The simplified form of the expression: [tex]\( -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} \)[/tex]
To simplify the expression [tex]\( \frac{15p^{-4}q^{-6}}{-20^{12}q^{-3}} \)[/tex], we can apply the rules of exponents and simplify each part of the expression separately.
First, let's rewrite [tex]\( -20^{12} \) as \( -(20^{12}) \)[/tex] to make it clear that the exponent applies to the entire term:
[tex]\[ \frac{15p^{-4}q^{-6}}{-(20^{12}q^{-3})} \][/tex]
Now, let's simplify each part:
1. \( p^{-4} \) can be rewritten as [tex]\( \frac{1}{p^4} \).[/tex]
2. \( q^{-6} \) can be rewritten as [tex]\( \frac{1}{q^6} \).[/tex]
3. [tex]\( 20^{12} \)[/tex] can be calculated.
[tex]\[ \frac{15}{-(20^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]
Now, let's calculate [tex]\( 20^{12} \):[/tex]
[tex]\[ 20^{12} = (2^2 \times 5)^{12} = 2^{24} \times 5^{12} \][/tex]
[tex]\[ = (2^4)^6 \times 5^{12} = 2^{24} \times 5^{12} \][/tex]
Now, we can rewrite the expression:
[tex]\[ \frac{15}{-(2^{24} \times 5^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]
[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^6 \times q^{-3}} \][/tex]
[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} \][/tex]
This is the simplified form of the expression.
Which answer best describes the shape of this distribution?
What is the answer for this equation?
36^-x+3=(1/216)^x+1
Write a quadratic equation whose solutions are 2i and -2i.
Answer:
answer= 2i
Step-by-step explanation:
Sin (2x -9)= Cos (x +30) to solve for x
A shipping container is in the shape of a right rectangular prism with a length of 13.5 feet, a width of 10.5 feet, and a height of 2.5 feet. The container is completely filled with contents that weigh, on average, 0.33 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
The weight of the contents in the container, to the nearest pound, is 117 pounds.
To calculate the weight of the contents, we first find the volume of the container, then multiply it by the weight per cubic foot.
Step 1: Calculate the volume of the container.
Volume = length × width × height
Volume = 13.5 ft × 10.5 ft × 2.5 ft
Volume = 354.375 cubic feet
Step 2: Calculate the weight of the contents.
Weight = Volume × Weight per cubic foot
Weight = 354.375 cubic feet × 0.33 pounds per cubic foot
Weight ≈ 116.8725 pounds
Rounded to the nearest pound, the weight of the contents is 117 pounds.
First, we find the volume of the container by multiplying its length, width, and height together. The formula for the volume of a rectangular prism is length × width × height. In this case, the dimensions are given as 13.5 feet for the length, 10.5 feet for the width, and 2.5 feet for the height.
Next, we multiply the volume of the container by the weight per cubic foot of the contents to find the total weight. The average weight per cubic foot is given as 0.33 pounds.
Finally, we round the calculated weight to the nearest pound to match the desired precision. In this case, the weight of the contents is rounded to 117 pounds.
Complete question:
A shipping container is in the shape of a right rectangular prism with a length of 13.5 feet, a width of 10.5 feet, and a height of 2.5 feet. The container is completely filled with contents that weigh, on average, 0.33 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Which ordered pair is a solution of y = x + 12?
(24, 12)
(9, 21)
(–12, –24)
(0, –12)
For bananas are to be selected from a group of seven in how many ways can this be done
Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $14 per hour at her job, and Jack is paid $7 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $770 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?
Answer:
20
Step-by-step explanation:
WILL GET BRAINLIEST
Which does NOT represent the interior angle measures of a triangle? A.5°, 75°, 100°B.10°, 80°, 90°C.20°, 60°, 100°D.45°, 45°, 45°E.50°, 50°, 80°
Solve the system of equations -4x + 3y = -2 y = x - 1
The solution to the system of equations -4x + 3y = -2 and y = x - 1 is x = -1 and y = -2.
What is the solution to the system of equations?Given the system of equations in the question:
-4x + 3y = -2
y = x - 1
Solve the system of equations by substituting the expression for y from the second equation into the first equation:
-4x + 3y = -2
Plug in y = x - 1:
-4x + 3( x - 1 ) = -2
Simplifying, we get:
-4x + 3x - 3 = -2
Solve for x:
-x = -2 + 3
-x = 1
x = -1
Now, plug x = -1 into equation 2 and solve for y:
y = x - 1
y = -1 - 1
y = -2
Therefore, the solution is x = -1 and y = -2.
Learn more about system of equations here: brainly.com/question/30319215
#SPJ3
Item 11 Solve y=4x+8x for x.
To solve the equation y = 4x + 8x for x, isolate x by combining like terms on the right side and dividing both sides by 12. The solution is x = y/12.
Explanation:To solve the equation y = 4x + 8x for x, we need to isolate x on one side of the equation.
We can start by combining the like terms on the right side:
12x = y
To find the value of x, divide both sides of the equation by 12:
x = y/12
So the solution to the equation is x = y/12.
To solve the equation y = 4x + 8x for x, combine like terms to get y = 12x and then divide both sides by 12 to find x = y/12.
