Answer:
When we are dividing exponents, there is this rule:
[tex]\frac{a^n}{a^m}=a^{(n-m)}[/tex]
So, in our case we have this:
[tex]\frac{16a^5b^3}{8ab} = \frac{16}{8}a^{(5-1)}b^{(3-1)}[/tex][tex]=2a^4b^2[/tex]
Is 1/6 rational or irrational
While Abbie is jogging, she moves forward 85 cm every second. How many seconds will Abbie take to jog 8.5 meters?
Thank you very much !!!!!! :D
Answer:
It will take Abbey 10 seconds to move 8.5 meters
Step-by-step explanation:
100 cm makes one meter
So 85 cm=85/100
85 cm. = 0.85 meter
So Abbey travels 0.85 meters every second
One second= 0.85 meters
Let the unknown time be x
X= 8.5 meters/0.85
X= 10 seconds
It will take Abbey 10 seconds to move 8.5 meters
2x²-y if x=3 and y=8
Answer:
10
Step-by-step explanation:
2(3)²-8
2(9)-9
18-8=10
Answer:
28
Step-by-step explanation:
Plug in the variable "meaning": (2 × 3)^2 - 82 × 3 = 6Plug 6 in: [tex]6^{2} - 8[/tex] [tex]6^{2}[/tex] = 6 × 6 = 36Plug 36: 36 - 836 - 8 = 28What is negative 300 minus 150
Answer: -450 since negative minus a positive makes it even more negative
for the equation f(x)=x^2-4x+1
f(x+h)-f(x)/h = ?
Answer: f(x)=x2-4x
Step-by-step explanation:
-5/2 (3x + 4) < 6 - 3x
Step-by-step explanation:
here is the ans
please check
What’s the writing in the form of a/b: -16 *
Answer:
-16/1
Step-by-step explanation:
-16 in the form a/b can be written as -16/1.
Neal is a coffee drinker. At the local coffee shop, the price
of a cup of coffee is $3. Neal's total benefits from
drinking coffee are indicated in the accompanying table.
Use this information to calculate Neal's marginal benefit
of consuming each cup of coffee.
Quantity of
coffee
(cups per day)
Total
benefits
2
3
$8
$14
SI8
$20
$21
4
5
a. The marginal benefit of the first cup is 5
b. The marginal benefit of the second cup is $
10
c. The marginal benefit of the third cup is $15
d. The marginal benefit of the fourth cup is 25
e. The marginal benefit of the fifth cup is s
f. Neil should consume
cups of coffee per day.
Answer and Step-by-step explanation: Marginal Benefit is the maximum a person is willing to pay for an additional good or service. It can be calculated as:
[tex]marginal=\frac{Change total benefit}{Change quantity}[/tex]
For each cup of coffee:
For the first cup, benefit is $8;
For the second:
[tex]marginal=\frac{14-8}{2-1}[/tex]
marginal = 6
For the third:
[tex]marginal=\frac{18-14}{3-2}[/tex]
marginal = 4
For the fourth:
[tex]marginal=\frac{20-18}{4-3}[/tex]
marginal = 2
For the fifth:
[tex]marginal=\frac{21-20}{5-4}[/tex]
marginal = 1
The cost of the coffe is $3, so comparing benefit and cost, Neal should consume 4 cups of cofee per day.
{...-3, -2,-1, 0, 1, 2, 3...}
Real Numbers
Whole Numbers
Natural Numbers
Integers
Rational
Answer:
they are integers and also rational numbers
A 1000 L tank now contains 240 L of water. How long will it take to fill the tank using a pump that pumps 25 L per minute
Answer:
30.4 minutes
Step-by-step explanation:
The tank already has 240L in it, so we need to fill 1000 - 240 = 760L of water.
Since the pump pumps 25L per minute, we can find how many minutes it takes to pump 760L.
760 / 25 = 30.4 minutes.
