The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
\(\sqrt[4]{a}^3\)
Consider an expression expressed as xⁿ
The expression can be expanded as
xⁿ = x * x * x .... in n places
Using the above as a guide, we have the following:
\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)
Apply the exponent rule of indices
\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)
Apply the power rule of indices
\(\sqrt[4]{a}^3 = a^\frac34\)
Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)
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Which statements about the reflection are true? Check all that apply.
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will remain in the same location as C because it is on the line of reflection.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
The statements that are true are:
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Options A, B, D, E, and F.
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
Clayton could use the relationship (x, y) → (y, x) to find the points of the image.
This is the y = x reflection rule.
This is true.
Clayton could negate both the x and y values in the points to find the points of the image.
Reflection of (x, y) along the x-axis and y-axis consecutively will give us
(-x, -y).
This is true.
C’ will remain in the same location as C because it is on the line of reflection.
This is not true.
C’ will move because all points move in a reflection.
This is true.
The image and the pre-image will be congruent triangles.
This is true.
The image and pre-image will not have the same orientation because reflections flip figures.
This is true.
Thus,
All statements are true except the statement:
C’ will remain in the same location as C because it is on the line of reflection.
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which equation has x=8 for a solution
2x + 3 = 13
4x + 6 = 38
3x - 5 = 29
5x - 8 = 48
Answer:
4x + 6 = 38
Step-by-step explanation:
Substitute x in for x and see which equation is true
2x + 3 = 13
2*8+3 = 16+3 = 19 this is not 13 so it is false
4x + 6 = 38
4*8+6 = 32+6 = 38
This is true
3x - 5 = 29
3*8 -5 = 24-5 = 19
False
5x - 8 = 48
5*8-8 = 40-8 = 32
False
Derrick and Janis are planting
150 strawberry plants.
The first day, Derrick plants 20% of
the strawberry plants. Janis plants
60% of the strawberry plants.
Eliezer
How many strawberry plants do Derrick and Janis plant on the first day?
Choose one option from each drop-down menu to answer the question.
On the first day, Derrick plants Choose... strawberry plants.
Janis plants Choose... strawberry plants.
Together, they plant a total of Choose... strawberry plants.
X
Derrick and Janis together plant a total of 30 + 90 = 120 strawberry plants on the first day.
To find out how many strawberry plants Derrick and Janis planted on the first day, we need to calculate the sum of the plants they individually planted.
Derrick planted 20% of the 150 strawberry plants:
20% of 150 = (20/100) * 150 = 30 strawberry plants.
Janis planted 60% of the 150 strawberry plants:
60% of 150 = (60/100) * 150 = 90 strawberry plants.
Therefore, on the first day, Derrick and Janis planted a total of 30 + 90 = 120 strawberry plants.
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Please help me i need help.
Answer:
5x+7 > 17 matches with 3.
1+3x > -5 matches with 2.
2x+1 < 3 matches with 1.
5-3x > 11 matches with 4.
Step-by-step explanation:
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 10% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 10% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 13 customers buy a magazine?
Answer:
0.55% probability that exactly 5 out of the first 13 customers buy a magazine
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of other customers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
10% of his customers buy a magazine
This means that \(P = 0.1\)
What is the probability that exactly 5 out of the first 13 customers buy a magazine?
This is P(X = 5) when n = 13. So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 5) = C_{13,5}.(0.1)^{5}.(0.9)^{8} = 0.0055\)
0.55% probability that exactly 5 out of the first 13 customers buy a magazine
Answer:
\( P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554\)
So then he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554
Step-by-step explanation:
Let X the random variable of interest "number of customers that buy a magazine", on this case we can model the variable of interest with this distribution:
\(X \sim Binom(n=13, p=0.1)\)
The probability mass function for the Binomial distribution is given as:
\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)
Where (nCx) means combinatory and it's given by this formula:
\(nCx=\frac{n!}{(n-x)! x!}\)
We want to find this probability:
\( P(X=5)\)
And using the probability mass function we got:
\( P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554\)
So then he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554
Composing ________________ is another way to compose two functions
Answer:
is there any options or answers I could see?
NEED SOME HELP HERE!!
Neil Down is doing some remodeling and needs to cut a triangular piece of wood such that the diagonal is 10 feet long, and the sides of the triangle are in a ratio 3:4. How long should each side be?
