)
I/Y (Interest per year) = 6%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
FV = $3,612.22
Total Interest $1,612.22
Investment of $3,612.22 for 8 years:N (# of periods) = 32 (8 years x 4)
I/Y (Interest per year) = 6%
PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)
PMT (Periodic Payment) = $0
Results:
FV = $5,816.85
Total Interest $2,204.63
Thus, the value of the account after 18 years was $5,816.85.
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Calculate the volume of a sphere that has a radius of 4 meters
Answer:
268.08
Step-by-step explanation:
use the formula 4/3πr^3Answer:
803.84 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
radius ⇒ 4m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 4 )³
V = 4 π × 64
V = 4 π × 64
V = 12.56 × 64
V = 803.84 m³
Decimals, fractions, and percents can all represent the same values.
True
False
The given statement that, decimal, fraction, and percent can all represent the same values is True.
Verification of the True Statement:
The ratio of two numbers results in a fraction which are often rational numbers (often integers). As an illustration, 11/59 is a fraction. Typically, absolute values for fractions should be larger than 0 and less than 1. A mixed fraction equivalent to 1 3/4 is 7/4.
A fraction stated in tenths are known as a decimal (or tenths of tenths, etc.). The decimal equivalent of one fourth, or 1/4 as a fraction, is 0.25 (which equals 25/100). (Remember that 1/100 is just a tenth of a tenth.)
Percentage (percent) is a decimal fraction multiplied by 100. Therefore, 0.25 is equivalent to 25 percent, for instance. The ratio of two numbers results in fractions, which are often rational numbers (often integers).
Let us take a number 3/5, this is a fraction.
Now, if we further divide, 3 by 5, we will get 0.6
This 0.6 is a decimal number, but it still represents the number 3/5
Similarly, it is equivalent to 60 percent which again represent the fraction 3/5 or decimal 0.6.
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A large hall has a capacity of 3481 seats. If the number of rows is equal to the number of seats in each row, then find the number of seats in each row
Answer:
59
Step-by-step explanation:
Suppose, The number of seats in each row = z
Number of rows = number of seats in each row 7 z
So, the total plants = z×z=z^2
As per question,
z^2=3481
z=59
So the seats in each row = 59.
Hi,
Could anyone help with this please?
Many thanks,
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.
Length
2.6 x 40 = 260
260 cm = 2.6 m
Width
4.5 x 40 = 180
180 cm= 1.8 m
Area
1.8 x 2.6 = 4.68 m
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
Part of the arena is being turned into a public darkroom. The floor needs covering in rubber tiles before work can begin on the dark room. The tiles are 20 cm by 30 cm. The dark room floor is 6 metres by 3 metres. Are 280 tiles enough? How many more/less tiles are needed?
The number of tiles used is 300 tiles.
According to the statement
We have given that:
The tiles are 20 cm by 30 cm. And the dark room floor is 6 meters by 3 meters.
And we have to find that the number of tiles used to prepare the dark room.
So, For this purpose we have to find the area of the room floor.
The area of the floor is 6 *3.
The area of the floor is 18 meter per square.
The area of the tile is 0.2*0.3
The area of the tile is 0.06 meter per square.
Now,
The number of tiles used is 18/0.06
The number of tiles used is 300.
So, The number of tiles used is 300 tiles.
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What is the value of 2 + (- 2/3)^2 ÷ 1/3 ?
16
3
-2
0
Answer:
3
Step-by-step explanation:
2+ (-2/3)^2 ÷ 1/3
make -2/3 postive because its being raised by an even exponent
you never divide by fractors so make 1/3 into 3 and make it multiplication
2+ (2/3)^2 × 3
raise the fraction to the power of 2
2+ (4/9)× 3
cancel out the GCF
2+ 4/3
add
10/3
simplify
3.3 ≅ 3
Question 5
Find the interest rate for a principal of $6570 and charged $30105 in interest for 12 years.
The Formula is
I
PT
x 100
Take the interest divide by the principal
then divide by the years
then times by 100
Round your answer to 1 decimal place.
Answer:
R=i
Step-by-step explanation:
R=i×100÷p×t
r=30105×100÷6570×12
r=3010500÷78840
r=38.18
Assume the graph is derivative f(x). Answer for f(x)
The intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
How to determine the intervals which the original function f(x) concave down?The information that completes the question are added as an attachment
The question requires that we determine the intervals which the original function f(x) concave down
From the attached graph, we have the following turning points
(-2, -4) and (3, 2)
From the domain of the graph, the curve starts at (-5, 0), turns at (-2, -4), also turns at (3, 2) and then stops at (5, 0)
So, we have:
(-5, 0), (-2, -4), (3, 2) and (5, 0)
Remove the y coordinates
x = -5, -2, 3 and 5
Express as intervals
(-5, -2) and (3, 5)
Hence, the intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
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The hypotenuse of an isosceles right triangle is 14 centimeters longer than either of its legs. Find the exact length of each side. (Hint: An isosceles right triangle is a right triangle whose legs are the same length.)