It will take 30.4 minutes to fill the tank completely.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, The 1000 L tank contains 240 L of water, therefore, the free space in the tank is :
1000-240
= 760 L
The pump fills the tank at a rate of 25 L per minute.
Therefore, it can be represented as:
25 L = 1 minute
1 L = (1/25) minutes
760 L = (1/25)×760 minutes
760 L = 30.4 minutes.
Hence, it will take 30.4 minutes to fill the tank completely.
Learn more about equations here:
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Joan has $375.24 in a savings
account. She deposits $37.50 each
week and makes no withdrawals.
Which expression represents the
amount of money in the account
in w weeks?
Answer:
C. 375.24 + 37.50w
Step-by-step explanation:
He already has 375.24
He adds 37.5 every week.
W = the number of weeks.
Example:
=> If he deposits for 10 weeks, then it will be
=> 375.24 + 37.5(10)
=> 375.24 + 375
=> 750.24
The correct expression to represent this problem is Option C.
Find the median for the given set of data.
5/8, 3/4, 1&1/8, 1&1/4
A. 15/16
B. 7/8
C. 13/16
In the 1970s, due to world events, there was a gasoline shortage in the United States. There were often long lines of cars waiting at gas stations. Part A: If there were 41 cars in a line that stretched 388 feet, what is the average car length? Assume that the cars are lined up bumper-to-bumper. Round your answer to the nearest tenth of a foot.
Answer:
Part A: The average car length is 9.1 feet to the nearest tenth foot
Part B: The line would be 9100 feet to contained 1000 cars
Step-by-step explanation:
* Lets explain how to solve the problem
# Part A:
- There were 62 cars in a line that stretched 567 feet
- The cars are lined up bumper-to-bumper
- That means there is no empty spaces between the cars
* To find the average length of the car we will divide the length of
the line by the numbers of the cars
∵ The average car length = length of the line/number of cars
∵ The length of the line is 567 feet
∵ The numbers of the cars is 62 cars
∴ The average car length = 567/62 = 9.1 feet
* The average car length is 9.1 feet to the nearest tenth foot
# Part B:
- There are 1000 cars
- We need to find the length of line which contained the cars
∵ The average car length = length of the line/number of cars
∵ The average of car length is 9.1 feet
∵ The number of the cars is 1000 cars
∴ 9.1 = length of the line/1000
- Multiply both sides by 1000
∴ The length of the line = 9.1 × 1000 = 9100 feet
∴ The line would be 9100 feet to contained 1000 cars
Which of the following has the largest value?
1/2 0.09 35%
Answer:
1/2
Step-by-step explanation:
its j the biggest its not that hard
Find the quotient of 9216 and 150
Answer: 61.44
Step-by-step explanation:
To find the quotient of 9216 and 150, it means to divide.
9216/150=61.44
For the following study identify the sources of sampling bias and describe how it might affect the study and conclusion and how you might alter the sampling method to avoid the bias.A nutritionist is interested in the eating habits of college students and observes what each student who enters a dining hall between 8:00 A.M. and 8:30 A.M. chooses for breakfast on a Monday morning.
Answer:
1. 1. Because convenient sampling is adopted here data is only gotten from students that eat in the hall in a given period of time so this is a source of bias
Also one study center that is the Hall of only one school is used this is also biased and may affect the result of the study
To avoid this bias a simple random sampling where each student have an equal chance of being selected in the study should be adopted
Dave has $11 to spend on a $8 book and two birthday cards (c) for his friends. How much can he spend on each card if he buys the same card for each card
Answer:
$1.50
Step-by-step explanation:
Luke earns $11.00 per hour. He works 32 1/2
hours per week. What is his weekly wage
Answer: 357.50
Step-by-step explanation:
Multiply 11.0 and 32.5 without the decimal points.
