Answers
The solution is Option D.
The value of the equation is A = 2a³b
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first expression be x = 18a⁶b²
Let the second expression be y = 9a³b
The equation A = x/y
Substituting the values in the equation , we get
A = 18a⁶b² / 9a³b be equation (1)
On simplifying the equation , we get
A = ( 18/2 ) ( a⁶ / a³ ) ( b²/b )
A = 2a³b
Therefore , the value of A is 2a³b
Hence , the equation is A = 2a³b
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Related Questions
You got a new Corvette Z06 for $146,331.90.
You paid $0 down to took the whole price out as a loan.
You are deciding between a 3-year loan at 2.16% (compound monthly) or a 6-year loan for 3.30% (compounded monthly).
How much more money in total will you pay for the 6-year over the 3-year?
Answers
The amount of money to be paid for 6 year loan at a given rate is $875764.76 more than 3 year loan.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The cost of the car is $146331.90.
And, the rate of interest for loan of 3 and 6 years are 2.16% and 3.30% respectively.
Since, it is the case of monthly compounding.
The time interval for both the cases are given as 3 × 12 = 36 and 6 × 12 = 72.
Similarly, rate can be 2.16/12 = 0.18% and 3.30/12 = 0.275.
Then, the amount to be paid for both cases are obtained as,
Plug corresponding values in the expression A = P(1 + r/100)ⁿ.
⇒ A = 146331.90(1 + 0.18/100)³⁶
⇒ A = 156119.08
And, A = 146331.90(1 + 0.275/100)⁷²
⇒ A = 1031883.84
Then, the difference can be calculated as 1031883.84 - 156119.08 = $875764.76.
Hence, the extra money to be paid for 6 year over 3 year is $875764.76.
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what is the answer for this question
Answers
The
number
of
pupils
that prefer
English
as their favorite subject from the table is 26
How to determine the total number
From the table provided, we have to fill the empty spaces before finding the sum of the numbers.
To calculate the
number
of girls that chose
English
= Total number of girls - sum of Mathematics and Sciences
= 38 - (20 + 12)
= 38 - 32 = 6
To calculate the exact number of boys that chose English, we have;
= Total for Mathematics- Girls that chose Mathematics
= 25 - 20 = 5
Also,
To find the
total
pupils for all the courses - total for girls in general
= 70 -38 = 32
Then,
= 32 - ( 5 + 7)
= 32 - 12 = 20
The total pupils that chose English
= 20 + 6
= 26 pupils
Thus, the
number
is 26
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1. Show that (a) exp(2±3лi) = -e²;
Answers
The given expression is proved above to its equivalent value.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is an exponential expression.
[tex]$e^{(2\pm3\pi i)} = -e^{2}[/tex]
We can write the given expression in two possible ways -
[tex]$e^{2} e^{3\pi i}[/tex] and [tex]$\frac{e^{2} }{e^{3\pi i} }[/tex]
Now, we know using the De - Moivre's theorem, we can write -
[tex]$e^{i\theta} =[/tex] cos(θ) + i sin(θ)
Now -
[tex]$e^{3\pi i} =[/tex] cos(3π) + i sin(3π) = - 1
So, we can write -
[tex]$e^{2} e^{3\pi i}[/tex] = - e²
and
[tex]$\frac{e^{2} }{e^{3\pi i} }=\frac{e^{2} }{-1}[/tex]
[tex]$\frac{e^{2} }{e^{3\pi i} }=-e^{2}[/tex]
Therefore, the given expression is proved above to its equivalent value.
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"It was a 20% chance of rain between noon and 1pm and there is a 60% chance that the dog walker may come at that time. What percentage that the dog walker will be walking in the rain with the dogs?"
please help me with this.
I know both events are independent but I'm not sure if this is the way to solve it:
20% = 1/5
60% = 3/5
1/5*3/5= 3/25 which is 12% that both events occur at the same time
is it correct?
if not... how can I practice this? is it compound probability?
Thank you very much!
Answers
Answer:
To find the probability that both events will occur at the same time, you need to use the formula for the probability of the intersection of two events. In this case, the probability that it will rain between noon and 1pm AND that the dog walker will come at that time is:
P(Rain AND Dog Walker) = P(Rain) * P(Dog Walker | Rain)
The probability that it will rain is 20%, or 1/5. The probability that the dog walker will come at that time given that it is raining is 60%, or 3/5. Plugging these values into the formula above, we get:
P(Rain AND Dog Walker) = (1/5) * (3/5) = 3/25 = 12%
So the probability that the dog walker will be walking in the rain with the dogs is 12%.
