Which is equivalent to √60n^11/256n^4 after it has been simplified completely? Assume n =0
Answers
Answer:
[tex]\large\boxed{\dfrac{n^3}{8}\sqrt{15n}}[/tex]
Step-by-step explanation:
[tex]\sqrt{\dfrac{60n^{11}}{256n^4}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\ \text{and}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\sqrt{\dfrac{60}{256}n^{11-4}}=\dfrac{\sqrt{60n^7}}{\sqrt{256}}=\dfrac{\sqrt{4n^{6+1}\cdot15}}{16}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\dfrac{\sqrt{4n^6\cdot15n}}{16}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt{4n^{3\cdot2}}\cdot\sqrt{15n}}{16}\qquad\text{use}\ (a^n)^m=a^{nm}[/tex]
[tex]=\dfrac{\sqrt{4(n^3)^2}\cdot\sqrt{15n}}{16}=\dfrac{\sqrt{4}\cdot\sqrt{(n^3)^2}\cdot\sqrt{15n}}{16}=\dfrac{2\!\!\!\!\diagup^1\sqrt{15n}}{16\!\!\!\!\!\diagup_8}=\dfrac{n^3\sqrt{15n}}{8}[/tex]
Related Questions
How much more will $28,000 earn in interest than $16,000 if both are
invested in savings accounts with APYs of 5.8% for a year?
Answers
Answer:
Final answer is $12696.
Step-by-step explanation:
Given that initial amount P = $28000
Interest rate r = 5.8% = 0.058
Time = 1 year
Then future value is given by :
[tex]A=P\left(1+r\right)^t[/tex]
[tex]A=28000\left(1+0.058\right)^1=29624[/tex]
Similarly calculate future value for 2nd case:
Given that initial amount P = $16000
Interest rate r = 5.8% = 0.058
Time = 1 year
Then future value is given by :
[tex]A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}[/tex]
[tex]A=16000\left(1+0.058\right)^1=16928[/tex]
then difference = 29624 - 16928 = 12696
Hence final answer is $12696.
Answer:
$696.
Step-by-step explanation:
We are asked to find the amount of interest earned on $28,000 than $16,000 with APYs of 5.8% for a year.
We will use simple interest formula to solve our given problem.
[tex]I=Prt[/tex]
[tex]I[/tex] = Amount of interest,
P = Principal amount,
r = Interest rate in decimal form,
t = Time in years.
[tex]5.8\%=\frac{5.8}{100}=0.058[/tex]
Let us find difference of interests as:
[tex]\$28,000\times 0.058-\$16,000\times 0.058[/tex]
[tex](\$28,000-\$16,000)\times 0.058[/tex]
[tex](\$12,000)\times 0.058[/tex]
[tex]\$696[/tex]
Therefore, it will earn $696 more in interest.
2x + x + x + 2y × 3y × y
Answers
Answer:
[tex]\large\boxed{4x+6y^3}[/tex]
Step-by-step explanation:
[tex]2x+x+x+2y\times3y\times y\\\\=(2x+x+x)+(2y\times3y\times y)\\\\=4x+(2\times3)(y\times y\times y)\\\\=4x+6y^3[/tex]
What is the solution of 3x+8/x-4 less than or equal to 0
Answer Choices
x less than or equal to -8/3 or x greater than 4
x less than -8/3 or x greater than 4
-8/3 less than or equal to x less than 4
-8/3 less than x less than 4
Answers
In solving the inequality, 3x+8/x-4 <= 0, we identify critical points and assign intervals based on them. The solution offers two possible scenarios: x is less than or equal to -8/3 or x is greater than 4.
Explanation:The inequality 3x+8/x-4 =< 0 can be divided into two possible scenarios by clarifying the critical points. To solve this inequality, you first need to identify where the expression equals zero, that's where 3x+8=0 and x=4. Solving 3x+8=0 yields x=-8/3, which is the first
possible solution. Another critical point is where the denominator is zero, which is x=4.
Next, we need to check the signs of these intervals: (-inf, -8/3), (-8/3, 4) and (4, inf). Testing these intervals on the given inequality gives us the
solution that x is less than or equal to -8/3 or x is greater than 4 . Remember, x cannot be equal to 4 because it makes denominator zero in the origin expression which is undefined in mathematics.
Therefore, the correct solution is 'x less than or equal to -8/3 or x greater than 4'.
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Jillian sold 12% of the candy bars the class sold to raise money for a new water cooler in the school. If she sold 36 candy bars, what was the total number before taxes?
Answers
Answer:
So we can write an equation to solve this:
12/100 = 36/x
And then we are going to solve for x
x(12/100) = 36
36 x (100/12) = 300
The total number of candy bars was 300
Jillian sold 12% of the class's candy bars, which amounts to 36 bars. To find the total, calculate what 1% would be by dividing 36 by 12, and then multiply by 100 to find that the class sold 300 candy bars in total.
The student is asking about a practical application of percentages in a real-world context, which is a common subject in middle school mathematics. To find the total number of candy bars sold by the class, we need to use the information that Jillian sold 12% of the total and that this amounted to 36 candy bars. The calculation is straightforward: if 12% equals 36, we want to find 100% (the total).
To do this, we set up a simple proportion: if 12% is 36, then 1% would be 36 divided by 12, which is 3 candy bars. Since we're looking for the total, we multiply the number of candy bars representing 1% (which is 3) by 100 to find that the class sold a total of 300 candy bars before taxes.
Step-by-Step Calculation:
Find 1% of the total by dividing 36 candy bars by 12%.
1% of the total = 36 candy bars / 12 = 3 candy bars.
Multiply the value of 1% by 100 to find the total amount.
Total candy bars = 3 candy bars × 100 = 300 candy bars.
What is 2852÷12? Please help!!
Answers
It is D.) 237 and 2/3... glad I was able to help!
2852/12 is ———————> (A) 237
Jovie is maintaining a campfire. She has kept the fire steadily burning for 10 hours with 15 logs. She wants to know how many hours (h), she could have kept the fire going with 9 logs. She assumes all logs are the same.
How many hours can Jovie keep the fire going with 9 logs?
Answers
Answer:
6 hours
Explaination
10/15=.66666667
.66666667*9=6 hours
need help ASAP
which graph shows the graph of a circle with the equation x^2 + (y + 3)^2 equals 9
Answers
Answer:
upper left
Step-by-step explanation:
The generic equation for a circle centered at (h, k) with radius r is ...
(x -h)^2 +(y -k)^2 = r^2
Comparing that equation to the one you have, you can see that ...
-h = 0
-k = +3
r^2 = 9
Then you have (h, k) = (0, -3) and a radius of 3.
The circle has its center on the y-axis 3 units below the x-axis and just touches the x-axis. This is a description of the graph at upper left.
explain how the perimeter of a polygon is calculated.
Answers
Multiply the side length by the number of sides to get the perimeter. The formula for finding the perimeter of a regular polygon is just the number of sides x the length of any side. Once you've multiplied those 2 numbers together, you've found the perimeter of the polygon
Final answer:
The perimeter of a polygon is calculated by adding together the lengths of all its sides. For regular polygons with equal side lengths, the perimeter is the side length multiplied by the number of sides. For irregular polygons, all unique side lengths must be measured and summed.
Explanation:
The perimeter of a polygon is the total length around the shape. It is calculated by summing the lengths of all its sides. For a regular polygon with all sides of equal length, like a square, if one side length is a, then the perimeter is simply 4a because there are four sides. In the case of irregular polygons, each individual side length must be measured and added together to find the total perimeter.
For instance, consider a rectangle with a length of l and a width of w; the perimeter would be 2l + 2w, because each opposite pair of sides are equal. The units used for the lengths will be the same units used for the perimeter, such as meters. Nonetheless, the calculation can become more complex with polygons of more sides. Each side must be accounted for precisely, and units must remain consistent.
HELP! 4/5n = 2/3. n = ?
A. 2/15
B. 5/6
C. 1 1/5
D. 1 7/15
Answers
ANSWER
[tex]n=\frac{5}{6} [/tex]
EXPLANATION
The given equation is
[tex] \frac{4}{5}n =\frac{2}{3} [/tex]
We multiply both sides of the equation by:
[tex]\frac{5}{4}[/tex]
[tex] \frac{5}{4}\times \frac{4}{5}n =\frac{2}{3}\times\frac{5}{4} [/tex]
Multiply and cancel out common factors
This implies that:
[tex]n=\frac{5}{6}[/tex]
Option B is correct.
Jason used the commutative property to write an expression that is equivalent to 3
4
+ 5.6b + 9.
3
4
+ 5.6b + 9 is equivalent to 9.0 + 56b + 3.4.
Answers
Answer: 0.22
Step-by-step explanation:
Answer:Jason is not correct as Jason changed the terms.
Step-by-step explanation:
Given the expression 34+5.6b+9.Jason used the commutative property to write the above expression changed to 9.0 + 56b + 3.4
We have to tell Jason work is correct or not.
Commutative property states that order does not matters but the terms remains same i.e a+b=b+aJason change the expression 34+5.6b+9 to 9.0 + 56b + 3.4here, Jason change the terms as well as order Jason is not correct as Jason changed the terms.
Find the length of the missing side of necessary round to the nearest tenth . If y’all a real one help me please
Answers
Answer:
19.4
Step-by-step explanation:
40^2=35^2+b^2
(Pythagorean Theorem)
b^2=375
b=19.4
the two lines y=2x+8 and y=2x-12 intersect at x-axis at P nad Q. work out the distance PQ
Answers
The x-coordinates of points P and Q, where lines y=2x+8 and y=2x-12 intersect the x-axis, are -4 and 6 respectively. Therefore, the distance between them, PQ, is 10 units.
Explanation:The two given lines are y = 2x + 8 and y = 2x - 12. These lines intersect the x-axis when y = 0. Setting y=0 in these two equations, we find the x co-ordinates of the intersection points P and Q.
For y = 2x + 8, solving 2x + 8 = 0 gives x = -4. Hence, Point P is at (-4,0).
Similarly, for y = 2x - 12, solving 2x - 12 = 0 gives x = 6. Hence, Point Q is at (6,0).
The distance PQ can then be calculated using the distance formula: "PQ = |Q - P| = |6 - (-4)| = 10 units".
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Sally is completely unprepared for a three-question multiple-choice pop quiz, so she randomly guesses the answer to each question. If each question has four choices, then what is the probability that she gets all three questions correct?
A) 0.02
B) 0.25
C) 0.42
D) 0.75
Answers
Answer:
Option A) 0.02
Step-by-step explanation:
The probability p that one of the questions is correct is
[tex]P = \frac{1}{4}[/tex]
The number of questions that will answer (number of trials) is [tex]n = 3[/tex].
We want to find out the probability that [tex]x = 3[/tex] three questions will be answered correctly.
To calculate this probability we use the binomial formula:
[tex]P(x) = \frac{n!}{x!(n-x)!} p^x(1-p)^{n-x}[/tex]
Where
[tex]x=3\\n=3\\p=0.25[/tex]
Then:
[tex]P(x=3) = \frac{3!}{3!(3-3)!} 0.25^3(1-0.25)^{3-3}[/tex]
[tex]P(3) =0.25^3[/tex]
[tex]P(3) = 0.0156[/tex]
P(3) = 0.0156≈0.02
Please help.