It should look like this: 110 × 325
After you solve this equation, count the numbers after the decimal points in 11.0 and 32.5. There is one number after the decimal point in 11.0, and one number after the decimal point in 32.5. In the number 35750, count from the last number and add a decimal point right before the 5.
Hope it helps!!
find the value of x2 values that separate the middle 90% from the rest of the distribution for 8 degrees of freedom
Answer:
With alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
Step-by-step explanation:
The significance level ∝ = 1- 0.9 = 0.1
But we need the area of the middle so we divide this significance level with 2
so that we get exactly the middle area .
Dividing 0.1/2= 0.05
So we will have two values for chi square
One with 0.9 + 0.05 = 0.95 alpha and one with 0.05 alpha . This is because the chi square is right tailed.
So with alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
This can be shown with a graph.
Lexie drives her car 204 miles using 12 gallons of gasHow many miles per gallon does her car get? not include the units in your answer
Answer: 17
Step-by-step explanation: 204/12 = 17
Answer:
204÷12=17
lexie used 17 per miles
Step-by-step explanation:
that if am right lol
What’s the difference/same with y/x and y1-y2/x2-x1? Are they both the same?
They are both similar but not entirely the same.
The first expression y/x means we divide y over x. We divide two values here and we are not subtracting first before division. This expression is useful for when you want to find the variation constant in the equation y = kx (for direct proportion equations).
The other expression (y2-y1)(x2-x1) is where we first subtract the y values, and do the same for the x values, before we divide. This computes the slope of the line through the two points (x1,y1) and (x2,y2). It's also useful to figure out the average rate of change (one application of slope). For problems involving time versus distance, the average rate of change is the average speed in which the object is moving.
Work the following area application problem.
You wish to paint a storage shed. Its four walls measure 5 ft. high and 8 ft. wide each. If one gallon of paint covers 160
sq. ft., how many gallons of paint will you need?
Gallons of paint required =
a. 1
b. 2
c. 3
d. 4
Answer: a. 1
Step-by-step explanation:
There are 4 walls in total, and each wall measures 5ft high, 8ft wide
5 × 8=40 ft² for each wall
4×40=160 ft² for 4 walls
------------------
stated one gallon cover 160 ft²
160 ÷ 160=1 gallon
Hope this helps!! :)
Please let me know if you have any question
1) Find an equation of the tangent line at each given point on the curve.x = t2 − 4, y = t2 − 2tat (0, 0)at (−3, −1)at (−3, 3)2) Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)Parametric Equations Intervalx= sqrt1a.gif t y=5t-4 0 ≤ t ≤ 13) Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an answer does not exist, enter DNE.)r = 2(1 − sin(θ))
Answer:
1) at ( 0,0) : y = x/2. at(-3-1) : y = -1. at(-3,3) : y = 2x +9
2) DNE ( does not exist )
Step-by-step explanation:
The general equation of tangent line
y - y1 = m( x - x1 )
attached below is the detailed solution on how i derived the answers above
I need a step by step of this equation please -2(3x+1)=26
Answer:
x = -14/3
Step-by-step explanation:
-2(3x + 1) = 26
Distribute the -2 to the number in the parentheses.
-6x - 2 = 26
Add 2 to both sides of the equation.
(-6x - 2) + 2 = 26 + 2
-6x = 28
Divide both sides of the equation by -6.
(-6x)/-6 = 28/-6
x = -28/6
x = -14/3
4(7-13)divided by 3 + (-4) times 2 - (6-2)
Answer:
[tex]24[/tex]
Step-by-step explanation:
[tex] \frac{4(7 - 13)}{3 + ( - 4)} \times \frac{2 - (6 - 2)}{1} = \frac{28 - 52}{3 - 4} = \frac{ - 24}{ - 1} = 24[/tex]
Hope this helps ;) ❤❤❤
Answer:
24 (Can I have a brainlist, please?)
