The given expression can be written in its simplest form by using the rule of exponents.
There are three components to the given expression, there is a negative base term -27, there is a base term with negative exponent x^-9, and both base terms have a fractional exponent 1/3.
Solving the term with negative exponent, the rule dictates that a term with a negative exponent can be written as its reciprocal. As x^-n=1/x^n,
x^-9=1/x^9
Hence, the expression becomes (-27/x^9)^1/3
The fractional exponent is applied to both the base terms. As (x^n)^m=x^nm,
(-27/x^9)^¹/₃=(-27)^1/3/(x^9*1/3)
Solving the negative term, the rule dictates that when there is a negative term with an odd number power, the negative sign can be extracted from the expression.
Hence,
(-27)^1/3=-(27^1/3)
Further simplifying the term, we know that 3^3=27,
-(27^1/3)=-(3^3*1/3)
Multiplying the powers for the entire expression,
-(3^3*1/3)/(x^9*1/3)=-3^1/x^3=-3/x^3
The simplest form of the expression (-27x^-9)^¹/₃ is -3/x^3
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determine the probabilities of being dealt each of the following hands from a poker deck of 52 cards. a.) three cards all of the same type. b.) four cards all of a different type (no pairs, three of a kind or four of a kind). c.) six cards of which exactly four are of the same suit.
A) 54,912 B) 2,598,960 C) 15
A) The number of ways to produce three of a kind (Num3) is equal to the product of the number of ways to make each independent choice. Therefore,
Num3 = 13C1 * 12C2 * 4C3 * 4C1 * 4C1
Num3 = 13 * 66 * 4 * 4 * 4 = 54,912
B) First, we count the number of five-card hands that can be dealt from a standard deck of 52 cards. This is a combination problem. The number of combinations is n! / r!(n - r)!. We have 52 cards in the deck so n = 52. And we want to arrange them in unordered groups of 5, so r = 5. Thus, the number of combinations is:
52C5 = 52! / 5!(52 - 5)! = 52! / 5!47! = 2,598,960
Hence, there are 2,598,960 distinct poker hands.
C) 6 C 4 = 6! / 4! (6-4)!
= 6*5*4! / 4!*2!
= 30 / 2
= 15
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Please help very quickly
The name of each midpoint and the segment it bisects include the following:
Point R bisects line segment PQ.Point X bisects line segment WY.Point Y bisects line segment WZ.Point D bisects line segment CA.What is a line segment?A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
In this scenario, the name of each midpoint and the segment it bisects include the following:
Point R bisects line segment PQ.Point X bisects line segment WY.Point Y bisects line segment WZ.Point D bisects line segment CA.Read more on midpoint and line segments here: https://brainly.com/question/28367319
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Complete Question:
Name each midpoint and the segment it bisects.
solve for x.
60°
8x-4
Answer: x=8
Step-by-step explanation: i did this exact question on OW
What is 4÷139 as a decimal answer ?
Please help me.
Answer:
0.025
Step-by-step explanation:
Divide 4 by 139 and get the number as a decimal
answer the question with a reason, please
Answer:
Diagram A
Step-by-step explanation:
a line of best fit can only be drawn if thier is strong negative or positive correlation
Drew is an artist. He paints portraits. The table below shows the number of portraits painted in hours. What is the constant of proportionality?
The constant of proportionality for the paints portraits is estimated as 5.
What is defined as the constant of proportionality?When two variables are proportional to one another, their relationship can be expressed as y = kx or y = k/x, in which k defines how the two factors are connected to one another. This k is recognized as the proportionality constant.The proportionality constant is the fixed value of the ratio of two proportional quantities. When the ratio or product of two varying quantities yields a constant, they are said to be in a proportional relationship.For, the given question;
The relation between the portraits and the time for their drawing made by Drew is-
In 5 hours ----> 1 portrait
Thus, 5/1 = 5
In 10 hours ------> 2 portrait
Thus, 10/2 = 5
In 15 hours -----> 3 portrait
Thus, 15/3 = 5 .....and so on.
Therefore, the constant of proportionality is found as 5.
