Answer:
A rational number is a number that can be written as a fraction.
A. 7.11
=> 711/100
So, the 1st option is a rational number.
B. 4.333....
=> 4 1/3
=> 13/3
So, the 2nd option is a rational number.
C. 8/11
=> This is in its fractional form.
=> So, the 3rd option is a rational number.
D. -2852664798743
=> This can't be written in a fractional form.
=> So, the 4th option is NOT a rational number.
I need help with this ! ❤️
Answer:
The correct answer is: (x,y)↦(x+ 8 ,y+ 16)
Hoped I helped
Simplify the expression below.
w^2-9
_____
w^2-4w-21
A. 3
_
4w+7
B. -9
—
-4w-21
C. w-3
___
w-7
D. w+3
___
w+7
Answer:
D
Step-by-step explanation:
w² - 9 can be factored as (w + 3)(w - 3) using the difference of squares. To factor w² - 4w - 21, we need to find 2 integers that have a sum of -4 and product of -21; these integers are -7 and 3 so the factored form is (w + 7)(w - 3). Therefore, the expression becomes:
(w + 3)(w - 3) / (w + 7)(w - 3)
Both the numerator and denominator have a factor of (w - 3) so that cancels out, leaving us with (w + 3) / (w + 7).
The price of a technology stock was $9.69 yesterday. Today, the price fell to $9.58 . Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answer:
1.1% decrease
Step-by-step explanation:
Use the formula, % change = (difference/original) x 100
Plug in the values:
% change = ((9.69 - 9.58) / 9.69) x 100
= 1.1% decrease
Micah was given $200 for his birthday. Each week he spends $15 on comic books. In how many weeks will his birthday money be gone?
Answer:
13 weeks
Step-by-step explanation:
V = -15 x + 200 x 213.33 weeks 6 = -15x + 200 after 13 weeks.
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
The number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.
Given,
Micah was given $200 for his birthday.
Each week he spends $15 on comic books.
We need to find in how many weeks will his birthday money be gone.
How to compare two units in proportion?We need to make sure we get the required value on the left side.
If 1 week = 7 days
Find how many days in 2 weeks
2 weeks = 2 x 7 days = 14 days
We have 2 weeks on the left side.
If 2 items = $5
5/2 x 2 items = 5/2 x $5
5 items = $25/2 = $12.5
Find the total amount Micah has.
= $200
Find the amount spend each week.
= $15
Find how many weeks she must spend to spend $200.
We have,
$15 = 1 week
Multiply 200/15 on both sides.
200/15 x $15 = 200/15 x 1 week
$200 = 13.33 weeks
This means 13 weeks.
Thus the number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.
Learn more about how to find the number of weeks equal to 56 days here:
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Identify the property illustrated by the statement.
(3 + 6) + 6 = (6 + 3) + 6
Commutative
Associative
Distributive
Closure
Answer:
Associative
Step-by-step explanation:
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .10 significance level. Let p_M and p_F be the proportion of Men and Women who own cats respectively.
Based on a sample of 80 men, 40% owned cats
Based on a sample of 80 women, 51% owned cats
What is the test statistic and the critical value? Reject or Fail to Reject Null hypothesis?
Answer:
The test statistics is [tex]t = -1.40[/tex]
The critical value is [tex]Z_{\alpha } = 2.33[/tex]
The null hypothesis is rejected
Step-by-step explanation:
From the question we are told that
The sample size for men is [tex]n_1 = 80[/tex]
The sample proportion of men that own a cat is [tex]\r p _M = 0.40[/tex]
The sample size for women is [tex]n_2 = 80[/tex]
The sample proportion of women that own a cat is [tex]\r p_F = 0.51[/tex]
The level of significance is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \r p _M = \ r P_F[/tex]
The alternative hypothesis is [tex]H_a : \r p _M < \r p_F[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{(\r p_M - \r p_F)}{\sqrt{\frac{(p_M*(1-p_M)}{n_1 } } + \frac{p_F*(1-pF)}{n_2 } }[/tex]
=> [tex]t = \frac{(0.40 - 0.51)}{\sqrt{\frac{(0.40 *(1-0.41)}{80} } + \frac{0.51*(1-0.51)}{80 } }[/tex]
=> [tex]t = -1.40[/tex]
The critical value of [tex]\alpha[/tex] from the normal distribution table is
[tex]Z_{\alpha } = 2.33[/tex]
The p-value is obtained from the z-table ,the value is
[tex]p-value = P( Z < -1.40) = 0.080757[/tex]
=> [tex]p-value = 0.080757[/tex]
Given that the [tex]p-value < \alpha[/tex] then we reject the null hypothesis
On average the number of drum sets sold in Michigan each year is 96,537, which is seven times the average number of drum sets sold each year in Vermont. How many drum sets, on average, are sold each year in Vermont?