The Pythagorean theorem states that:
[tex]a^2+b^2=c^2[/tex]
a and b are two legs of a right trianglec is the hypotenuseThe Quadratic Formula[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Solving the QuestionLet a represent the length of one leg.
Because the hypotenuse is 14 cm longer than a leg, we can say that the hypotenuse's length is 14 + a.
Plug these into the Pythagorean theorem:
[tex]a^2+b^2=c^2\\a^2+a^2=(14+a)^2\\2a^2=14^2+2(14)a+a^2\\2a^2=196+28a+a^2\\a^2=196+28a\\a^2-196-28a=0\\a^2-28a-196=0[/tex]
Factor using the quadratic formula:
[tex]a=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]a=\dfrac{-(-28)\pm \sqrt{(-28)^2-4(1)(-196)}}{2(1)}\\\\a=14\pm14\sqrt{2}\\\\a=14+14\sqrt{2}[/tex]
We know that it's plus because subtracting results in a negative value, and length cannot be negative.
This is the length of each side.
Because the hypotenuse is 14 cm longer, we can say that the hypotenuse is [tex]28+14\sqrt{2}[/tex].
AnswerLeg length = [tex]14+14\sqrt{2}[/tex]
Hypotenuse length = [tex]28+14\sqrt{2}[/tex]
Take 4x + 2 from 8x + 5.
4x + 3
4x - 3
-4x - 3
Answer:
4x + 3 just take away rhe values
how is the e - lambda figured out as 0.00248?
Answer:
Step-by-step explanation:
e^-6 = 1/e^6 = about 0.00248
Solve the differential equation. (x^2 + 11)y' = xy
Separate the variables.
[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]
Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].
[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]
[tex]\ln|y| = \frac12 \ln|u| + C[/tex]
[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]
[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]
[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]
Using separation of variables, the solution to the differential equation is:
y = ksqrt(x² + 11)
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
(x² + 11)y' = xy
Applying separation of variables, we have that:
y'/y = x/(x² + 11)
[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]
[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]
[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]
[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]
Hence the solution is:
y = ksqrt(x² + 11)
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A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze and the second brand is 55% pure antifreeze. In order to obtain 160 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
64 gallons 30%96 gallons 55%Step-by-step explanation:
The amount of each brand can be found by writing and solving an equation that makes use of the given relations.
SetupLet x represent the quantity of 55% pure antifreeze needed in the mixture. Then the quantity of the 30% brand is (160-x). The amount of pure antifreeze in the mixture is ...
0.55x +0.30(160 -x) = 0.45(160)
SolutionSubtracting 0.30(160), we have ...
x(0.55 -0.30) = 160(0.45 -0.30)
x = 24/0.25 = 96 . . . . . simplify, divide by the coefficient of x
96 gallons of the 55% brand, and 64 gallons of the 30% brand must be used.
__
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Tyson uploaded 500 videos to the Internet. Sarita uploaded fewer videos than Tyson. Write an inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded.
→WILL MARK BRAINLIEST←
The inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
Inequalitynumber of videos Sarita uploaded = vnumber of videos Tyson uploaded = 500Total videos updated = yInequality for number of videos Sarita uploaded:
v - 500 < y
Therefore, the inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
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Answer:
- v < 500
Step-by-step explanation:
question:
|x-2|, if x > 5
simplify without the absolute value sign
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its positive numerical value.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
List the angles in order from the largest to the smallest for ΔABC. AB⎯⎯⎯⎯⎯⎯⎯=14, AC⎯⎯⎯⎯⎯⎯⎯⎯=15, BC⎯⎯⎯⎯⎯⎯⎯⎯=16
Answer:
BC 1
AC 2
AABC 3
Step-by-step explanation:
BC=16
AC = 15
AABC= 15
Answer: C, B, A
Step-by-step explanation: It just is
Find the area of rhombus JKLM given the coordinates of the vertices. Round to the nearest tenth if necessary.
J(-2, -4), K(2, 2), L(6, -4), M(2, -10)
Answer:
The area of rhombus JKLM is 48 units²=====================================
Given Rhombus JKLM,Vertices at J(-2, -4), K(2, 2), L(6, -4), M(2, -10).To find The area of rhombus JKLMSolutionWe know that diagonals of rhombus are perpendicular to each other.
Hence its area is half the product of diagonals.
The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.
Let's find the length of diagonals, using the difference of coordinates:
JL = 6 - (-2) = 8 units,KM = 2 - (-10) = 12 units.Now find the area:
A = JL*KM /2 = 8*12 / 2 = 48 units²Which of the following is NOT part of a scatter plot graph?
Key
Source
Labels
Scale
Which of the following is the scale on each axis based on?
