The direct variation of x to y implies that x and y increases at the same time, and the formula of x in terms of z is [tex]x = 4z^3[/tex]
How to determine the formula for x?The direct proportion of x to y is represented as:
[tex]x\ \alpha\ y^2[/tex]
As an equation, we have:
[tex]x\ =\ ky^2[/tex]
The direct proportion of y to z is represented as:
[tex]y\ \alpha\ z^3[/tex]
As an equation, we have:
[tex]y\ =\ kz^3[/tex]
Square both sides
[tex]y^2 = k^2z^3[/tex]
Substitute [tex]y^2 = k^2z^3[/tex] in [tex]x\ =\ ky^2[/tex]
[tex]x =k^3z^3[/tex]
When z = 2, x = 32.
So, we have:
[tex]32 =k^3 * 2^3[/tex]
Evaluate
[tex]32 =k^3 * 8[/tex]
Divide both sides by 8
[tex]k^3 =4[/tex]
Substitute [tex]k^3 =4[/tex] in [tex]x =k^3z^3[/tex]
[tex]x = 4z^3[/tex]
Hence, the formula of x in terms of z is [tex]x = 4z^3[/tex]
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what value makes the following equation true? x + 10 = 18
x=8
Solution:In order to determine the value of x that makes the equation true, we need to subtract 10 from both sides:x+10=18x=18-10x=8Therefore, when x=8, the equation x+10=18 is true.Hope it helps.
Do comment if you have any query.
Answer:
8 + 10 = 18
Step-by-step explanation:
no need for explanation simple addition
A solid shape is made by joining two cones.
Each cone has the same radius.
One cone has
slant height = 2 × radius
The other cone has slant height = 3 × radius
The total surface area of the shape is 135. 21 cm²
Curved surface area of a cone = tırl where r is the radius and / is the slant height
Work out the radius.
The surface area of the solid shape is the amount of space on it
The radius of the two cones is 2.93 cm
How to determine the radius?The given parameters are:
Cone 1: slant height, l = 2rCone 2: slant height, L = 3rSurface area = 135. 21 cm²The surface area of the shape is calculated using:
T = πr(L + l)
So, we have:
135.21 = πr(2r + 3r)
Evaluate
135.21 = 5πr²
Divide both sides by 5π
r² = 135.21/5π
Evaluate the quotient
r² = 8.61
Take the square root of both sides
r = 2.93
Hence, the radius of the cones is 2.93 cm
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The area of the rectangle below is greater than or equal to 18.13 square units. The inequality 3.7w ≥ 18.13 represents this
situation?
Answer:
so the answer is tyrany because i love to talk aboutheaarts so this is waht happened
Step-by-step explanation:
Brianna was offered a job that paid a salary of $77,000 in its first year. The salary
was set to increase by 2% per year every year. If Brianna worked at the job for 5 years,
what was the total amount of money earned over the 5 years, to the nearest whole
number?
Answer:776
Step-by-step explanation:
77
Brianna earned a total of approximately $400,652 over the 5 years.
What is an expression?A grouping of variables, symbols, and/or numbers used to represent a mathematical quantity or relationship is known as an expression in mathematics. Expressions might be straightforward with just one number or variable or complex with many terms, operations, and functions.
To find the total amount of money Brianna earned over 5 years, we need to calculate her salary for each of the 5 years and add them up.
In the first year, Brianna's salary was $77,000.
In the second year, her salary increased by 2%, so it became:
$77,000 + 0.02 x $77,000 = $78,540
In the third year, her salary increased by another 2%, so it became:
$78,540 + 0.02 x $78,540 = $80,106.80
In the fourth year, her salary increased by 2% again, so it became:
$80,106.80 + 0.02 x $80,106.80 = $81,700.94
In the fifth and final year, her salary increased by 2% once again, so it became:
$81,700.94 + 0.02 x $81,700.94 = $83,303.11
To find the total amount of money Brianna earned over the 5 years, we just need to add up her salaries from each year:
$77,000 + $78,540 + $80,106.80 + $81,700.94 + $83,303.11 = $400,651.85
Therefore, Brianna earned a total of approximately $400,652 over the 5 years.
