To simplify the expression (3x^4y^-5)^3, apply the power rule to each term, calculate the result, and combine them. The simplified form is 27x^12y^-15.
How to Simplify the Expression (3x^4y^-5)^3:
Let's simplify the given expression step by step:
Apply the power rule of exponents to the entire expression. This means raising each term inside the parentheses to the given power:(a^m * b^n)^p = a^(m*p) * b^(n*p)
So, (3x^4y^-5)^3 becomes:
(3^3) * (x^(4*3)) * (y^(-5*3))
Calculate each term separately:3^3 = 27x^(4*3) = x^12y^(-5*3) = y^-15Putting it all together, we get:
27x^12y^-15
Simplified Form:In conclusion, the simplified form of (3x^4y^-5)^3 is 27x^12.y^-15.
Dakota’s dance troupe sold T-shirts as a fundraiser so that they could go to summer camp. When the girls began their fundraiser, 600 people wanted their T-shirts. They were actually short by 210 T-shirts, so the troupe ordered more. They raised the price in hopes of earning more profit, but when the price increased, the demand went down. Use the given information to analyze what happened with the fundraiser.
What happens when the quantity is above the equilibrium point?
Answer:
If the quantity is above the equilibrium point, there is an oversupply.
Step-by-step explanation:
The demand and supply curves intersect at a point called the equilibrium point. At this point, the price and quantity of equilibrium are determined. If we increase the price of the products, there is a decrease in the quantity demanded.
If demand and supply are perfectly elastic, when the price increases, the quantity demanded decreases proportionally. Given this, we can deduce that the collection of funds did not vary from what they would have obtained by selling the rest of the t-shirts at the same price.
If the quantity is above the equilibrium point, there is an oversupply.
Have a nice day!
A recipe for cookies calls for 3 1/4 cups of sugar. Amy already put in 3 1/9 cups. How many more cups does she need to put in
(-3,2) 90 degrees about the origin clockwise
Choose all the answers that apply.
The greenhouse effect is:
a) slowly increasing global temperature
b) caused when atmospheric gases trap heat
c) melting the polar ice caps
d) slowly increasing sea levels
e) increasing because of carbon dioxide emissions
Answer:
The greenhouse effect is the process by which radiation from a planet's atmosphere warms the planet's surface to a temperature above what it would be without this atmosphere.So following options are correct options
slowly increasing global temperaturecaused when atmospheric gases trap heatincreasing because of carbon dioxide emissionsAnswer:
A - slowly increasing global temperature
B - caused when atmospheric gases trap heat
E - increasing because of carbon dioxide emissions
Step-by-step explanation:
Estella buys 1.8 pounds of walnuts for a total of $5.04. She solves the equation 1.8p=5.04 to find the price p in dollars of one pound of walnuts. what does one pound of walnuts cost?
1.8p = 5.04
p = 5.04/1.8
p = 2.8
it cost $2.80 per pound
Estella buys 1.8 pounds of walnuts for a total of $5.04. She solves the equation 1.8p=5.04 to find the price p in dollars of one pound of walnuts. what does one pound of walnuts cost?
Solution: Let the cost of one pound of walnuts= $p
So, The cost of 1.8 pound of walnuts=$1.8p
Whereas, The cost of 1.8 pound of walnuts=$5.04
So, 1.8p=5.04
Now, To solve for p, Let us isolate p
To isolate p, Let us divide by 1.8 on both sides
[tex] \frac{1.8}{1.8} p=\frac{5.04}{1.8} [/tex]
On dividing 5.04 by 1.8, we get 2.8
[tex] \frac{1}{1} p=\frac{2.8}{1} [/tex]
So, p=2.8
Cost of one pound walnuts is $2.80
Walt received a package that is 2 1/3 inches long, 6 3/4 inches high, and 8 1/2 inches wide. What is the surface area of the package?
Answer : The surface area of the package is, [tex]185.9inch^3[/tex]
Step-by-step explanation :
The given package is in cuboid shape. Now we have to calculate the surface area of the package by using volume of cuboid.
