Answers
Since power ³ is outside parenthesis, you should put the power to each expression inside parenthesis as below
2³(g⁵)³ / 4³(h²)³
in the multiplication of exponents, you add the indices
8(g⁵⁺³) / 64(h²⁺³)
8g⁸ / 64h⁵
it simplifies into
1g⁸ / 8h⁵
Your answer is D) g⁸ / 8h⁵
Related Questions
The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of the earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 325 miles above the earth's surface?
Answers
180 = k/(3900)² → k = 180 x 3900² → k = 2,737,800,000
If he is at 325 miles ABOVE the earth, the distance becomes: 3,900+325=4,225 miles and his weight becomes:
Weight = k/(distance)² → Weight = 2,737,800,000/(4225)² = 153.37
Weight = 153.37 lb
If an investment of $3000 grows to $4432.37 in eight years with interest compounded annually , what is the interest rate?
Answers
[tex]\bf 4432.37=3000\left(1+\frac{r}{1}\right)^{1\cdot 8}\implies \cfrac{4432.37}{3000}=(1+r)^8 \\\\\\ \sqrt[8]{\cfrac{4432.37}{3000}}=1+r\implies \sqrt[8]{\cfrac{4432.37}{3000}}-1=r \\\\\\ 0.0500001086\approx r\qquad\qquad\cfrac{r\%}{100}\approx 0.0500001086 \\\\\\ r\%\approx 100\cdot 0.0500001086\implies r=\stackrel{\%}{5}[/tex]
Please help me with this problem.
The diagram shows the floor plan of a one-bedroom apartment. Find the area of the living room in square feet. Round to nearest square foot.
Answers
The area of the living room is approximately 238 square feet.
To find the area of the living room, we need to multiply its length by its width.
First, let's convert the dimensions from feet and inches to feet. We have:
Length: 12 feet + 4 inches = 12 + 4/12 = 12.33 feet
Width: 19 feet + 4 inches = 19 + 4/12 = 19.33 feet
Now, we can multiply the length and width to find the area:
Area = length × width = 12.33 feet × 19.33 feet = 238.1289 square feet
Rounding to the nearest whole square foot, the area of the living room is approximately 238 square feet.
Please help me with this problem.
The diagram shows the floor plan of a one-bedroom apartment. Find the area of the living room in square feet. Round to nearest square foot.
The dimensions of living room are 12' 4" x 19' 4"
On rounding off to nearest feet we get the area of the living room as 238 ft²
In the figure it is given that the dimensions of the living room are 12' 4" x 19' 4". This means that the dimensions are:
12 ft 4 in x 19 ft 4 in
To get the area in feet, we need to convert the dimensions into feet. This can be done by using the conversion factor that 1 foot = 12 inch
So, 12 ft 4 in can be converted into feet as follows:
[tex]12\ \text{ft}\ 4\ \text{in} = 12\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 12.333\ \text{ft}[/tex]
19 ft 4 in can be converted into feet as follows:
[tex]19\ \text{ft}\ 4\ \text{in} = 19\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 19.333\ \text{ft}[/tex]
Now to calculate the area we multiply the dimensions of the living room (as the living room is a rectangle and area of rectangle is product of its length and breadth):
[tex]area = 12.333 \times 19.333 =238.433889[/tex] ft²
On rounding of to nearest feet we get the area as 238 ft². So, the area of the living room is 238 ft²
Use the regression line for the data in the scatter plot to answer the question. On average, how many more goals will a player score for every additional hour of practice?
A. )1/2 of a goal
B. )3/4of a goal
C.) 1 goal
D.) 4/3 goals
Answers
Answer:
Step-by-step explanation:
Given is a scatter plot and the regression line using least squares.
We are required to find out how many more goals a player will score for every additional hour of practice.
In other words, we are to find the slope of the regression line.
By taking two points on the line we can find slope of the line.
(1.5,2) and (6.5,6) are points on the line
Find slope using two point formula
Slope = [tex]\frac{y2-y1}{x2-x1} =\frac{6-2}{6.5-1.5} \\=\frac{4}{5}[/tex]
near slope is 3/4
Hence answer is option b.
On average, the goals a player scores for every additional hour of practice will be 3/4.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
We need to find out how many more goals a player will score for every additional hour of practice.
In other words, we have to find the slope of the regression line.
By taking two points on the line we can find the slope of the line.
Lets (1.5,2) and (6.5,6) are points on the line
So, the slope will be
Slope = y-y₁ / (x-x₁)
= 6- 2 / 6.5 - 1.5
= 4/5
Thus, the near slope is 3/4. Option B is correct.
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The perimeter of a rectangle is 99 inches. It’s width is 11 inches. What is the length of the rectangle? Solve algebraically and arithmetically.