Answer:
13791
Step-by-step explanation:
Take 96,537 and divide by 7
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between and minutes. Find the probability that a randomly selected passenger has a waiting time minutes. 0 7 greater than 1.25
Complete Question
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answer:
The probability is [tex]P(X > 1.25) = 0.8214[/tex]
Step-by-step explanation:
From the question we are told that
The start time is a = 0 minutes
The end time is b = 7 minutes
Generally the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes is mathematically represented as
[tex]P(X > 1.25) = 1 - P(X \le 1.25)[/tex]
=> [tex]P(X > 1.25) = 1 - \frac{1.25 - a}{ b- a }[/tex]
=> [tex]P(X > 1.25) = 1 -0.1786[/tex]
=> [tex]P(X > 1.25) = 0.8214[/tex]
If a data set produces SSR = 400 and SSE = 100, then the coefficient of determination is a. .10. b. .80. c. .25. d. .40.
Answer: 0.8
Step-by-step explanation:
Given the following :
Sum of Square Error Error (SSE) = 100 which is the difference between the actual and predicted value.
Sum of Square due to regression (SSR) = 400
The Coefficient of determination (R^2) :
(Sum of Square Regression(SSR)) / Sum of Squared total (SST))
Sum of Squared total (SST) = SSE + SSR
Sum of Squared Total = (100 + 400) = 500
R^2 = 400 / 500
R^2 = 0.8
A company that prints Blue Books for exams makes a profit according to the number of books sold. Suppose that the Profit is
Answer:
The answer is not complete. I will explain the concept of profit to you.
Step-by-step explanation:
We can determine profit deducting direct costs (cost price) of commodities from sales (selling prices) of the commodities.
Profit = Selling Price - Cost Price
Example:
A trader buys some dresses for #2,500 in May and agrees to pay for it in three months’ time. He sells off all the dresses in August for #4,500. The profit for the month is #2,000.
The formula for percentage profit is [tex]\frac{profit * 100}{cost price}[/tex]
The formula for gross profit is Revenue – Cost of Sold Items
Profit Margin = [tex]\frac{Total Income}{Net Sales}[/tex] * 100
While Gross Profit Margin can be calculated as [tex]\frac{Gross Profit}{Net Sales}[/tex] * 100
Any of these formulas can be used to calculate profit-related questions.
can someone help me pllzz
Answer:
directrix: y=4
focus: (-3,2)
vertex: (-3,3)
Step-by-step explanation:
would you use the Law of Sines or the law of cosines to solve a triangle if. given all three sides of the triangle?
a. the Law of Sines
b. the Law of Cosines
Answer:
b. [tex]\displaystyle Law\:of\:Cosines[/tex]
Step-by-step explanation:
You would use this law under two conditions:
One angle and two edges defined, while trying to solve for the third edgeALL three edges definedHence, you have your answer.
* Just make sure to use the inverse function towards the end, or elce you will throw your answer off!
_______________________________________________
Now, you would use the Law of Sines under three conditions:
Two angles and one edge defined, while trying to solve for the second edgeOne angle and two edges defined, while trying to solve for the second angleALL three angles defined [of which does not occur very often, but it all refers back to the first bullet]* I HIGHLY suggest you keep note of all of this significant information. You will need it going into the future.
I am delighted to assist you at any time.
Answer:
Conditions for SINE RULE:
If two angles and any side is given.If two sides and an angle opposite one of the side is given.Conditions for COSINE RULE:
If two sides and an inclined angle is given.If all the three sides are give.Step-by-step explanation:
Side is the number in m/cm.
Angle is the number with degree/in degree. Like this: ° ° °
With all these, it means you should COSINE rule.
Find the value of 83 - [59 - (22 - 18)].
