The value of the constant of variation is 2,199 feet. The speed of the another rider is 87.96 feet/sec.
What is the directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
A.) The time it takes to complete a go-cart course is inversely proportional to the average speed of the go-cart. Therefore, the relationship can be written as,
Average speed ∝ (1/time)
Now, if the constant of variation is introduced then the relationship can be written as,
Average speed = k(1/time)
Substituting the values, we will get,
[tex]73.3\frac{ feet}{second}= k \times \dfrac{1}{30\ seconds}\\\\73.3 \frac{ feet}{second}\times 30\ seconds = k\\\\k = 2,199\ feet[/tex]
Hence, the value of the constant of variation is 2,199 feet.
B.) The speed of the another rider is,
Average speed = k(1/time)
Average speed = 2,199×(1/25) feet/sec
Average speed = 87.96 feet/sec
Hence, the speed of another rider is 87.96 feet/sec.
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I have no idea what to do for these 2 questions, somebody please help
Answer:
Step-by-step explanation:
2.2:
[tex]3^2(6)(3.14) = 169.56 in^3[/tex]
3.3
[tex]9^2(5)(3.14) = 1287.4 un^3[/tex]
Mick recently had new carpet installed. the cost of the carpet including installation was $8.14 per square foot before any discounts. the rectangular room he had carpeted measured 24 feet long and 18 feet wide. if mick actually paid $3,235.16, what discount percentage did he receive? assume there are no taxes.
Answer:
8%
Step-by-step explanation:
Let’s first determine the cost before any discount.
To do so, we first need to determine the area to be carpeted:
Area of Rectangle = Length × Width = 24 ft × 18 ft = 432 square feet.
To find the cost before discount we need to multiply the area by the cost per square foot:
Cost Before Discount = Area × Cost per square foot
Cost Before Discount = 432 square feet × $8.14 per square foot
Cost Before Discount = $3,516.48
We can now determine the discount percentage he received:
Cost After Discount = Cost Before Discount − (Discount % × Cost Before Disc.)
$3,235.16 = $3,516.48 – (Discount % × $3,516.48)
To solve, it is easiest to plug in each answer to see which discount percentage is the correct solution (i.e. “work backwards” from the given answers) or use the equation solver on our calculator.
We find that a discount of 8% is the correct solution.
If you instead prefer to use algebra to solve for the discount percentage, here are the steps.
We will rewrite the equation, using x to represent “Discount %”.
$3,235.16 = $3,516.48 − (x × $3,516.48)
$3,235.16 = $3,516.48 − $3,516.48x
Factoring out $3,516.48 we have:
$3,235.16 = $3,516.48(1 − x)
Note: Once you get comfortable with this type of problem you should skip straight to the step above.
Dividing both sides by $3,516.48 we have:
$3,235.16$3,516.48=1−x
0.92 = 1 − x
x = 0.08 = 8%
A doctoral student wants to determine the relationship between steps per minute and the time it takes to walk 100 feet in
minutes. Thirty trials are completed and the correlation coefficient between steps per minute and time in minutes is determined
to be -0.543. Therefore, fewer steps per minute were related to longer time spans. How is the correlation affected if the units for
time are changed from minutes to seconds? (3 points)
The correlation and time measurement would change proportionally to one another.
The correlation would increase because changing the units for time would result in an increase in time values.
It is impossible to determine the amount of change experienced by the correlation.
The correlation would decrease because only the units for one of the variables changed.
The correlation would stay the same because the change in units for time would have no effect on it.
Using correlation coefficients, it is found that that the correct option is given as follows:
The correlation would stay the same because the change in units for time would have no effect on it.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.The correlation coefficient does not have units, hence if the units of the measures is changed, the coefficient remains constant, which means that the correct option is given by:
The correlation would stay the same because the change in units for time would have no effect on it.
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If a circular playground has an area of 144 m2. What is the diameter of the playground?
Answer:
The diameter is about 13.55m
Step-by-step explanation:
Calculator
convert 0.29 to a percentage
Answer:
0.29 as a percentage is the same as 29%
Step-by-step explanation:
it’s going to be 29% because you just pretend that there isn’t a 0. In front of the 29 and you have 29%.
The decimal number 0.29 is equivalent to 29% when expressed as a percentage.
Given decimal is 0.29.
To convert a decimal number to a percentage, multiply it by 100 and add the percentage symbol (%).
In this case, to convert 0.29 to a percentage
= 0.29 x 100
= 29
Therefore, 0.29 is equivalent to 29% as a percentage.
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What is the area of adef with vertices d(-1,-5), e(4.-5),
and f(4,7)?
Answer:
Step-by-step explanation:
30 square unit is the area of the triangle DEF.
