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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Find the prime factorization of 1296
METHOD WAY!
Answer:
[tex]1296 = 6 \times 6 \times 6 \times 6 = {6}^{4} = {2}^{4} \times {3}^{4} [/tex]
How Do You Graph This Equation
Answer:
Rearrange both inequalities to make y the subject.
Momentarily swap the inequality sign for an equals sign in order to calculate two points for each line.
Inequality 1
[tex]2y \leq x-10[/tex]
[tex]\implies y < \dfrac{1}{2}x-5[/tex]
[tex]x=0\implies y=\dfrac{1}{2}(0)-5 \implies (0,-5)[/tex]
[tex]x=4 \implies y=\dfrac{1}{2}(4)-5 \implies (4,-3)[/tex]
Inequality 2
[tex]x+y\leq -3[/tex]
[tex]\implies y\leq -x-3[/tex]
[tex]x=0\implies y=-(0)-3\implies (0,-3)[/tex]
[tex]x=4\implies y=-(4)-3\implies (4,-7)[/tex]
When graphing inequalities
< or > : dashed line
≤ or ≥ : solid line
< or ≤ : shade below the line
> or ≥ : shade above the line
Therefore,
Inequality 1: plot points (0, -5) and (4, -3) and draw a solid line through them.
Inequality 2: plot points (0, -3) and (4, -7) and draw a solid line through them.
Shade the area below both lines from where the lines intersect.
Answer:
See below ~
Step-by-step explanation:
Inequality 1 :
Convert into y = mx + b form2y ≤ x - 10y ≤ x/2 - 5Taking 2 points :
0 ≤ x/2 - 5x/2 ≥ 5x ≥ 10⇒ Point 1 = (10, 0)y ≤ 0 - 5y ≤ -5⇒ Point 2 = (0, -5)Inequality 2 :
x + y ≤ -3y ≤ -x - 3Taking 2 points :
0 ≤ -x - 3x ≤ -3Point 1 = (-3, 0)y ≤ 0 - 3y ≤ - 3Point 2 = (0, -3)Plot the two 2 lines using the 2 points and shade as per the sign of the inequality. The result will be this graph :
Please help don’t understand radical
Simplified
[tex]x\sqrt[3]{x}[/tex]
Can you create a data set which contains median=6 and mode=4?
1, 4, 6, 9, 15, 4, 3, 12, 11
Answer:
hey!
Step-by-step explanation:
b) Your father uses text messaging to communicate with his employees. If he sends an
average of 19 text messages each day, how many more text messages does he
send than you? Write an equation and solve for the unknown value. (2 points)
Answer:
father sends 7 more
19-12=7
Need help please answer ASAP!
25&26
Answer:
40° and 6
Step-by-step explanation:
25. Let's suppose the angles as 2x and 7x
Then,
2x + 7x = 180°
or, 9x = 180°
or, x = 180°/9
or, x= 20°
Now, 2x is smaller
So, 2x = 2× 20° = 40°
26. Solution,
Each exterior angle = 360°\n
or, 60° = 360°/n
or, 60°n = 360 °
or, n = 360°/60°
or, n=6
As, Hexagon has 6 sides.
#26
Any polygon has sum of exterior sides as 360°
No of sides
360/60=6#25
Let the angles be 2x and 7x
2x+7x=1899x=180x=180/9x=20°Smallest angle=2(20)=40°
whats the probability of Rolling an even number on a dice, then flipping a coin to get a tails
Answer:the probabilities of getting a head and a tail are equal to 12 . The probability of getting an even number on a die is 36=12
Step-by-step explanation:because among 6 results there are 3 even numbers.
please give answer asap i’ll give brainlist to correct answer
Answer:
I believe the answer is; The median is 4.5 inches.
let me know if this is right for you! :)
Step-by-step explanation:
I need help on this please
Answer:
9.45 ounces
Step-by-step explanation:
The formal definition of the standard deviation of a population is that it is the square root of the mean of the squares of the differences between the data values and their mean.
The calculation can be done more simply as the root of the difference between the mean of the squares and the square of the mean. That is the calculation shown in the attachment.
The population standard deviation is about 9.45 ounces.
_____
Additional comment
The easier way to do the calculation is to use the calculator or spreadsheet function that gives the result directly. For the Desmos calculator shown, that function is stdevp(w) for the definition of w that we used. The function has the same name in many spreadsheet programs.
The relationship between the number of pounds (lb) of almonds and the price in dollars is shown in the graph. What is the unit price of almonds?
