Answer:
1/(8b^2a^8)
Step-by-step explanation:
The given expression can be simplified using the rules of exponents.
[tex]ba^4\times(2ba^4)^{-3}=\dfrac{ba^4}{(2ba^4)^3}=\dfrac{ba^4}{8(ba^4)^3}=\dfrac{1}{8(ba^4)^2}=\boxed{\dfrac{1}{8b^2a^8}}[/tex]
__
The applicable rules of exponents are ...
a^-b = 1/a^b
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
__
Additional comment
It can be useful to think of an exponent as indicating repeated multiplication: 2^3 = 2×2×2, for example. Of course, the repeated multiplication can be nested: (4^2)^3 = (4^2)×(4^2)×(4^2) = (4×4)×(4×4)×(4×4) = 4^6
Numerator and denominator factors cancel in the usual way.
Which expression is equivalent to 16 4 6 a x , when a > 0 and x > 0?
The expression of [tex]\sqrt{[/tex](16a^4x^6) is an algebraic expression
The equivalent expression of [tex]\sqrt{[/tex](16a^4x^6) is 4a^2x^3
How to determine the equivalent expression?The expression is given as:
[tex]\sqrt{[/tex](16a^4x^6)
Expresss 16 as the square of 4
[tex]\sqrt{[/tex](16a^4x^6) = [tex]\sqrt{[/tex](4^2a^4x^6)
Evaluate the square root of each factor in the expression
[tex]\sqrt{[/tex](16a^4x^6) = 4a^2x^3
Hence, the equivalent expression of [tex]\sqrt{[/tex](16a^4x^6) is 4a^2x^3
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Find the equation to graph when 5x-4<0
Hey there!
5x-4<0
=> 5x < 0 + 4
=> 5x < 4
Divide both sides by 5
=> 5x/5 < 4/5
=> x < 4/5
x < 0.8
Graph in image
Joslynn makes $8.25 per hour babysitting. If she made $123.75 last week, then how
many hours did she work last week?
Answer:
We already know that Joslynn makes $8.25 per hour.
Equation:
123.75 divided by 8.25= worked hours
123.75 divided by 8.25 = 15 hours
So last week Joslynn worked 15 hours to make $123.75.
Use the ordered pairs below. (10,20), (11, 21), (12, 22) What patterns are used to create the ordered pairs?
Answer:
The x and y points are increasing by 1
Step-by-step explanation:
(x + 1, y + 1)
The x and y points are increasing by 1
(10, 20) => (10 + 1, 20 + 1) => (11, 21)
(11, 21) => (11 + 1, 21 + 1) => (12, 22)
(10, 20), (11, 21), (12, 22)
Hope this helps!
Can someone help me with this
Answer:
56x
Step-by-step explanation:
Think of it an a triangle and a rectangle. The area of the rectangle is obviously 13 x 4x, which is 52x
for triangle, the hypotenuse is C, Right hand side is B and the side that is in the shape is B.
Area of triangle = (bh) / 2
B = 13 - 9, so B = 4
A = 6x - 4x, so A = 2x
the area is 2x x 4, which is 8x.
8x / 2 = 4x
The area is 4x + 52x, so the final answer is 56x
Will give brainiest!!
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If segment AD = 4 cm, what is the smallest diameter of wrapper that will fit the candy bar?
Triangle ABC in which point E is between points A and B, point D is between points A and C, point F is between points B and C, segments AE and EB are congruent, segments BF and FC are congruent, and angles AED, ABF, and DFC are right angles.
7 cm
8 cm
9 cm
10 cm
The diameter of wrapper is the line that passes through its circumference
The smallest diameter of wrapper that will fit the candy bar is 8 cm.
How to determine the smallest diameter?The diven parameter is:
AD = 4 cm
AD = DC
AC = AD + DC
Substitute AD = DC in AC = AD + DC
So, we have:
AC = AD + AD
AC = 2AD
Substitute 4 for AD
AC = 2 * 4
AC = 8
Hence, the smallest diameter of wrapper that will fit the candy bar is 8 cm.
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Answer:
B. 8cm
Hope this helps! :D
Step-by-step explanation:
10.
(07.02 MC)
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If segment AD = 4 cm, what is the smallest diameter of wrapper that will fit the candy bar? (1 point)
A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question. Confidence Level 90% 95% 99% z*-score 1. 645 1. 96 2. 58 Remember, the margin of error, ME, can be determined using the formula M E = StartFraction z times s Over StartRoot n EndRoot EndFraction. 128. 75 to 147. 25 130. 98 to 145. 02 132. 10 to 143. 90 137. 38 to 138. 62.
