Answer:
see below
Step-by-step explanation:
given:
LCM(a,b) = 20160, a=60
find:
smallest possible value of b
solution;
60, b = 20,160
b = 20,160 / 60
b = 336
60 x 336 = 20,160
= 2⁶ x 3² x 5 x 7
= (2² x 3 x 5) x (2⁴ x 3 x 7)
= (60) x (336)
LCM(60,336) = 1680
consider the 2² x 3 to get the prime number:
= 336 x 12
= 4032
therefore,
LCM(60,4032) = 20160
The smallest possible value of b is 336.
What is Prime Factorization?Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.
We have been given that
LCM(a,b) = 20160 and a = 60
We have to determine the smallest possible value of b
Since the product of two numbers equals the product of their HCF and LCM.
⇒ 60 × b = 20,160
⇒ b = 20,160 / 60
⇒ b = 336
⇒ 60 × 336 = 20,160
We need to write 20160 as the product of its prime factors, which is 20160.
⇒ 2⁶ × 3² × 5 × 7
⇒ (2² × 3 × 5) x (2⁴ × 3 × 7)
⇒ (60) × (336)
⇒ LCM(60,336) = 1680
Therefore, the smallest possible value of b is 336.
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Solve all these to be marked the brainlest
Divide. 1/3 ÷ 4/5 Express your answer in simplest form. Enter your answer in the box.
1/3 divided by 4/5 = 5/12
What is x=to in this? 3x + 18 = 4x + 10
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
[tex]3x+18=4x+10[/tex]
Subtract 18 from both sides:
[tex]3x+18-18=4x+10-18[/tex]
[tex]3x=4x-8[/tex]
Subtract 4x from both sides:
[tex]3x-4x=4x-8-4x[/tex]
[tex]-x=-8[/tex]
Divide both sides by -1:
[tex]\frac{-x}{-1}=\frac{-8}{-1}\\[/tex]
[tex]x=8[/tex]
If f(x) = 2 - x, express 2f(a) + f(2a) in simplest form.
Answer:
6 - 4a
Step-by-step explanation:
From the question given,
f(x) = 2 - x
2f(a) + f(2a) =.?
First, we shall obtain f(a). This can be obtained as follow:
f(x) = 2 - x
x = a
f(a) = 2 - a
Next, we shall obtain 2f(a). This is can be obtained as follow:
f(a) = 2 - a
2f(a) = 2(2 - a)
2f(a) = 4 - 2a
Next, we shall obtain f(2a). This can be obtained as follow:
f(x) = 2 - x
x = 2a
f(2a) = 2 - 2a
Finally, we shall determine 2f(a) + f(2a) as follow:
2f(a) = 4 - 2a
f(2a) = 2 - 2a
2f(a) + f(2a) =?
2f(a) + f(2a) = (4 - 2a) + (2 - 2a)
2f(a) + f(2a) = 4 - 2a + 2 - 2a
2f(a) + f(2a) = 4 + 2 - 2a - 2a
2f(a) + f(2a) = 6 - 4a
Therefore, 2f(a) + f(2a) is equivalent to 6 - 4a
Which rules define the function graphed below?
Answer:
y = 2x + 3; y = -1/3 x + 3
Step-by-step explanation:
Both lines have y-intercept 3.
The slopes are 2 and -1/3.
The equations are
y = 2x + 3; y = -1/3 x + 3
Answer:
A
y = 2x + 3; y = -1/3 x + 3
13. Which is the range of the relation
below?
х
0 2 468
Ly-2 -1012
A 0, 2, 4, 6,8
B-2, -1,0, 1, 2
C-2, -1,0, 1, 2, 4, 6,8
D 0,2
The range is all y-values.
In the relation, all the y-values are in the
second row.
-2, -1, 0, 1, 2
Therefore, the answer is B.
Best of Luck!
There are 30 students in a sixth grade class. 60% of the students are girls. How many of the students are girls?
Answer:
18
Step-by-step explanation:
30 students * 60/100= 18
Complete the recursive formula of the geometric sequence 56\,,-28\,,\,14\,,-7,...56,−28,14,−7,...56, comma, minus, 28, comma, 14, comma, minus, 7, comma, point, point, point. d(1)=d(1)=d, left parenthesis, 1, right parenthesis, equals d(n)=d(n-1)\cdotd(n)=d(n−1)⋅d, left parenthesis, n, right parenthesis, equals, d, left parenthesis, n, minus, 1, right parenthesis, dot
Answer:
Step-by-step explanation:
[tex]r=\frac{-28}{56}=-\frac{1}{2}\\a_{n}=\frac{-1}{2}a_{n-1}[/tex]
The recursive formula for the sequence is aₙ = (-1/2) * aₙ₋₁
What is a Geometric Series?A sequence of numbers such that the consecutive term is increasing or decreasing by a fixed ratio is called a geometric series.