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What did i do wrong here
Answer: Everything lol
Step-by-step explanation:
help math thx!!! dont haft to explain
Answer:
Step-by-step explanation:
try number 1
From the value found for the x, the angle ABD is 37° and the angle DBC is 58°.
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.
The question gives that the angle ABC is 95°. The angle ABC is composed of the angles ABD and DBC. Thus, you should sum the angles ABD and DBC, for finding x.
2x+23+9x-5=95
11x+18=95
11x=95-18
11x=77
x=7
Like x=7, you can find the angles ABD and DBC
Angle ABD = 2*7+23=14+23=37°Angle DBC = 9*7-5=63-5=58°Learn more about the algebraic expression here:
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A square picture with an area of 100 cm² is mounted on a square piece of matting. The matting has 2.5 times the area of the picture. If the picture is centred on the matting, what width of matting is visible around the outside of the picture? Give your answer to the nearest tenth of a centimetre.
150cm² is the area of matting visible.
What exactly are mathematical operations?An operation, also known as an "operand" or "argument," is a mathematical function that converts zero or more input values into a precisely defined output value.The arity of the operation is influenced by the number of operands.Unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication, are the operations that are most frequently studied.A constant is an operation of arity zero, also known as a nullary operation.The mixed product serves as an example of a ternary operation, which is an operation of arity 3.So, the area of matting is 100 × 2.5:
100 × 2.5 = 250cm²Now, the area of the matting is visible:
250 - 100 = 150cm²Rounding to nearest tens: 150cm²
Therefore, the area of matting visible is 150cm².
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please help me solve 4 +6.5x< 36.5
The solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.
What is the solution to the given inequality?Given the inequality in the question;
4 + 6.5x < 36.5
First, move all terms not containing x to the right side of the inequality.
4 + 6.5x < 36.5
6.5x < 36.5 - 4
Subtract 4 from 36.5
6.5x < 36.5 - 4
6.5x < 32.5
Divide both sides by the coefficient of x
6.5x < 32.5
6.5x/6.5 < 32.5/6.5
x < 32.5/6.5
x < 5
The solution in inequality form is x < 5
The solution in interval notation is ( -∞,5 ).
Therefore, the solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.
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Answer:
X < 5
Step-by-step explanation:
The solution is so subtract the 4 with the 4 and 36.5 you cross out the 4 and subtract 4 form 36.5 which leaves you with 32.5. Then to get the variable by itself you divide 6.5 on both sides, then cross out the 6.5 and divide 6.5 on 32.5 which gives you 5. (I solved it by myself)
-9x-9+5^3x4^4 I need step by step pleas
Answer:
32081.
Step-by-step explanation:
-9x-9+5^3x4^4
Using PEMDAS, the exponents are calculated first:
= -9 x -9 + 125 x 256
Next the multiplications:
= 81 + 32000
= 32081.
What is the radius of D
A. 6 cm
B. 12 cm
C. 3 cm
D. 24 cm
Help me ASAP!
what is 37x1000 plases help
Answer:
Step-by-step explanation: 37 times 1000 equals 37000 if you times anything by 1000 just add 2 zeros to the end
How would this word problem be solved?
A phone call costs $0.58 per minute for the first three minutes and $0.15 per minute for each additional minute. If the total charge for the call was $4.29, how many minutes long was the call?
Answer:
31 minutes in total
Step-by-step explanation:
Going step by step, where m = minutes after the first 3:
0.58 + 0.15m = 4.78
We want to solve for m, so we need to isolate it. The first step is to get rid of 0.58 to simplify our equation.
0.15m = 4.78 - 0.58
Now we have:
0.15m = 4.20
To isolate further, we need to remove 0.15.
m = 4.20 / 0.15
m = 28
Now, we add the first 3 minutes to m to get our total time.
28 + 3 = 31
A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (\text{kpx}kpxstart text, k, p, x, end text) of a kitchen scene and renders another 90\,\text{kpx}90kpx90, start text, k, p, x, end text each minute. The computer has rendered 960\,\text{kpx}960kpx960, start text, k, p, x, end text of a garden scene and renders 60\,\text{kpx}60kpx60, start text, k, p, x, end text more pixels each minute. After how many more minutes will the scenes have the same amounts rendered?
