What would you use for the
least common denominator?
Simplify each first.
Help please
Answers
The least common denominator is [tex]$&\frac{2}{3 b q}[/tex].
The smallest number that is precisely divisible by each denominator of a group of fractions is known as the lowest common denominator.
What is meant by least common denominator?The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.
When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.
The smallest number that is precisely divisible by each denominator of a group of fractions is known as the lowest common denominator. It is occasionally referred to as the lowest common denominator.
a) [tex]$\frac{2 q}{3 b q^2}$$[/tex]
Apply exponent rule:
[tex]$\frac{x^a}{x^b}=\frac{1}{x^{b-a}}$[/tex]
substitute the values in the above equation, we get
[tex]$&\frac{q^1}{q^2}=\frac{1}{q^{2-1}} \\[/tex]
simplifying the above equation, we get
[tex]$&=\frac{2}{3 b q^{2-1}}[/tex]
Subtract the numbers,
[tex]$=\frac{2}{3 b q^1}$$[/tex]
Apply exponent rule:
[tex]$&q^1=q \\[/tex]
[tex]$&=\frac{2}{3 b q}[/tex]
b) [tex]$\frac{3 b^2}{7 b^4 q}$$[/tex]
Apply exponent rule, we get
[tex]$\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}$[/tex]
substitute the values in the above equation, we get
[tex]$&\frac{b^2}{b^4}=\frac{1}{b^{4-2}} \\[/tex]
[tex]$&=\frac{3}{7 b^{4-2} q}[/tex]
Subtract the numbers:
[tex]$=\frac{3}{7 b^2 q}$$[/tex]
[tex]$\frac{4 q^2}{8 b^2 q^5}$$[/tex]
Factor the number:
[tex]$=\frac{4 q^2}{4 \cdot 2 b^2 q^5}$$[/tex]
Cancel the common factor,
[tex]$=\frac{q^2}{2 b^2 q^5}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{q^2}{q^5}: \frac{1}{q^3}$[/tex]
[tex]$=\frac{1}{2 b^2 q^3}$$[/tex]
Therefore, the correct answer is option a) [tex]$&\frac{2}{3 b q}[/tex].
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Related Questions
Based on historical data, three hospital trauma centers in ontario have 50, 30, and 20 percent of cases. the probability of a case resulting in a malpractice lawsuit in each of the three hospitals is .001,.005, and .008 respectively. if the malpractice suit is filled, what is the probability that it originated in hospital 1?
Answers
The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A) =
To solve this problem we will use Baye's theorem which states
P(B1 |A) = P(A/B1)P(B1) / P(A|B1)P(B1) + P(A|B2)P(B2) + P(A|B3)P(B3) (1)
where P(A|B) is the probability of event A occurring given that event B has already taken place.
Probability of hospital 1 having the case = P(B1) = 50
Probability of hospital 2 having the case = P(B2) = 30
Probability of hospital 3 having the case = P(B3) = 20
Probability of case resulting in malpractice in hospital 1= P(A/B1) =0.001
Probability of case resulting in malpractice in hospital 2= P(A/B2) =0.005
Probability of case resulting in malpractice in hospital 3= P(A/B3) =0.008
The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A)
Using equation (1)
P(B1|A) = (0.001)(50) / (0.001)(50) + (0.005)(30) + (0.008)(20)
= 0.05 / ( 0.05 + 0.15 + 0.16 )
= 0.05 / 0.36
= 0.138
Problem based on Bayes's theorem
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please help trying to do a test
(x + 1) a factor of 2x ^ 4 - 9x ^ 3 - 20x ^ 2 + 147x - 180 Find out by using the Factor theorem.
Answers
Answer:
Step-by-step explanation:
4
Ivan borrowed money from a credit union for 5 years and was charged at an annual rate 9% .The total interest that he paid was $2700.How much money did he borrow
Answers
The formula to calculate the total interest paid is:
[tex]I=P((1+r)^n-1)[/tex]Where:
• I, is the total interest paid
,• P, is the amount borrowed
,• r, is the interest rate
,• n, is the times that the interest was compounded
Solving this formula for P,
[tex]\begin{gathered} I=P((1+r)^n-1) \\ \\ \Rightarrow P=\frac{I}{(1+r)^n-1} \end{gathered}[/tex]Using the data given,
[tex]\begin{gathered} P=\frac{2700}{(1+\frac{9}{100})^5-1} \\ \\ \Rightarrow P=5012.77 \end{gathered}[/tex]Therefore, we can conclude that he borrowed $5,012.77
Can some one solve this
Answers
A(2,12) and B(-1,17)
Slope of the line that is parallel to AB is given by formulae y2-y1/x2-x1
=> m = 17-12/-1-2 = 5/-3=-5/3
Also parallel lines run in same direction and hence have same slope!
Answer them please. I need help ASAP!!!!!
Answers
Answer:
A. -26, -12.7, -9/2, 2/100, 7, 11 1/4, 41/2, 35
B. |-12.7| = 12.7, |-11 1/4| = |-45/4| = 45\4
B Optional 45/4 = 11.25 as decimal form
Step-by-step explanation:
For the mixed fractions you have to divide it. For the whole fraction
11 1/4
1. 11 x 4=44
Then add the 1. 44+1=45
The denominator doesn't change
45/4 then divide if it ask for the decimal form which is 11.25.
I'm not entirely sure of the answers. Good luck :)
–26.1 as a mixed number.
Answers
Answer:
-26 [tex]\frac{1}{10}[/tex]
Step-by-step explanation:
.1 as a fraction is 1/10
Answer:
________________________________________________
Step-by-step explanation:
______________________________________________________________________________________________
What is greater 1.0079 or 100.8
Answers
Answer:
100.8 is the correct answer
Answer:
100.8
Step-by-step explanation:
100.8 > 1.0079
(30 points) Circle A is____ to circle B.
A. Tangent
B. Concentric
C. Coplanar
D. Congruent
Answers
Answer:Co planar
Step-by-step explanation:
There are different types of relation between circles,
Congruent circles: Two circles are congruent to each other if they have same size( radius, diameter or circumference).
Concentric circles: If two circles have the same center,
Co planar : When the two circles lie on the same plane.
Tangent circle : Circles in a common plane that intersect in a single point.
⇒ They are only co-planer circles.
In the figure above, ABCD is a square. What is the value of x?
Answers
Answer:
6x-1 is x=-1
5x+7 is x=7
Step-by-step explanation:
Tell which definition, postulate, or theorem gives the justification.
- Geometry
Answers
The condition m∠GLA + m∠ALD = m∠GLD is proved by the Angle Addition Postulate.
What is termed as the Angle Addition Postulate?According to the Angle Addition Postulate, the measure of an angle made of two angles adjacent to each other is the sum of the two angles' measures. The Angle Addition Postulate can be employed to compute the angle formed by two or more angles, as well as to compute the assessment of a missing angle. The Angle Addition Postulate states that if two angles are placed side by side, the measure of a resulting angle would be equal to the sum of the original two angle measures. This postulate requires that the vertices, that are the angle's corner points, be placed together.For the given question;
A is the interior angle of ∠GLD.
m∠GLA + m∠ALD = m∠GLD is proved by the Angle Addition Postulate.
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work it out pleasee :)
Answers
Answer:
18
Step-by-step explanation:
18 is the HCF of 36 and 90 , then
[tex]\frac{36}{90}[/tex] ( divide numerator/ denominator by 18 )
= [tex]\frac{2}{5}[/tex] ← in simplest form
Korey is planning to open a comic book store. His store will cost $12,500 to open and will come with an $8,000 total annual operational cost. If his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for Korey to see an overall profit in his business (where total profits exceed total expenses)? A = P (1 + r) superscript t
Answers
It will take 3 years for Korey to see an overall profit in his business.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
We have,
Cost of the store to open = $12500
Cost of the operational cost = $8000
Profit store makes each year = $12000
Profit increase each year = 6%
Profit = Income - Total cost
First-year:
Profit = 12000 - (12500 + 8000) = -8500
There is no profit in the first year.
2nd year:
Profit = 2 x (12000 + 6% of 12000) - (12500 + 2 x 8000)
= 25440 - 28500
= -3060
There is no profit in the second year.
Third-year:
Profit = 3 x (12000 + 6% of 12000) - (12500 + 3 x 8000)
= 38160 - 36500
= 1660
We see that there is a profit of 1600 in the third year.
Thus,
It will take 3 years for Korey to see an overall profit in his business.