The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
Suppose that we have:
Sample size n > 30Sample mean = [tex]\overline{x}[/tex]Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Then the confidence interval is obtained as
Case 1: Population standard deviation is known[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown.[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}[/tex]
For this case, we're given that:
Sample size n = 90 > 30Sample mean = [tex]\overline{x}[/tex] = 138Sample standard deviation = s = 34Level of significance = [tex]\alpha[/tex] = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).At this level of significance, the critical value of Z is: [tex]Z_{0.1/2}[/tex] = ±1.645
Thus, we get:
[tex]CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90][/tex]
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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Using the equation 4x-7=13 , choose all the steps that are used to solve the equation.
Answer:
see below
Step-by-step explanation:
4x-7=13
Add 7 to each side
4x-7+7 = 13+7
4x=20
Divide each side by 4
4x/4 = 20/4
x = 5
Answer:
x=5
Step-by-step explanation:
[tex]\hookrightarrow 4x-7=13 \\\\\hookrightarrow 4x=13+7\\\\\hookrightarrow 4x=20\\\\\hookrightarrow x=20/4\\\\\hookrightarrow x=5[/tex]
find the median of first 10 prime numbers
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER PLEASE
Answer:
1st answer was wrong
area of circle - quarter
Step-by-step
100pi- (100pi÷4)
100pi - 25pi
75pi
Write a story problem to go with the multiplication problem 3 x
7
8
. Then, solve the problem.
Answer:
Each order of rings comes with 3 rings. There are 78 order to pack how many rings is there going to be?
Step-by-step explanation:
solve for Surface Area
Answer:
325.76
Step-by-step explanation:
72+104+149.76
Moussa owns a small business selling clothing. He knows that in the last week 92 customers paid cash, 5 customers used a debit card, and 25 customers used a credit card.
If next week, he is expecting 1600 customers, about how many would you expect to pay with cash? Round your answer to the nearest whole number.
Answer:
1207
Step-by-step explanation:
Total number of customers last week: 92 + 5 + 25 = 122
Number of customers who paid cash: 92
Percent of customers who paid cash last week: 92/122 × 100% = 75.4%
Next week:
Total number of customers: 1600
Expected number of customers paying cash:
75.4% of 1600 = 0.754 × 1600 = 1207
What is the value of x?
Answer:
53
Step-by-step explanation:
This is because the total angle is 90, which is a complementary angle. So what you do is you subtract the total which is 90 from 37 to find x which is 53
a coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to buy each player a bottle of water and an energy bar. The price of one energy bar is $2. w equal the price of a bottle of water. Write an equation that represents the situation.
Answer:
$1.5 per water bottle.
Step-by-step explanation:
One energy bar is equal to $2.
$2 * 22 players is equal to $44.
$44 - $77 is equal to $33.
$33 ÷ 22 players is $1.5.
the reason I divided $33 by 22 players is because you need to know how many dollars did he pay for each bottle of water so you divide the amount of dollars by the amount of players to get the amount of dollars of each water bottle.
help pls i cant figure this out
Answer:
answer is 1 metre
Step-by-step explanation:
We can assume the width be 'x'
Now we would get the equation
(2x+10)(2x+14)=192
on solving we get x=1
Diana is trying to choose a broker who will help her purchase a par value $1,000 corporate bond from deegan pharmaceuticals. broker p charges a commission of 4.4% of the market value of each bond purchased, and broker q charges a flat fee of $32.50 for each bond purchased. if bonds from deegan pharmaceuticals are selling at 104.682, which broker will give diana the better deal, and by how much? a. broker p’s commission will be $9.47 less than broker q’s. b. broker p’s commission will be $27.89 less than broker q’s. c. broker q’s commission will be $13.56 less than broker p’s. d. broker q’s commission will be $11.50 less than broker p’s.
Broker q’s commission with a charge of $32.50 will be $11.50 less than broker p’s commission of 4.4%
What is a bond?A bond is a fixed-income instrument that represents a loan made by an investor to a borrower.
Par value of bond = $1,000
Commission on this by broker p= 4.4% = 1000*(4.4)/100= $44
So, the total price spent to purchase this bond = $1044
Par value of bond = $1,000
Commission on this by broker q= $32.50
So, the total price spent to purchase this bond =1000+32.50 = $1032.50
Difference between both deals = 1044-1032.50 = $11.50
Therefore, broker q’s commission will be $11.50 less than broker p’s.
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Answer:
C. Broker Q's commission will be $13.56 less the Broker P's.
Step-by-step explanation:
I just took the test and got it right.
Help pleaseee i am awful at math
Step-by-step explanation:
use the above process and answer is $3.60
help worth a lot of pounts
You want to buy a new computer that costs $2250. You check your savings-account balance and realize that to buy the computer, you will need $125 more than what you have in your savings account. How much money do you have in your savings account?
Equation:
Define the Variable:
How much money in your savings account?
Answer:
See below.
Step-by-step explanation:
Let x = amount of money you have in your account.
The money in your account plus the $125 extra that you need equals the total cost of the computer.
The equation is:
x + 125 = 2250
Now we solve the equation by subtracting 125 from both sides.
x = 2125
Answer: You have now $2125 in your account
Answer:
$2125Step-by-step explanation:
A rocket is shot off from a launcher. The accompanying table represents the height of
the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a
quadratic regression equation for this set of data, rounding all coefficients to the
nearest hundredth. Using this equation, find the height, to the nearest foot, at a time
of 14.7 seconds.
Time in Seconds (x) Height in Feet (v)
1.1
301
2
518
3.1
756
3.6
833
4.3
956
Copy Valoes for Calculator
Open Statistics Calculator
Regression Equation:
Final Answer:
Submit Answer
Answer:The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :y = - 15.57x² + 179.32x + 0.20height = yx = time Using the model obtained;The height, to the nearest foot, at a time, x = 6.4 seconds.y = - 15.57x² + 179.32x + 0.20y = - 15.57(6.4^2) + 179.32(6.4) + 0.20y = 510.1008y = 510
Step-by-step explanation:
A rugby match lasts for 80 mins. 20 mins of a match have been played. a) what Fraction of he match has been played? b) what percentage of the match is there left to play?
Answer:
a, 1/4
b, 75%
Step-by-step explanation:
a, total mins meant to be played = 80mins
mins being played = 20mins
fraction of the match being played = 20 /80 = 1/4
b, percentage of the match left to be played
= 80 - 20 = 60
then we find the fraction of the match meant to be played
60 / 80 = 3 /4
then we multiply by 100 to get the percentage
3/4 × 100 = 75 %
if this helped pls give brainliest
in a single drawer, erin has some socks of different colors: 3 black and 9 orange. if she pulls one sock out of the drawer what's the likelihood the sock is black??
The girls bought 20 blue hair bows, lost 4 bows, and gave 3 away. What percent of the bows do the girls still have?
Answer:
65%
Step-by-step explanation:
4 + 3 = 7
7/20 = 35/100
100 - 35 = 65
I may be wrong but yknow
Why didn't the physics teacher marry the biology teacher
Answer: There wasn't chemistry in them?
XD I dunno ._. >w<
Find a linear equation with two variables that, together with the
equation 10x + 5y = 1, would comprise a system
without a solution.
Answer:
10x+5y=2
Step-by-step explanation: You have the equation 10x+5y=1 and from the problem, we are trying to find an equation that does not produce a solution with 10x+5y=1. To do this know 1 is your y-intercept and if you put 10x+5y=1 into slope-intercept form you'll get y=-2x+1/5. Solve the problem know that you can use any number besides 1 on the right side and have the same slope to fit the question. What I mean is that let's say I have 10x+5y=2, I put it into a slope-intercept form I'll have y=-2x+2/5. The two equations y=-2x+1/5 and y=-2+2/5 will not meet because their slopes are PARALLEL. So in short have a different y-intercept but the same slope to not get a solution. Additional note you could have other y-intercepts such as 3,4,5,6,7,8, or 9 in your standard form equation 10x+5y= to get a equation that does not make a solution with 10x+5y=1.
If the area of a circular cricket ground is 15,400 m2, then find its circumference. (Take π≈22/7)
Answer:
440m^2
Step-by-step explanation:
15400/(22/7)=4900, which is r^2, so r=70. Now we can find the circumference by doing 22/7*2*70, which is 440.
Find the radius of the circle:
Area of a circle = pi x r^2
15,400 = 22/7 x r ^2
Divide both sides by 22/7
4900 = r^2
Take the square root of bothe sides:
R = 70
The radius of the circle is 70 meters.
now find the circumference:
Circumference = 2 x pi x radius
Circumference = 2 x 22/7 x 70
Circumference = 440 meters
answer: 440 meters
[tex]solve \: the \: following \: problems \: below[/tex]
please answer it correctly I need It now
please none sense report
Answer:
1. Find the circumference, then multiply that by 120 turns.
Formula for circumference;
C = 2πr
But, we need to find the radius which is 1/2(half) of the diameter, so,
D/2 = R
D = Diameter
R = Radius
20/2 = 10 is the radius.