Answers
22+2x=99
2x=77
X=77/2
Width=77/2
simplify each expression -(5p+3)
Answers
Answer:
-5p-3
Step-by-step explanation:
use the distributive property
Find the area of the surface. the part of the paraboloid z=4-x^2-y^2 that lies above the xy-plane
Answers
[tex]\mathbf s(u,v)=\langle u\cos v,u\sin v,4-u^2\rangle[/tex]
with [tex]0\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex]. Then the surface element is
[tex]\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|=u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]
The area of [tex]\mathcal S[/tex] is then given by the surface integral
[tex]\displaystyle\iint_{\mathcal S}\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=2}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=2}u\sqrt{1+4u^2}\,\mathrm du=\dfrac{(17^{3/2}-1)\pi}6\approx36.1769[/tex]
what is 260% as a fraction in simplest form
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Find the probability that your friend is at least 20 minutes late
Answers
If the graph has 1/3 length…
At least 20 minutes late: this would mean 20 minutes late or more.
20 or more minutes goes from 20 to 30. So that is a difference of 30 – 20 = 10. The distance of your rectangle is 10.
Length * width = (1/30) * 10 = 1/3 or 0.3333. The probability the friend is at least 20 minutes late is 0.3333.
What is the quotient? −4 1/2 ÷ (−2 2/3) Enter your answer as a mixed number, in simplified form, in the box. Will Mark Brainliest
Answers
The quotient of −4 1/2 ÷ (−2 2/3) would be equal to 1 1/16 as a mixed number, in simplified form.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
Thus,
[tex]\dfrac{a}{\frac{b}{c}} = a \times \dfrac{1}{\frac{b}{c} } = a \times \dfrac{c}{b} = \dfrac{a \times c}{b}[/tex]
We have been given that [tex]-4 \dfrac{1}{2}[/tex] ÷ (-[tex]2 \dfrac{2}{3}[/tex])
But first convert the mixed fraction into simple fraction
[tex]-4 \dfrac{1}{2}[/tex] = -9/2
(-[tex]2 \dfrac{2}{3}[/tex]) = -8/3
Thus, we have to divide the terms;
[tex]-4 \dfrac{1}{2}[/tex] ÷ (-[tex]2 \dfrac{2}{3}[/tex])
-9/2 ÷ -8/3
-9/2 x -3/8
27/ 16
In a mixed fraction; [tex]1\dfrac{1}{16}[/tex]
Hence, the quotient of −4 1/2 ÷ (−2 2/3) would be equal to 1 1/16 as a mixed number, in simplified form.
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Resolva o sistema a seguir:
2x - 4y = 8
x . y = 6
Answers
2x-4y=8
2x-4(6)=8
2x-24=8
+24. +24
2x=32
X=16
Using polar coordinates, evaluate the integral ∫∫rsin(x2+y2)da where r is the region 16≤x2+y2≤81.
Answers
[tex]\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_{\theta=0}^{\theta=2\pi}\int_{r=4}^{r=9}r\sin(r^2)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\pi\int_{s=16}^{s=81}\sin s\,\mathrm ds[/tex]
where we take [tex]s=r^2[/tex] so that [tex]\mathrm ds=2r\,\mathrm dr[/tex].
[tex]=\pi(\cos16-\cos81)[/tex]
The value of the integral is: πcos(16)- πcos (81)
What are polar coordinates?The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a from a reference point and an angle from a reference direction.
Given:
∫∫ r sin(x²+y²)dA and 16≤x²+y²≤81.
Now,
x =rcosϕ
y=rsinϕ
I=r
Find the integration limits:
ϕ∈[0,2π]
16≤x²+y²≤81
16≤r² cos² Ф + r²sin² Ф≤81
16≤r²≤81
4≤r≤9
So, r∈[4,9]
Now,
∫∫ r sin(x²+y²)dA=
= [tex]\int\limits^9_4 {dr} \int\limits^{2\pi}_0 {rsin \;(r^{2}) } \, d\phi[/tex]
=2π [tex]\int\limits^9_4 {rsin \;(r^{2}) } \, dr[/tex]
Let r² = u
2rdr=du
Also, limit will change from 16 to 25.
5→25
4→16
So,
= π[tex]\int\limits^{81}_{16} {sin \;(u) } \, du[/tex]
=−π|cos (u)∣[tex]^{81}_{16}[/tex]
= πcos(16)- πcos (81)
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One option in a roulette game is to bet $2 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $2 you paid to play the game and you are awarded $2. If the ball lands elsewhere, you are awarded nothing and the $2 that you bet is collected. Find the expected payback for this roulette game if you bet $2 on red.
Answers
The expected payback for betting $2 on red in a roulette game is -$0.62. This indicates an expected average loss, making it not a profitable bet.
Explanation:The expected payback for betting $2 on red in a roulette game is -$0.62. This means that on average, you would expect to lose 62 cents per game if you play this game repeatedly over a long string of games. The expected value indicates an expected average loss, so it is not a profitable bet.
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a rectangle is 9ft long and 40 in wide what is its area in square feet?