To practice solving problems like this, you can try solving similar problems where you are given different probabilities for the two events. This will help you become more comfortable with using the formula for the probability of the intersection of two events.
Step-by-step explanation:
This figure is made up of two rectangular prisms what is the volume
Answers
The required volume of the given figure is 1134 cubic in.
What is volume?
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Given that,
A figure made up of two rectangular prisms has shown, we have to determine the volume of the prism.
Here,
The required volume of the figure is given as,
Volume = Volume of the bottom prism + Volume of the top prism
Volume = [7 ×2 × 21 ] + [12 × 10 × 7]
Volume = 294 + 840
Volume = 1134 cubic in.
Thus, the required volume of the given figure is 1134 cubic in.
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Melissa receives a daily wage of $50 for each shift at the mall as well as a commission of 3% on her sales. Her sales range from $0 per day to $2000 per day
a. Graph her earnings and write an equation for the relation
B. State the y-intercept and its meaning
C. Create a data table with 4 possible data points on the graph
Answers
a. The linear function that models her earnings is given as follows:
y = 50 + 0.03x.
The function is graphed on the image given at the end of the answer.
b. The y-intercept of 50 represents her fixed pay of $50 per shift.
c. Four points from the graph are given as follows:
(0, 50), (100, 53), (1000, 80), (2000, 110).
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the rate of change of the linear function.b is the y-intercept, representing the value assumed by the linear function when x assumes a value of zero.Melissa receives a daily wage of $50, hence the intercept b is given as follows:
b = 50.
She also earns a commission of 3% on her sales, hence the slope m is given as follows:
m = 0.03.
Meaning that the function is defined as follows:
y = 50 + 0.03x.
The domain of the function is given as follows:
0 ≤ x ≤ 2000.
As it is the amount of sales that she can earn per day.
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the area of a rectangular city park is 25/54 square miles. The length of the park is 5/9 miles. What is the width,in miles of the park
Answers
If the area of the rectangular city park is 25/54 square miles and the length is 5/9 miles, the width of the park, in miles, is 5/6 miles.
What is the formula for the area?The area is the product of the length and width of a rectangle.
To determine one side given the area and another side, we divide the area by the given side's length.
Area = 25/54 square miles
Length = 5/9 miles
Area = Length x Width
Width = 25/54 ÷ 5/9
= 25/54 x 9/5
= 5/6
Thus, the width is 5/6 miles.
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Ill give brainliest for the answer
Answers
Answer:
x = 5Step-by-step explanation:
according to the thereom
both equation are equal as line passes through parallel lines
so,
23x -5 = 21x +5
23x - 21x = 5 + 5
2x = 10
x = 5
Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.
Mangos Used Smoothie Size
Angela 1 9 oz
Kim 3 27 oz
Bri 4 36 oz
Which statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
The ratio of smoothie size to mangos used for Kim is 1:9, and the ratio of smoothie size to mangos used for Bri is 4:27.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 9:1, and the ratio of smoothie size to mangos used for Angela is 4:36.
Answers
The correct statement is "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela".
The correct answer option is option A
How to solve ratio?Mangos Used Smoothie Size
Angela 1 9 oz
Kim 3 27 oz
Bri 4 36 oz
Check the given options to determine which statement is correct;
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
Kim = 27 : 3 = 9 : 1
Angela = 9 : 1
True
The ratio of smoothie size to mangos used for Kim is 1:9, and the ratio of smoothie size to mangos used for Bri is 4:27.
Kim = 27 : 3 = 9 : 1
Bri = 36 : 4 = 9 : 1
False
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
Angela = 9 : 1
Kim = 27 : 3 = 9 : 1
False
The ratio of smoothie size to mangos used for Bri is 9:1, and the ratio of smoothie size to mangos used for Angela is 4:36.
Bri = 36 : 4 = 9 : 1
Angela = 9 : 1
False
Therefore, Kim and Angela has equal ratio of smoothie size to mangoes used.