Formula used for volume of cuboid is:
[tex]V=2(lb+bh+hl)[/tex]
where,
V = volume of package
l = length of package = [tex]2\frac{1}{3}inch=\frac{7}{3}inch[/tex]
b = width of package = [tex]8\frac{1}{2}inch=\frac{17}{2}inch[/tex]
h = height of package = [tex]6\frac{3}{4}inch=\frac{27}{4}inch[/tex]
Now put all the given values in the above formula, we get:
[tex]V=2\times [(\frac{7}{3}\times \frac{17}{2})+(\frac{17}{2}\times \frac{27}{4})+(\frac{27}{4}\times \frac{7}{3})][/tex]
[tex]V=2\times [\frac{119}{6}+\frac{459}{8}+\frac{63}{4}][/tex]
[tex]V=185.9inch^3[/tex]
Therefore, the surface area of the package is, [tex]185.9inch^3[/tex]
Amir is operating a machine that adds sand to a concrete mixture. The machine adds 110 ton of sand to the mixture in 45 minute. Enter a number in each box to complete the statements. Write the ratio that compares 110 ton of sand to 45 minute. The ratio in ton(s) per minute(s) is $$ .
During bowling practice, Marley rolled 14 strikes out of 70 attempts. What percent of Marley’s attempts were strikes?
Answer:
No, the correct answer should be 20 percent!
Step-by-step explanation:
14 divided by 70 = 0.2, which equals to 20%
Percentage of Marley's attempts were strikes = 20%
Step-by-step explanation:
Given :
Marley rolled 14 strikes.
Total attempts of Marley = 70
Calculation :
Percentage of Marley's attempts were strikes is
[tex]= \dfrac {14 \times 100}{70}[/tex]
= 20 %
For more information, refer the link given below
https://brainly.com/question/22056199?referrer=searchResults
Sean is raising funds for an event at his school. He has collected $25 each from x people, and he is still $100 short of his goal.
The expression that gives his goal is
Given that 2x - 3y = 8 and 4x + 3y = -2, what is the product of x and y?
Please answer I give out Brainliest, I thank, and I give out stars!
Mr Nickelson tells the class that they double the least common denominator for 1/2 3/5 and 9/15 to find the number of the day what number is the number of the day
Given fractions are [tex] \frac{1}{2} ,\frac{3}{5} ,\frac{9}{15} [/tex]
To find the least common denominators of the given fractions, we need to find the least common multiple (L.C.M.) of the numbers given in denominators i.e. 2, 5, and 15.
Finding the LCM of 2, 5, and 15 :-
2 = 1 x 2
5 = 1 x 5
15 = 3 x 5
So least common multiple of 2, 5, and 15 would be (1 x 2 x 3 x 5) = 30.
Hence, common denominator would be 30.
The teacher tells us to double the common denominator to find the answer that is the number of the day.
So we need to double the value of common denominator i.e. 2 x 30 = 60.
It means that 60 is the number of the day.
Hence, 60 is the final answer.
The number of the day is 4.
Explanation:Least common denominator for 1/2 3/5 and 9/15
To find the least common denominator (LCD) for fractions, we need to find the smallest multiple that is common to all the denominators.
For 1/2, 3/5, and 9/15, the denominators are 2, 5, and 15 respectively.
To find the LCD, we need to double the smallest denominator, which is 2, resulting in an LCD of 4.
Therefore, the number of the day is 4.
Learn more about Least Common Denominator here:https://brainly.com/question/12127721
#SPJ11
Which property changes when a figure is reflected across a line?
When a figure is reflected across a line the orientation of the figure or shape changes when it is a reflected across a line. Also, the x-coordinate and y-coordinate change places
What is reflection?
A reflection is a mirror image of the shape.