Solve 3(x+2) > x
Answers
Answer: Last option
{x| x>-3}
Step-by-step explanation:
We have the following inequality 3 (x + 2)> x
To solve the inequality, apply the following steps:
1) Apply distributive property
[tex]3 * x + 3 * 2> x\\\\3x + 6> x[/tex]
2) Subtract 6 on both sides of the inequality
[tex]3x +6 -6> x-6\\\\3x> x-6[/tex]
3) Subtract x on both sides of the inequality
[tex]3x-x> x-x-6\\\\2x> -6[/tex]
3) Divide by 2 both sides of the inequality
[tex]x> -3[/tex]
The solution is all numbers greater than -3
ANSWER
{x|x>- 3}
EXPLANATION
The given inequality is;
[tex]3(x+2) \: > \: x[/tex]
Expand the parenthesis to obtain,
[tex]3x+6>x[/tex]
Group like terms
[tex]3x-x \: > \: -6[/tex]
[tex]2x>-6[/tex]
Divide both sides by 2
[tex]x \: > \: - 3[/tex]
The correct choice is D.
In year 13 the scientist will put tree wrap around tree 1 to protect it from the winter snow. The height of the tree wrap needs to be 45 inches the wrap is priced by the square foot. To the nearest square foot, how many square feet of wrap does she need
Answers
Answer:
22 feet²
Step-by-step explanation:
We are given:
height of tree h = 45 inches
Circumference= πd × inches
But d = 22.2inches
Therefore area will be
Area = 22.2π × 45 inches²
Area = 3137 inches²
Let's convert from inches² to feet², we have:
1 foot = 12 inches.
Therefore,
1 square foot = 1foot × 1foot = 12inches×12inches
= 3137inches² / 144 inches²
= 22feet²
Note: I attached missing data which states that diameter at year 13 is 22.2inches
To calculate the square footage of the tree wrap needed, we multiply the circumference of the tree trunk by the desired height. Assuming the tree trunk is cylindrical, we use the formula for the circumference of a circle: C = 2πr. Then, we convert the height to feet and calculate the square footage.
Explanation:To calculate the square footage of the tree wrap needed, we need to find the circumference of the tree trunk and multiply it by the desired height. Assuming the tree trunk is cylindrical, we can use the formula for the circumference of a circle: C = 2πr. We can then multiply the circumference by the desired height to get the square footage. Since we know the height is 45 inches, we need to convert it to feet by dividing by 12. Let's say the circumference of the tree trunk is 10 feet. The square footage of the tree wrap needed would be C * H = (2πr) * H = (2π * 5) * 3.75 = 47.12 square feet (rounded to the nearest square foot).
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Anwser These Questions they are hard
Answers
If you would like to show the questions to us, would be fine!
The shoreline pictured below used to extend about 10 meters farther out into the ocean. A warming climate and rising sea levels have weakened the soil and brought more water up against the shoreline than in the past. Image courtesy of Benjamin Jones, USGS Which of the following statements about the shoreline pictured above is true?
A. Rain and wind have built up the shoreline through physical weathering.
B. The ocean has built up the shoreline through the process of deposition.
C. Rain and wind have broken down the shoreline through chemical weathering. D. The ocean has eroded the shoreline by carrying earth materials out to sea.
20 points!!!
Answers
Answer:
D. The ocean has eroded the shoreline by carrying earth materials out to sea
Step-by-step explanation: I don't actually know why, I just did it on Study Island
Answer:
The ocean has eroded the shoreline by carrying earth materials out to sea.
Step-by-step explanation:
I had to do study island. Apparently, this answer was correct.
Which triangle has a bigger area:
1. A triangle with sides measuring 300, 400, and 500.
2. A triangle with sides measuring 300, 400, and 700.
Answers
Hello there!
Answer:
Triangle 2
Step-by-step explanation:
To determine which triangle has the bigger area, we would need to figure our the area of the triangles.
To solve for the area of the triangles, we would use the formula length × width × height or l × w × h
They gave us the information to the triangles in the question, so we would just solve.
Triangle 1: [tex]300 *400*500= 60,000,000[/tex]
Triangle 2: [tex]300*400*700=84,000,000[/tex]
When you finish solving, you would see that triangle 2 has the bigger area.
Triangle 2 would be the CORRECT answer because it has a bigger area than Triangle 1.
Triangle 2. Area is length x width x height
Which of the following are true about x? Check all that apply.
Answers
Answer:
x∈B
x∈A∪B
x∈A∪C
x∈A∩B
Step-by-step explanation:
As can be seen from the Venn diagram, x is the shaded portion between the intersection of 3 circles A, B and C.
hence x belong to b, and x belong to A union B, x belong to A union C and x belong to A intersection B !
Answer:
The following are correct:
B
C
D
E
F
Step-by-step explanation
Given s(x) = 3x - 6 and t(x) = 6 - 3x.
Find the simplified formula and domain for v(x)=(s/t)x and w(x)=(t/s)x
Answers
Answer with step-by-step explanation:
We are given the following two functions:
[tex]s(x) = 3x - 6[/tex]
[tex]t(x) = 6 - 3x[/tex]
We are to find the simplified formula and domain for [tex] v ( x ) = \frac { s ( x ) } { t ( x ) } [/tex] and [tex] w ( x ) = \frac { t ( x ) } { s ( x ) } [/tex].
[tex]\frac{3x-6}{6-3x}=\frac{3(x-2)}{3(2-x)}=\frac{x-2}{2-x}=\frac{x-2}{-(x-2))}=-1 [/tex]
So the domain for this function is (-∞, +∞) for v(x) = -1.
[tex]\frac{6-3x}{3x-6}=\frac{3(2-x)}{3(x-2)}=\frac{2-x}{x-2}=\frac{2-x}{-(-x+2)}=\frac{2-x}{-(2-x)}=-1[/tex]
The domain of this function is (-∞, +∞) for w(x)= -1
ANSWER
v(x)=-1
Domain: (-∞,2)U(2,+∞)
EXPLANATION
We have the given function
s(x) = 3x - 6 and t(x) = 6 - 3x.
We want to find the simplified formula and domain for
[tex]v(x) =( \frac{s}{t} )(x)[/tex]
[tex]v(x) = \frac{s(x)}{t(x)} [/tex]
[tex]v(x) = \frac{3x - 6}{6 - 3x} [/tex]
This function is defined if and only if
[tex]6 - 3x \ne0[/tex]
[tex]x \ne2[/tex]
Hence the domain is:
[tex]x \ne2[/tex]
We now simplify to obtain;
[tex]v(x) = \frac{ - (6 - 3x )}{6 - 3x} = - 1[/tex]
In need of help. Please help!!!
Answers
Answer:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
The answer is 9x10 to the positive 16 power
The sum of the given equation in the scientific notation should be [tex]9 \times 10^{16}[/tex]
Calculation of the sum:Here we Move the decimal due to this there is one non-zero digit to the left of the decimal point. In the case when the decimal is being moved to the right, so the exponent will be negative and vice versa.
So,
[tex]= (2 \times 10^{16}) + (7 \times 10^{16}) = 9 \times 10^{16}[/tex]
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There is a 30% chance of snow tomorrow. What is the likelihood of the event given it’s probability
Answers
The likelihood of an event stating the 30% chance of snow means that, in 100 identical weather circumstances, we would predict it to snow during 30. This does not deliver any information on the quantity of snow.
Explanation:The likelihood of an event given its probability represents the chance of that event taking place. When we say that there is a 30% chance of snow tomorrow, this means that out of every 100 similar weather scenarios, we would expect it to snow in 30 of them. Hence, the likelihood of it snowing tomorrow is 30%. It's important to understand that probability is a way to quantify the uncertainty associated with events predicted to occur, based on the known conditions.
