Answer:
0.25.
Step-by-step explanation:
To find the common difference, you need to find the number that each value increases by.
1.75 - 1.5 = 0.25.
1.5 - 1.25 = 0.25.
1.25 - 1 = 0.25.
All values apparently increase by 0.25. So, that is your common difference.
Hope this helps!
Answer:
0.25
Step-by-step explanation:
The common difference is the value added to the first term to get the second term, then added to the second to get the third and so on.
To find the common difference, subtract the first term from the second. Then check by subtracting the second term from the third.
The sequence is: 1,1.25,1.5,1.75
second term - first term
1.25- 1= 0.25
third term- second term
1.5 -1.25= 0.25
The common difference in the arithmetic sequence is 0.25
Find the probability of winning a lottery with the following rule. Select the winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Complete Question
Find the probability of winning a lottery with the following rule. Select the six winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Answer:
The probability is [tex]P(winning ) = 7.435 *10^{-7}[/tex]
Step-by-step explanation:
From the question we are told that
The total winning numbers n = 34
The total number to select is r = 6
The total outcome of lottery is mathematically represented as
[tex]t_{outcome}) = \left n } \atop {}} \right. C_r[/tex]
[tex]t_{outcome}) = \frac{n! }{(n-r )! r!}[/tex]
substituting values
[tex]t_{outcome}) = \frac{ 34 ! }{(34 - 6 )! 6!}[/tex]
[tex]t_{outcome}) = \frac{ 34 ! }{28 ! 6!}[/tex]
[tex]t_{outcome}) =1344904[/tex]
The number of desired outcome is
[tex]t_{desired} = 1[/tex]
this is because the desired outcome is choosing the six winning number
The probability of winning a lottery is mathematically represented as
[tex]P(winning ) = \frac{t_{desired}}{t_{outcome}}[/tex]
substituting values
[tex]P(winning ) = \frac{1}{1344904 }[/tex]
[tex]P(winning ) = 7.435 *10^{-7}[/tex]
Zanna rounded these numbers.
7,494 7,540
7,452
First, she rounded them to the tens place. Then, she rounded them to
the hundreds place. Finally, she rounded them to the thousands place.
At which place were the rounded numbers all the same? What was the
rounded number?
Answer:
hundredths place, 7,500.
Step-by-step explanation:
They would be the same when they are all rounded all of the numbers to the the hundredths place. And that number would be 7,500.
When rounding its 5 or higher round up, if its 4 or lower round down.
It takes amy 8 minutes to mow 1/6 of her backyard. At that rate how many more minutes will it take her to finish mowing her backyard
Answer:
40 minutes
Step-by-step explanation:
If it takes her 8 minutes to mow 1/6 of it, we can find the total amount of time it will take by multiplying 8 by 6, since 1/6 times 6 is 1 (1 represents the whole lawn mowed)
8(6) = 48
The question asks for how many more minutes it will take, so subtract 48 by 8.
48 - 8 = 40
= 40 minutes
Answer:
40 minutes
Step-by-step explanation:
We can use ratios to solve
8 minutes x minutes
------------------- = ----------------
1/6 yard 1 yard
Using cross products
8 * 1 = 1/6 x
Multiply each side by 6
8*6 = 1/6 * x * 6
48 = x
48 minutes total
She has already done 8 minutes
48-8 = 40 minutes
How do you evaluate this?
[tex]_6C_3=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20[/tex]
Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b
The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
What is a triangle?Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
In the given figure, three triangles is shown with base and height. Here,
The base 1 is matched with height 2, as the height shown in figure 2 is the dimension of the elevation from the opposite peak to the length of the base 1.Similarly, base 2 is matched with height 3.Base 3 is matched with height 1.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
Learn more about the base and height of the triangle here;
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1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident
Answer:
math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.
Learn more:
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I need help please help meee I don’t understand
Answer:
204
Step-by-step explanation:
To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.
For height of the prongs, take 4 from 6.
6 - 4 = 2
Divide by 2 as there are 2 prongs.
2 / 2 = 1
Remember L * W * H
6 * 3 * 1 = 18
Remember that there are two prongs!
3 + 4 = 7
6 * 7 * 4 = 168
168 + 2(18) = 204
A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.
Answer:
6344
Step-by-step explanation:
Find 26% of 24400
24400 * 26%
24400 * .26
6344
If A = {2,4,6,8,10) and B = [4,8,10), then which of the following statements is false?
A n B = B
B C B
A C B
A C B because all elements of A are not found in B
An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99
Answer:
The width is [tex]w = \$ 729.7[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma = \% 1,000[/tex]
The sample size is [tex]n = 50[/tex]
The sample mean is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
=> [tex]\alpha = 1\%[/tex]
=> [tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 364.9[/tex]
The width of the 99% confidence interval is mathematically evaluated as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 364.9[/tex]
[tex]w = \$ 729.7[/tex]
A box contains 40 identical discs which are either red or white if probably picking a red disc is 1/4. Calculate the number of;
1. White disc.
2. red disc that should be added such that the probability of picking a red disc will be 1/4
Use the graph showing Phillip's account balance to answer the question that follows. ^
What is the interest rate on Phillip's account?
A - 3.3%
B - 6.7%
C - 9.0%
D - 15.3%
Answer:
A - 3.3%
Step-by-step explanation:
From the graph
Where x= 0
Amount =$ 450
It shows that$450 is the capital
Then
When x= 3
Amount=$494.55
So interest generated within 3 years
= $494.55-$450
=$ 44.55
When x= 9
Amount = $583.65
So interest generated within 9 years
= $583.65-$450
=$ 133.65
PRT/10= Interest
450*x*3/100= 44.55
1350x= 4455
X= 4455/1350
X= 3.3
So the rate is =3.3%
please help !! Solve –2.5x ≤ 25
Answer:
x ≥-10
Step-by-step explanation:
–2.5x ≤ 25
Divide each side by -2.5, remembering to flip the inequality
–2.5x/-2.5 ≥ 25 /-2.5
x ≥-10
Answer:
[tex]x\leq -10[/tex]
Step-by-step explanation:
[tex]-2.5x\leq 25[/tex]-----> Multiply by -1:
[tex]2.5x\geq -25[/tex]-----> Divide by 2.5:
[tex]x\geq -10[/tex]
Hope this helps!
According the the U.S. Department of Education, full-time graduate students receive an average salary of $15,000 with a standard deviation of $1,200. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 100 randomly selected students and finds their average salary is $16,000. Use a significance level of 0.05 to test if there is evidence that the dean's claim is correct. What are the hypotheses
Answer:
Step-by-step explanation:
Given that :
population Mean = 15000
standard deviation= 1200
sample size n = 100
sample mean = 16000
The null and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o : \mu = 15000 }\\ \\ \mathtt{H_1 : \mu > 15000}[/tex]
Using the standard normal z statistics
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]
[tex]z = \dfrac{16000 -15000}{\dfrac{1200 }{\sqrt{100}}}[/tex]
[tex]z = \dfrac{1000}{\dfrac{1200 }{10}}[/tex]
[tex]z = \dfrac{1000\times 10}{1200}[/tex]
z = 8.333
degree of freedom = n - 1 = 100 - 1 = 99
level of significance ∝ = 0.05
P - value from the z score = 0.00003
Decision Rule: since the p value is lesser than the level of significance, we reject the null hypothesis
Conclusion: There is sufficient evidence that the Dean claim for his graduate students earn more than average salary of $15,000
Dean's Claim of Average Salary = 16000, ie greater than 15000 : is correct
Null Hypothesis [ H0 ] : Average Salary = 15000
Alternate Hypothesis [ H1 ] : Average Salary > 15000
Hypothesis is tested using t statistic.
t = ( x - u ) / ( s / √ n ) ; where -
x = sample mean , u = population mean , s = standard deviation, n = sample size
t = ( 16000 - 15000 ) / ( 1200 / √100 )
= 1000 / 120
t {Calculated} = 8.33,
Degrees of Freedom = n - 1 = 100 = 1 = 99
Tabulated t 0.05 (one tail) , at degrees of freedom 99 = 1.664
As Calculated t value 8.33 > Tabulated t value 1.664 , So we reject the Null Hypothesis in favour of Alternate Hypothesis.
So, conclusion : Average Salary > 15000
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Two sides of a triangle are equal length. The length of the third side exceeds the length of one of the other sides by 3 centimeters. The perimeter of the triangle is 93 centimeters. Find the length of each of the shorter sides of the triangle
Answer:
30 cm
Step-by-step explanation:
let x be the lenght of the two sides of equal lenghts, so the other is x+3
and the perimeter is x+x +x +3
P=3x+3
P=3(x+1)
93=3(x+1)
31=x+1
x=30
so the shorter sides are of 30 centimeters and the longest is 33
Explain how to solve the inequality (x + 1)(x – 2) ∙ (x – 3) > 0. Explain in your own words, each step necessary to solve the inequality, making sure to follow the proper order of operations. Is this inequality accurate? Explain why or why not.
Answer:
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
Step-by-step explanation:
Given
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Required
Solve; with steps
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Start by splitting the inequality as follows
[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or [tex]x - 3 > 0[/tex]
Solve the inequalities one after the other
Solving: [tex]x + 1 > 0[/tex]
Subtract 1 from both sides
[tex]x + 1 - 1 > 0 - 1[/tex]
[tex]x > -1[/tex]
Solving: [tex]x - 2 > 0[/tex]
Add 2 to both sides
[tex]x - 2 +2 > 0 +2[/tex]
[tex]x > 2[/tex]
Solving: [tex]x - 3 > 0[/tex]
Add 3 to both sides
[tex]x - 3 +3> 0+3[/tex]
[tex]x > 3[/tex]
Hence, the solution to the inequality is
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
A population consists of 100 elements. We want to draw a simple, random sample of 20 elements from this population. On the first selection, the probability of any particular element being selected is ____.
Answer:
1/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event /total outcome
Since the population consists of 100 elements, the total outcome of event = 100.
If random sample of 20 element is drawn from the population, the expected outcome = 20
On the first selection, the probability of any particular element being selected = 20/100 = 1/5
Find the polynomial for the area.
The area is
Answer: ¹/₂( x² - 10y² + 10xy - xy )
Step-by-step explanation:
From the diagram area of the triangle = ¹/₂ ˣ base ˣ height
where the base = x + 10y and the height = x - y
Therefore putting these into the formula above
Area = ¹/₂ [( x + 10y )( x -y )]
= ¹/₂( x² - xy + 10xy - 10y²)units²
= ¹/₂( x² - 10y² + 10xy - xy )
How do you write 30,8608
Answer:
it should be 308,608. the comma is after every three in this scenario.
Step-by-step explanation:
33 points
1. A sandwich vendor offers a choice of hamburger, chicken, or fish on
either a plain or sesame seed bun. How many different types of
sandwiches are there to choose from?
*
4
6
12
3
Answer:
6 sandwiches to choose from because
3×2 = 6
HELP ME!
A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the state. Approximately how many of these students would have I.Q.s above 140?
Answer: approx 1196 students.
Step-by-step explanation:
As known for normal distribution 95.4% of all results are situating at +-2*s distance from the mean. (s is the standard deviation)
2s=16*2=32 . The mean +2s= 104+32=136 = approx 140.
95.4% from 52000 = 49608 students. The residual amont ( which is out of the border mean+-2s)= 52000-49608=2392
Because of the normal distribution simmetry the number of the students which has IQ 140 and more is twice less than 2392.
N=2392:2=1196
if given the diameter how can you find the radius
Answer:
Divide the diameter by 2.
Step-by-step explanation:
The radius of any circle is always the end to the center.
The diameter is a point of the circle to the opposite side.
This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.
Hope this helped!
Answer:
Divide the diameter by 2. d/2=r
Step-by-step explanation:
If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.
If the diameter was 10, the radius would 10/2=5.
PLZ HELPPPPPP. 25 POINTS.
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
A. y=12/x
B. y=12x
C. y=12+x
D. y=12−x
Answer:
b
Step-by-step explanation:
because its right dummy
Find (fºg)(2) and (f+g)(2) when f(x)= 1/x and g(x) = 4x +9
[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]
Which defines a line segment?
two rays with a common endpoint
O a piece of a line with two endpoints
O a piece of a line with one endpoint
all points equidistant from a given point
Answer:
O a piece of a line with two endpoints
Step-by-step explanation:
O a piece of a line with two endpoints
A piece of a line with two endpoints.
What is a line segment?In geometry, a line segment is a part of a line this is bounded by distinct end points and includes every point on the line this is between its endpoints.
What are the examples of line segments in real life?A ruler, a scale, a stick, a boundary line.Learn more about line segments here https://brainly.com/question/2437195
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Sugar, flour, and oats are stored in three drawers. The first drawer is labeled "oats", the second is labeled, "flour", the third is labeled "oats or flour". The label of each drawer does not correspond to what is stored inside of it. In which drawers is what stored?
Answer:
first = flour, second = oats, third = sugar
Step-by-step explanation:
Since the labels are "wrong", we know that the third drawer doesn't have oats or flour, therefore it has sugar. Since the first doesn't have oats, it must have flour and that makes the second drawer oats.
Answer:
first drawer has flour, second has oats, third is sugar
Step-by-step explanation:
on the first drawer, it is labelled oats, so it cannot be oats. on the second it cannot be flour, and on the third it cannot be oats or flour, which means it HAS to be sugar leaving oats and flour to be in either the first, or second.
i know it may sound a little confusing but please let me know if you dont understand
Karim has two investments, one in Company A, and another in Company B. Karim purchased 3,000 shares in company A at $2.65 per share. Since purchasing the shares, the price per share increased to $2.95 per share, after which point Karim decided to sell, realizing a profit. At the same time, Karim purchased 2,000 shares in Company B at $1.55 per share. Since purchasing the shares, the share price fell to $1.30 per share, after which Karim decided to sell the shares, suffering a loss. Karim is required to pay tax at a rate of 28% on the combined profit from both investments. Calculate how much tax Karim must pay.
Answer:
A:$2478
B:$728
Total:$3206
Step-by-step explanation:
2.95x3000=8850
1.30x2000=2600
8850x0.28=2478
2600x0.28=728
2478+728=3206
22 tons is equivalent to ______ kilograms.
Answer:
20000 kg
Step-by-step explanation:
Recall that 1 kg = 2.2 lb approximately. Then:
22 tons 1 kg 2000 lb
------------ * ------------ * -------------- = 20000 kg
1 2.2 lb 1 ton
Compute (3/4)*(8/9)*(15/16)*(24/25)*(35/36)*(48/49)*(63/64)*(80/81)*(99/100) Express your answer in the simplest way possible. (Suggestion: First, try computing 3/4*8/9 then 3/4*8/9*15/16 and so on. Look for patterns.
Answer:
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
Step-by-step explanation:
Given
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})[/tex]
Required
Simplify
For clarity, group the expression in threes
[tex]((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the first group [Divide 8 by 4]
[tex]((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 9 by 3]
[tex]((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex]((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 15 by 3]
[tex]((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 16 by 2]
[tex]((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the second group [Divide 35 and 25 by 5]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 49 by 7]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 24 by 3]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Merge the first and second group
[tex]((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the last group [Divide 99 by 9]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))[/tex]
[Divide 63 by 9]
[tex](\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))[/tex]
[Divide 64 and 80 by 8]
[tex](\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))[/tex]
[Divide 10 and 4 by 2]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))[/tex]
[Divide 100 by 5]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})[/tex]
[tex]1*(\frac{11}{20})[/tex]
[tex]\frac{11}{20}[/tex]
Hence;
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
2/3a - 1/6 =1/3 please help me
Answer:
[tex]a = \frac{3}{4}[/tex]
Step-by-step explanation:
Let's convert everything to sixths to make it easier to work with.
[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]
Add 1/6 to both sides:
[tex]\frac{4}{6}a = \frac{3}{6}[/tex].
Dividing both sides by 4/6:
[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]
Hope this helped!