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Answer:b
Step-by-step explanation:
i got it correct
Graph all of the following points on the same coordinate plane.a. (4,2)
b. (2,−4)
c. (−2,−4)
d. (4,−2)
e. (−4,2)
f. (−2,4)
Answers
Answer:
Answer in image
Step-by-step explanation:
-Hope this helped
Solve for x.
9 / (x-6 ) = 27/(2x+4)
Answers
Answer:
X=22
Step-by-step explanation:
Cross multiply the two sides.
Group the like terms.
Solve the equation.
Answer:
Step-by-step explanation:
15 + 12 + 9.6 + ...; n = 40
Answers
The sum of the first 40 terms of the geometric sequence 15 + 12 + 9.6 is given as follows:
75.
How to obtain the sum?The sum for this problem is defined as follows:
15 + 12 + 9.6 + ..., n = 40.
The ratio between the consecutive terms of the sequence is given as follows:
12/15 = 9.6/12 = 0.8.
This means that the sequence is a geometric sequence, for which:
The first term is of [tex]a_1 = 15[/tex]The common ratio is of q = 0.8.The sum of the first n terms of a geometric sequence is given by the equation presented as follows:
[tex]S_n = \frac{a_1(q^n - 1)}{q - 1}[/tex]
Considering the numeric values of the parameters [tex]a_1[/tex] and q, the numeric value of the sum is given as follows:
S = 15 x (0.8^40 - 1)/(0.8 - 1)
S = 75.
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Sharon has (6t-5) oranges. If she gives (2t+1) oranges to Harry, (t-3) oranges to Tom and twice as many to Tammy, how many oranges in terms of t, does she have left?
Answers
Answer:
Step-by-step explanation:
i did this in 10 seconds it might be wrong
(6t-5)-(2t+1)-(t-3)-2(t-3)
6t-5-2t-1-t+3-2t-6
t-9
3. Students from 4 classes at Franklin Elementary School are going on a field trip to the theater. Each
class has 30 students. There will also be 6 teachers and 14 parents on the trip. There are 20 seats in
each row at the theater. How many rows should be reserved for the field trip?
A 2
B 7
C 74
D 140
Answers
Answer:
B) 7
Step-by-step explanation:
Given information:
Number of classes = 4Number of students in each case = 30Number of teachers = 6Number of parents = 14Number of seats per row = 20If there are 30 students in each class, and there are 4 classes, the total number of students is:
[tex]\begin{aligned}\implies \textsf{Total students}&=\textsf{Students per class} \times \textsf{Number of classes}\\&=\sf 30 \times 4\\&=\sf 120\end{aligned}[/tex]
Therefore, the total number of people going on the trip is:
[tex]\begin{aligned}\implies \textsf{Total number of people}&=\sf Students+Teachers+Parents\\&=\sf 120+6+14\\&=\sf 140\end{aligned}[/tex]
As there are 20 seats in each row at the theater, to calculate how many rows should be reserved for the trip, divide the total number of people by the number of seats per row:
[tex]\begin{aligned}\implies \textsf{Rows to reserve}&=\sf \dfrac{\sf Total\;people}{\sf Seats\;per\;row}\\\\&=\sf\dfrac{140}{20}\\\\&=\sf 7\end{aligned}[/tex]
Therefore, 7 rows should be reserved for the field trip.
Question 9 of 10
Solve |6 x+3|=27.
A. x=-4 and x=5
B. x=-4 and x=-5
C. x=4 and x=-4
D. x=4 and x=-5
Answers
The correct solution after solving |6x+3|=27 is x=4 and x=-5
Hence, option (D) is the correct .
Step-by-Step Approach:
STEP 1: Value in Absolute Formula entered: |6x+3|=27
Rearrange this Absolute Value Equation.
|6x+3| = 27 was entered as the absolute value equality.
STEP 2Clear the Absolute Value Bars.
By dividing the equation into two cases, one for the Positive case and the other for the Negative case, the absolute-value bars will be removed.
|6x+3| is the Absolute Value phrase.
We'll take the negative example, -(6x+3)
Use (6x+3) for the positive case.