Answer:
28
Step-by-step explanation:
83 - [59 - (22-18)]
= 83 - [59 - 4]
= 83 - 55
= 28
Write an equation of the line below.
Answer:
y = x - 1
Step-by-step explanation:
sing the Divergence Theorem, find the outward flux of F across the boundary of the region D. F = x2i + y2j + zk; D: the solid cube cut by the coordinate planes and the planes x = 2, y = 2, and z = 2
Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]
Div and Curl:
[tex]\displaystyle \text{div \bf{F}} = \nabla \cdot \textbf{F}[/tex][tex]\displaystyle \text{curl \bf{F}} = \nabla \times \textbf{F}[/tex]Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]
First, let's define what we are given:
[tex]\displaystyle \text{F} = x^2 \hat{\i} + y^2 \hat{\j} + z \hat{\text{k}}[/tex]
Region D is the solid cube cut by coordinate planes and planes [tex]x = 2[/tex]. [tex]y = 2[/tex], and [tex]z = 2[/tex]
Step 2: WorkIn order to use the Divergence Theorem, we first must find div F. We use partial differentiation and differentiation properties found under "Calculus" to attain div F:
[tex]\begin{aligned}\nabla \cdot \text{F} & = \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial z}(z) \\& = 2x + 2y + 1 \\\textbf{div} \ \text{F} & = \boxed{2x + 2y + 1}\end{aligned}[/tex]
∴ [tex]\displaystyle \boxed{ \textbf{div} \ \text{F} = 2x + 2y + 1 }[/tex]
In order to find the outward flux of F across region D, we now must use the Divergence Theorem. Substitute our knowns into the Divergence Theorem Formula listed under "Multivariable Calculus":
[tex]\displaystyle \iiint_D \nabla \cdot \textbf{F} \, dV = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz[/tex]
We can now evaluate the Divergence Theorem integral using basic + advanced integration techniques listed under "Calculus" and learned from "Multivariable Calculus":
[tex]\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dz \, dy \, dx \\& = \int\limits^2_0 \int\limits^2_0 {(2x + 2y + 1)z \bigg| \limits^2_0} \, dy \, dx \\& = 2 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dy \, dx \\& = 2 \int\limits^2_0 {\bigg( 2xy + y^2 + y \bigg) \bigg| \limits^2_0} \, dx \\\end{aligned}[/tex]
[tex]\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = 2 \int\limits^2_0 {4x + 6} \, dx \\& = 2 \bigg[ 2x^2 + 6x \bigg] \bigg| \limits^2_0 \\& = 2(20) \\& = \boxed{40} \\\end{aligned}[/tex]
∴ the integrals evaluates to 40.
Answer:[tex]\displaystyle \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz = \boxed{40}[/tex]
___
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___
Topic: Multivariable Calculus
Unit: Stokes' Theorem and Divergence Theorem
Kara needs to fence her yard. How many feet of fencing is needed?
A. 370 feet
B. 500 feet
C. 13, 700 feet
D. 15, 000 feet
Answer:
newzz new new me he new new
Answer:
oiuhj90pkomnjhb vcfgtyu789i0op,lmkn bvghyu7890opklmnjbhgvfty67890-p[lkjhngvty67u890-op[l;',
Step-by-step explanation:
Pythagorean Theorem:a2 + b2 = c2 Re−write the formula solving for b2 .
Answer: c2 - a2 = b2
Step-by-step explanation: to isolate b2 you have to subtract a2 from both sides to get c2 - a2 = b2
Find the missing term in the
geometric sequence.
13,[ ? 1,208
Answer:
Step-by-step explanation:
Step 1: the first term a is 13
Which means a=13 let's make this equation i
And the third term ar^3-1 = 1208
= Ar²= 1208 let's make this equation ii
Step 2: subtititute equation i into equation ii
= 13r²=1208
Divide both sides by 13 it gives us
13r²/13 = 1208/13
r²= 92.92
r= 9.64
So the second term ar^2-1
=ar
= 13. 9.64
= 125.32
The average age of Iowa residents is 37 years. Amy believes that the average age in her hometown in Iowa is not equal to this average and decided to sample 30 citizens in her neighborhood. Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311. What is the p-value of the test statistic? Answer choices are rounded to the hundredths place.