The standard equation for geometric series is
Tₙ = a₁ rⁿ⁻¹
The formula above represents the explicit formula to determine the nth term of the sequence.
The recursive formula is used to determine the nth term when (n-1) th term is given.
The geometric sequence is,
56, -28, 14, -7,.................
The first term of the sequence is 56
The common ratio is determined by taking the ratio of the second term to the first term.
r = -28/56 = -1/2
The recursive formula is represented by,
aₙ = r * aₙ₋₁
aₙ = (-1/2) * aₙ₋₁
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Camila is seamstress and is creating a wedding dresses. She has 144 yards of silk fabric. For each dress, the skirt requires 3 yards of silk and the bodice requires 1 yard of silk. How many dresses can she make with the amount of silk she has?
Answer:
either 36 or 24
Step-by-step explanation:
The number of dresses can she make with the amount of silk she has is 48.
Given that,
She has 144 yards of silk fabric. For each dress, the skirt requires 3 yards of silk and the bodice requires 1 yard of silk.Based on the above information, the calculation is as follows:
[tex]= 144 \div 3[/tex]
= 48
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I need help if anyone can help me and explain it how to do it
Step-by-step explanation:
h(x) = f(g(x)), so h(x) is the same as g(x) substituted into f(x).
In this case, we can say f(x) = √x, and g(x) = 5x + 30.
f(g(x)) = √(5x + 30)
If UV = 5, VW = 4x − 1, and UW = 5x + 2, what is UW? Simplify your answer and write it as a proper fraction, mixed number, or integer. Could you type in step by step so I could understand it too?
Answer:
12
Step-by-step explanation:
UV + VW = UW
[tex]5+(4x-1)=5x+2[/tex]
Remove brackets:
[tex]5+4x-1=5x+2[/tex]
Solve [tex]5-1=4:[/tex]
[tex]4x+4=5x+2[/tex]
Subtract 4 from both sides:
[tex]4x+4-4=5x+2-4[/tex]
[tex]4x=5x-2[/tex]
Subtract 5x from both sides:
[tex]4x-5x=5x-2-5x[/tex]
[tex]-x=-2[/tex]
Divide both sides by -1:
[tex]\frac{-x}{-1}=\frac{-2}{-1}[/tex]
[tex]x=2[/tex]
[tex]UW=5x+2=5(2)+2=10+2=12[/tex]
Does the ordered pair (−1,−3) satisfy the following system of equations? {2x+5y=−17−4x+3y=−5
Answer:
yes
Step-by-step explanation:
Try it and see:
2(-1) +5(-3) = -2-15 = -17 . . . . . works in the first equation
-4(-1) +3(-3) = 4 -9 = -5 . . . . . . works in the second equation
Yes, the ordered pair (-1, -3) satisfies the equations.
__
Or, you can check the solution using a graphing calculator.
A company makes a profit of 35$ per video game. The company can produce at most 200 software programs and at most 300 video games per week. How many items of each kind should be produced per week in order to maximize the profit? Use linear programming to solve. Show all your work.
Answer:
Let x = software program
Let y = video game
x < 200 ; y < 300
x + y < 425
50x ; 35y
x = 200 ; y = 225
50(200) + 35(225) = 10,000 + 7,875 = 17,875
x = 125 ; y = 300
50(125) + 35(300) = 6,250 + 10,500 = 16,750
x = 175 ; y = 250
50(175) + 35(250) = 8,750 + 8,750 = 17,500
It is more profitable to maximize production of software program when working within the limits provided.
Step-by-step explanation:
Which angle pairs in the diagram are supplementary angles? Check all that apply.
∠3 and ∠6
∠1 and ∠4
∠5 and ∠6
∠4 and ∠5
∠6 and ∠7
Answer:
1 and 4
4 and 5
6 and 7
Answer:
∠1 and ∠4
∠4 and ∠5
∠6 and ∠7
Step-by-step explanation:
took the edge quiz
Question 5: The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days.
74 73 74 77 75 68 73 69 69 69
70 71 73 72 72 71 62 63 66 65
65 64 68 67 67
Find the percentile rank of 73. % =
Answer:
The percentile rank of the data value 73 is 84.
Step-by-step explanation:
In this problem, you want to find the percentile rank of the data value 73 in the data set.
The percentile rank represents the percent of numbers in the data set that have value equal or less than 73.
Take note that there are 25 data values in this data set. It's helpful to sort them in ascending order.
Of these 25 data values, 21 are less than or equal to the data value 73. To find the percentile rank of 73, apply the formula:
percentile rank = (L/N)(100)
where L is the number of data values that are less than or equal to 73, and N is the size of the data set.