STEP 3: Solve the Negative Case. -(6x+3) = 27
⇒-6x-3 = 27
⇒ -6x = 30
⇒-x=5
⇒x= -5
STEP 4: Solve the Positive Case. (6x+3) = 27
⇒(6x+3) = 27
⇒6x=24
⇒x=4
STEP 5: Conclude with the solution.
x= -5
x= 4
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Find c for the inequality 5/7c +2greater than or equal to 4/7
Answers
The solution for the given inequality (5/7)*c + 2 ≤ 4/7 is the one on the third option:
c ≤ -2
How to solve inequality?Here we want to solve the following inequality:
(5/7)*c + 2 ≤ 4/7
We want to solve this for the variable c, to do so, we need to isolate that variable.
We can start by subtracting 2 in both sides, so we will get:
(5/7)*c + 2 ≤ 4/7
(5/7)*c +2 - 2 ≤ 4/7 - 2
(5/7)*c ≤ 4/7 - 14/7
(5/7)*c ≤ -10/7
Now we can multiply both sides by 7/5 to get:
(7/5)*(5/7)*c ≤ (-10/7)*(7/5)
c ≤ -10/5
c ≤ -2
Then the correct option is the third one.
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Question 4 Find the additive inverse of the linear expression. -4 - 7x
please help
Answers
Answer:
4 +7x
Step-by-step explanation:
You want the additive inverse of -4-7x.
Additive inverseThe additive inverse of an expression is the value that gives zero when added to the expression. It is the expression multiplied by -1.
-1 · (-4 -7x) = 4 +7x
The additive inverse is 4 +7x.
__
Additional comment
(-4 -7x) + (4 +7x) = 0
The moon is in an orbit around the earth, and the length of this
orbit is 3.844 × 100,000 kilometers.
1. What is the shortcut for multiplying 3.844 by 100,000?
Answers
The product of given numbers is 384400.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Given that, the moon is in an orbit around the earth, and the length of this
orbit is 3.844×100,000 kilometers.
Here, 3.844 multiplied by 1 we get 3.844
When multiplying decimals by 100000, the digits shift five places to the left.
That is, 384400.0
Therefore, the product of given numbers is 384400.
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Evaluate the expression when a = 1/4 and b = 6 12a + (b - a - 4)
Answers
Answer:
1
Step-by-step explanation:
Substitute a and b .
12 * 1/4 + ( 6 - 4 - 4)
Calculate the difference
12 * 1/4 + ( -2 )
Cancel out the greatest common factor of 4
3 + ( -2 )
When there is a + in front of an expression in the parentheses, the expression remains the same
3 - 2
Subtract the numbers
1
So the solution is, 1
For a company picnic, Dale ordered a box of fresh-backed gingerbread cookies and sugar cookies. He got 49 gingerbread cookies and 1 sugar cookie. What percentage of the cookies were gingerbread. Write your answer using a percent sign (%).
Answers
The percentage of the cookies that were gingerbread was 98%.
What is the percentage?We refer to a percentage as a ratio of a number.
Percentages are expressed over 100 as fractional values, like probabilities, ratios, and proportions.
The percent sign (%) is used to denote percentages.
We can compute the percentage of gingerbread cookies by adding up the total cookies (the denominator), making the number of gingerbread cookies the numerator, which is multiplied by 100.
The number of gingerbread cookies that Dale got = 49
The number of sugar cookies that Dale got = 1
The total number of cookies that Dale ordered = 50
The percentage of gingerbread cookies to the total cookies = 98% (49/50 x 100)
Thus, Dale ordered a box of fresh-baked gingerbread cookies and sugar cookies but got 98% gingerbread.
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Put these numbers in order from least to greatest 7.9 7.5 7.541 8.401 7.19
Answers
Answer: 7.19, 7.5, 7.541, 7.9, 8.401
Step-by-step explanation: I would recommend creating a number line and plotting to points, this may help you visual it from least-> great :)
f(x) = 6(0.4)^x-1 in recursive form
Answers
Recursive functions create a sequence of phrases by repeating or using their own prior terms as inputs.
What is a recursive equation?Recursive functions create a sequence of terms by iterating over or using their own prior terms to calculate new terms. Typically, we study this function using the arithmetic-geometric sequence, which has terms with a shared difference.
The factorial, which multiplies an integer by itself while decrementing it incrementally, is an example of a recursive function. Recursive functions include a wide variety of self-referential functions used in loops.
Any term of a sequence defined by a recursive formula is defined in terms of the term before it (s). Examples include Arithmetic sequences can be recursively written as a = an-1 + d. For a geometric series, a = an-1r is the recursive formula.
