The simplified form is [tex]6x^{3}[/tex].
What are indices in maths?
An index, or a power, is the small floating number that goes next to a number or letter.The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.The equation is -
[tex]\sqrt{\frac{2160x^{3} }{60x^{2} } }[/tex]
We can rewrite this using property of multiplication to obtain
[tex]\sqrt{\frac{2160}{60} * \frac{x^{8} }{x^{2} } }[/tex]
We simplify variable expression in the radicand using
[tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]
[tex]\sqrt{36 * x^{8 - 2} }[/tex]
[tex]\sqrt{36 * x^{6} }[/tex]
[tex]\sqrt{36 * (x^{3})^{2} }[/tex]
[tex]\sqrt{36} * \sqrt{(x^{3})^{2} }[/tex]
[tex]6 * x^{3}[/tex]
Therefore, the simplified form is [tex]6x^{3}[/tex]
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A recipe requires 150 grams of sugar to make 6 serves of a special desert how much sugar will be needed to make 15 serves of this desert?
Answer:
150g for 6 servings
x grams for 15 servings
150/6 = 25
15 x 25 = 375
375g of sugar will be required to make 15 servings.
Your team decides to erect 8 tent frames that can each hold a tarp to provide shade and cover if needed. The area under each tarp is 25 feet wide and 40 feet long, and the top of the tarp will run the length of your seating area. Your tarp needs a slope of to allow runoff in case of rain. The frame will be 10 feet high around the outside.
How high does the center of the frame need to be?
The height of the frame is 15 feet.
How to calculate the height?From the information given, the following can be depicted:
b - 10/a = 2/5
2a = 5b - 50
2a - 5b = -50
Also, slope of AC:
= (b - 10(/(a - 5) = 2/5
2a - 50 = -5b + 50
2a + 5b = 100
Both equations will be solved
The height of the frame will be:
= 5 + 10
= 15 feet
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What is the solution to the inequality?
A. y > 32
B. y > 2
C. y < 2
D. y < 32
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
An inequality [tex]\sf{-\cfrac{y}{4}+7 > -1}[/tex]✏[tex]\bigstar\textsf{To\quad find:-}[/tex]✏
y -- ?▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex]✏
First, subtract both sides by 7:-
[tex]\sf{-\cfrac{y}{4} > -1-7}}[/tex]
[tex]\sf{-\cfrac{y}{4} > -8}[/tex]
Now multiply both sides by 4:-
[tex]\sf{-y > -8*4}[/tex]
[tex]\sf{-y > -32}[/tex]
last step:-
[tex]\sf{y < 32}[/tex]
`hope it was helpful to u ~
[tex] \implies \: \sf{ - \dfrac{y}{4} \: + \: 7 \: > \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 7 \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 8} \\ \\ \implies \: \sf{ \cancel- \: \dfrac{y}{4} \: > \: \cancel- \: 8} \\ \\ \implies \: \sf{ \dfrac{y}{4} \: < \: 8} \\ \\
\implies \: \sf{ y \: < \: 8 \times 4} \\ \\ \implies \: \bf{ y \: < \: 32}[/tex]
Expand the following using the Binomial Theorem and Pascal’s Triangle. Show your work
2. (x-4)^4
3. (2x+3)^5
4. (2x-3y)^4
Answer:
2
Step-by-step explanation:
If 3 square feet of fabric costs $3.75. what would 7 square feet cost?
Answer:
8.75
Step-by-step explanation:
3.75/3=1.25
1.25=1 square feet
1.25(7)=8.75
PLEASE HELP IM STUCK
Hello, the solution of the problem is in this photo.
If the graph of the line falls from left to right, then the slope is negative.
Find the remainder when:
(75*56)^28+(58*34)^31 is divided by 19
Answer:
Exact form: 19 multiply 4200^28 + 1972^31 / 19
Decimal form: 3.55481422 multiply 10^101
From Dan's ranch one road is built to get to Andy's house two roads are built to get wo Willies house. How many way are there now to get from Andys house to Willies house?
Answer:
the answer you can find onlinde \\\\
Step-by-step explanation:
Two students compared the scores on their math tests. Their results on 9 tests are shown in the box plots below.
Compare the box plots. Which statements are true? Check all that apply.
Ben has the smaller range of test scores.
The lower quartile and upper quartile of Nadia’s data are both higher than the lower quartile and upper quartile of Ben’s data.
The median of Nadia’s data is equal to the median of Ben’s data.
Nadia had the highest score on a test.
Ben’s lowest score was equal to Nadia’s lowest score
The statements that are true for the box plots are:
C. The median of Nadia’s data = median of Ben’s data.
D. Nadia had the highest score on a test
How to Find the Median of a Box Plot?The median of a data set is the center value, which is indicated on a box plot by a vertical line that divides the box.
Given the two box plots, we can conclude that:
Median for the data of Nadia is 92, which is the same for Ben.
The extreme whisker to the right for Nadia is at 100, which is the highest value for Nadia while that of Ben is 99.
The true statements are:
C. The median of Nadia’s data = median of Ben’s data.
D. Nadia had the highest score on a test
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Answer:
"C" and "D"
Step-by-step explanation:
took test on edge 2023
Triangle ABC is transformed to triangle A′B′C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles?
A. m
B. m
C. m
D. m
The triangle ABC was reflected over the x axis to form triangle A'B'C, hence the measures of the corresponding angles are congruent.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The triangle ABC was reflected over the x axis to form triangle A'B'C, hence the measures of the corresponding angles are congruent.
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An aircraft seam requires 21 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 23% of all seams need reworking, what is the probability that a rivet is defective
For Part A the probability is 0.0095 and for Part B the probability is
0.0043.
What does defective mean in probability?Probability of defect is perhaps the most important indicator of a manufacturing process's quality. It's a statistical technique used to indicate how often a product will fail during its lifespan, which in turn allows you to estimate the likelihood that an item will result in customer dissatisfaction.
Part A:
The number of rivets=22 rivets
Probability that no rivet is defective= [tex](1-p)^{22}[/tex]
The probability that at least one rivet is defective=1-[tex](1-p)^{22}[/tex]
For 19% of all seams need reworking, probability that a rivet is defective is given by
1-[tex](1-p)^{22}[/tex] = 0.19
[tex](1-p)^{22} = 1-0.19\\(1-p)^{22} = 0.81\\ p=1-\sqrt[22]{0.81} \\p=0.0095[/tex]
Part B:
For 9% of all seams need reworking, probability of a defective rivet is:
1-[tex](1-p)^{22}[/tex] = 0.09
[tex](1-p)^{22} = 1-0.09\\(1-p)^{22} = 0.91\\ p=1-\sqrt[22]{0.91} \\p=0.0043[/tex]
Hence, For Part A the probability is 0.0095 and for Part B the probability is 0.0043.
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When I flip a coin, the outcome can be either heads or tails; it is uncertain. However, in a large number of flips, the distribution of heads and tails is very regular. We say that flipping a coin is Group of answer choices predictable. deterministic. none of the above. random.
If the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is: D. random.
What is a fair coin?A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly flipped or tossed by anybody.
This ultimately implies that, the outcome of flipping a fair coin is generally going to produce only one of two results and these include the following:
HeadTailIn this context, we can infer and logically conclude that if the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is considered as being random.
In conclusion, it is important to note that a fair coin is considered as being random when the distribution of heads and tails of a fair coin is very regular in a large number of flips.
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For 2-3, Name a postulate or theorem that can be used to prove that the two triangles are similar. Then, write a similarity statement.
Postulate: AA
Similarity statement: [tex]\triangle CBA \sim \triangle FED[/tex]
What is the missing number in the synthetic division problem below? NEED HELP FAST!
Answer:
9
Step-by-step explanation:
3 + 0 = 3
-2 + 6 = 4
2 + 18 = 20
From this:
1 + 8 = 9
Answer:
A.9
Step-by-step explanation:
✓3 + 0 = 3
✓ -2 + 6 = 4
✓ 1 + 8 = 9
✓ 2 + 18 = 20 beacuse of this the answer is 9
Trigonometry, please provide a simple explanation
Answer:
C
Step-by-step explanation:
cosecΘ = [tex]\frac{1}{sin0}[/tex] = [tex]\frac{2}{\sqrt{3} }[/tex] ( cross- multiply )
2sinΘ = [tex]\sqrt{3}[/tex] ( divide both sides by 2 )
sinΘ = [tex]\frac{\sqrt{3} }{2}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{2}[/tex] ) = 60°
Answer:
C. 60°
Step-by-step explanation:
by definition, cosec(θ) is the reciprocal of sin(θ)
In other words ,
[tex]\text{cosec} \left( \theta \right) =\frac{1}{\sin \theta }[/tex]
Then
[tex]\text{cosec} \left( \theta \right) =\frac{2}{\sqrt{3} }[/tex]
[tex]\Longleftrightarrow \frac{1}{sin \left( \theta \right) } =\frac{2}{\sqrt{3} }[/tex]
[tex]\Longleftrightarrow sin \left( \theta \right) =\frac{\sqrt{3} } {2}[/tex]
Then
θ = 60°
WILL MAKE BRAINLIEST!! What will the coordinates of triangle are RST after it is translated four units right and three units up type your answer in as a coordinate pair X, Y for each point enter your answer and also provide a one sentence explanation that describes how are you determine your answer review the Rubik be slow to see how you will be evaluated?
The coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)
How to determine the coordinates?From the figure, the coordinates of the triangle RST are:
R = (-4, 2)
S = (3, 5)
T = (-4, -4)
The rule of translation is given as:
Four units rightThree units upThis is represented as:
(x, y) = (x + 4, y + 3)
So, we have:
R' = (-4 + 4, 2 + 3) = (0, 5)
S' = (3 + 4, 5 + 3) = (7, 8)
T = (-4 + 4, -4 + 3) = (0, -1)
Hence, the coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)
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A paper bag contains a mixture of 3 types of candy. there are 10 packs of fuzzy peaches, 7 packs of sour keys, and 3 packs of nerds. suppose a game is played in which a candy is randomly taken from the bag, replaced, and then a second candy is drawn from the bag. if you are allowed to keep the second candy only if it was the same type a the one that was drawn the first time, calculate the probability of each of the following: a) you will keep a pack of fuzzy peaches b) you will be able to keep any of the candy c) you will not be able to keep any of the candy
The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.
How to calculate the probability?a. Based on the information given, the probability that the person will be able to keep a pack of fuzzy peaches will be:
= 10/(10 + 7 + 3) × 10/(10 + 7 + 3)
= 10/20 × 10/20
= 1/4
= 0.25
The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.
b. The probability to be able to keep any of the candy will be:
= (10/20 × 10/20) + (7/20 × 7/20) + (3/20 × 3/20)
= 100/400 + 49/400 + 9/400
= 158/400
= 0.395
The probability to be able to keep any of the candy will be 0.395.
c. The probability that you will not be able to keep any of the candy will be:
= (10/20 × 10/20) + (7/20 × 13/20) + (3/20 × 17/20)
= 100/400 + 91/400 + 51/400
= 242/400
= 0.605
The probability that you will not be able to keep any of the candy will be 0.605.
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A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 3 feet per minute. Find the rate at which the area is changing at the instant the radius is 4 feet.
The rate of change of area when radius = 4feet is 75.36 feet²/min.
What is area?Area definition, any particular extent of space or surface.
Area of circle = πr²
Let the area of the circle be πr²
dr/dt = 3feet/min (GIVEN)
Differentiating both sides with respect to time:
A = πr²
dA/dt = π(2r).(dr/dt)
dA/dt = (2 * 3.14 * r).(dr/dt)
The rate of change of area when radius = 4feet
dA/dt = (2 * 3.14 * 4).(3)
dA/dt = 75.36
Hence, the rate of change of area is 75.36feet²/min.
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If c(x) = 4x − 2 and d(x) = x² + 5x, what is (c.d)(x)?
4x³ + 18x² – 10x
x² + 9x-2
16x² + 4x-6
4x² + 20x-2
Answer:
[tex]4x^2+20x-2[/tex]
Step-by-step explanation:
To find (c.g)(x) we basically use the function d(x) as your variable, x, and plug it into c(x). So we replace every x in c(x) with the function d(x), [tex]x^{2} +5x[/tex]
c(g(x))=4(x^{2} +5x)-2
c(g(x))4[tex]x^2[/tex]+20x-2
HELP!! Which of the following represents the graph of the equation y = 1/2 x +1
ANSWER - The first seems more accurate according to my view it's A
The ratio of boys to girls who play soccer in Mr. Fraser’s class is 14:6. If there were 400students in the school, how many boys would likely play soccer?
Answer:
280
Step-by-step explanation:
Set up a ratio to solve.
Mr. Fraser's class has 20 soccer playing students, and 14 are boys.
14/20 = x/400
Cross multiply. 20x= 5600
Divide by 20 to solve
x= 280
The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5 She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales Now she has 14 more books of fairy tales than encyclopedias How many picture books does she have?
Using a system of equations, it is found that she has 9 picture books.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of picture books.Variable y: Number of encyclopedias.Variable z: Number of fairy tale books.The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5, hence:
[tex]\frac{x}{y} = \frac{3}[4}, \frac{x}{z} = \frac{3}{5}, \frac{y}{z} = \frac{4}[5}[/tex]
She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales. Now she has 14 more books of fairy tales than encyclopedias, hence:
z + 5 - 0.5y = 14.
z - 0.5y = 9
From the ratios, we have that:
[tex]y = \frac{4}{3}x, z = \frac{5}{3}x[/tex]
Hence we solve for x to find the number of picture books:
[tex]z - \frac{y}{2} = 9[/tex]
[tex]\frac{5}{3}x - \frac{2}{3}x = 9[/tex]
x = 9.
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Ahmad has containers of two different sizes. The total capacity of 16 containers of one size is x gallons, and the total capacity of 8 containers of the other size is also x gallons, and . In terms of x, what is the capacity, in gallons, of each of the larger containers?
Answer:
x/8 gallons.
Step-by-step explanation:
The 8 containers have the larger capacity as the 2 totals are x and the other containers are 16 in total.
Capacity of each of the large containers = x/8 gallons.
The sum of two numbers is 140, and their difference is 20. What are the two numbers?
Answer:
60 and 80.
Step-by-step explanation:
If the numbers are x and y:
x + y = 140
x - y = 20 Adding:
2x = 160
x = 80
So y = 140 - 80 = 60.
Answer:
80 and 60
Step-by-step explanation:
Expressing the Word Problem mathematically.
Let the first number be X.
Let the second number be Y.
From the question,
[tex]x + y = 140 - - - - - (1) \\ x - y = 20 - - - - - (2) \\ From \: equation \: (2) \\ x = 20 + y - - - - - - (3) \\ Substitute \: equation \: 3 \: into \: 1 \\ 20 + y + y = 140 \\ 20 + 2y = 140 \\ 2y = 140 - 20 \\ 2y = 120 \\ Dividing \: bothsides \: by \: 2 \\ \frac{2y}{2} = \frac{120}{2} \\ y = 60 \\ Substitute \: y \: into \: quation \: 3 \\ x = 20 + 60 \\ x = 80 \\ Therefore, \: x = 80 \: and \: y = 60[/tex]
The two numbers are 80 and 60
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.
(x + 2y ) 2
The expansion of the expression (x + 2y)² is x² + 4xy + 4y².
How to illustrate the information?The given expression is (x + 2y)². The expansion of the expression will be:
(x + 2y)²
= (x + 2y)(x + 2y)
= x² + 2xy + 2xy + 4y².
= x² + 4xy + 4y²
The expansion is x² + 4xy + 4y².
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What's the answer to this question?
Answer:
C
Step-by-step explanation:
The solution to a system equations is the point(s) of intersection of the 2 graphs.
Assuming that each square grid represents 1 unit, the coordinates of the point intersection is (-2, 2). This is because drawing a vertical line straight down from the point of intersection, we notice that the x-coordinate of the solution is 2 square units on the left of the origin. Drawing a horizontal line from the point of intersection to the y-axis gives us the y-coordinate of y= 2. Thus, the solution is (-2, 2) and the answer is C.
This method of finding the solution is also known as graphical method, where the graphs of the 2 equations are drawn, and the solution is where the lines cuts through each other.
Alternative methods of solving equations include substitution and elimination methods.
*Origin is the point (0, 0) on the graph, and it is the point in which the two axes intersect.
Additional:
For an example of solving by substitution, do check out the following!
https://brainly.com/question/16296725The water was pumped out of a backyard pond. What is the domain of this graph?
quick answer (A)
ALL real numbers less than or equal to 8
You are playing the new Simpsons board game and it comes with a six sided dice with one of the following colors on each side, red, blue, green, purple, indigo and orange. If you roll orange you win a donut, if you roll green you get eaten by Maggie. What is the probability that you will roll anything but orange
The probability that person will be eaten by Maggie is 16.67%.
Given there are 6 sided coloured dice. Colours are red, blue,green,purple, indigo and orange.
We have to find the probability that the person will be eaten by Maggie.
Probability is the likeliness of happening an event among all the possible events. It lies between 0 and 1. The probability is the numberof items divided by the total number of items.
Number of green coloured sides=1
Total number of sides=6
Probability of getting green when the dice is rolled 1 time=1/6=0.1667
We have been told that if green comes then person will be eaten by Maggie so the probability that the person will be eaten by Maggie is 0.1667 which is 16.67%.
Hence the probability that the person will be eaten by Maggie is 16.67%.
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Question is incomplete as the complete question is :
What is the probability that the person will eaten by Maggie?
If rick has 35 oranges and he divide them into equally into 7 bags. what fraction represents the number of oranges rick puts in each bag?
A classroom fish tank contains x goldfish the tank contains four times as many cups as goldfish enter an equation that represents the total number of guppies y in the fishtank