Substituting in values for this problem, we have:
percentile rank = (21/25)(100)
percentile rank = (0.84)(100)
Percentile ranks are always expressed as whole numbers.
Evaluating the multiplication above and rounding to the nearest whole number we have:
percentile rank = 84
Interpreting our answer, 84% of the numbers in the data set have values less than or equal to 73.
Find two decimals that are equivalent to (4x10)+(7x1/100)
Answer:
4.700 and 4.70Step-by-step explanation:
step one:
Since the number is basically a representation of numbers to the powers of 10, that is the place value of each digit corresponds to the power of 10
step two:
now given the expression
(4x10)+(7x1/100)
this can be written as
4.700
and this Could also be equivalent to
4.70 and 4.7 since
What is the vertex of the graph of y = 1/4 (x - 2)^2+ 6?
(0,7)
(4,7)
(2,6)
(-2,-6)
Answer:
focus | (2, 7)
vertex | (2, 6)
semi-axis length | 1
focal parameter | 2
eccentricity | 1
directrix | y = 5
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(-1,9) and (-7,1)
Answer:
1 1/3
Step-by-step explanation:
m=y2-y1/x2-x1
or rise over run
m=1-9/(-7)-(-1)= (-8)/(-6)= 1 1/3
Answer:
11/3
Step-by-step explanation:
Which describes an atom that has fewer neutrons and protons and more electrons than protons
Answer:
Negative charged ion :)
Answer:
Negative charged ion
Step-by-step explanation:
Help me solve step by step
Solve the equation: 2^2 − 9 + 10 = 0 Step by step
Step-by-step explanation:
2^2 − 9 + 10 = 0
4-9+10=0
4+1=0
5=0
False
[7,8] is the difference between
2 vectors with components [a, 5] and
(-4,-3). What is a
Answer:
The value of [tex]a[/tex] is 3.
Step-by-step explanation:
Let be [tex]\vec a = \langle a, 5 \rangle[/tex] and [tex]\vec b = \langle -4,-3 \rangle[/tex], the difference between the two vectors is:
[tex]\vec c = \vec b - \vec a[/tex]
[tex]\vec c = \langle a, 5\rangle - \langle -4,-3 \rangle[/tex]
[tex]\vec c = \langle a+4,8 \rangle[/tex]
If we know that [tex]\vec c = \langle 7,8 \rangle[/tex], the value of [tex]a[/tex] is:
[tex]\langle 7, 8 \rangle = \langle a+4, 8\rangle[/tex]
In which,
[tex]a + 4 = 7[/tex]
[tex]a = 3[/tex]
The value of [tex]a[/tex] is 3.
Identify a reasonable approximation for the solution of this system
Answer:
Add a picture of the system
Step-by-step explanation:
Describe the difference in how the pie chart and the Pareto chart show patterns in the data. Choose the correct answer below.
O A. The pie chart shows the percentages as parts of the whole. The Pareto chart shows the rankings of the seasons.
OB. The pie chart shows the individual responses. The Pareto chart shows the distribution of the seasons.
O C. The pie chart shows the distribution of the seasons. The Pareto chart shows the individual responses.
OD. The pie chart shows the rankings of the seasons. The Pareto chart shows the percentages.
Click to select your answer.
Answer:
A. The pie chart shows the percentages as parts of the whole. The Pareto chart shows the rankings of the seasons.
Step-by-step explanation:
hope this helps
A pie chart shows the percentages as parts of the whole. The Pareto chart shows the rankings of the seasons.
What is a pie chart?"A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice is proportional to the quantity it represents."
What is a Pareto chart?"A Pareto chart is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line."
Therefore, a pie chart shows the percentages as parts of the whole. The Pareto chart shows the rankings of the seasons.
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1 A line passes through (0, 2) and has a slope of 3. Which function's graph is parallel to this line?
A. f(x) = 2
B. f(x) = 3
C. f(x) = 2x
D f(x) = 3x
Pleaseee. helpppl
Find the most important variable in the problem.
There are 13 fish in an aquarium. Seven of the fish are guppies. How many
non-guppies are in the aquarium?
A. the total number of fish
B. the number of guppies
c. the number of non-guppies
Answer:
C. the number of non-guppies
Step-by-step explanation:
The number of non-guppies is the only variable the other two options have defined values.
Answer:
C, The number of non- guppies is the most important variable.
Step-by-step explanation:
The answer is the unknown variable that you're trying to find and the entire problem is to help you find the unknown.
What is equivalent to
5[4 + 3(x – 6)]?
Answer:
odk
Step-by-step explanation:
-(4+H)=3h
Solve for h
Rita is developing an equation that will represent the same proportional relationship as the graph.
It's d. The quotient of the coordinates will be a coeffficient in the equation
HELPPPP PRECALC WILL GIVE BRAINLIEST
Answer:
500
600
500
Step-by-step explanation: