Answer:
Yes it is reasonable to conclude the mean rate charged is greater than 14%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.14[/tex]
The sample size is [tex]n = 10[/tex]
The sample mean is [tex]\= x = 0.1564[/tex]
The standard deviation is [tex]\sigma = 0.01561[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o: \mu = 0.14[/tex]
The alternative hypothesis is [tex]H_a : \mu > 0.14[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]
[tex]t = 3.322[/tex]
Now the p-value obtained from the z-table is
[tex]p-value = P(t > 3.322) = 0.00044687[/tex]
Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that the mean rate charged is greater than 14%
Please Solve
F/Z=T for Z
Answer:
F /T = Z
Step-by-step explanation:
F/Z=T
Multiply each side by Z
F/Z *Z=T*Z
F = ZT
Divide each side by T
F /T = ZT/T
F /T = Z
Answer:
[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]
Step-by-step explanation:
[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]
AB is dilated from the origin to create A'B' at A' (0, 8) and B' (8, 12). What scale factor was AB dilated by?
Answer:
4
Step-by-step explanation:
Original coordinates:
A (0, 2)
B (2, 3)
The scale is what number the original coordinates was multiplied by to reach the new coordinates
1. Divide
(0, 8) ÷ (0, 2) = 4
(8, 12) ÷ (2, 3) = 4
AB was dilated by a scale factor of 4.
Which one is correct? in need of large help
Answer:
Option C. x + 12 ≤ 2(x – 3)
Step-by-step explanation:
From the question, we obtained the following information:
x + 12 ≤ 5 – y .......(1)
5 – y ≤ 2(x – 3) ....... (2)
To know which option is correct, do the following:
From equation 2,
5 – y ≤ 2(x – 3)
Thus, we can say
5 – y = 2(x – 3)
Now, we shall substitute the value of 5 – y into equation 1 as shown below:
x + 12 ≤ 5 – y
5 – y = 2(x – 3)
x + 12 ≤ 2(x – 3)
From the above illustration, we can see that if x + 12 ≤ 5 – y and 5 – y ≤ 2(x – 3), then x + 12 ≤ 2(x – 3) must be true.
Option C gives the correct answer.
Brainliest! Jared uses the greatest common factor and the distributive property to rewrite this sum: 100 + 75 Drag one number into each box to show Jared's expression. Brainliest!
Answer:
25(4 + 3)
Step-by-step explanation:
100 = 2^2 + 5^2
75 = 3 * 5^2
GCF = 5^2 = 25
100 + 75 =
= 25 * 4 + 25 * 3
= 25(4 + 3)
Two fraction have the same denominator, 8.the some of two fraction is 1/2.if one of the fraction is added to five times the order, the result is 2,find the number.
Answer:
1/8, 3/8
Step-by-step explanation:
Let x and y represent the two fractions. Then we are given ...
x + y = 1/2
x + 5y = 2
Subtracting the first equation from the second, we get ...
(x +5y) -(x +y) = (2) -(1/2)
4y = 3/2 . . . . . simplify
y = 3/8 . . . . . . divide by 4
x = 1/2 -3/8 = 1/8
The two numbers are 1/8 and 3/8.
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario
Answer:
The test statistic is [tex]t = 2.79[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 59.3[/tex]
The sample size is [tex]n = 79[/tex]
The sample mean is [tex]\= x = 62.4[/tex]
The standard deviation is [tex]\sigma = 9.86[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]
[tex]t = 2.79[/tex]
Figure out if the figure is volume or surface area.
(and the cut out cm is 4cm)
Answer:
Surface area of the box = 168 cm²
Step-by-step explanation:
Amount of cardboard needed = Surface area of the box
Since the given box is in the shape of a triangular prism,
Surface area of the prism = 2(surface area of the triangular bases) + Area of the three rectangular lateral sides
Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(6)(4)[/tex]
= 12 cm²
Surface area of the rectangular side with the dimensions of (6cm × 9cm),
= Length × width
= 6 × 9
= 54 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Surface area of the prism = 2(12) + 54 + 45 + 45
= 24 + 54 + 90
= 168 cm²
You are going to your first school dance! You bring $20,
and sodas cost $2. How many sodas can you buy?