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3. Writing to Explain At a cat and dog hospital, 9 of the patients
were cats, 17 were dogs. Use this fact to write two ratios.
Explain what each ratio means.
Answers
Answer:
[tex]\frac{9}{17}[/tex] or 9:17 This is the ratio of cats to dogs.
[tex]\frac{17}{9}[/tex] or 17:9 This is the ratio of dogs to cats.
Step-by-step explanation:
Dave Bowers collects U.S. gold coins. He has a collection of 51 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $710, how many of each denomination does he have?
Answers
The number of $10 coins and $20 coins in a coin collection will be 31 and 20, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Dave Bowers collects U.S. gold coins. He has a collection of 51 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $710.
Let 'x' be the number of $10 coins and 'y' be the number of $20 coins. Then the equations are given as,
x + y = 51 ...1
10x + 20y = 710 ...2
From equations 1 and 2, then we have
10(51 - y) + 20y = 710
510 - 10y + 20y = 710
10y = 200
y = 20
The value of 'x' is given as,
x + 20 = 51
x = 31
The number of $10 coins and $20 coins in a coin collection will be 31 and 20, respectively.
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Answer the question below. View the rubric linked above for help if needed.
Simplify the expression (6²a⁻³ / b⁻¹c)⁻². Show all work and explain each step.
Answers
Answer:
[tex] \frac{ {a}^{ 6 } {c}^{2} }{1296 {b}^{2} } [/tex]
Step-by-step explanation:
By Using
[tex] {(\frac{a}{b} )}^{ - n} = {(\frac{b}{a})}^{n} [/tex]
Express the phrase as a positive power
We apply power in fractions for a
Six to two power can be multiplied, then multiplying the number behind A, 36
Now because on top of a fraction there is a negative power, it transferred to below the deduction, but we make the power positively
Now it's a "A" turn
After sorting the phrase "A" to the back of "c" of the phrases to power two
[tex] \frac{ {a}^{6} {c}^{2} }{1296 {b}^{2} } [/tex]
On his inline skates, Jamal covered a steep 20-mile route in 2 hours and 22 minutes. After a
break for lunch, he took same path back to where he started from. It was mostly downhill, so
he made the return trip in just 1 hour. What was his average speed during the trip?
Write your answer as a whole number or as a decimal rounded to the nearest tenth.
miles per hour
Submit
Work it out
Answers
The average speed during the trip is 11.9 miles per hour.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Total distance covered.
= 20 miles + 20 miles
= 40 miles
Total time.
= 2 hours + 22 minutes + 1 hour
= 3 hours 22 minutes
= 180 + 22 minutes
= 202 minutes
= 3.36 hours
Now,
Average speed.
= 40/3.36
= 11.9 miles per hour
Thus,
The average speed is 11.9 miles per hour.
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supply the missing numerator or denominator
Answers
Answer:
You need to find a pattern in order to solve (check explanation)
Step-by-step explanation:
The easiest way to find a pattern is by knowing the difference between two numbers; in this case, it's 3 and 6 (a-numerators), 3 - 6 = 3 we know you could get this by multiplying 3 x 2
Now that you know this-- the other a-numerators are products of 3
A) 3, 6 , 9 , 12 , 15, 18
20
____
I'm not so sure as for the b problem, I genuinely don't want to give a bad answer, but possibly using the same tactic could work, it does seem like the denominator is more important for b.
PLEASE HELP ASAP. Name the marked angle in 2 different ways.
Answers
2.) ∠MKN
As long as the vertex is the middle letter, the angles can be identified in a couple different ways. Notice that “K” is in the middle of both names? That’s because point K is the vertex and is always the middle letter of an angle name.
Sams total bill was $39.57. If she left $50.50 how much did she tip the waiter?
Answers
Answer:
$10.93
Step-by-step explanation:
Select the correct answer.
You are a delivery driver for an online retail company. The table shows your statistics for total, successful, and missed shipments.
Day Total Shipments Successful Shipments Missed Shipments
1 58 51 7
2 79 72 7
3 82 80 2
4 64 58 8
Which day in the table has incorrect information?
A.
day 1
B.
day 2
C.
day 3
D.
day 4
Answers
Answer:
sorry I i get this wrong but it is c
Answer:
D. day 4
Step-by-step explanation:
Because 58 + 8 = 66 Not 64