Explanation:The student's question requires us to solve the given equation for x. The original equation provided is y = 4x + 8x. To solve for x, we first combine like terms on the right side of the equation.
Combine like terms: y = 4x + 8x becomes y = 12x.Divide both sides of the equation by 12 to isolate x: x = y/12.The solution for x is x = y/12. This is a straightforward algebraic manipulation that involves combining like terms and using division to solve for the unknown variable.
What is the y-intercept of the line whose equation is y = x - 3?
Answer:
-3
Hope this helps! Please mark as brainliest.
10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 48t + 160 The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.
The Average rate of change of f(t) from t = 3 seconds to t = 5 seconds is - [tex]v_{avg} = -80\;ft/s[/tex]
We have a equation -
[tex]f(t) = -16t^{2} +48t+160[/tex]
that calculates the height of the ball from sea level in feet at different times.
We have to find the average rate of change of f(t) from t = 3 seconds to t = 5 seconds.
What is Average velocity?The rate of change of displacement per unit time is called average velocity. Mathematically -
[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]
We have -
[tex]f(t) = -16t^{2} +48t+160[/tex]
For time t = 3 seconds, f(t) is -
[tex]f(3) = -16(3)^{2} + 48(3) + 160\\f(3) = -144 +144 +160\\f(3) = 160\; feets\\[/tex]
For time t = 5 seconds, f(t) is -
[tex]f(5) = -16(5)^{2} + 48(5) + 160\\f(5) = -400+240+160\\f(5) = -400 + 400\\f(5) = 0 feet[/tex]
The formula for average velocity is -
[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]
According to question -
[tex]t_{2} = 5s[/tex] and [tex]t_{1} = 3s[/tex]
[tex]d_{2} = f(5) = 0 feet[/tex] and [tex]d_{1} = f(3)=160[/tex]
Substituting the values in the formula of average velocity, we get -
[tex]v_{avg} = \frac{0 - 160}{5 - 3} \\v_{avg} = \frac{-160}{2\\} \\v_{avg} = -80\;ft/s[/tex]
Hence, average rate of change of f(t) from t = 3 seconds to t = 5 seconds is [tex]v_{avg} = -80\;ft/s[/tex].
To solve more questions on calculating the average rate of change of height with time, visit the following link -
https://brainly.com/question/22257105
#SPJ2
I need help
Simplify 4z2 + z2 + 6a.
4z2 + 7a
5z2 + 6a
3z2 + 6a
11az2
Which equation is NOT true?
A. 15x + 55 = 6x + 4x
B. 15x + 55 = 26x
C. 25x + 55 = 180
D. m ∠S = 6x + 4x
Answer:
C
Step-by-step explanation:
Answer:
A. 15x + 55 = 6x + 4x
Step-by-step explanation:
Process of elimination the rest are true so this one is not. The angles of one side are supplementary with these angles which means they are not congruent.
I really need this answer to be correct
Select ALL the expressions that are equivalent to the polynomial below.
(4x+5)(-3x-1)
(-16x^2 + 10x - 3) + (4x^2 - 29x - 2)
3(x - 5) - 2(6x^2 + 9x + 5)
2(x - 1) - 3(4x^2 + 7x + 1)
(2x^2 - 11x - 9) - (14x^2 + 8x - 4)
(-15x^2 + 9x - 10) + (3x^2 - 10x - 5)
(4x^2 - 13x - 7) - (16x^2 + 9x - 5)
Please help due tomorrow! Math
the bottle of water contains 32 fluid ounces of water. How many cups of water are in a bottle.
There are 4 cups of water in a bottle containing 32 fluid ounces.
We have,
The number of cups in a bottle of water depends on the conversion rate from fluid ounces to cups.
1 cup is equivalent to 8 fluid ounces.
To find the number of cups in a bottle containing 32 fluid ounces of water, we can divide the total number of fluid ounces by the conversion rate:
So,
= 32 fluid ounces / 8 fluid ounces per cup
= 4 cups
Therefore,
There are 4 cups of water in a bottle containing 32 fluid ounces.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ6
Consider the following graph of a piecewise-defined function.
When x<-2, f(x)=
A: -3
B: 5
C: 2
When -2
A: x+2
B: 2x+2
C: 2x
When x>3, f(x)=
A: -3
B: 5
C: 2
Answer:
When x<-2, f(x) = 5
When -2<x<3, f(x)= 2x+2
When x>3, f(x)= -3
Step-by-step explanation:
Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle b. Round to the nearest tenth. A. 10.2° B. 11.2° C. 59.3° D. no solution Please select the best answer from the choices provided
The Nichols family consists of 8 children and 2 adults. The family minivan can safely transport a total of 7 family members, including an adult driver.
Which number line illustrates the capacity of the Nichols minivan as an inequality?
If the sum of two numbers is 20 and one of those numbers is three times the other, what is the smaller number?
Let logba=3 logbc=2 logbd=5 what is the value of logba^3d^4/c^2
Answer:
25
Step-by-step explanation:
15 is 10 % of what number
15*10=150
15 is 10% of 150
What is the value of x
The monthly rent of Marilyn's house went from $500 to $400, if p is the percent decrease in the rent, which proportion can be used to calculate p?
Answer:
D
Step-by-step explanation:
doing the test right now
Find the domain of the function :
Can you show the steps
please help asap 48 pts