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f(x)=-3x+12find f(-6)
Answers
Answer:
f(-6)=18d
Step-by-step explanation:
Answer:
-3x-72f
Step-by-step explanation:
Blank x + 16 + x = – 3 x – 4
Answers
The value of x from given linear equation is -4.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
Given that x + 16 + x = – 3 x – 4
To find the value of x solving the given linear equation
x + 16 + x = – 3 x – 4
⇒ 2x + 16 = -3x - 4
⇒ 2x + 3x = -4 -16
⇒ 5x = -20
⇒ x = -20/5
⇒ x = -4
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find 9th term for 2,5,8,11
Answers
Answer: 26
Step-by-step explanation:
2+3=5
5+3=8
8+3=11
11+3=14
14+3=17
17+3=20
20+3=23
23+3=26
11. What is the least common
70 ?
multiple of 30, 40, and
Answers
Answer:
i think 840 i searched it up
Step-by-step explanation:
84 km a centímetros
Alguien sabe como se resuelve
Answers
8400000cm
84 kilometer is 8400000 centimeter.
How to convert kilometer to centimeter?In the International System of Units, a Centimeter or centimeter is a unit of length equal to one hundredth of a meter, with centi being the SI prefix for a factor of 1/100.A centimeter is a metric length measurement unit. One centimeter equals ten millimeters or one meter. A cheerio is typically one centimeter in diameter.One kilometer equals 1000 meters. When we need to travel from one location to another, we use kilometers to calculate the distance. Kilometers can be used to calculate the distance between cities or the distance traveled by a plane.
Here given 84 km ,
We know that 1 km = 1000 meter
so 84 km = 84 x 1000 meter
= 84000 meter
and 1 meter = 100 cm
so here 84000 meter = 84000 x 100 cm
= 8,400,000 Centimeters
∴ 84 km = 8400000cm
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HELP PLEASE
Which one of the following absolute value equations and inequalities have a solution set that is NOT the empty set?
O |2x-51|-3 = -2
O |5x-1| +8 < 6
O 3|x-4|+5 < 4
O 2|x + 7| +3 = 2
Answers
For the given absolute value equations and inequalities the following have solution set which is not empty set.
a. |2x-51|-3 = -2 has solution set x = 25 or 26.
b |5x-1| +8 < 6 has empty set.
c. 3|x-4|+5 < 4 has empty set.
d. 2|x + 7| +3 = 2 has solution set x = -15/2 or -13/2.
As given in the question,
Solution set of the absolute value equations and the inequalities are as follow:
a. |2x-51|-3 = -2
⇒ |2x-51| = -2+3
⇒ |2x-51| = 1
⇒ 2x -51 = 1 or 2x -51 = -1
⇒ 2x = 52 or 2x = 50
⇒ x= 26 or 25
Solution set is x = 25 or 26.
b. |5x-1| +8 < 6
⇒|5x-1| < -2
⇒5x -1 < -2 or 5x -1 > 2
⇒ x< -1/5 or x > 3/5
Empty set.
c. 3|x-4|+5 < 4
⇒3|x-4| < -1
⇒x -4 < -1/3 or x -4 > 1/3
⇒ x< -11/3 or x > 13/3
Empty set.
d. 2|x + 7| +3 = 2
⇒2|x + 7| = -1
⇒|x + 7| = -1/2
⇒ (x+7) = -1/2 or (x+7) = 1/2
⇒x= -15/2 or -13/2
Solution set is x= -15/2 or -13/2.
Therefore, For the given absolute value equations and inequalities the following have solution set which is not empty set.
a. |2x-51|-3 = -2 has solution set x = 25 or 26.
b |5x-1| +8 < 6 has empty set.
c. 3|x-4|+5 < 4 has empty set.
d. 2|x + 7| +3 = 2 has solution set x = -15/2 or -13/2.
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WILL GIVE BRAINLIST TO BEST ANSWER PLUS EXTRA POINTS
A company rents a Popcorn machine. Customers are charged a fixed amount plus a rate based on the number of hours the machine is rented. The company uses the function shown below to determine the total charges, in dollars, for the customer.
ƒ (x) = 40 + .15x
What does f(x) represent?
What does the 40 represent?
What does the 0.15 represent?
What does the ‘x’ represent?