Please write and solve an equation (for x sodas), and
explain how you set it up.
Answer:
10
Step-by-step explanation:
Let the no. of sodas be x
Price of each soda = $2
Therefore, no . of sodas you can buy = $2x
2x=20
=>x=[tex]\frac{20}{2}[/tex]
=>x=10
you can buy 10 sodas
Answer: 10 sodas
Step-by-step explanation:
2x = 20 Divide both sides by 2
x = 10
If I brought 20 dollars and I want to by only sodas and each sodas cost 2 dollars, then I will divide the total amount of money that I brought by 2 to find out how many sodas I could by.
consider the bevariate data below about Advanced Mathematics and English results for a 2015 examination scored by 14 students in a particular school.The raw score of the examination was out of 100 marks.
Questions:
a)Draw a scatter graph
b)Draw a line of Best Fit
c)Predict the Advance Mathematics mark of a student who scores 30 of of 100 in English.
d)calculate the correlation using the Pearson's Correlation Coefficient Formula
e) Determine the strength of the correlation
Answer:
Explained below.
Step-by-step explanation:
Enter the data in an Excel sheet.
(a)
Go to Insert → Chart → Scatter.
Select the first type of Scatter chart.
The scatter plot is attached below.
(b)
The scatter plot with the line of best fit is attached below.
The line of best fit is:
[tex]y=-0.8046x+103.56[/tex]
(c)
Compute the value of x for y = 30 as follows:
[tex]y=-0.8046x+103.56[/tex]
[tex]30=-0.8046x+103.56\\\\0.8046x=103.56-30\\\\x=\frac{73.56}{0.8046}\\\\x\approx 91.42[/tex]
Thus, the Advance Mathematics mark of a student who scores 30 out of 100 in English is 91.42.
(d)
The Pearson's Correlation Coefficient is:
[tex]r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot \sum X^{2}-(\sum X)^{2}][n\cdot \sum Y^{2}-(\sum Y)^{2}]}}[/tex]
[tex]=\frac{14\cdot 44010-835\cdot 778}{\sqrt{[14\cdot52775-(825)^{2}][14\cdot 47094-(778)^{2}]}}\\\\= -0.7062\\\\\approx -0.71[/tex]
Thus, the Pearson's Correlation Coefficient is -0.71.
(e)
A correlation coefficient between ± 0.50 and ±1.00 is considered as a strong correlation.
The correlation between Advanced Mathematics and English results is -0.71.
This implies that there is a strong negative correlation.
Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula. A. an=44−6n B. an=41−6n C. an=35−6n D. an=43−6n
Answer:
The answer is option AStep-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 38
d = 32 - 38 = - 6 or 20 - 26 = - 6
Substitute the values into the above formula
A(n) = 38 + (n - 1)-6
= 38 - 6n + 6
We have the final answer as
A(n) = 44 - 6nHope this helps you
Answer:
a
Step-by-step explanation:
you're welcome!
What is the value of the product (3 – 2i)(3 + 2i)?
Answer:
13
Step-by-step explanation:
(3 - 2i)(3 + 2i)
Expand
(9 + 6i - 6i - 4i^2)
Add
(9 - 4i^2)
Convert i^2
i^2 = ([tex]\sqrt{-1}[/tex])^2 = -1
(9 - 4(-1))
Add
(9 + 4)
= 13
Answer:
13.
Step-by-step explanation:
(3 - 2i)(3 + 2i)
= (3 * 3) + (-2i * 3) + (2i * 3) + (-2i * 2i)
= 9 - 6i + 6i - 4[tex]\sqrt{-1} ^{2}[/tex]
= 9 - 4(-1)
= 9 + 4
= 13
Hope this helps!
According to the local union president, the mean gross income of plumbers in the Salt Lake City area follows a normal distribution with a mean of $48,000 and a population standard deviation of $2,000. A recent investigative reporter for KYAK TV found, for a sample of 49 plumbers, the mean gross income was $47,600. At the 0.05 significance level, is it reasonable to conclude that the mean income is not equal to $47,600? Determine the p value. State the Null and Alternate hypothesis: State the test statistic: State the Decision Rule: Show the calculation: What is the interpretation of the sample data? Show the P value
Answer:
Step-by-step explanation:
Given that:
population mean [tex]\mu[/tex] = 47600
population standard deviation [tex]\sigma[/tex] = 2000
sample size n = 49
Sample mean [tex]\over\ x[/tex] = 48000
Level of significance = 0.05
The null and the alternative hypothesis can be computed as follows;
[tex]H_0 : \mu = 47600 \\ \\ H_1 : \mu \neq 47600[/tex]
Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.