Step-by-step explanation:
4(7-13)/3 + (-4)2-(6-2)
First we solve the problems in the paraenthesis:
4(7-13)/3 + (-4)2-(6-2)
4(-6)/3 + -4 × 2 -(4)
Now we multiply the ones that are needed to be multiplied:
4(-6)/3 + -4 × 2 -(4)
-24/3 + -8 -(4)
-24/3 + 32
Now we divide:
-24/3 + 32
-8 + 32
And finally we solve the last:
-8 + 32
= 24
Hope that helped!
Charlie had a -$38.65 balance in his checking account. He deposited $126.00 into the account. What is his new balance?
Answer: $87.35
Step-by-step explanation:
Answer:
$164.65
Step-by-step explanation:
$38+$126.65=$164.65
Find the Autocorrelation function of the following periodic function: X(t) = A sin(wt +θ) 21 With T=2π/w the period, A, θ, and w are constants.
Answer:
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
Step-by-step explanation:
To find Autocorrelation function of the following periodic function
Given that:
X(t) = A sin(wt +θ)
with the period T=2π/w , A, θ, and w are constants.
The autocorrelation function of periodic function with period and phase θ can be expressed as:
[tex]R(\tau) = \dfrac{1}{T} \int \limits ^{T/2}_{-T/2} x(t) *x(t - \tau) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{T} \int \limits ^{T/2}_{-T/2} \ A sin ( \omega t + \theta)*A sin [ \omega (t- \tau ) + \theta] \ dt[/tex]
where;
[tex]sinAsin B = \dfrac{1}{2}[cos (A-B) -cos (A+B)][/tex]
Then;
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( \omega t- \omega \tau + \theta - \omega t - \theta) - cos (\omega t - \omega \tau + \theta + \omega t + \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) - cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) \ dt - \dfrac{1}{2T} \int \limits ^{T/2}_{-T/2} cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
The term 2 is the cosine wave of frequency and the phase = [tex]- w \tau + 2 \theta[/tex]
if we integrate that, the second term in the expansion for R(t) = zero
As such,
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits^{T/2}_{-T/2} \ cos ( - \omega \tau ) dt[/tex]
where ;
[tex]cos (-\omega \tau )[/tex]is constant
Then :
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) [t]^{T/2}_{-T/2}[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{T}{2}+ \dfrac{T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{2T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times T[/tex]
[tex]R(\tau) = \dfrac{A^2}{2} cos (-\omega \tau)[/tex]
since [tex]cos (-\omega \tau) = cos (\omega \tau)[/tex]
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
Segments AB and CD intersect to form an angle of 88.5° as shown. What is the measure
of <2
Answer:
91.8°
Step-by-step explanation:
180-88.2=91.8°
For each point find the coordinates of the image point under a half turn about the origin
a(3,0)
b(3,4)
c(-1,-4)
d(r,s)
Answer:
see explanation
Step-by-step explanation:
Under a half turn about the origin
a point (x, y ) → (- x, - y ) , thus
(3, 0 ) → (- 3, 0 )
(3, 4 ) → (- 3, - 4 )
(- 1, - 4 ) → (1, 4 )
(r, s ) → (- r, - s )
The coordinates of the image point under a half-turn about the origin(3, 0 ) is (- 3, 0 ), (3, 4 ) is (- 3, - 4 ), (- 1, - 4 ) is (1, 4 ), (r, s ) is (- r, - s ).
What is a mirror image of a point in coordinate geometry?The mirror image of a point in coordinate geometry is the image formed with respect to the x-axis, y-axis, or origin.
A point (x, y ) has image point (- x, - y )
Thus,
The coordinates of the image point under a half-turn about the origin(3, 0 ) is (- 3, 0 )
The coordinates of the image point under a half-turn about the origin(3, 4 ) is (- 3, - 4 )
The coordinates of the image point under a half-turn about the origin(- 1, - 4 ) is (1, 4 )
The coordinates of the image point under a half-turn about the origin(r, s ) is (- r, - s )
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Which of the following is a rational number