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please hurry!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
the radius of circle s is point,radius,arc,
A. 5
B. 7
C. 2.6
D. 5.5
Answer:
A 5 is the distance between
Step-by-step explanation:
(-2 -2)^2 + ( 0-3)^2 = d^2
d = 5
pls help!! i rlly need this quick
Answer:
See below ~
Step-by-step explanation:
Combination Rule
ⁿCₓ = n! / (n - x)! x!#1) ²²C₂₀
²²C₂₀ = 22! / 2! 20!22 x 21 x 20! / 2! x 20!22 x 21 / 211 x 21231#2) ¹²C₈
¹²C₈ = 12! / 4! 8!12 x 11 x 10 x 9 x 8! / 4! x 8!12 x 11 x 10 x 9 / 4 x 3 x 211 x 5 x 999 x 5495Answer:
[tex]\displaystyle ^{22}C_{20} =231[/tex]
[tex]\displaystyle ^{12}C_{8} =495[/tex]
Step-by-step explanation:
Binomial Coefficients
[tex]\displaystyle \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{(n-r)! \, r!}[/tex]
[tex]\begin{aligned}\displaystyle \implies ^{22}C_{20} & = \frac{22!}{(22-20)! \, 20!}\\\\ & =\frac{22!}{2! \, 20!}\\\\ & =\frac{22 \cdot 21 \cdot 20!}{2! \, 20!}\\\\ & =\frac{22 \cdot 21}{2 \cdot 1}\\\\ & =\frac{462}{2}\\\\ & =231\end{ailgned}[/tex]
[tex]\displaystyle \begin{aligned} \implies ^{12}C_{8} & = \frac{12!}{(12-8)! \, 8!}\\\\ & =\frac{12!}{4! \, 8!}\\\\ & =\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{4! \, 8!}\\\\ & =\frac{12 \cdot 11 \cdot 10 \cdot 9}{4 \cdot 3 \cdot 2 \cdot 1}\\\\ & =\frac{11880}{24}\\\\ & =495\end{aligned}[/tex]
If there are two angles that are supplementary, and the first angle has a measure of 137°, what is the measure of the second angle? A. 43 degrees B. 90 degrees C. 72 degrees
Answer:
Step-by-step explana what grade math is this?
i need help its 7th grade area surface
Answer:
729 square inches
Step-by-step explanation:
9^3 or 9×9×9
(im not sure but i think thats it)
if p=1(l+b), express b in terms of p and l:b=
Step-by-step explanation:
=> p=1(l+b)
=> P = 1l + 1b
=> 1l - P = 1b
=> b = 1l - P/1
~Done~
Or
p=1(l+b)
Step 1: Flip the equation.
b+l=p
Step 2: Add -l to both sides.
b+l+−l=p+−l
b=−l+p
Answer:
b=−l+p
Lilly has two cousins. One of the cousins is 7 years older than Lilly. The other cousin is 3 years younger than Lilly. The product of Lilly’s cousins' ages is 24. How old is Lilly?
Write a statistical question that you might ask to gather information about the recycling habits of your neighbors
Answer:
How often do you recycle?
Step-by-step explanation:
Statistical questions are questions where results may vary meaning that depending on who you ask this question you can get very different but measurable answers.
If CDEF is a kite, CD =15 find CG
Answer:
Step-by-step explanation:
CD = 15, so we have the hypotenuse.
DF = 18, but we can find a leg by 18/2 which is 9
using our pyth. theorem, 15^2=9^2+CG^2
CG = 12
Hope this helped
How to do the circumference of a semicircle with a radius of 7 1/2.
Answer:
38.6 units (nearest tenth)
Step-by-step explanation:
Formulae
Diameter = 2r Circumference = 2πr(where r is the radius)
Circumference of a semicircle = diameter + half the circumference
⇒ Circumference of a semicircle = 2r + πr
Given:
[tex]\sf radius\:{(r)=7\frac12=7.5[/tex][tex]\begin{aligned}\implies \textsf{Circumference of semicircle} & = 2(7.5) + \pi(7.5)\\ & = 15+7.5 \pi\\ & = 38.5619449...\\ & = 38.6\:\sf units\:(nearest\:tenth)\end{aligned}[/tex]
Circumference
πr+2rr(π+2)7.5(3.14+2)7.5(5.14)38.6units²20 points given and brainiest for correct answer
Answer:
B is correct
I = (5200)(0.06)(2.5)
Step-by-step explanation:
Brainliest would be very much appreciated
PLEASE HELP just need a quick answer!!! will give brainly!!!