The test statistics can be calculated by using the formula:
[tex]z= \dfrac{\overline X - \mu }{\dfrac{\sigma}{ \sqrt{n}}}[/tex]
[tex]z= \dfrac{ 48000-47600 }{\dfrac{2000}{ \sqrt{49}}}[/tex]
[tex]z= \dfrac{400 }{\dfrac{2000}{ 7}}[/tex]
[tex]z= 1.4[/tex]
Conclusion:
Since 1.4 is lesser than 1.96 , we fail to reject the null hypothesis and that there is insufficient information to conclude that the mean gross income is not equal to $47600
The P-value is being calculate as follows:
P -value = 2P(Z>1.4)
P -value = 2 (1 - P(Z< 1.4)
P-value = 2 ( 1 - 0.91924)
P -value = 2 (0.08076 )
P -value = 0.16152
A raffle offers one $8000.00 prize, one $4000.00 prize, and five $1600.00 prizes. There are 5000 tickets sold at $5 each. Find the expectation if a person buys one ticket.
Answer:
The expectation is [tex]E(1 )= -\$ 1[/tex]
Step-by-step explanation:
From the question we are told that
The first offer is [tex]x_1 = \$ 8000[/tex]
The second offer is [tex]x_2 = \$ 4000[/tex]
The third offer is [tex]\$ 1600[/tex]
The number of tickets is [tex]n = 5000[/tex]
The price of each ticket is [tex]p= \$ 5[/tex]
Generally expectation is mathematically represented as
[tex]E(x)=\sum x * P(X = x )[/tex]
[tex]P(X = x_1 ) = \frac{1}{5000}[/tex] given that they just offer one
[tex]P(X = x_1 ) = 0.0002[/tex]
Now
[tex]P(X = x_2 ) = \frac{1}{5000}[/tex] given that they just offer one
[tex]P(X = x_2 ) = 0.0002[/tex]
Now
[tex]P(X = x_3 ) = \frac{5}{5000}[/tex] given that they offer five
[tex]P(X = x_3 ) = 0.001[/tex]
Hence the expectation is evaluated as
[tex]E(x)=8000 * 0.0002 + 4000 * 0.0002 + 1600 * 0.001[/tex]
[tex]E(x)=\$ 4[/tex]
Now given that the price for a ticket is [tex]\$ 5[/tex]
The actual expectation when price of ticket has been removed is
[tex]E(1 )= 4- 5[/tex]
[tex]E(1 )= -\$ 1[/tex]
anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
The limit of a function is the value it approaches.
In #37, as x approaches infinity (far to the right), the curve f(x) approaches 1. As x approaches negative infinity (far to the left), the curve f(x) approaches -1.
lim(x→∞) f(x) = 1
lim(x→-∞) f(x) = -1
In #38, as x approaches infinity (far to the right), the curve f(x) approaches 2. As x approaches negative infinity (far to the left), the curve f(x) approaches -3.
lim(x→∞) f(x) = 2
lim(x→-∞) f(x) = -3
If f(x) = 2x2 – 3x – 1, then f(-1)=
The value of function at x= -1 is f(-1) = 4.
We have the function as
f(x) = 2x² - 3x -1
To find the value of f(-1) when f(x) = 2x² - 3x -1, we substitute x = -1 into the expression:
f(-1) = 2(-1)² - 3(-1) - 1
= 2(1) + 3 - 1
= 2 + 3 - 1
= 4.
Therefore, the value of function at x= -1 is f(-1) = 4.
Learn more about Function here:
https://brainly.com/question/32020999
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Consider the surface f(x,y) = 21 - 4x² - 16y² (a plane) and the point P(1,1,1) on the surface.
Required:
a. Find the gradient of f.
b. Let C' be the path of steepest descent on the surface beginning at P, and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane.
c. Find parametric equations for the path C' on the surface.
Answer:
A) ( -8, -32 )
Step-by-step explanation:
Given function : f (x,y) = 21 - 4x^2 - 16y^2
point p( 1,1,1 ) on surface
Gradient of F
attached below is the detailed solution
Simplify . 7+ the square root of 6(3+4)-2+9-3*2^2 The solution is
Answer:
7+sqrt(37)
Step-by-step explanation:
7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)
Which graph shows the polar coordinates (-3,-) plotted
Which function below has the following domain and range?
Domain: { -6, -5,1,2,6}
Range: {2,3,8)
{(2,3), (-5,2), (1,8), (6,3), (-6, 2)
{(-6,2), (-5,3), (1,8), (2,5), (6,9)}
{(2,-5), (8, 1), (3,6), (2, - 6), (3, 2)}
{(-6,6), (2,8)}
Answer:
{(2,3), (-5,2), (1,8), (6,3), (-6, 2)
Step-by-step explanation:
The domain is the input and the range is the output
We need inputs of -6 -5 1 2 6
and outputs of 2 3 and 8
evaluate the expression 4x^2-6x+7 if x = 5
Answer:
77
Step-by-step explanation:
4x^2-6x+7
Let x = 5
4* 5^2-6*5+7
4 * 25 -30 +7
100-30+7
7-+7
77
The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.
Answer:
7/11 = 0.6363...
Step-by-step explanation:
7 + 4 = 11
probability of winning: 7/11 = 0.6363...
The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]
Given that the odds of the horse winning the race is 7:4
Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:
[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]
From the given question;
The probability of the horse winning the race is:
[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]
[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]
Learn more about probability here:
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A normal distribution has a mean of 30 and a variance of 5.Find N such that the probability that the mean of N observations exceeds 30.5 is 1%.
Answer:
109
Step-by-step explanation:
Use a chart or calculator to find the z-score corresponding to a probability of 1%.
P(Z > z) = 0.01
P(Z < z) = 0.99
z = 2.33
Now find the sample standard deviation.
z = (x − μ) / s
2.33 = (30.5 − 30) / s
s = 0.215
Now find the sample size.
s = σ / √n
s² = σ² / n
0.215² = 5 / n
n = 109
A fair die is tossed once, what is the probability of obtaining neither 5 nor 2?
Answer:
4/6 or 66.666...%
Step-by-step explanation:
If you want to find the probability of obtaining neither a 5 nor a 2 you find how many times they occur and add them together in this case 5 occurs once and 2 also occurs once out of 6 numbers so 1/6 + 1/6 equals 2/6, you now know that 4/6 of them won't be a 5 nor a 2 and because it is a fair die the likelihood of it falling on a number is the same for all sides so the answer is 4/6 or 66.67%.
Evaluate integral _C x ds, where C is
a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)
b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)
Answer:
a. [tex]\mathbf{36 \sqrt{5}}[/tex]
b. [tex]\mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]
Step-by-step explanation:
Evaluate integral _C x ds where C is
a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)
i . e
[tex]\int \limits _c \ x \ ds[/tex]
where;
x = t , y = t/2
the derivative of x with respect to t is:
[tex]\dfrac{dx}{dt}= 1[/tex]
the derivative of y with respect to t is:
[tex]\dfrac{dy}{dt}= \dfrac{1}{2}[/tex]
and t varies from 0 to 12.