The minutes when the scenes have the same amounts rendered is 14 minutes.
How to illustrate the expression?The expression for the kitchen is illustrated as 540 + 90t.
The expression for the garden is illustrated add 960 + 60t.
Therefore, for the same amount, this will be:
540 + 90t = 960 + 60t.
Collect like terms
90t - 60t = 960 - 540
30t = 420
Divide
t = 420 / 30
t = 14 minutes
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Solve each equation. Check your answers. ln x=-2
After solving the equation ln x = -2, x is the value of equal to [tex]e^{-2}[/tex]
We have been asked to find x in ln x = -2
⇒ ln x = -2
⇒ x = [tex]e^{-2}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Mrs. White ordered 6 large boxes and 9 small boxes of crayons for the school art classes. Each large box has 189 crayons, and each small box has 90 crayons. Which is the best estimate of the number of crayons Mrs. White ordered
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 18 times t squared plus 54 times t end quantity over the quantity t squared plus 7 times t plus 10 end quantity comma where the time, t is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations.
The domain of the function C(t) is R - { -5. -2}.
What is a domain?The domain of a function is the set of all values for which the range of the function is defined.
To achieve an immediate response to a particular drug's effects the concentration, C, in mg/L, of a particular medication after being injected into a patient is given by the function
C(t) = [tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex] where t represents time in hours.
We know that a function is undefined when its denominator becomes zero.
∴ We have to factor the quadratic equation t² + 7t + 10 which is,
t² + 5t + 2t + 10 = 0.
t(t+5)+2(t+5) = 0.
(t+5)(t+2) = 0.
So, t = -5 or t = -2 are the two values of this equation which makes the function c(t) undefined.
∴ The domain of the function [tex]\frac{-18t^2 + 54t}{(t+5)(t+2)}[/tex] is all real numbers except -2 and - 5 which can be written as
Domain of C(t) is R - { -5, -2}, where R represents all real numbers.
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what number can equal 2x² -50=
The number that can be equal to 2x² -50 = 2(x + 5)(x - 5).
What is defined as the quadratic equation?A quadratic equation has a single factor of degree two. It has the general form ax² + bx + c = 0,, at which x is the variable, a, b, and c are constants, and a = 0.This same standard form of a quadratic equation is given to us in the question as - ax² + bx + c = 0,When we compare the statement in the question to the definition discussed above, we can conclude that the given statement is correct. The standard form of the a quadratic equation is ax² + bx + c = 0,, where a, b, and c are constant real numbers. The constant 'a' cannot be zero as it will indeed reduce the degree of the equation to one.For the given equation;
= 2x² -50
Take 2 common;
= 2(x² - 25)
This could be written as;
= 2(x² - 5²)
Now use per the property of (a² - b²) = (a + b)(a - b).
= 2(x + 5)(x - 5)
Thus, the given expression 2x² -50 can be represented as 2(x + 5)(x - 5).
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Can u help me mates Like im dum
Answer:
U: (-7, 0)
S: (-7, -2)
T: (3, -2)
Step-by-step explanation:
Moving a point 6 to the left is the same as subtracting 6 from its x value. Moving a point up 1 is the same as adding 1 to its y value.
Point=(x-6, y+1) where x is the point's original x value and y is the point's original y value.
U: (-1-6, -1+1)=(-7, 0)
S: (-1-6, -3+1)=(-7, -2)
T: (9-6, -3+1)=(3, -2)
Based on the diagram, which of the following statements must be true?
A. No lines are parallel
B. a || b and l || m
C. l || m
D. a || b
Answer: The answer is B. a||b and l||m
Step-by-step explanation: I hope this helps.
$10,000, time to double is 12 years, what is the annual rate & amount after 10 years?
well, double of 10000 is 20000, so hmmm happens in 12 years, ok
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20000\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]20000=10000\left(1+\frac{~~ \frac{r }{100 } ~~}{1}\right)^{1\cdot 12} \implies \cfrac{20000}{10000}=\left( 1+\cfrac{r}{100} \right)^{12} \\\\\\ 2=\left( \cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{2}=\cfrac{100+r}{100}\implies 100\sqrt[12]{2}=100+r \\\\\\ 100\sqrt[12]{2}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{5.95}\approx r \end{array}}[/tex]
now, what will it be after 10 years assuming we use 5.95%? mind you that's a rounded figure, but close enough.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 5.95\%\to \frac{5.95}{100}\dotfill &0.0595\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=10000\left(1+\frac{0.0595}{1}\right)^{1\cdot 10} \implies {\LARGE \begin{array}{llll} A \approx 17824.18 \end{array}}[/tex]
When thinking about the small group as a system, what is the key component that connects all of the system's relevant parts?
a. equifinality
b. summativity
c. multifinality
d. communication
e. minifinality
When thinking about the small group as a system, the key component that connects all of the system's relevant parts is D. Communication.
How to illustrate the information?It should be noted that the system framework is important as it reminds us that the piece of puzzle interacts with each other.
Therefore, when thinking about the small group as a system, the key component that connects all of the system's relevant parts is communication.
The sender, also known as the communicator or source, is where communication starts. The sender wishes to share some kind of information with the recipient(s), such as a request, query, or idea.
Understanding comes through good communication. Four essential elements make up the communication process. These elements consist of encoding, transmission medium, decoding, and feedback.
It should be noted that communication links the parts together.
Therefore when thinking about the small group as a system, the key component that connects all of the system's relevant parts is Communication.
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90x - 128 = 24x + 50
Greetings from Brasil...
90X - 128 = 24X + 50
90X - 24X = 50 + 128
X = 89/33Solve the equation for a.
−7(a+13)=−6(−3a+10)
a=
Answer:d=-3743
Step-by-step explanation:
help me please i need to know how to do this
Answer:
12'
Step-by-step explanation:
Pythagoras theorem = a² = b²+c²
*a² is always the hypothenuse (the longest side if the triangle)
you could use b² as the base and c² as the height
to find the height i.e., c² you transpose and substitute what we know so that'll be
13'² = 5'² + c²
you expand which will then give you
169 = 25 + c²
you then take over the 25+ which when addition goes over the equal sign becomes subtraction so that'll now give you
169 - 25 = c²
144 = c²
we want to find for c not c² so to do that we find the square root of 144 which is equal to 12.
so the height is equal to 12'
hope this helps
Tonya is paid a salary of $650 a month at her sales job. She also earns a commission on her sales in this way: 3% on all sales up to $32,000 in a month
and 8% on all higher sales. What were Tonya's total earnings for a month where her total sales were $80,000?
Tonya's total earnings for a month where her total sales were $80,000 is $5,450
What made up Tonya's total earnings?
Tonya's total earnings in any month comprises the basic salary of $650 , 3% of sales as sales commission on sales revenue of up to $32,000 and 8% as commission on sales in excess of $32,000
total earnings=basic salary+(3%*sales of up to $32,000)+(8%*sales of above $80,000)
basic salary=$650
3%*sales of up to $32,000=3%*$32,000
3%*sales of up to $32,000=$960
8%*sales of above $80,000=8%*($80,000-$32,000)
8%*sales of above $80,000=8%*$48,000
8%*sales of above $80,000=$3,840
Tonya's total earnings for a month=$650+$960+$3,840
Tonya's total earnings for a month=$5,450
Note that the total earnings based on the basic salary of $650 and sales revenue of $80,000 is $5,450
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8 1/2 - 4 2/3?????????
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}} ~\hfill \stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}~~ - ~~\cfrac{14}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~ - ~~(2)14}{6}}\implies \cfrac{51~~ - ~~28}{6}\implies \cfrac{23}{6}\implies {\LARGE \begin{array}{llll} 3\frac{5}{6} \end{array}}[/tex]
I need help! Thank you
Find f(4) when f(x) = x 2-3x + 3
Step-by-step explanation:
f(x) = x² - 3x + 3
f(4) = 4² - 3.4 + 3
f(4) = 16 - 12 + 3
f(4) = 7