Plug in values now:-
C = 2(3.14) x 10
C = 6.28 x 10
C = 62.8 is the circumference, now we multiply this by 120 to get the total amount of centimetres it'll go.
62.8(120)
= 7,536 cm it'll go.
2. Find the circumference, then multiply that by 750 turns/revolutions.
C = 2πr
Find radius,
D/2 = R
50/2 = 25 is the radius.
Plug in values now:-
C = 2(3.14) x 25
C = 6.28 x 25
C = 157 cm it'll go.
3. Same thing, find circumference then compare values.
Given that radius is 10,
Use the formula for circumference;
C = 2πr
Replace values:-
C = 2(3.14) x 10
C = 6.28 x 10
C = 62.8 cm is the circumference of the first circle.
Now the second circle, (use same formula)
C = 2πr
Find radius,
D/2 = R
10/2 = 5 is the radius.
Replace values:-
C = 2(3.14) x 5
C = 6.28 x 5
C = 31.4 cm is the circumference for the second circle.
Now subtract the second circle's circumference from the first:
62.8 - 31.4
= 31.4, 31.4 cm is how much greater the second circle is than the first.
4 - 5. Find circumference, (using circumference formula)
C = 2πr
Find radius,
D/2 = R
760/2 = 380
Replace values:-
C = 2(3.14) x 380
C = 6.28 x 380
C = 2,386.4 km is the distance he'll travel.
If he wants to travel around it with 2,000 km, he'll need to travel at least once.
What is the volume of this figure?
6004 in³
6624 in³
9936 in³
10,488 in³
The volume of the figure is the amount of space in the figure
The volume of the figure is 10488 cubic inches
How to determine the volume?The figure is a composite figure, and it contains:
A rectangular prism A triangular prismThe volume (V1) of the rectangular prism is:
V1 = Length * Width * Height
V1 = 18 in * 23 in * 16 in
V1 = 6624 cubic inches
The volume (V2) of the triangular prism is:
V2 = 0.5 * Base * Width * Height
V2 = 0.5 * 23 in * 16 in * 21 in
V2 = 3864 cubic inches
Add the volumes of both figures
V = V1 + V2
V = 6624 cubic inches + 3864 cubic inches
V = 10488 cubic inches
Hence, the volume of the figure is 10488 cubic inches
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Answer:
The answer is D: 10488
Step-by-step explanation:
What are the inputs of the function below? x –8 2 4 6 f(x) –6 –3 1 5 –6, –3, 1, 5 –6, –3, 4, 6 –8, 2, 4, 6 –8, 2, 1, 5
The inputs of the function are -8, 2, 4, and 6.
What is the input function?The input is the number that we put into the given function to get the output function.
x and y of the function are given below
X –8 2 4 6
f(x) –6 –3 1 5
From the given table, the inputs are given as the set of x values.
outputs are given as the set of y values. here, x is the input value that gives the output f(x).
Since x represents the input values and y represents the output values.
So, inputs of the function are -8, 2, 4 and 6
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a tether ball is tied to a rope and can rotate 230 degrees. If the rope has a radius of 6 ft, find the actual length the ball can travel in one rotation of 230 degrees
The actual length the ball can travel in one rotation of 230 degrees is approximately 24.06 feet.
How to find the relation between angle subtended by the arc, the radius and the arc length?[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
We are given that;
The angle= 230 degrees
Radius of rope= 6ft
Now,
If the tether ball is tied to a rope with a radius of 6 ft and can rotate 230 degrees, then the length of the rope that the ball travels in one rotation can be found using the formula for the circumference of a circle, which is:
C = 2πr
where C is the circumference of the circle, r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14).
To find the length the ball can travel in one rotation of 230 degrees, we first need to convert 230 degrees to radians by multiplying it by π/180.
230 degrees * π/180 ≈ 4.01 radians
Now we can calculate the length of the rope that the ball travels in one rotation of 230 degrees using the formula:
L = rθ
where L is the length of the rope traveled by the ball, r is the radius of the circle (the length of the rope), and θ is the angle traveled in radians.
L = 6 ft * 4.01 radians
L = 24.06 ft
Therefore, by the given angle the answer will be approximately 24.06 feet.
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