we all know that:
[tex]ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \ \ dt[/tex]
∴
[tex]\int \limits _c \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt[/tex]
[tex]= \int \limits ^{12}_{0} \ \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2}) \ dt[/tex]
[tex]= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0[/tex]
[tex]= \dfrac{\sqrt{5}}{4}\times 144[/tex]
= [tex]\mathbf{36 \sqrt{5}}[/tex]
b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)
Given that:
x = t ; y = 3t²
the derivative of x with respect to t is:
[tex]\dfrac{dx}{dt}= 1[/tex]
the derivative of y with respect to t is:
[tex]\dfrac{dy}{dt} = 6t[/tex]
[tex]ds = \sqrt{1+36 \ t^2} \ dt[/tex]
Hence; the integral _C x ds is:
[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]
Let consider u to be equal to 1 + 36t²
1 + 36t² = u
Then, the differential of t with respect to u is :
76 tdt = du
[tex]tdt = \dfrac{du}{76}[/tex]
The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145
Thus;
[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]
[tex]\mathtt{= \int \limits ^{145}_{0} \sqrt{u} \ \dfrac{1}{72} \ du}[/tex]
[tex]= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}[/tex]
[tex]\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}[/tex]
[tex]\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]
Researchers recorded that a certain bacteria population declined from 450,000 to 900 in 30 hours at this rate of decay how many bacteria will there be in 13 hours
Answer:
30,455
Step-by-step explanation:
Exponential decay
y = a(1 - b)^x
y = final amount
a = initial amount
b = rate of decay
x = time
We are looking for the rate of decay, b.
900 = 450000(1 - b)^30
1 = 500(1 - b)^30
(1 - b)^30 = 0.002
1 - b = 0.002^(1/30)
1 - b = 0.81289
b = 0.1871
The equation for our case is
y = 450000(1 - 0.1871)^x
We are looking for the amount in 13 hours, so x = 13.
y = 450000(1 - 0.1871)^13
y = 30,455
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k)left parenthesis, k, right parenthesis she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.
How many kilometers can Pamela drive with 12 liters of fuel?
Answer:
132 kilo meters
Step-by-step explanation:
Pro por tions:
9 lite rs ⇒ 99 km
12 lite rs ⇒ P km
P = 99*12/9
P = 132 km
Answer:
132
Step-by-step explanation:
give person above brainliest :))
A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.
(a) If the initial distribution for states A, B, and C is P0 = ( 1／3 , 1／3 , 1／3 ), find the distribution of X2
(b) Find the steady state distribution by solving πP = π.
Answer:
A) distribution of x2 = ( 0.4167 0.25 0.3333 )
B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]
Step-by-step explanation:
Hello attached is the detailed solution for problems A and B
A) distribution states for A ,B, C:
Po = ( 1/3, 1/3, 1/3 ) we have to find the distribution of x2 as attached below
after solving the distribution
x 2 = ( 0.4167, 0.25, 0.3333 )
B ) finding the steady state distribution solving
[tex]\pi p = \pi[/tex]
below is the detailed solution and answers
Which of the following is an even function? f(x) = (x – 1)2 f(x) = 8x f(x) = x2 – x f(x) = 7
Answer:
f(x) = 7
Step-by-step explanation:
f(x) = f(-x) it is even
-f(x)=f(-x) it is odd
f(x) = (x – 1)^2 neither even nor odd
f(x) = 8x this is a line odd functions
f(x) = x^2 – x neither even nor odd
f(x) = 7 constant this is an even function
Answer:
answer is f(x)= 7
Step-by-step explanation:
just took edge2020 test
99 litres of gasoline oil is poured into a cylindrical drum of 60cm in diameter. How deep is the oil in the drum?
Answer:
35 cm
Step-by-step explanation:
The volume of a cylinder is given by ...
V = πr²h
We want to find h for the given volume and diameter. First, we must convert the given values to compatible units.
1 L = 1000 cm³, so 99 L = 99,000 cm³
60 cm diameter = 2 × 30 cm radius
So, we have ...
99,000 cm³ = π(30 cm)²h
99,000/(900π) cm = h ≈ 35.01 cm
The oil is 35 cm deep in the drum.
solve the equation
Answer:
x = 10
Step-by-step explanation:
2x/3 + 1 = 7x/15 + 3
(times everything in the equation by 3 to get rid of the first fraction)
2x + 3 = 21x/15 + 9
(times everything in the equation by 15 to get rid of the second fraction)
30x+ 45 = 21x + 135
(subtract 21x from 30x; subtract 45 from 135)
9x = 90
(divide 90 by 9)
x = 10
Another solution:
2x/3 + 1 = 7x/15 + 3
(find the LCM of 3 and 15 = 15)
(multiply everything in the equation by 15, then simplify)
10x + 15 = 7x + 45
(subtract 7x from 10x; subtract 15 from 45)
3x = 30
(divide 30 by 3)
x = 10