Averages
Percents
Data
Number of data poin
The first step in the area method to estimate the line of best fit is to ______.
divide the data points equally with a horizontal line
draw a line around all of the data points
place two x's centered in each half of the data points
divide the data points equally with a vertical line
The complete statements are:
The Key is not part of a scatter plotThe scale on the axes of a scatter plot is based on the number of data pointsThe first step in the area method to estimate the line of best fit is to draw a line around all of the data pointsHow to complete the statementsPart of a scatter plot
The parts of a scatter plot are
LabelSourceScaleThe dataThe axesThis means that the Key is not part of a scatter plot
The scale on the axes
Here, the scale is determined by the number of data points that exists on the scatter plot
This means that scatter plots that have 10 and 100 data points might not be represented on the same scale
The line of best fit
This is determined by drawing a line through the data points on the scatter plot.
The line is know as the line of best fit
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Compute (x4 - 5x3+4x² - 15x + 3) = (x² + 3).
Check the attached file.
Two sides of a triangle are 12cm and 8cm. Complete the inequality to show the possible lengths for the third side.
The inequalities that represents the third side of the triangle is c ≥ 4 or c ≤ 20
How to find the third side of a triangle?The triangle inequality theorem states that that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, the two sides of the triangle are 12 cm and 8 cm.
A triangle with sides a, b and c follows the principle below;
a + b ≥ c.
Therefore,
let
c = third sides
12 + 8 ≥ c
20 ≥ c
c + 8 ≥ 12
c ≥ 4
c + 12 ≥ 8
Therefore, the third third should be greater than or equals to 4 or less than or equals to 20
c ≥ 4 or c ≤ 20
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According to a recent poll at a university,70.7 % of high school seniors in a certain region had a driver's license. A sociologist thinks this rate has declined. The sociologist surveys randomly selected high school seniors and finds that have a driver's license. a. Pick the correct null hypothesis. b. Pick the correct alternative hypothesis. c. In this context, what does the symbol p represent?
your mother i swear
Step-by-step explanation:
ask yo mom
Which statement best reflects the solution(s) of the equation? ASAP
The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Given the equation:
1 / (x - 1) + 2/x = x / (x - 1)
Multiplying through the equation by x(x - 1):
x + 2(x - 1) = x(x)
x² - 3x + 2 = 0
x² - 2x - x + 2 = 0
(x - 2)(x - 1) = 0
x = 2; and x = 1
The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1
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Ronaldo specializes in creating sewing patterns for dresses, and wants to set up his own website to sell electronic copies. He pays $120 for a domain name and web hosting services for the first year. Ronaldo makes $14.25 for each electronic pattern that he sells. How many patterns must he sell to cover the cost of the website for the first year? Round your answer to a whole number.
Answer:
8
Step-by-step explanation:
120/14.25=8.4 rounded off to a whole number is 8
Someone please help me with this question thank youuu
Answer: 148 degrees
Step-by-step explanation:
The total measure of all exterior angles of a convex pentagon is 360 degrees.
If four of them equal 53 degrees then all those together is 212 degrees
53 times 4 = 212
Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!
Hope this helps :)
Please Help!!!
Type the correct answer in the box. Use numerals instead of words.
The surface area of a cone is square units. The height of the cone is times greater than the radius.
What is the length of the radius of the cone to the nearest foot?
The radius is about
feet.
Answer:
Step-by-step explanation:
9.05737
The length of the radius of the cone to the nearest foot is 5 feet.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, The surface area of a cone is 216π sq units and the height of the cone is (5/3) times of the radius.
∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.
∴ πrl = 216π.
√{(34/9)r³ = 216.
1.9r³ = 216.
r³ = 113.7.
r = 4.8 feet Or 5 feet.
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Find the number if 11% of it is 55
Answer:
Step-by-step explanation:
.11x = 55
11x = 5500
x = 500
Drag the tiles to the correct boxes to complete the reasoning of the proof. Not all tiles will be used.
May this help other people in the near future!!!!!
The missing reasons for each of the given statements are respectively;
1) Substitution
2) Definition of a Straight angle because a straight angle is 180°.
3) Congruent Angles have equal measures
How to prove angles in a triangle?
We are given that;
m∠1 = 90°
m∠1 + m∠2 = m∠5
∠3 ≅ ∠4
Statement 1; 90° + m∠2 + m∠4 = 180°
Reason 1; Substitution
Statement 2; m∠1 + m∠2 + m∠3 = 180°
Reason 2; Definition of a Straight angle because a straight angle is 180°.
Statement 3; m∠3 = m∠4
Reason 3; Congruent Angles have equal measures
Thus, the missing reasons for each of the given statements are respectively;
1) Substitution
2) Definition of a Straight angle because a straight angle is 180°.
3) Congruent Angles have equal measures
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Question 1 Which number has the greatest value? O 0.095 O 1.24 1.215 O 0.365 Confident
Answer:
1.24
Step-by-step explanation:
because 1.24>1.215>0.365>0.095
There are 96 football players at all levels at Davenport High School. If two-thirds of the players make the honor roll for their grades how many olayers are on the list?
64 players
48 players
72 players
54 players