What is Coordinate system?In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space
Given,
A figure is reflected across a line
The orientation of the figure or shape changes when it is a reflected across a line
Also, the x-coordinate and y-coordinate change places
Hence, When a figure is reflected across a line the orientation of the figure or shape changes when it is a reflected across a line. Also, the x-coordinate and y-coordinate change places
Learn more about Reflection and Coordinate system here
https://brainly.com/question/26259511
#SPJ2
The orientation of a figure changes when it is reflected across a line while its shape and size stay consistent, creating a mirror image with symmetry relative to the line of reflection.
When a figure is reflected across a line, its orientation changes, whereas the shape and size of the figure remain the same. The Law of Reflection implies that each point of the figure maintains its distance from the line of reflection but on the opposite side, creating a 'mirror image' or symmetric counterpart. This mirror image aligns with the original figure if an imaginary line were drawn perpendicular to the mirror (line of reflection) at each point, these perpendiculars would be equal in length on both sides. This reflection transformation is an example of a linear transformation, preserving the straightness of lines and parallelism of parallel lines.
A six sides dice rolls twice. What is the probability that the first roll is a even number and the second roll is a number greater than 4?
this is algabra 1 i need 7,13, and 14
Can u guys help me with the visual question please
Simplify the expression. Show each step.
–5 × 1 × 11 × 4.
Cereal is packaged in a box shaped like a rectangular prism with a base 7.5 inches by 2 inches and a height of 10 inches. Manufacturing each box requires 10% more cardboard than the box's surface area. How much cardboard is needed to make each box?
Answer: 1032
Step-by-step explanation: you welcome
Is 100 a reasonable estimate 915.25 divided by 88.22
The reasonable estimate is 10.
We can approximate 915.25 to 900.
We can approximate 88.22 to 90.
Then we divide them: [tex]\frac{915.25}{88.22}\approx\frac{900}{90}=10[/tex].
So the reasonable estimate is 10.
Learn more: https://brainly.com/question/21764393
100 is not a reasonable estimate for the operation 915.25 divided by 88.22, as the actual answer is approximately 10.37. While estimates don't provide exact numbers, the difference here is too great for 100 to be considered reasonable, depending on the level of accuracy needed.
Explanation:In mathematics, estimation is commonly used when you do not need the exact answer, but rather a ballpark number close to the actual value. The student's question revolves around whether 100 is a reasonable estimate for the operation 915.25 divided by 88.22. We can check this by performing the actual division: 915.25 / 88.22 equals approximately 10.37. Although this is not exactly 100, it is within an order of magnitude which might make the estimate reasonable depending on the context. Therefore, as a quick estimate, 100 might not be suitable for high-precision contexts.
It's important to understand how estimates work. Their value is not in providing exact numbers, but in giving a quick understanding of a situation, especially when the exact numbers are complex or cumbersome. Here, however, the difference between the actual result (10.37) and the estimate (100) is quite significant, which suggests that 100 might not be a reasonable estimate in this case, depending on the level of accuracy needed.
Learn more about Estimation here:https://brainly.com/question/14992908
#SPJ11
A new car is purchased for 20300 dollars. The value of the car depreciates at 8.75% per year. What will the value of the car be, to the nearest cent, after 12 years?
Answer:
$6,765.35.Step-by-step explanation:
Here we have to use the rate of depreciation, the initial value and the total time to find the final value with this formula
[tex]A=A_{0}(1-r)^{t}[/tex]
Where [tex]A[/tex] is the final value, [tex]A_{0}[/tex] is the initial value, [tex]r[/tex] is the rate of depreciation and [tex]t[/tex] is the time.
Replacing all values, we have
[tex]A=20300(1-0.0875)^{12}[/tex]
[tex]A=6765.35[/tex]
Therefore, after 12 years the car will value $6,765.35.
If a company's revenue is 50 billion USD a year, how much money does it make per hour?
A scale drawing of a billboard uses the scale 4cm:9 ft. The length of the billboard in the drawing is 11 cm. How long is the actual billboard
The length of the actual billboard is 24.75 ft.
What is Scale Factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure.
Given:
Scale: 4cm : 9 ft
So, 1 cm = 9/4 ft
Then, length = 11cm
= 11 x 9/4
= 99/4
= 24.75 ft
Hence, the length is 24.75 feet.
Learn more about scale factor here:
https://brainly.com/question/29464385
#SPJ3
Chad has a rope that is 20 yards long. How many pieces of rope measuring 4/7 of a yard can he divide his rope into?
Answer:
[tex]35\ pieces[/tex]
Step-by-step explanation:
we know that
To find the number of pieces of rope 4/7 of a yard, divide the total length of the rope by 4/7
we have that
The total length of the rope is 20 yards
so
[tex]\frac{20}{(4/7)}=\frac{20*7}{4}=35\ pieces[/tex]
Answer:
28 is the answer
Step-by-step explanation:
Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is s4. There is also a single shipping charge of $2. How many books can he afford without spending more than his gift voucher amount?
General Idea:
When we are working with word problems, we need to follow the below steps:
Step 1: Assign variable for the unknown that we need to find.
Step 2: Write a meaningful mathematical equation using the sentence given
Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.
Applying the concept:
Step 1: Let x be the number of books that Brett can afford without spending more than his gift voucher amount.
Step 2: Writing mathematical equation based on the given sentence "Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2"
[tex] Online \; Gift \; Voucher=Number \; of \; books \; \times \; Cost\;per \; Book \; + \; Single \; shipping \; charge [/tex]
[tex] 30=4x+2 [/tex]
Step 3: Solving equation
[tex] 4x+2=30\\ Subtract \; 2 \; on \; both \; sides\\ \\ 4x+2-2=30-2\\ Combine \; like \; terms\\ \\ 4x=28\\ Divide \; 4 \; on \; both \; sides\\ \\ \frac{4x}{4}= \frac{28}{4} \\ Simplifying \; fraction \; on \; both \; sides\\ \\ x=7 [/tex]
Conclusion:
The number of books that Brett can afford without spending more than his gift voucher amount is 7 !!
Will mark brainliest and 20 points
How many 1-inch cubes do you need to create a cube with an edge length of 7 inches?
If James can swim 10 laps in 23 minutes, what would be his expected time for 15 laps?
Jeremy is making a cube using blocks. The cube is solid and has no holes. How many cubes did Jeremy use? A. 125 B. 75 C. 25 D. 15
Ms.Gibson made an initial deposit of $500 when opening a bank account. After the initial deposit, she deposited the same amount of money each month. The table below shows the total amount of money, a, she deposited into the account after a certain number of months, t, since opening it. Write an equation to model the relationshipbetween t and a.
To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we can use the equation a = 500 + 500t.
Explanation:To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we need to find the pattern. According to the information given, Ms. Gibson made an initial deposit of $500 and then deposited the same amount each month. This means that the total amount of money, a, deposited after a certain number of months, t, can be represented by the equation:
a = 500 + 500t
Learn more about Equation to model relationship between time and money deposited here:https://brainly.com/question/9802576
#SPJ12
Choose the correct simplification of the expression a^7b^8/a^4b^4
A: a^11b^12
B: a^3b^4
C: 1/a^3b^4
D: 1/a^3b^2
Eder needs 6 cookies and 2 brownies for every 4 plates he makes for a bake sale. Drag cookies and brownies into the box to show how many Eder needs for 10 plates.
Answer:
Eder needs 15 cookies and 5 brownies for every 10 plates he makes.
Step-by-step explanation:
In order to know hoy many cookies and brownies Eder needs for 10 plates, given the fact that he needs 6 cookies and 2 brownies for every 4 plates, we need to perform the following calculation:
6C + 2B = 4X (plates)
6/4C + 2/4B = X
1.5C + 0.5 B = X
So, as we can see, 1.5 cookies and 0.5 brownies are needed for every plate. To know how many of those are needed for ten plates, we ned to multiply those numbers by 10.
1.5 x 10 = 15
0.5 x 10 = 5
Eder needs 15 cookies and 5 brownies for every 10 plates he makes.
Betty is participating in a walk a thon. For every .25 miles she walks, she earns a donation. Betty walks 2.50 miles. How many donations did she earn?