Answers
1. F(x) represents the total cost function for renting a Popcorn machine.
2. The 40 in the equation represents the Fixed Cost per day of the rental.
3. The 0.15 represents the variable cost per hour.
4. The x represents the number of hours the machine is rented.
What is a function?A function is a mathematical expression, rule, or law defining the mathematical relationship between the independent variable and the dependent variable.
Mathematical functions are used to define the mathematical relationships that show how the dependent variable can be determined, given an independent variable. They are written with the equal sign (=).
Thus, we can conclude that the rental cost function ƒ (x) = 40 + .15x shows the total amount that a customer would be charged each day for renting a Popcorn machine.
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Answer for (4)(4+2^2-4) ???
Answers
1. The polynomial function F(x) = x² + 6x + 8 has a known factor of (x + 4). Rewrite F(x) as a product of
linear factors.
Answers
Answer:
f=12
Step-by-step explanation:
F(4) = 4^(2) + 6(4) + 8
Solve the compound inequality.
x + 6 <0 or 6x > - 18
Answers
Answer: 6x - 18 = 6 • (x - 3)
Step-by-step explanation: Pulling out like terms
Which expression can be used to check the answer to 56÷(-14)= -4?
Answers
the given expression is,
56 /(-14)
[tex]\begin{gathered} =\frac{56}{-14} \\ =-4 \end{gathered}[/tex]so the answer is -4.
you can check the answer
by multiplying the (-14) to -4,
[tex]\begin{gathered} \frac{56}{-14}=-4 \\ 56=-14\times-4 \\ 56=56 \end{gathered}[/tex]LHS = RHS so we use the expression -14 x -4 to check the answer.
7. What is the equation of the line in slope intercept
form that passes through (6,8) and (-2,4)
Answers
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{6}}} \implies \cfrac{ -4 }{ -8 } \implies \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{6}) \\\\\\ y-8=\cfrac{ 1 }{ 2 }x-3\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 2 }x+5 \end{array}}[/tex]
Can some one help please I don’t know their
Answers
Answer: 2 complex solutions; the discriminant is less than zero
Step-by-step explanation:
When the D<0 there are no real solutions because the quadratic does not intercept the x-axis on the graph.
4 x 10 to the power of 5
Answers
Answer:
400000
Step-by-step explanation:
Have a Good Day!
Write an equation of the line that passes through(0, -2) and(4,10)
Answers
Answer: y = 3x -2
Step-by-step explanation:
1) slope formula
y2 - y1 / x2 - x1
2) find the y's and x's
y2 = 10
y1 = -2
x2 = 4
x1 = 0
3) plug them into the equation
10 - (-2) / 4 -0
10+2/4
12/4
4) simplify
slope = 3
5) write out equation
y = 3x + b
6) plug in coordinates
(0,2)
-2 = 3(0) + b
7) find the y intercept
-2 = b
8) plug in y intercept
y = 3x -2
Thank you to who ever answers this question. Have a good rest of your day!
Answers
Answer:
Step-by-step explanation:
Answer: HI! I believe that the answer would be this symbol (I put it below)
>
Step-by-step explanation:
So sorry if this is wrong
Which of the following functions translates the graph of the parent function f (2) = 2? left 2 units?
Answers
f (x) = x^2, translated left ,2 units
Is a parabola
Vertex is at (0,0)
left translation is (x +2)
(-2 + 2)= 0
Then answer is
Option A ) h(x)= (x+2)^2
Somebody help!!!!! I don’t know the answer
Answers
Given expression
[tex][(\cfrac{20}{5}*\cfrac{1}{5})^{-1}]^2[/tex]Step 1Simplify the parenthesis:
[tex][(\cfrac{20}{5}*\cfrac{1}{5})^{-1}]^2=[(\cfrac{4}{5})^{-1}]^2[/tex]Step 2Apply the negative exponent rule:
[tex]a^{-1}=1/a[/tex][tex][(\cfrac{4}{5})^{-1}]^2 = [(\cfrac{5}{4})^{1}]^2[/tex]Step 3Apply the product of a power rule:
[tex](a^b)^c=a^{bc}[/tex][tex](\cfrac{5}{4}})^{1*2}=(\cfrac{5}{4}})^2[/tex]Step 4Apply product of the product law:
[tex]a^2=a*a[/tex][tex](\cfrac{5}{4}})^2=(\cfrac{5}{4}})^(\cfrac{5}{4}})=\cfrac{25}{16}[/tex]