A moving-van rental company uses the polynomial 130 + 0. 75(m – 200) to calculate the rental charges if a customer drives a van more than 200 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 200 miles in one day
Answer:
im not sure but i think this is the answer
Step-by-step explanation:
I think it would be 130 + 0.75m
Which simplified could be 130.75m Hope it helps! :)
0.75m - 20
[tex]130+0.75\left(m-200\right)\ =\ 0.75m-20[/tex]
Step-by-step explanation:[tex]0.75(m-200) + 130[/tex]
The slope is 0.75
Substitute m for 0 ( [tex]0.75(-200) + 130[/tex])
Evaluate the equation ( [tex]0.75(-200) + 130[/tex]) = -20, this is the y-intercept
now the equation is [tex]slope + intercept[/tex] = [tex]0.75 -20[/tex]
A rectangle measures 9 4/5 meters 5 3/4 meters. What is its area?
Answer:
56.35 meters squared
Step-by-step explanation:
lmk if its inches
A music store charges for lessons
according to the table below. If the store
charges a constant rate of dollars to time,
which of the following could fill the empty
row?
Time (min) Cost
a. 50 minutes for $40
o Yes O No
b. 60 minutes for $42
o Yes No
c. 70 minutes for $56
o Yes No
d. 90 minutes for $72
o Yes No
Rate of change:-
(30,24)(40,32)Slope:-
m=32-24/40-30m=8/10=4/5So
Next time is off course 50 .
Price should be calculated
y=50(4/5)=10(4)=40Option A✓
Check all
Option B:-
42=(4/5)(60)42=4(12)No
Option C
56=4/5(70)56=4(14)yes
Option D
72=4/5(90)72=4(18)Yes
. . . .. . . ................................
Answer:
4 1/10
Step-by-step explanation:
:) Hope this helps
Write a multiplication expression that can be used to solve 2/3a = 30.
a=45
Solution:We need to multiply both sides by 3 in order to get rid of the denominator, 3:2/3a•3=30•32a=90Divide both sides by 2:a=45Hope it helps.
Do comment if you have any query.
Identify the radius, height, and diameter of the cylinder.
30 in.
12 in
Radius:
inches
Height:
inches
Diameter:
inches
Answer:
Radius: 12 inches
Height: 30 inches
Diameter: 24 inches
Step-by-step explanation:
Radius: 12 inches
Height: 30 inches
Diameter: 24 inches
Find the circumference and area of a circle with diameter 4 cm.
HELP ASAP PLS
Step-by-step explanation:
the formulas can be easily found on the internet.
remember, the diameter of a circle is 2 times the radius.
so, the radius of our circle here is 4/2 = 2 cm.
circumference :
2×pi×r = 2×3.14×2 = 12.56 cm
area :
pi×r² = 3.14×2² = 3.14×4 = 12.56 cm²
hey, your teacher gave you the circle, where the circumference and the area have the same quantity ! funny !
so, make double sure you use the correct unit dimensions (remember, a distance has only one dimension, an area has 2 dimensions, and a volume has 3 dimensions).
giving brainlist for correct answers =}
Answer:
Step-by-step explanation:
the answer is uniform
Answer:
Skewed right :)
Step-by-step explanation:
The most data points are to the left and there is barely any to the right. That is why it is skewed right :)
Have an amazing day!!
Please rate and mark brainliest!!
Credits to: hautauv!!!
Which description compares the vertical asymptote(s) of Function A and Function B correctly?
Function A: f(x) = 1/x-1
Function B: (see photo)
A. Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x = 0.
B. Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x=−3.
C. Function A has a vertical asymptote at x=−1.
Function B has a vertical asymptote at x=−3.
D. Both functions have the same vertical asymptote.
Answer:
B. Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x=−3.
Step-by-step explanation:
You can see from the diagram that the asymptope is x = -3, but to find the asymtope for the function make denominator equal to 0 and solve because the denominator can never equal 0, (you divide a number by 0, which is mathematically impossible) therefore the function will never reach that line.
Please Help With This!!!
Will try to give out brainliest!!!
Answer: [tex]2^4,4^2,16^1[/tex]
Step-by-step explanation:
Let's evaluate each expression
Remember the little number that is the exponent means to multiply that number by itself that amount of times
[tex]8^2=[/tex]8×8=64 this is not 16
[tex]2^4=[/tex]2×2×2×2=4×4=16
[tex]2^8[/tex] we already know [tex]2^4[/tex] was enough so this must be over 16 and incorrect
[tex]4^2=[/tex]4×4=16
[tex]16^1[/tex]=16
Determine the area of the shaded region. Pool Use 3 for
[tex]\pi[/tex]
Answer:
36 sq in
Step-by-step explanation:
First find the area of the square: 12*12 = 144 in^2
next find the area of 1 circle, im assuming the circles are tangent to the sides of the square and to each other, so each circle has a radius of 12/4 or 3in, the area of each circle is then pi*3^2 or 27 in^2
the total area of the 4 circles is then 27*4 = 108in^2
144-108=36in^2
can someone please help with This !
Answer:
A. E
B. D
C. A
Trust me on this one! I used a calculator.
A survey of customers at a restaurant revealed that 7 out of 10 customers preferred the restaurants new spaghetti sauce. Which graph shows a relationship between y, the number of customers who preferred the new spaghetti sauce, and x, the total of customers?
The graph that shows the proportional relationship y = 0.7x is Graph A.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, 7 out of 10 customers preferred the restaurants new spaghetti sauce, hence the constant is given by:
k = 7/10 = 0.7.
And the equation is:
y = 0.7x.
When x = 0, y = 0, which already eliminates graphs C and D. When x = 10, y = 7, which means that Graph A is the answer to this question.
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5 5/8 as an improper fraction
The improper fraction is 45/8.
Answer:
45/8
Step-by-step explanation:
to get an improper fraction, you multiply the denominator by the whole number and add the numerator to the total. So for this problem 5(8)=40+5= 45/8
A 2-column table with 6 rows. the first column is labeled week with entries 1, 2, 4, 6, 8, 10. the second column is labeled miles run with entries 5, 8, 13, 15, 19, 20. rita is starting a running program. the table shows the total number of miles she runs in different weeks. what is the equation of the line of best fit for the data? state each number to the thousandths place. y ≈ x
The line of best fit for the data of week and the corresponding miles run is evaluated to be: y = 4.699 + 1.671x
How does linear regression works?Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.
The following data for the Week and miles run variables are provided to construct linear regression model:
Week miles run
1 5
2 8
4 13
6 15
8 19
10 20
The independent variable is Week(represented by x), and the dependent variable is miles run(represented by y). In order to compute the regression coefficients, the following table needs to be used:
Let week = x, and miles run = y, then we get this table:
x y xy [tex]x^2[/tex] [tex]y^2[/tex]
----------------------------------------------------
1 5 5 1 25
2 8 16 4 64
4 13 52 16 169
6 15 90 36 225
8 19 152 64 361
10 20 200 100 400
-----------------------------------------------------
Sum = 31 80 515 221 1244
Based on the above table, the following is calculated:
[tex]\bar X = \frac{1}{n} \sum_{i=1}^{n} X_i = \frac{ 31}{ 6} \approx 5.167[/tex]
[tex]\bar Y = \frac{1}{n} \sum_{i=1}^{n} Y_i = \frac{ 80}{ 6} \approx 13.33[/tex]
[tex]\large SS_{XX} = \sum_{i=1}^{n} X_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right)^2 = 221 - 31^2/6 \approx 60.833[/tex]
[tex]\large SS_{YY} = \sum_{i=1}^{n} Y_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} Y_i\right)^2 = 1244 - 80^2/6 \approx 177.33[/tex]
[tex]\large SS_{XY} = \sum_{i=1}^{n} X_i Y_i - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right) \left(\sum_{i=1}^{n} Y_i\right) = 515 - 31 \times 80/6 \approx 101.67[/tex]
Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:
[tex]m = \frac{SS_{XY}}{SS_{XX}} \approx \frac{ 101.67}{ 60.833} \approx 1.6712[/tex]
[tex]n = \bar Y - \bar X \cdot m = 13.33- 5.167 \times 1.6712 = 4.6986[/tex]
Therefore, we find that the regression equation is:
miles run = 4.6986 + 1.6712 Week
y = 4.6986 + 1.6712x (approximately)
To the thousandths place, it becomes:
y = 4.699 + 1.671x
Therefore, based on the information provided above, the following scatter plot and regression plot are obtained as the image attached below.
Thus, the line of best fit for the data of week and the corresponding miles run is evaluated to be: y = 4.699 + 1.671x
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Answer:
y-1.671
4.699
Step-by-step explanation: