Answer:
All real numbers.
Step-by-step explanation:
So we have the equation:
[tex]6y-8=2(3y-4)[/tex]
First, distribute the right side:
[tex]6y-8=6y-8[/tex]
As we can see, both expressions on both sides of the equation are the exact same. In other words, every value of y will make the equation true. Thus, the answer is all real numbers.
Answer:
infinite solutions
Step-by-step explanation:
1 solution means that only 1 number can replace that variable
No solution means that no numbers can replace that variable. If the 2 sides of the question cannot be solved or they are different, then that equation has no solutions.
Infinite solution means that any number can replace that variable. If the 2 sides of the equation the same, then it is an infinite solution.
6y - 8 = 2(3y - 4)
=> 6y - 8 = 6y - 8
Since both sides of the equations are the same, "y" can be any number.
So, this equation has infinite solutions.
Part B
Write an expression that represents the net change in Rylee's bank account balance after paying for fuel at the gas station.
Answer:
Rylee spent $25 for fuel at the gas station. This money is leaving her bank account, so represent the amount with a negative sign: -$25.
Step-by-step explanation:
None. the expression explains it.
Percy spent money on new shirts for the summer each shirt cost $7 he spent $42 all together how many shirts did Percy buy
The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 4 − x2, 0 ≤ x ≤ 3
Answer:
The area of the surface is 2.72 units
Step-by-step explanation:
The area of a curve y = (x) a ≤x ≤ b rotated about the y axis is given by:
[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]
y = 4 - x²
dy / dx = -2x
(dy/dx)² = (-2x)² = 4x²
Hence:
[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\\\s=\int\limits^0_3 {2\pi x\sqrt{1+4x^2} } \, dx\\\\Let\ u = 1+4x^2\ \\\frac{du}{dx}=8x\\\frac{du}{8x}=dx\\\\Substituting\ value\ of\ u \ and\ dx:\\ \\s=\int\limits^0_3 {2\pi x\sqrt{u} } \, \frac{du}{8x} \\\\s=\frac{\pi }{4} \int\limits^0_3 {\sqrt{u} } \, du\\\\s=\frac{\pi }{4}|\frac{2}{3}u^{3/2}|_0^3\\\\s=\frac{\pi }{4}*\frac{2}{3}(5.196)\\\\s=2.72\ units[/tex]
The area of the surface is 2.72 units
The area of the resulting surface is [tex]37.3437\pi[/tex].
Curve:
A curve is an object that is similar to a line, but that does not have to be a straight line. A curve may be regarded as a trace left by a moving point.
Given:
[tex]y=4-x^{2}[/tex] , [tex]0 \leq x\leq 3[/tex]
Surface area[tex]=2\pi \int_{a}^{b}x\sqrt{1+\left ( \frac{dx}{dy} \right )^{2}dy}[/tex]
[tex]x=\sqrt{4-y} \ , \ \frac{dx}{dy}=-\frac{1}{2\sqrt{4-y}}[/tex]
when [tex]x=0 \ , \ y=4[/tex]
[tex]x=3 \ , \ y=-5[/tex]
Area of surface[tex]=2\pi \int_{-5}^{4}\sqrt{4-y}\sqrt{1+\frac{1}{4\left ( y-4 \right )}dy}[/tex]
[tex]=2\pi \int_{-5}^{4}\sqrt{4-y+\frac{4-y}{4\left ( y-4 \right )}dy} \\ =2\pi \int_{-5}^{4}\sqrt{4-y+\frac{1}{4}dy} \\ =\frac{2\pi }{2}\int_{-5}^{4}\sqrt{17-y} \ dy \\ =\pi \int_{-5}^{4}\sqrt{17-y} \ dy[/tex]
Solving with calculator:
[tex]\Rightarrow \pi\left [ \frac{1}{6}\left ( 37\sqrt{37}-1 \right ) \right ][/tex]
[tex]=37.3437\pi[/tex]
Learn more about the topic Curve: https://brainly.com/question/8771120
Please help me out!!!!
Answer:
You should multiply the exponents "-3" and "-6"
Then your answer is:
4^18Hope this helps..
Best of luck!
Answer:
4^18Step-by-step explanation:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(4^{-3}\right)^{-6}=4^{-3\left(-6\right)}\\\\-3\left(-6\right)=18\\\\=4^{18}[/tex]
Consider the following. (Round your answers to four decimal places.)f(x, y) = yex(a) Evaluate f(2, 1) and f(2.5, 1.65) and calculate Δz(b) Use the total differential dz to approximate Δz.
Answer:
Step-by-step explanation:
Given the function f(x,y) = ye^x
To evaluate f(2,1), we will substitute x = 2 and y = 1 into the given function to have;
f(2,1) = 1×e^2
f(2,1) = e^2
f(2,1) = 7.3891(to 4dp)
For f(2.5, 1.65), x = 2.5 and y =1.65
f(2.5, 1.65) = 1.65e^2.5
f(2.5, 1.65) = 1.65×12.1825
f(2.5, 1.65) = 15.2281 (to 4dp).
∆z = f(2.5, 1.65) - f(2, 1)
∆z = 15.2281-7.3891
∆z = 7.8390
dz = fxdx + fydy
fx is the differential of the function with respect to x keeping y constant.
Since f(x,y) = ye^x
fx = ye^x + 0e^x
fx = ye^x
dx = x2-x1 = 2.5-2
dx = 0.5
fy = e^x
dy = (y2-y1) = 1.65-1
dy = 0.65
Using the point (2, 1) for x and y and substituting the values gotten into dz function:
dz =ye^x(0.5) + e^x(0.65)
If x = 2 and y = 1
dz = 1e^2(0.5) + e^2(0.65)
dz = 7.3891(0.5)+7.3891(0.65)
dz = 7.3891(0.5+0.65)
dz = 7.3891(1.15)
dz = 8.4975
A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.84mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.24mm. Would this outcome warrant a refund (meaning that it would be unusual)?
Answer:
4.32%; no
Step-by-step explanation:
The value of 0.24 differs from the mean by 0.84 -0.24 = 0.60. 2 standard deviations from the mean would be a difference of 2×0.35 = 0.70.
A statistical calculator says the probability of a depth less than 0.24 mm for the given distribution is about 4.32%.
The value differs from the mean by less than 2 standard deviations, so is not considered unusual.
What is the area of rectangle whose
height is 2.5 in and base is 12 in?
Step-by-step explanation:
Area of a rectangle is base times height.
A = bh
A = (12 in) (2.5 in)
A = 30 in²
Let α ∈ S n α∈Sn for n ≥ 3 . n≥3. If α β = β α αβ=βα for all β ∈ S n , β∈Sn, prove that α α must be the identity permutation; hence, the center of S n Sn is the trivial subgroup.
Answer:
Sn is the trivial subgroup
Step-by-step explanation:
To prove that α must be the identity permutation and also Sn is the trivial subgroup we have to make assumptions :
when we assume α is not an identity permutation
α(i) = -j but since n ≥ 3 we will make another assumption of a number k
hence we will choose : β = ( i k )
from these assumptions we can deduce that
αβ (i) = α(k) ≠ -j since α(i) = -j
also βα (i) = β(-j) = -j
from the equations above we can conclude that
αβ ≠ βα which is in contradiction to the expression : αβ=βα . this simply shows that α must be the identity permutation, and the number of permutations of Sn is true for every number of permutation of Sn provided it is other than the identity
hence the center Sn is the trivial subgroup
The first Ferris wheel took 9 minutes to make a complete revolution. How fast was the wheel moving?
M=undefined, x-int=(3,0)
Answer:
x = 3
Step-by-step explanation:
Maybe you want the equation of the line.
__
A vertical line has undefined slope. Its equation is of the form ...
x = constant
In order for the line to go through a point with an x-coordinate of 3, the constant must be 3.
x = 3 . . . . equation of the line
the peak of Mt. johnson is 19,360 feet above sea level. The top of Mt. Harrison is 23,350 feet above sea level. round each height to the nearest thousand to estimate the difference in elevation of these two peaks.
How is a coefficient different than a constant... please give me an example as well thank you.. I’m giving max points
Answer:
A coefficient is a number that is in front of a variable. A number that is multiplied by a variable in a variable expression; in an expression such as 3ab, the numerical coefficient of ab is 3. The word constant means unchanging. Since a number’s value never changes, a number with no variable factors is a constant. A constant is a numerical term in an expression. a term that has no variables
Example: 5a+4 The coefficient is 5 and the constant is 4 because it does not have a variable in front of it.
Hope this helps
The rate of growth of mice is inversely proportional to the square of the population:__________
Answer:
The value is [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]
Step-by-step explanation:
From the question we told that are
The rate of growth of mice is inversely proportional to the square of the population
This above statement can be mathematically represented as
[tex]\frac{d y }{dt} \ \ \ \alpha \ \ \frac{1}{\sqrt{y(t)} }[/tex]
Here [tex]y(t)[/tex] is the population
=> [tex]\frac{d y }{dt} = \frac{k}{\sqrt{y(t)} }[/tex]
=> [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]
n(n+p)-n; use n=5, and p=3
Answer:
45
Step-by-step explanation:
We can first expand the expression:
n(n+p) - n
= n^2 + np + n
Then, we can plug in values of n and p into the expression:
n^2 + np + n = (5)^2 + (5)(3) + 5 = 25 + 15 + 5 = 45
Answer:
35
Step-by-step explanation:
Substitute the value of the variable into the expression and simplify
Solve 6x+57=2x+315 . A. x=−911 B. x=911 C. x=119 D. x=−119
Explanation:
Remember: we have to isolate the variable x, so that means we have to get x by itself.
Step 1:
Let’s look at our equation:
[tex]6x+57=2x+315[/tex]
Let’s subtract 2x from both sides of the equation, since our goal is to isolate the variable. You could also subtract 6x from both sides, but you would end up with a negative number, and I find it easier to deal with positive numbers.
[tex]6x(-2x)+57=2x(-2x)+315\\4x+57=315[/tex]
Step 2:
Now, let’s subtract 57 from both sides of our equation.
[tex]4x+57(-57)=315(-57)\\4x=258[/tex]
Step 3:
Since we have to isolate x, let’s divide both sides of the equation by 4.
[tex]4x/4=x\\258/4=64.5[/tex]
Our final answer: x = 64.5
None of your options is the correct answer. Notify your teacher, tutor, etc. since there none of the options are correct.
9 less than one-fifth of c
Answer: The equation in math form is [tex]\frac{1}{5}c[/tex] - 9.
Step-by-step explanation:
So the givens are:
9 less than one-fifth of c
Let's put this equation in math form:
[tex]\frac{1}{5}c[/tex] - 9
Hence your answer!
A box is 15cm long, 4cm wide and 8cm high. Another box is 10cm long, 9cm wide and 4cm high. which box has a larger volume? what is the difference in volume between the two boxes
Answer:
Differences=
[tex] {120cm}^{3} [/tex]
Step-by-step explanation:
Volume of first box=15cm×4cm×8cm
[tex]480 {cm}^{3} [/tex]
Volume of second box=10cm×9cm×4cm
[tex] {360cm}^{3} [/tex]
Two cars traveling toward each are 200 miles apart. Car A is traveling 20 miles per hour faster than car B. The cars pass after 2 hours. How fast is each car traveling?
Answer:
Step-by-step explanation:
d = 200 miles
B rate = x
A Rate = x + 20
Each has traveled two hours
The total distance each travels after two hours is 200 miles (they pass each other).
d = r * t
2*x + 2*(x + 20) = 200 Remove the brackets
2x + 2x + 40 = 200 Combine like terms
4x + 40 = 200 Subtract 40 from each side
4x = 200 - 40
4x = 160 Divide by 4
x = 160/4
x = 40
There B's rate is 40 miles / hour
A's rate is 40 + 20 = 60 miles / hour
A group of 8 children and 8 adults are going to a movie. Child tickets cost $2, and adult tickets cost $6. How much will the movie tickets cost in all? ANSWER PLEASE LOTS LOTS OF POINTS.