What are the properties of Triangle?The properties of the triangle are:
The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.We can use the coordinates of the three vertices of the triangle to find the length of its base and height, and then use the formula for the area of a triangle.
The base of the triangle is the line segment from point E to point F, which has a length:
|EF| = √[(4-4)^2 + (7-(-5))^2] = √(0^2 + 12^2) = 12
The height of the triangle is the perpendicular distance from point D to the line containing the base, which is the horizontal line y = -5.
Therefore, the height of the triangle is the vertical distance from point D to the line y = -5, which is 5 units.
The area of the triangle is then:
Area = (1/2) x (base) x (height)
= (1/2) x 12 x 5
= 30 square units.
Therefore, the area of triangle DEF is 30 square units.
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Match each problem with its solution.
200
6
5
15
Jason is a party planner. In 124 packages, he has a total
of 1,860 balloons. If each package has the same number
of balloons, how many balloons are there in each package?
arrowRight
A plane has to travel 2,800 miles at an average speed of
560 miles per hour. How many hours will it take to reach
its destination?
arrowRight
An adult seal at a marine park consumes 2,400 kilograms
of food in one year. If it consumes the same amount of
food every month, how many kilograms of food does the
seal consume per month?
arrowRight
Andy and his roommates consume 180 bottles of orange
juice in 30 days. If they consume the same amount of
orange juice each day, how many bottles of orange juice
do they consume each day?
please let me know if you have an answer
The number of balloons on each package will be 15
How to calculate the problems?From the information, Jason is a party planner. In 124 packages, he has a total of 1,860 balloons and each package has the same number.
Therefore, the number of balloons on each package will be:
= 1860 / 124
= 15
When a plane has to travel 2,800 miles at an average speed of 560 miles per hour. The number of hours used will be:
= 2800/560
= 5
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Kara wants to buy a game that is on sale. the original price of the game is p, but it is on sale for 30% off the original price. she uses the expression p(i - 0.3) to model the price. which expressions are equivalent to kara's expression? select all correct answers and the answers are
p - 0.3
1 - 0.3p
0.7p
p - 0.3p
1.3p
The expressions equivalent to kara's expression are 0.7p and p-0.3p
How to find discount of original price?Original price = pDiscount = 30%Discount price expression = p(1 - 0.3)
= p - 0.3p
= 0.7p
Check for equivalent expression
p - 0.3
Not equivalent
1 - 0.3p
Not equivalent
0.7p
Equivalent
p - 0.3p
Equivalent
1.3p
Not equivalent
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the distance midpoint between A (-6, 8) & B (6, -2)
Answer:
I think 2
Step-by-step explanation:
6-2is 4 8-6 2 both have common 6 and 2 multiple of 6is 2
Out of a population of 1,500 students, 100 were asked by a random sampling to choose their favorite national park. their responses are shown in the table below. national parks favorite park number of students acadia 19 carlsbad caverns 14 rocky mountain 30 grand canyon 23 yosemite 14 using proportional reasoning, about how many students out of the 1,500 would you expect to pick yosemite for their favorite national park? 14 86 210 244
Answer:
210
Step-by-step explanation:
the sample is one 15th of the total population, and thus Yosemite's 14 should be scaled back by 15
1500/100 = 15
15 * 14 = 210
Answer:
210
Step-by-step explanation:
I did the test
A flower shop charged $124.44 for 3 bouquets of flowers. This price included a $7.50 service and delivery fee.
What was the cost of one bouquet?
A car traveled 200 miles on 8 1/2 gallons of gas. How much gas will it take to drive 1 mile?
Answer:
23 1/2 gallons of gas to travel one mile
Step-by-step explanation:
Given the car can travel 200 miles on 8 1/2 gallons of gas, we divide 200 by 8 1/2.
8 1/2 = 8.50 = 8.5
200/8.5 = 23.5 = 23.52 = 23 1/2
Answer:
17/400 gallons or 0.0425 gallons
Step-by-step explanation:
Take the ratio of the scale and the actual values :
200 miles : 8 1/2 gallons = 1 mile : x gallons200/(8.5) = 1/x400/17 = 1/xx = 17/400 gallons or 0.0425 gallons[tex]\huge\color{yellow}\underline \colorbox{violet} {\color{red}{QUESTION}}[/tex]
Direction:Write TRUE if the statement is true and FALSE if not.
1.Non standard units cannot be used to measure volume.
2.To find the volume of rectangular prism multiply the length width and height.
3.When the non-standard unit used in small,more units are needed to fill a container.When the non-standard unit used is bigger.Few units are needed to fill the container.
correct answer=brainles
nice answer=rate 5 star
explanation=heart
incorrect=report
no explanation=report
Answer:
FALSETRUETRUEStep-by-step explanation:
1.
Non-standard units can be used to measure volumeExamples : m³, in³, cm³, mm³, L2.
The volume of a rectangular prism can be found by multiplying the length, width, and heightV = lwh3.
If there are smaller units, then naturally more of the units will be usedIf there are larger units, then less of the units will be usedA cylinder has a circumference of 16pi inches and a height of 20 inches. what is the surface area of a cylinder in square inches?
Answer:
1407.43
Step-by-step explanation:
The eqaution for surface area of a cylinder is 2πr+2π[tex]r^{2}[/tex]'
but you already got the circumference so you work backwards
16pi/pi=16
16/2=8
r=8
h=20
So you plug it into the eqaution
2π8*20+2π8^2=1407.43
Find the slope of the line that goes through the given points! A(2,8) and B(4,6)
(WHOEVER ANSWERS FIRST AND CORRECTLY WILL BE BRAINLIEST!!!)
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
Find the slope of the line that goes through (2, 8) and (4, 6)
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
The slope formula will help us find the slope, Here it is:-
[tex]\Large\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]
Now, replace y2 with 6, y1 with 8, x2 with 4, and x1 with 2:-
[tex]\Large\text{$\displaystyle\frac{6-8}{4-2}$}[/tex]
Simplifying,
[tex]\Large\text{$\displaystyle\frac{-2}{2}$}[/tex]
Simplifying further,
[tex]\hookrightarrow\underline{\boxed{\sf{Slope=-1}}}[/tex]
Good luck with your studies.#TogetherWeGoFar
[tex]\rule{300}{1}[/tex]
Answer:
[tex]\sf \boxed{-1} \ \ is \ the \ slope[/tex]
Explanation:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given points: A(2,8) and B(4,6)
Find slope (m):
[tex]\sf \rightarrow \dfrac{6-8}{4-2}[/tex]
simplify
[tex]\sf \rightarrow -1[/tex]
AdditionalTo find equation:
[tex]\sf y-y_1 = m(x-x_1)[/tex]
[tex]\rightarrow y-8 = -1(x-2)[/tex]
[tex]\rightarrow y = -x+2+8[/tex]
[tex]\rightarrow y = -x+10[/tex]
The triangle below is equilateral. Find the length of side X in simplest radical form with a rational denominator.
Answer:
kinda hard
Step-by-step explanation:
h² = c² + c²
([tex]\sqrt{11}[/tex])² = ([tex]\sqrt{11}[/tex]/2)² + x²
x² = ([tex]\sqrt{11}[/tex])² - ([tex]\sqrt{11}[/tex]/2)²
answer: x = [tex]\sqrt{11}[/tex] - [tex]\sqrt{11}[/tex]/2
14.
If we flip a coin eight times, how many possible sequences of eight coin faces (i.e., heads or tails) can we have?
1,024
512
256
2,048
Using the Fundamental Counting Theorem, the number of possible sequences of eight coin faces is of 256.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, there are 8 events, each with 2 possible outcomes, hence:
[tex]n_1 = n_2 = \cdots = n_8 = 2[/tex]
Hence, the total number of sequences is given by:
[tex]N = 2^8 = 256[/tex].
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Answer:
C) 256
Step-by-step explanation:
Essentially, each coin flip is a decision, and heads or tails is the choice offered. Therefore, we calculate that there are 28 possible sequences, or 256.
Took the quiz ;)
Solve for x in the equation below.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.
x-6 = 7
e
Answer:
x=13
Step-by-step explanation:
The graph of f(x) = x2 was transformed to create the graph of g(x) = (2x)2 – 4. Which of these describes the transformation from the graph of f to the graph of g?
Answer:
A. Horizontal Stretch and vertical shift down 4
Step-by-step explanation:
When multiplying by a number greater than one, its a stretch. When it is less than one it is a compression.
2 is greater than 1 so its a horizontal stretch.
When there is a number outside of the () then that number determines how high or how low you go depending on the sign.
Our number is -4 so we go down 4.
3B What is the value of account after 10 years,
if interest is paid at 3.7%, if no other deposits
or withdrawals are made?
Initial deposit $6500, then compounded annually
Answer:
$9,347.62
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $6,500r = 3.7% = 0.037n = 1t = 10 yearsSubstituting the given values into the formula and solving for A:
[tex]\implies \sf A=6500\left(1+\frac{0.037}{1}\right)^{10 \times 1}[/tex]
[tex]\implies \sf A=6500\left(1.037\right)^{10}[/tex]
[tex]\implies \sf A=9347.617232[/tex]
Therefore, the value of account after 10 years is $9,347.62
Let's see
[tex]\\ \rm\Rrightarrow A=P(1+r)^t[/tex]
P=6500r=3.7%t=10yearsSo
A:-
[tex]\\ \rm\Rrightarrow 6500(1+0.037)^{10}[/tex]
[tex]\\ \rm\Rrightarrow 6500(1.037)^{10}[/tex]
[tex]\\ \rm\Rrightarrow \$ 9347.6[/tex]
THE IMAGE OF TRIANGLE ABC AFTER A 180 DEGREE ROTATION THE ORIGIN IS
The image of triangle ABC is a A'B'C' after rotating about the origin with an angle of 180 degree.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
If we rotate the triangle ABC with the origin (0, 0) about 180 degree it will form an image of the triangle ABC which is A'B'C'
Here the coordinates for ABC are not given so we are assuming the triangle ABC has a image which is A'B'C' (refer attached picture)
Thus, the image of triangle ABC is a A'B'C' after rotating about the origin with an angle of 180 degree.
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what is the area, in square centimeters, of the isosceles trapezoid below?
Answer:
65.28
Step-by-step explanation:
1/2 × (15.2+5.2) × 6.4 = 65.28
hope this helps ;)
The principal sent a message to 25 students to ask them to
help pick up litter after school. Only 8 of them showed up.
What percentage of the students came to pick up litter?
Answer: 32%
Step-by-step explanation:
100 / 25= 4
4 x 8 = 32%
I'll mark as Brainliest, Please answer ASAP, Ihave MCAS tomorrow. How could this be true?? Please Explain.
Answer:
See below
Step-by-step explanation:
The number of loaves of bread remaining can only go as low as ZERO (you can't have negative loaves) ...and can only go as high as when h = 0
so 0 = 42-3.5 h
3.5 h = 42
h = 12 and min is h = 0 ( when there are 42 loaves to start)
So:
0≤ h ≤ 12
What binomial do you have to add to the polynomial 2x^2+3y^2-5xy+1 to get the following?
a polynomial that does not contain the variable y
Answer:
-3y^2+5xy
Step-by-step explanation: Just cancel out all of the numbers with the variable "y"
Binomial [tex]-3y^{2}+5xy[/tex] when added to polynomial [tex]2x^{2} +3y^{2} -5xy+1[/tex] gives polynomial that does not contain the variable y .
What is binomial?A mathematical expression consisting of two terms connected by a plus sign or minus sign .
Example: x + 2 is a binomial, where x and 2 are two separate terms.
What is polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer
According to the question
polynomial [tex]2x^{2} +3y^{2} -5xy+1[/tex]
when added with [tex]-3y^{2}+5xy[/tex]
= [tex]2x^{2}+1[/tex] (as [tex]3y^{2} -5xy[/tex] got cancelled )
that does not contain the variable y
Hence, Binomial [tex]-3y^{2}+5xy[/tex] when added to polynomial [tex]2x^{2} +3y^{2} -5xy+1[/tex] gives that does not contain the variable y .
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GR. 9 QUESTION 1/ VRAAG 1: Simplify the following: / Vereenvoudig die volgende: 1.1 -8xy-6xz + 10xy + 9xz - 4yx
1.2 m² - 4m - 1 + m² - 8m + 5-6m² +3m - 1
Answer:
Below in bold.
Step-by-step explanation:
-8xy-6xz + 10xy + 9xz - 4yx (Note 4yx = 4xy)
Bringing like terms together we have:
-8xy + 10xy - 4xy - 6xz + 9xz
= -2xy + 3xz.
m² - 4m - 1 + m² - 8m + 5-6m² +3m - 1
= m² + m² - 6m² - 4m - 8m + 3m - 1 + 5 - 1
= -4m² - 9m + 3.
pleas send help this is due today
Answer:
y = -3x
Step-by-step explanation:
Equation of the line going through the origin: y = mx
Substitute any point in the above equation.
Here, Chosen point( 1 ,-3)
-3 = m*1
m = -3
Equation of the line: y = -3x
6 + 33 divided by 9 what is it
Answer:
I think its 4.9
Step-by-step explanation:
i used a calculator
Answer:
6+33/9 ≈ 9.67
Step-by-step explanation:
first you have to divide 33 by 9 getting roughly 3.67
once you have that u add 6
roughly giving you 9.67
Find a number “a so that the numbers 42, 46, a, a, a have a mean and mode both equal.
Answer:
44
Step-by-step explanation:
The mode will be a as it is the most in frequency.
Calculating 'a' by taking the mean
42 + 46 + a + a + a / 5 = a88 + 3a = 5a2a = 88a = 44Help ASAP NEED ANSWER NOW
Answer:
A.
Step-by-step explanation:
bc, it's high preasured. meaning its going 2b snowy.