Answers
you can buy 5 cans of green beans at the Village Market for $2.20 you can buy at 10 of the same cans of beans at Sam's Club for $5.10 Which places is the better buy
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and at Sams they are $.51 ----- 5.10/10= .51
Adding Rational Expressions
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The temperature in mariah’s town was at 5.2 f midnight. the temperature decreased at a steady rate of 1.1 per hour until 7:00 a.m. at 7:00 a.m. the temperature increased by a total of 4.9until noon. what was the temperature at noon?
Answers
The temperature at noon was 2.4 degrees Fahrenheit.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
To determine the temperature at noon, we need to first calculate the temperature decrease between midnight and 7:00 a.m. and then add the temperature increase from 7:00 a.m. to noon.
The temperature decreased at a rate of 1.1 degrees Fahrenheit per hour, and it took 7 hours from midnight to 7:00 a.m., so the temperature decreased by a total of 7 hours x 1.1 degrees per hour = 7.7 degrees.
The temperature at 7:00 a.m. would therefore be 5.2 degrees - 7.7 degrees = -2.5 degrees Fahrenheit.
At noon, the temperature increased by a total of 4.9 degrees, so the temperature at noon would be -2.5 degrees + 4.9 degrees = 2.4 degrees Fahrenheit.
Thus, the temperature at noon was 2.4 degrees Fahrenheit.
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When Kaitlin divided a fraction by 1/2, the result was a mixed number. Was the original fraction less than or greater than 1/2? Explain your reasoning
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Evaluate (x + y)0 for x = -3 and y = 5.
A. -1/2
B. 0
C. 1
D. 2
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0
Answer: B).
*All you have to do is add negative three plus five and make it 2, then multiply 2 times zero to get the answer.
Kimmy bought a 5kg mg can of peanuts for $4.50 what is the unit price
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8/10 divided by 1/3 Help Needed
Answers
flip the sign and the second number
8/10 (3/1)
multiply across
24/10
simplify
12/5
12/5 is your answer
hope this helps
8/10*3/1= 24/10
Divide
24/10= 2.4 or 2 4/10= 2 2/5
Complete the inequality statement. 2/7___5/14
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>
=
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hope this helps
What is the most appropriate way to report the distance driven using the cars odometer
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You are ordering a hamburger and can get up to 77 toppings, but each topping can only be used once. you tell the cashier to surprise you with the toppings you get. what is the probability that you get 00 toppings? express your answer as a fraction or a decimal number rounded to four decimal places.
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You are building a rectangular garden and would like the area to be 32 square feet and the length twice the size as the width. What should the dimensions of your garden be?
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what's the length? well, isn't it 2w?
Which best describes the formula for the perimeter of a rectangle? A. It’s twice the length plus the width. B. P = 2l + 2w is the perimeter of a shape. C. Double the length and width to get the perimeter. D. The formula for the perimeter of a rectangle is P = 2l + 2w.
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The firmula for the perimeter of a rectange of dimensions L and W is
P = 2L + 2W.
Tomas plans to work in his garden on a day when it is least likely to rain.
He checks the weather forecast for the following week
probability of rain
Monday 18%
Tuesday 12%
Wednesday 73%
Thursday 61%
Friday 20%
Tomas plans to work in his garden on Tuesday.
What is the probability that it will not rain on Tuesday?
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Given the function h(x) = 4x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
Answers
[tex]\dfrac{h(1)-h(0)}{1-0}=\dfrac{4-0}{1-0}=4[/tex]
Average rate of change in Section B:
[tex]\dfrac{h(3)-h(2)}{3-2}=\dfrac{12-8}{3-2}=4[/tex]
As you can see, the average rates of change are the same, as expected. [tex]h(x)=4x[/tex] is linear, which means it has a constant rate of change over any interval in its domain.
Answer:
The rate of change of section A is 3 and rate of change of section B is 48.
Step-by-step explanation:
The given function is
[tex]h(x)=4^x[/tex]
Formula for average rate:
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Section A is from x = 0 to x = 1, the average rate of change of section A is
[tex]m_1=\frac{h(1)-h(0)}{1-0}=\frac{4-1}{1}=3[/tex]
Section B is from x = 2 to x = 3, the average rate of change of section B is
[tex]m_2=\frac{h(3)-h(2)}{3-2}=\frac{64-16}{1}=48[/tex]
Therefore rate of change of section A is 3 and rate of change of section B is 48.
[tex]m_1\times k=m_2[/tex]
[tex]3\times k=48[/tex]
[tex]k=12[/tex]
Therefore average rate of change of Section B is 12 times of Section A.
The given function is an exponential function and rate of change is not constant.
Jake walks a mile to work. If Jake has already walked two-fifths of a mile, how many more feet must he walk to get to work?
Answers
1 mile = 5280 feet
5280 * 3/5 = 3168 feet more to go
A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix? $7.00 $18.00 $24.00 $42.00
Answers
Answer:
18 just took the test