Answer:
B
Step-by-step explanation:
Slope is change of y over change of x
Y is going up by 8 and x is going over by 1
Therefore, $8/1 lb
The average speed of a car on the highway is 65 miles per hour? How many feet per
second is this?
Answer:
95.3333 ft/s
Step-by-step explanation:
Can someone answer this problem??
Answer: The answer is 9
Answer:
9% of her monthly income is spent on 'Other expenses'
Step-by-step explanation:
[tex]900+120+80+100+320=1820[/tex]
but if you divide 180 by 2000 you'll get 0.09 but times that by 100 you'll get 9%
12250 depreciates by 6% per year how much is the tractor worth after six years
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &12250\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=12250(1 - 0.06)^{6}\implies A=12250(0.94)^6\implies A\approx 8450.90[/tex]
I really need help with this. This is for AP Calculus. I just need to find the derivative for this function.
Answer: 40x^4 + 56x^3 − 16x − 14
Step-by-step explanation:
1. For any two functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.
2. The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0.
3. Simplify
4. Multiply 4x^2 + 7x^1 times 6x^2
5. Multiply 2x^3 - 2 times 8x^1 + 7x^0
6. To multiply powers of the same base, add their exponents.
7. Simplify
8. Combine like terms
9. For any term t, t^1 = t
10. For any term t except 0, t^0 = 1
If segment A is perpendicular to segment B, then they intersect at a 90° angle.
Choose the equivalent statement.
A. If segment B is not perpendicular to segment A, then they
intersect at a 90° angle.
B. If segment A is perpendicular to segment B, then they do not
intersect at a 90° angle.
C. If segments A and B do not intersect at a 90° angle, then they are
not perpendicular to each other.
The vertices of a feasible region are (14, 2), (0, 9), (6, 8), and (10, 3). what is the maximum value of the objective function p if p = 180x 250y? 2,940 3,020 3,080 3,250
The maximum value of the objective function p if p = 180x + 250y is 3020
How to determine the maximum value?The coordinates of the feasible region are given as;
(14, 2), (0, 9), (6, 8), and (10, 3)
The objective function is given as:
P = 180x + 250y
Substitute the coordinates of the feasible region in the above function
P = 180 * 14 + 250 * 2 =3020
P = 180 * 0 + 250 * 9 = 2250
P = 180 * 6 + 250 * 8 = 3080
P = 180 * 10 + 250 * 3 = 2550
The maximum value in the above computation is:
P = 180 * 14 + 250 * 2 =3020
Hence, the maximum value of the objective function p if p = 180x + 250y is 3020
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Linear Programming Quiz - Edge
Question 1: D
Question 2: D
Question 3: D
Question 4: B
Question 5: C
Question 6: C
Question 7: D
Question 8: A
Question 9: C
Question 10: C
It says I can't add anymore attachments but the rest are correct trust me
How many different trains can you make of length three?
Using the combination formula, and supposing that you have n parts, it is found that the number of trains you can make is of:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
The order in which the parts are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 3 parts are taken from a set of n, hence the total number of trains is given by:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
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A rectangle sticker had a perimeter of 32 centimeters and a area of 48 square centimeters. what are the dimensions of the sticker
Answer:
4 cm ×12 cm
Step-by-step explanation:
To find the dimensions of the sticker, start by forming 2 equations for its area and perimeter.
Perimeter of rectangle= 2(length +breadth)
Let the length and breadth of the rectangle be L and B cm respectively.
2(L +B)= 32
Divide both sides by 2:
L +B= 16 -----(1)
Area of rectangle= length ×breadth
LB= 48 -----(2)
From (1): L= 16 -B -----(3)
Substitute (3) into (2):
(16 -B)(B)= 48
Expand:
16B -B²= 48
B² -16B +48= 0
(B -4)(B -12)= 0
B -4= 0 or B -12= 0
B= 4 or B= 12
Substitute into (3):
L= 16 -4 or L= 16 -12
L= 12 or L= 4
Thus, the dimensions of the sticker is 4 cm ×12 cm.
HELP ASAP PLS
a survey asked two age groups about the car color that they most preferred. the results are down in the table below. which car color eat most preferred by people ages 16-24 and what is the relative frequency within this age group?
A.) Blue, 71.4%
B.)Red, 60.6%
C.)Blue, 26.8%
D.)33.9%
Answer:
blue i think good luck
Does anybody know this? I don't have much time and Also it is not the forth option. What is the approximate surface area of the cylinder shown?
Answer:
C) [tex]628\:\text{cm}^2[/tex]
Step-by-step explanation:
[tex]SA=2\pi rh+2\pi r^2\\\\SA=2\pi(\frac{10}{2})(15)+2\pi(\frac{10}{2})^2\\ \\SA=150\pi+50\pi\\\\SA=200\pi\:\text{cm}^2\approx628\:\text{cm}^2[/tex]
At devon's new job he spent $12.99, $10.50, $9.89, $6.90, and $7.58 on lunch the first week.
in the second week, he spent $2 more in total for the 5 lunches than the first week.
what is the increase in the mean for the second week compared to the first?
round the answer to the nearest penny.
A mean is an arithmetic average of a set of observations. The increase in the mean for the second week compared to the first is 0.4.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]
Given the spending in the first week is $12.99, $10.50, $9.89, $6.90, and $7.58, therefore, the mean will be,
[tex]\rm (Mean)_1 = \dfrac{\$12.99 + \$10.50 + \$9.89 + \$6.90 + \$7.58 }{5} = \$9.57[/tex]
Also, the spending in the second week is $2 more than the total of the first week, therefore, the mean will be
[tex]\rm (Mean)_2 = \dfrac{\$12.99 + \$10.50 + \$9.89 + \$6.90 + \$7.58 + \$2}{5} = \$9.97[/tex]
Hence, the increase in the mean for the second week compared to the first is 0.4.
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Which is equivalent to (3√125)*?
Answer:
33.5410196625 ????
Step-by-step explanation:
is 0.4285714285714 a rational number
Answer:
No it is not a rational number
Step-by-step explanation:
A rational number is a number that can be written in the form
p
q
, where
p
and
q
are integers and
q
≠
o
.
All fractions, both positive and negative, are rational numbers. A few examples are
4
5
,
−
7
8
,
13
4
,
and
−
20
3
Which equation gives the line shown on the graph?
y
y = 22 +4
10
9
8
y = 224
7
6
三一z-4
5
u
3
y= 22 + 4
N
1
O
0 1 2 3 4 5 6 7 8 9 10
Done >
Answer:
6
Step-by-step explanation:
line graph start at 5 equations
A graph shows the horizontal axis numbered 4 to 16 and the vertical axis numbered 4 to 12. points and a line show an upward trend. which is most likely the correlation coefficient for the set of data shown? –0.872 –0.191 0.191 0.872
Answer:
Its 0.191
Step-by-step explanation:
Answer:
c) 0.191
Step-by-step explanation:
In a bag, there are oranges and bananas. If we give away 135 bananas, the percentage of fruits in the bag that are bananas will decrease from 60% to 15%. How many oranges are there in the bag
The number of oranges that are in the bag is 120.
How many oranges are in the bag?The equation that represents the initial amount of bananas in the bag is: bananas / total number of fruits = 0.60
bananas = 0.60t equation 1
The equation that represents the number of bananas in the bag after 135 was removed is:
(b - 135) / t = 0.15
b - 135 = 0.15t equation 2
Where :
b - total number of bananas t = total number of fruitsSubstitute for b in equation 2 using equation 1
0.6t - 135 = 0.15t
0.6t - 0.15t = 135
t = 135 / (0.6 - 0.15)
t = 300
The initial number of bananas : 0.6 x 300 = 180
Number of oranges = 300 - 180 = 120
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What is the length of DE?
A. 5
B. 7
C. 6
D. 8
Answer:
the answer is 5. I think because it's a trian
A. 5 I think.....the length of DE is 5.
Check all statements that are true. If none are true click “None”
A- Since it is a repeating decimal, 14.19 is irrational.
B- Since it is a terminatingdecimal, 12.19 is rational.
C- Since 16 is a perfect square,
16 is irrational
D- Since 6 is not a perfect square, 6 is rational.
E- Since it’s a ratio of two integers 11/3 is rational
Answer:
B and E are True.
Step-by-step explanation:
B 12.19 is a terminating decimal so it is rational.
E its a ratio of 2 integers so its rational.
A - is not repeating so this is false.
C. a perfect square is rational - 16 can be written as 16/1.
D. 6 is rational because it can be written as 6/1 not because its not a perfect square.
Practice solving problems involving the area Assignment Which are true about the area of a circle? Check all that apply. The diameter is used in the formula. The units are always squared. The area can be found when given the diameter by first finding the radius. The area is the distance around the circle. Circumference can be used to find area.
Factorize algebraic expressions by pulling out highest commom factor.
10x - 15y
Answer:
5(2x-3y)
Step-by-step explanation:
10x-15y
=(5)(2x)-(5)(3y)
=5(2x-3y)