Regarding the example, if we know that 'If it snows more than three inches, the schools are mandated to close.' and we see that 'The schools closed.' we can infer that 'It snowed more than three inches.' This however has no direct relation to the probability of snow tomorrow.
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help again yall are life savers
question: which could be the base of a rectangle prism that has a volume of 60 cubic units?
A.#1 B.#2 C.#3 D.#4
Answers
Answer:
Base #2
Step-by-step explanation:
For this question, we need to find the base that's volume is a factor of 60.
Base #1 Volume = 7 * 3 or 21
21 is not a factor of 60, so it cannot be the base.
Base #2 Volume = 5 * 3 or 15
15 is a factor of 60, so it is the base.
Answer: I think it's base 4. Don't rely on me, 'cause I can't understand this right now.
A real estate agent sells two sites for Rs. 18000 each. On one he gains 25% and on the other he loses 25 %. What is his loss or gain percent?
Answers
In this situation of selling two properties for the same price but with different gain and loss percentages, the real estate agent does not break even but incurs an overall loss of 6.25%.
Explanation:This is essentially a problem in profit and loss calculations in the domain of Mathematics. Since the selling price of both the sites is the same, the loss and gain percent will cancel out each other, resulting in no overall gain or loss. Here's why:
The real estate agent gains 25% on the first site. Hence, the cost price will be Rs. 18000 x 100/125 = Rs. 14400.The real estate agent loses 25% on the second site. Here, the cost price will be Rs. 18000 x 100/75 = Rs. 24000.The total cost price is Rs. 14400 + Rs. 24000 = Rs. 38400 and the total selling price is Rs. 18000 + Rs. 18000 = Rs. 36000. So, the real estate agent has incurred an overall loss. To find the percentage of loss, use the formula face: [(Loss) / (Cost Price)] * 100 = [(Rs. 38400 - Rs. 36000) / Rs. 38400] * 100 = 6.25% loss.
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Please help will give BRAINLIEST answer
Answers
Answer:
45 m
Step-by-step explanation:
The height at time of launch is at x = 0
Substitute x = 0 into f(x)
f(0) = - 5(0 + 1)(0 - 9) = - 5(1)(- 9) = 45 m
If f(x)=x+6 and g(x)=x^4 find G(F(x))
Answers
You plug in f(x) into where x is within g(x) so you get G(f(x))=(X+6)^4
Answer:
[tex]\large\boxed{g(f(x))=(x+6)^4}[/tex]
Step-by-step explanation:
[tex]f(x)=x+6\\\\g(x)=x^4\\\\g(f(x))\to\text{put}\ x+6\ \text{to the equation of}\ g(x)\\\\g(f(x))=(x+6)^4[/tex]
a snow globe has a volume of 3349 cm3 what is the radius
Answers
Answer: Apply the formula for the volume of a sphere.
Step-by-step explanation:
The volume of a sphere is
4
π
r
3
3
We just need to insert
r
=
2
c
m
into this to get the volume.
4
π
2
3
3
=
32
3
π
The exact volume is
32
3
π
c
m
3
The approximate volume is
33.5103217
which expression is equivalent to x^2-17x-60
Answers
Answer:
The expression is equivalent to x^2-17x-60 would be (x - 20)(x + 3)
Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60
Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -17 .
-60+1= -59
-30+2= -28
-20+3= -17
Final (x + 3) • (x - 20)
what are like terms and how to do them.
Answers
Answer:
So like terms are terms that have the same VARIABLE...
Step-by-step explanation:
So 2n + 3n is 5n and you can do that because they are like terms. you only need like terms for adding and subtracting
multiplying: 2n * 3n^2 = 6n^3
hope this helps!
What is the differences in length between the shortest and longest crayons
Answers
My answer would be 8.. I may not be correct, but I tried. So, I placed the numbers from least to greatest and split it 1’s and 2’s VS 3’s and 4’s. I just added 1 plus 2 plus 2 and a half plus 2 and a half and got 8. I also added (3+3+3)+3 and a half plus 3