Answer:
64 dollars
Step-by-step explanation:
8 children and 8 adults
2 dollars for a child and 6 dollars for an adult
cost for children
8 children * 2 dollars each = 16
cost for adults
8 adults * 6 dollars each = 48
Add the two costs together
16+48 =64
Answer:
8×2=16
8×6=48
48+16=64
how do you simplify 15/40
Answer:3/8
Step-by-step explanation:
The simplest form of
15 /40 is 3 /8 .
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 15 and 40 is 5
Divide both the numerator and denominator by the GCD
15 ÷ 5
40 ÷ 5
Reduced fraction:
3 /8
Therefore, 15/40 simplified to lowest terms is 3/8.
solve for P in the scientific formula PV = nRT
[tex]PV=nRT\implies P=V^{-1}nRT[/tex].
Hope this helps.
Find the distance between the points (-74,-76) and (-35,4)
Answer:
The answer is
[tex]89 \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-74,-76) and (-35,4)
The distance between the points is
[tex]d = \sqrt{( { - 74 + 35})^{2} + ({ - 76 - 4})^{2} } \\ = \sqrt{ ({ - 39})^{2} +( { - 80})^{2} } \\ = \sqrt{1521 + 6400} \\ = \sqrt{7921} [/tex]We have the final answer as
[tex]89 \: \: units[/tex]Hope this helps you
ID: A
17. N.Q.1-2 ULHS has a student that can run 100 yds in 15 seconds. Mrs. Duke's class converted his speed to
miles per hour below and determined he can run 4.55 miles per hour. Is the conversion correct? If not, explain
what the class did wrong and then work it out using dimensional analysis. You MUST Show all work.
100 yds
60 sec
60 min 1 mile
= 4.55 mph
15 sec
1 min 1 hr 5280 yds
its hard to explain and show work but so you know the answer is no and its because they converted yards to miles and did the formula for ft to miles instead of yd to miles they did 5280 ft per mile and not 1760 yd per miles
Answer:
13.63 miles per hour
Step-by-step explanation:
100 yards / 15 sec converted to miles per hour
100 yards x 60 sec x 60 min x 1 mile = 13.63 miles/hr
15 sec 1 min 1 hr 1760 yards
the mistake on Mrs Dukes is the conversion from miles to yards.
1 mile = 1760 yards NOT 5280 yards
calculate the area of area of a rectangular with a base of 10cm and a height of 6cm
Answer:
60cm²
Step-by-step explanation:
Length = 6cm
Breadth = 10cm
Area of rectangle = l×b
=( 10 ×6)cm
= 60cm²
Hope it helps.
Answer:
[tex]\Huge \boxed{\mathrm{60 \ cm^2 }}[/tex]
Step-by-step explanation:
Area of a rectangle is length × width.
The length of the rectangle is 10 cm.
The width of the rectangle is 6 cm.
[tex]\Rightarrow 10 \cdot 6 \\\\\\ \Rightarrow 60[/tex]
The area of the rectangle is 60 cm².
Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $300. The store allows the coupons to be combined. Which coupon should be applied first, and what is the final purchase price?
Answer:
Apply the 15% discount first, and the final purchase price is $332.50.
Step-by-step explanation:
The 15% discount of the two coupons should be applied first so that the final price is cheaper.
The final purchase price at the department store is $332.5.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Cost = $450
Two coupons.
Offer = 15% discount
off = $50
Now,
15% discount first and then $50 off.
(450 - 15/100 x 450) - 50
= (450 - 67.5) - 50
= $332.5
Now,
$50 off first and then the 15% discount.
(450 - 50) = 400
400 - 15/100 x 400
= 400 - 60
= $340
We see that,
When the 15% discount is applied first the final price is cheaper.
Thus,
15% discount should be applied first.
The final purchase price is $332.5.
Learn more about percentages here:
https://brainly.com/question/11403063
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Please help me with the question below
Answer:
1/8x + 1/2 y
Step-by-step explanation:
Charlotte gets 1/4x from dayna
Charlotte now has
1/4x+y
She lends 1/2 of this
1/2 ( 1/4x +y)
1/8x + 1/2 y
The radius of the wheel on a bike is 21 inches. If the wheel is revolving at 154 revolutions per minute, what is the linear speed of the bike, in miles per hour
Answer:
The linear speed of the bike is 19.242 miles per hour.
Step-by-step explanation:
If sliding between the bottom of the wheel and ground can be neglected, the motion of the wheel can be well described by rolling, which is a superposition of coplanar pure rotation and translation, The speed of the bike occurs at the center of the wheel, where resulting instantaneous motion is pure translation parallel to ground orientation. The magnitude of the speed of bike ([tex]v_{B}[/tex]), measured in inches per second, is:
[tex]v_{B} = R\cdot \omega[/tex]
Where:
[tex]R[/tex] - Radius, measured in inches.
[tex]\omega[/tex] - Angular speed, measured in radians per second.
Now, the angular speed must be converted from revolutions per minute into radians per second:
[tex]\omega = \left(154\,\frac{rev}{min} \right)\cdot \left(2\pi\,\frac{rad}{rev} \right)\cdot \left(\frac{1}{60}\,\frac{min}{s} \right)[/tex]
[tex]\omega \approx 16.127\,\frac{rad}{s}[/tex]
The speed of the bike is: ([tex]R = 21\,in[/tex] and [tex]\omega \approx 16.127\,\frac{rad}{s}[/tex])
[tex]v_{B} = (21\,in)\cdot \left(16.127\,\frac{rad}{s} \right)[/tex]
[tex]v_{B} = 338.667\,\frac{in}{s}[/tex]
Lastly, the outcome is converted into miles per hour:
[tex]v_{B} = (338.667\,\frac{in}{s} )\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(\frac{1}{63360}\,\frac{mi}{in} \right)[/tex]
[tex]v_{B} = 19.242\,\frac{mi}{h}[/tex]
The linear speed of the bike is 19.242 miles per hour.
Calculate the first, second, and third quartiles of the following sample. 5 8 2 9 5 3 7 4 2 7 4 10 4 3 5
Answer:
3 ; 4.5 ; 7.25
Step-by-step explanation:
Given the sample :
8 2 9 5 3 7 4 2 7 4 10 4 3 5
Calculate, the first, second, and third quartiles
Arranging the data in ascending order :
2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 7, 8, 9, 10
First quartile :
Q1 = [(n + 1) /4]th value
n = 14
Q1 = [(14 + 1) /4]th = (15/4)th = 3.75 value
Taking the average of the 3rs and 4th observation:
(3 +3) / 2 = 3
Second quartile :
Q2 = [2(n + 1) /4]th value
Q2 = 2(15)/4 = (30/4)th value
Q2 = 7.5 ; taking the 7th and 8th value
Q2 = (4 +5) /2 = 9/2 = 4.5
Q3 = [3(n + 1) /4]th value
Q2 = 3(15)/4 = (45/4)th value
Q2 = 11.25 ; taking the 11th
Q2 = 7 + 0.25 = 7.25
Hank invested a total of $20,000, part at 7% and part at 10%. How much did he invest at each rate if the total interest earned in one year was $1640?
Answer:
We have a total investment of $20,000 in two different amounts A and B.
Then:
A + B = $20,000.
And we know that the interest of the amount A is 7%, and the interest of the amount B is 10%. (i will assume that both interests are yearly interest)
And after one year, Hank earns $1,640 thanks to those interests, then we have that:
(7%/100%)*A + (10%/100%)*B = $1,640
And we can write this as:
0.07*A + 0.1*B = $1,640
Then we have a system of equations:
A + B = $20,000
0.07*A + 0.1*B = $1,640
To solve this, the first step is isolating one of the variables in one of the equations.
Let's isolate A in the first equation:
A + B = $20,000
A = $20,000 - B.
Now we can replace this in the other equation:
0.07*A + 0.1*B = $1,640
0.07*($20,000 - B) + 0.1*B = $1,640
$1,400 - 0.07*B + 0.1*B = $1,640
0.03*B = $1,640 - $1,400 = $240
B = $240/0.03 = $12,000
Then we have:
A = $20,000 - $12,000 = $8,000
Hank invests $12,000 in the 10% account and $8,000 in the 7% one.
What expression is equivalent to (8^2)^-4
Answer:
(64)^-4= 1/64^4= 1/16777216