Answer:
0.10
Step-by-step explanation:
Average age of Iowa residents = 37 years
Amy believes that the average age in her hometown in Iowa is not equal to this average
Alternative hypothesis : µ ≠ 37
Sample size = 30
t - test statistic = 1.311
The p-value of the test statistic can be obtained using the online p-value calculator :
The p- value obtained using a t-test statistic value of 1.311 and a degree of freedom (df =N-1; 30 - 1 = 29) at a 0.05 significance level = 0.100072 = 0.10 ( nearest hundredth)
Answer:
0.20
Step-by-step explanation:
In order to find the p-value we first need the degrees of freedom because we are running a t-test. The df = n-1 = 30-1 = 29. If Amy is using the alternative hypothesis, µ ≠ 531, this is a two-tailed test. In order to find the p-value, we simply need to find the probability of being as extreme or more extreme as our current test statistic in one-tail and then multiply it by 2. Another way to describe this is it is the tail probability/area. If we go to the df row of 29 and then scan to the right we see 1.311 is in the 0.10 column. So if we multiply this by 2, we find 0.20 or 20% in both of the tails. So the p-value is 0.20.
is -3/8 greater than - 2/7
What is the result of subtracting the polynomial (x²+3x) from the polynomial (-2x + 4x² + 5) ? A 3x² - x -5 B -3x²+x +5 C 3x² - 5x + 5 D -3x² + 5x - 5
Answer:
C
Step-by-step explanation:
We need to first rewrite the equation the proper way.
(-2x+4x²+5)-(x²+3x)
We need to distribute the negative thought the 2nd set of parenthesis.
-2x+4x²+5-x²-3x
combine the same terms
3x²-5x+5
Find the least whole number that can replace _
to make the statement true.
_ ÷ 17 > 99
The _ can be replaced with?
Answer:
1684
Step-by-step explanation:
x ÷ 17 > 99
x > 17 * 99
x > 1683
The least whole number that is greater than 1683 is 1684.
Answer: 1684
Answer:
1683
Step-by-step explanation:
To undo the problem you do 99 times 17 which is 1683. Then you know that 1683 divided by 17 is 99.
solve for p 7(p-9)=34.3
Answer: p = 13.9
Step-by-step explanation: 7(p-9) = 34.3 multiply 7 into p and -9
7p - 63 = 34.3 add 63 into both sides
7p = 97.3 divide 7 into both sides.
p = 13.9
This question can be solved in two ways
the equation given is 7(p-9)=34.3
The first step to take is to divide both sides of the equation by 7
p - 9 = 34.3 / 7
p - 9 = 4.9
The second step is to combine similar terms
p = 4.9 + 9 = 13.9
A second method
the equation given is 7(p-9)=34.3
1. expand the bracket
7p - 63 = 34.3
2. Combine similar terms
7p = 34.3 + 63
7p = 97.3
3. Divide both sides of the equation by 7
p = 13.9
A similar question was solved here: https://brainly.com/question/20432589?referrer=searchResults
If you have 200 cupcakes and you give 90 how many do you have left
Answer:
110 cupcakes are left
Step-by-step explanation:
200-90 is 110
Answer:
110 cupcakes
Step-by-step explanation:
If you have 200 cupcakes and you give away 90, that means you only have [tex]200-90[/tex] cupcakes left.
[tex]200 - 90 = 110[/tex]
So you have 110 cupcakes left.
Hope this helped!
Torricelli's hypothesis was consistent with the hypothesis that nature abhors a vacuum.
a. True
b. False
Answer:
False
Step-by-step explanation:
Torricelli once carried out a tube and mercury experiment to test the scientific claim that nature abhors a vacuum.
In his experiment, he used glassblowers to make a long glass tube which was 4 ft long with a closed end.
He filled the tube with mercury and put his finger over the open end. Thereafter, he turned the tube upside down, dipped the open end in a bowl of mercury, and then removed his finger from the open end. He discovered that the mercury in the tube didn't completely run out as it fell to around 30 inches above the bowl before it stopped.
The gap between the sealed top end of the tube and the top end of the fallen mercury was an empty space which is a vacuum.
The hypothesis that "nature abhors a vacuum" would have implied that the vacuum would have pulled the mercury and held it up in the tube. However, that wasn't the case with his experiment and it proves that nature doesn't abhor a vacuum.
Thus, it is false.
A mountain biker gets halfway up a hill and realizes he forgot his water, so he returns to his starting point.