Answer:
6 and 8
Step-by-step explanation:
Pythagorean theorem: a² + b² = c²
Given this,
(3x)² + (4x)² = 10²
9x² + 16x² = 100
25x² = 100
Divide both sides by 25
x² = 4
x = 2
Substitute this into 3x and 4x.
3x = 3 * 2 = 6
4x = 4 * 2 = 8
Thus, the answer is 6 and 8
Analyze the proportion below and complete the instructions that follow.
1+3x 5
=
4 2
A. 7
5
52
Solve the proportion for x.
'B. 3
C. 5
D. 6
Please select the best answer from the choices provided
The value of x is 4/3 for equation 1+3x=5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 1+3x=5
One plus three times of x equal to five
We need to solve for x
1+3x=5
Subtract 1 from both sides
3x=5-1
3x=4
Three times of x equal to four
Divide both sides by 3
x=4/3
Hence, the value of x is 4/3 for equation 1+3x=5.
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answer and i give you brainlest
Answer:
Volume=l×b×h
=6×5×10 mm³
=300mm³
Please help meee
Mr larson only wears his kilts on days he doestn ride his motorcycle. He owns 12 kilts and 10 motorcycles. He randomly picks one each day and returns it when he gets home. If you bumped into mr larson on Monday and Tuesday what is the percent probability that he was riding his motorcycle on both days?
Yall im crying help meee
On solving the provided question, we can say that there is a probability 20.66% chance that Mr. Larson rode his motorbike on both Monday and Tuesday.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Assuming that his decisions for the two days are independent, we must multiply the chance that he rides his motorbike on Monday by the probability that he rides it on Tuesday in order to get the likelihood that he does so on both Monday and Tuesday. Considering that his decisions on the two days are separate, Hence, the likelihood is:
(10/22) x (10/22) = 100/484 = 0.2066 or 20.66%
Hence, there is a roughly 20.66% chance that Mr. Larson rode his motorbike on both Monday and Tuesday.
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A parallelogram is transformed according to the rule (x,y) - (x,y). Which is another way to state the transformation?
A. Ro.90
B. RO, 180
C. R0,270
D. RO,360°
Help me this is time sensitive so please help
⭐️⭐️⭐️⭐️⭐️
The probability of rolling a total of 9 is 1/9.
The probability of rolling a total of 10 is 1/12.
The probability of rolling a total of 11 is 1/18.
We have,
To calculate the probabilities of rolling specific totals with a pair of dice, we need to consider all possible combinations of numbers on each die.
Probability of rolling a total of 9:
There are four combinations that can result in a total of 9: (3, 6), (4, 5), (5, 4), and (6, 3).
Since each die has six sides, there are 6 * 6 = 36 equally likely outcomes when rolling two dice.
The probability of rolling a total of 9 is 4/36, which can be simplified to 1/9.
Probability of rolling a total of 10:
There are three combinations that can result in a total of 10: (4, 6), (5, 5), and (6, 4).
The probability of rolling a total of 10 is 3/36, which can be simplified to 1/12.
Probability of rolling a total of 11:
There are two combinations that can result in a total of 11: (5, 6) and (6, 5).
The probability of rolling a total of 11 is 2/36, which can be simplified to 1/18.
Thus,
The probability of rolling a total of 9 is 1/9.
The probability of rolling a total of 10 is 1/12.
The probability of rolling a total of 11 is 1/18.
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Graph the equation y = 3/2x -2
Graph these twο pοints (0, -2) & (4/3, 0) and yοu have yοur slοpe graphed fοr the equatiοn y = 3/2x -2.
What is an equatiοn?
An equatiοn is a mathematical statement containing two algebraic expressiοns flanked by equal signs (=) on either side.
It shows that the relationship between the left and right printed expressiοns is equal.
All fοrmulas have LHS = RHS (left side = right side).
Yοu can sοlve equatiοns tο determine the values οf unknοwn variables that represent unknοwn quantities.
If a statement does not have an equals sign, it is not an equatiοn. A mathematical statement called an equatiοn cοntains the symbοl "equal tο" between twο expressiοns οf equal value.
Tο find the x-intercept, substitute y = 0 and sοlve fοr x. Tο find the y-intercept, substitute x = 0 and sοlve fοr y.
y = 3/2(0) -2
y = -2
⇒ (0, -2)
And for x
0 = 3/2x -2
2 = 3/2x
x = 4/3
(4/3, 0)
Now graph these two points and you have your slope graphed
Hence, The graph of the equation is given below.
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A bag has eight balls labeled A, B, C, D, E, F, G, and H. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing a letter from A to D. If there is more than one element in the set, separate them with commas. Samplespace: Event of choosing a letter from A to D:
We will have the following:
All the outcomes for the event of choosing a letter from A to D are:
\(\frac{4}{8}=0.5\)So half the times a ball is picked there should be one from letter A to D.
***Explanation***
We have the following set:
\(\mleft\lbrace A,B,C,D,E,F,G,H\mright\rbrace\)So, the set has a magnitude of 8 [Since it has 8 components].
When we pick any given value from the set we will have that we will have to pick 1 value from the total set, that is:
\(\frac{1}{8}\)But, when we are asked of the event of taking specific values from to D we are asked to pick 4 specific values:
\(\mleft\lbrace A,B,C,D\mright\rbrace\)That set has a magnitude of 4. So, in order to determine the event of picking a value from the second set on the first set, we will have:
\(p=\frac{4}{8}\Rightarrow p=\frac{1}{2}\Rightarrow p=0.5\)This event is represented by "p" the probability of that happening. So, the probability of the event happening [Selecting one of the balls of the specific set] is 1/2; in other words, each time you pick there is a 50% chance you will get one of the values of the smaller set.
Solve: -(1/4)m + 5 = 16
Answer:
m=-44
Explanation: distribute the negative and add -1/4 to m and then take the 5 away from 16 and then multiply both sides
Answer:
M = - 44
Step-by-step explanation:
You will start by subtracting 5 on both sides of the equation.
- (1/4)m + 5 =16
-5 -5
Simplify
- 1/4 m =11
Multiple both sides by - 4
(-1/4m)(-4)= 11 (- 4)
The final result is m equals negitive 4.
M = -44
differenciate the Function 1/ X3
Step-by-step explanation:
To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:
Write the function: f(x) = 1/x^3.
Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).
Differentiate the function: In our case, n = -3, so the derivative is:
f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.
Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.
11 divided by 8 + 9 divided by 3
Answer:
Step-by-step explanation:
4.375
Tell the kind of symmetry this figure has: point, line, plane (select all
Answer:
Line
Step-by-step explanation:
Answer:
LIIIIINE
Step-by-step explanation:
What is the constant of proportionality for this table?
Time (hr) 2 4 5 9
Pay ($) 16 32 40 72
Question 4 options:
1/8
16
8
2
I WILL MARK BRAINLIEST
Answer: the answer is 1/8
Step-by-step explanation: you divide 2 to 16 the you would get 0.125 and if you divide 4 to 32 its also 0.125 and if you make 0.125 a form of a fraction it is 1/8.
Help with this ? It’s troubling
Answer:
y=50x
Step-by-step explanation:
give brainliest?
Answer:
A. y = 50x
Explanation:
coordinates: ( 50 , 1 ) , ( 100 , 2 )
slope: (y2-y1)/(x2-x1) = (100-50)/(2-1) = 50
equation using: y = mx +b....where m is slope and b is y-intercept
equation: y = 50x + 0
y = 50x
The value of a coin in 2010 was $40. The value of the coin has increased in value at a rate of 16.9% annually.
What was the value of the coin in 2019?
Enter your answer in the box rounded to the nearest dollar.
The value of the coin in 2019 would be approximately $132.
To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.
Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:
Value in 2019 = Initial value * (1 + Rate)^n
where Rate is the annual increase rate and n is the number of years between 2010 and 2019.
Plugging in the values:
Value in 2019 = $40 * (1 + 0.169)^9
Value in 2019 ≈ $40 * 2.996
Value in 2019 ≈ $119.84
Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.
However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.
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After working satisfactorily for 6 months, Collin will be eligible for a 7% raise. How much will Collin's
gross salary be, after her raise, for each 2-week pay period? His current gross salary is $1,083.34.
Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.
To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.
Collin's current gross salary is $1,083.34.
To find the raise amount, we multiply his current gross salary by 7% (or 0.07):
Raise amount = $1,083.34 \(\times\) 0.07
= $75.8338 (rounded to two decimal places)
Now, we add the raise amount to his current gross salary to find the new gross salary:
New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)
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Write the equation in standard form. y - 2 = -2(x - 9)
I believe that the answer is y=-2x +20. please correct me if I am wrong.
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis.
y
=
11
−
x
,
y
=
0
,
x
=
3
,
x
=
9
Using the shell method, the volume of the solid generated when R is revolved about the y-axis is V= 324π cubic units.
The shell method refers to a method of finding volumes of the solid by decomposing a solid of revolution into cylindrical shells. It is one of the methods to find the volume of the solid. This solid is generated when region R is rotated about an axis or the y-axis. In case it is y-axis then the following formula is used:
V= ∫_a^b▒〖2πx [f(x)-g(x)]dx〗
Where y = f(x), y = g(x), and the interval is considered as [a,b].
The given curves are: y = 11 − x, y = 0, x = 3, x = 9
V= ∫_3^9▒〖2πx [11-x-0]dx〗
V= 2π∫_3^9▒〖(11x-x^2)dx〗
V= 2π[11/2 x^2- 1/3 x^3]
V= 2π[11/2 9^2- 1/3 9^3- 11/2 3^2+ 1/3 3^3]
V= 2π[891/2- 729/3- 99/2+ 27/3]
V= 2π[729/2- 702/3]
V= 2π[396-234]
V= 2π[162]
V= 324π cubic units
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CHIJ (KATONG) PRIMARY MILESTONES WHOLE NUMBERS 1: FACTORS AND MULTIPLES (3) Alarm Clock A rings every 9 minutes. Alarm Clock B rings every 12 minutes. If both alarm clocks rang together at 2 p.m., at what time will the two alarm clocks ring together again?
Answer:
The two alarm clocks will ring together again at 2:54 p.m
Solve to find the area:
Answer:
16cm^2
Step-by-step explanation:
well if you multiply 4 x 8 to find the area it would be 32 but it is a triangle so divide 32 by 2 to get 16
Answer:
16 cm²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Triangle: A = 1/2bhStep-by-step explanation:
Step 1: Define
Base b = 8 cm
Height h = 4 cm
Step 2: Find A
Substitute [Area]: A = 1/2(8 cm)(4 cm)Multiply: A = (4 cm)(4 cm)Multiply: A = 16 cm²
Find the percent of change.
From 25 teachers to 30 teachers.
Answer:
To calculate the percent change of two numbers, such as 25 to 30, you use the Percent Change Formula, where a is the start value and b is the end value.
(b - a)/a × 100
When we insert a = 25 and b = 30 in the formula above, then we get the following that we can simplify and solve to get the percent change from 25 to 30.
(30 - 25)/25 × 100
5/25 × 100
Change = 20%
Step-by-step explanation:
solve the equation and give the verified answer 9 Y - 5 (2 Y - 3) is equals to 1 - 2 y
Answer:
y= -14
Step-by-step explanation:
First, distribute to get 9y-10y+15=1-2y
Then, combine like terms: -y+15=1-2y
Then, bring the 2y over and the 15 over: y= -14
Hope this helped!
Please solve this questions. Just write True or False. I think its simple for you.
Answer: Provided the questions, we need to select true or false about any mathematical statement given in the question 1-10. the answers are as follows:
\(\begin{gathered} (1)\Rightarrow\text{ True } \\ (2)\Rightarrow\text{ True} \\ (3)\text{ }\Rightarrow\text{ True} \\ (4)\text{ }\Rightarrow\text{ True} \\ (5)\Rightarrow\text{ True} \\ (6)\text{ }\Rightarrow\text{ True} \\ (7)\Rightarrow\text{ True} \\ (8)\Rightarrow\text{ True} \\ (9)\text{ }\Rightarrow\text{ True} \\ (10)\Rightarrow\text{ True} \end{gathered}\)Why should we learn the limit definition of the derivative when we could just learn shortcut rules for differentiation?
Answer:
Step-by-step explanation:
I think this is a very essential question to ask. While a lot of people want shortcuts to get things done(i used to too, when I was a student), shortcuts doesn't always cut it short. The reason is just as simple as that of any other subject that deals with theory.
Learning the limit definition gives ample knowledge about how the whole derivation works in general. Yes, quite alright, you can get the basic differentiation done when you don't learn that, but as someone who has gone far in calculus, I'd tell you for free, a time will come during computation where you'd get stuck because you never had that prior knowledge of definition.
Further along the line in calculus, you would be doing derivatives where you'd have to apply your knowledge of the definition of limit, and how would you be able get that done if you hadn't already learnt it?
Exactly!