Answer:
True
Explanation:
1/2 (up the hill) - 1/2 (down the hill) = 0
Your math professor gives you a set of 10 problems and tells you that the final exam will consist of a random selection of 5 of them. If you figured out how to do 7 of the problems, what is the probability that you answer correctly (a) all 5 problems
Answer:
0.083
Step-by-step explanation:
To solve the above question, we use the combination method.
C(n, r) = nCr = n!/r!(n - r)!
Probability of answering (all 5 correctly)
= Probability of answering ( 5 out of 7 correctly)/ Probability of answering (5 out of 10 problems)
Probability of answering ( 5 out of 7 correctly) = 7C5
nCr = n!/r!(n - r)!
= 7!/5! (7 - 5)!
= 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (2 × 1)
= 21 ways
Probability of answering (5 out of 10 problems) = 10C5
nCr = n!/r!(n - r)!
= 10!/5! (10 - 5)!
= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (5 × 4 × 3 × 2 × 1)
= 252 ways
Probability of answering (all 5 correctly)
= 21/252
= 0.0833333333
Approximately = 0.083
PLEASE HELP ME, I DON'T UNDERSTAND THIS! :(
Answer:
1/204
Step-by-step explanation:
6/18 * 5/17 * 4/16 * 3/15
= 1/3 * 5/17 * 1/4 * 1/5
= 1/204
A medical researcher wants to compare the pulse rates of smokers and non-smokers. He believes that the pulse rate for smokers and non-smokers is different and wants to test this claim at the 0.01 level of significance. A sample of 75 smokers has a mean pulse rate of 76, and a sample of 73 non-smokers has a mean pulse rate of 72. The population standard deviation of the pulse rates is known to be 9 for smokers and 10 for non-smokers. Let µ1 be the true mean pulse rate for smokers and µ2 be the true mean pulse rate for non-smokers.
Step 1 of 5: State the null and alternative hypotheses for the test.
Step 2 of 5: Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 5: Find the p-value associated with the test statistic. Round your answer to four decimal places.
Step 4 of 5: Make the decision for the hypothesis test.
Step 5 of 5: State the conclusion of the hypothesis test.
Answer:
We conclude that the pulse rate for smokers and non-smokers is equal.
Step-by-step explanation:
We are given that a medical researcher wants to compare the pulse rates of smokers and non-smokers.
A sample of 75 smokers has a mean pulse rate of 76, and a sample of 73 non-smokers has a mean pulse rate of 72. The population standard deviation of the pulse rates is known to be 9 for smokers and 10 for non-smokers.
Let [tex]\mu_1[/tex] = true mean pulse rate for smokers
[tex]\mu_2[/tex] = true mean pulse rate for non-smokers
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that the pulse rate for smokers and non-smokers is same}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that the pulse rate for smokers and non-smokers is different}
The test statistics that will be used here is Two-sample z-test statistics because we know about the population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1}+\frac{\sigma_2^{2} }{n_2}} }[/tex] ~ N(0,1)
where, [tex]\bar X_1[/tex] = sample mean pulse rate of smokers = 76
[tex]\bar X_2[/tex] = sample mean pulse rate of non-smokers = 72
[tex]\sigma_1[/tex] = population standard deviation of the pulse rates of smokers = 9
[tex]\sigma_2[/tex] = population standard deviation of the pulse rates of non-smokers = 10
[tex]n_1[/tex] = sample of smokers = 75
= sample of smokers = 73
So, the test statistics = [tex]\frac{(76-72)-(0)}{\sqrt{\frac{9^{2} }{75}+\frac{10^{2} }{73}} }[/tex]
= 2.56
The value of the z-test statistics is 2.56.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 2.56) = 1 - P(Z [tex]\leq[/tex] 2.56)
= 1 - 0.9948 = 0.0052
For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0052 = 0.0104.
Now, at a 0.01 level of significance, the z table gives a critical value of -2.58 and 2.58 for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the pulse rate for smokers and non-smokers is equal.
Solve and graph the following inequality
Answer:
x is greater than 4
Step-by-step explanation:
4x + 5 is greater than 13
you want to find out what x is
4 - 4 x + 5 is greater than 13 - 4 ( whatever you do to one side you have to do to the other)
x + 5 is greater than 9
x + 5 - 5 is greater than 9 - 5
x is greater than 4