Answer:
y = (x - 4)² + 2 , x ≥ 4.
Step-by-step explanation:
Finding the inverse of
f(x) = 4 + √(x - 2)
Begin by swapping the x and y variables in the equation:
x = 4 + √(y - 2)
Subtract 4 from both sides:
x - 4 = √(y - 2)
Square both sides:
(x - 4)² = y - 2
Add 2 to both sides to get your equation:
y = (x - 4)² + 2
However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.
If nine of every 11 trick-or-treaters that came to your house last Halloween were dressed as pirates what proportion of trick-or-treaters were not dressed as pirates
Answer:
11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.
Answer: Ratio is 2:11
Step-by-step explanation:
So your ratio of pirates to non-pirates would be 9:11
So you subtract number of pirates from total trick-or-treaters and get 2.
So the proportion of non-pirates would be 2:11.
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?
Answer:
3lbs
Step-by-step explanation:
From a group of graduate students including 25 men and 22 women, 37 are chosen to participate in a presentation. What is the probability that exactly 19 men and 18 women are chosen
Answer:
25.02% probability that exactly 19 men and 18 women are chosen
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
19 men, from a set of 25
18 women, from a set of 22
[tex]D = C_{25,19}*C_{22,18} = \frac{25!}{19!6!}*\frac{22!}{18!4!} = 1295486500[/tex]
Total outcomes:
37 people from a set of 25 + 22 = 47. So
[tex]T = C_{47,37} = \frac{47!}{37!10!} = 5178066751[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1295486500}{5178066751} = 0.2502[/tex]
25.02% probability that exactly 19 men and 18 women are chosen
Which of the following shows the intersection of the sets? {1, 5, 10, 15} {1, 3, 5, 7}
Answer:
{1,5}
Step-by-step explanation:
The intersection of the sets are all of the numbers that appear in both sets. In this case, the only numbers that appear in both are 1 and 5.
Answer:
{ 1,5}
Step-by-step explanation:
The intersection is what the two sets have in common
{1, 5, 10, 15}∩ {1, 3, 5, 7}
= { 1,5}
A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function f(x)=-5x2+6x+100 (graphed below) represents this situation where x is time and y is the distance off of the ground. will mart brainliest yeah
Answer:
a) The domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex] [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex], b) The range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex], c) The ball is 73 meters off of the ground at x = 3 seconds.
Step-by-step explanation:
The complete statement is: A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function [tex]f(x) = -5\cdot x^{2} + 6\cdot x + 100[/tex] represents this situation where x is time and y is the distance off of the ground.
a) What domain does the function make sense?
b) What range does the function make sense ?
c) How far off the ground is the ball at time x = 3 seconds?
a) Let [tex]x[/tex] and [tex]f(x)[/tex] be the time, measured in seconds, and the distance of the ground, measured in meters, respectively. Time is a positive variable, so domain corresponds to the interval when [tex]f(x) \geq 0[/tex] and [tex]t \geq 0[/tex]. That is:
[tex]-5\cdot x^{2} + 6\cdot x + 100 \geq 0[/tex]
[tex]-(x-5.112\,s)\cdot (x+3.912\,s) \geq 0[/tex]
Therefore, the domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex] [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex]
b) The distance off of the ground is also a positive variable, where ball is thrown upward at a height of 100 meters and hits the ground at a height of 0 meters. Hence, the range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex]
c) The distance of the ball off of the ground at x = 3 seconds is found by evaluating the function:
[tex]f(3\,s) = -5\cdot (3\,s)^{2} + 6\cdot (3\,s) + 100[/tex]
[tex]f(3\,s) = 73\,m[/tex]
The ball is 73 meters off of the ground at x = 3 seconds.
find the value of x if (1.1)^x=100
Answer:
x ≈ 48.3177
Step-by-step explanation:
This is what logarithms are for (among other things).
log(1.1^x) = log(100)
x·log(1.1) = 2
x = 2/log(1.1) ≈ 48.3177
how many different four letter permutations can be formed using four letters out of the first 12 in the alphabet?
Answer:
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Permutations of four letters from a set of 12 letters. So
[tex]P_{(12,4)} = \frac{12!}{(12-4)!} = 11800[/tex]
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Answer: it’s 11,880
not 11800
A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
The required length of the line is given as 14.4 feet, as of the given conditions.
As given in the question, A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow, to determine the length of the line.
What are Pythagorean triplets?In a right-angled triangle, its side, such as the hypotenuse, is perpendicular, and the base is Pythagorean triplets.
Here,
let the length of the line be x,
The scenario formed is right angle triangle,
Apply Pythagoras' theorem,
x² = 12² + 8²
x = √208
x = 14.4
Thus, the required length of the line is given as 14.4 feet, as of the given conditions.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ2
Give the three-letter name of each of the angles in the drawing below. Lines and Angles a. ∠1 b. ∠2 c. ∠3 d. ∠4
Answer:
a. AEB
b. BEC
c. CED
d. AED
Step-by-step explanation:
Each angle is made up of three points. All three points in order is the name of the angle.
Answer:
a. ∠1 = ∠AEB or ∠BEA
b. ∠2 = ∠BEC or ∠CEB
c. ∠3 = ∠CED or ∠DEC
d. ∠4 = ∠DEA or ∠AED
Step-by-step explanation: Penn <3
In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows: JG JH JM GJ GH GM HJ HG HM MJ MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The event A is defined as follows: A = event that Helen gets first prize List the outcomes that comprise the event ~A (not A).
Answer:
1. JG (Jim gets first prize, George gets second prize)
2. JH (Jim gets first prize, Helen gets second prize)
3. JM (Jim gets first prize, Maggie gets second prize)
4. GH (George gets first prize, Helen gets second prize)
5. GJ (George gets first prize, Jim gets second prize)
6. GM (George gets first prize, Maggie gets second prize)
7. MJ (Maggie gets first prize, Jim gets second prize)
8. MG (Maggie gets first prize, George gets second prize)
9. MH (Maggie gets first prize, Helen gets second prize)
Step-by-step explanation:
The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.
The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.
Jeff worked 4 and 2/3 hours in the morning and 3 and 3/4 hours in the afternoon. How many total hours did he work
1. 8 and 1/2 hours
2.7 and 5/7 hours
3.7 and 5/12 hours
4.8 and 5/12 hours
Answer:
4. 8 5/12
Step-by-step explanation:
4 2/3 + 3 3/4 =
= 4 + 2/3 + 3 + 3/4
= 4 + 3 + 8/12 + 9/12
= 7 + 17/12
= 7 + 12/12 + 5/12
= 7 + 1 + 5/12
= 8 5/12
pls help me help me
Answer:
A
Step-by-step explanation:
Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets.
Complete Question
Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. Could they take 9 children and 4 adults to both shows? Show your work. A yes or no answer is not sufficient for credit.
Answer:
Yes it is possible to take the 9 children and 4 adults to both shows
Step-by-step explanation:
From the question we are told that
The cost of the Matinee tickets for a child is z = $4
The cost of the Matinee tickets for an adult is a = $ 4
The cost of the Evening tickets for a child is k = $6
The cost of the Evening tickets for an adult is b = $8
The maximum amount to be spent on Matinee tickets is m = $80
The maximum amount to be spent on Evening tickets is e = $100
The number of child to be taken to the movies is n = 9
The number of adults to be taken to the movies is j = 4
Now the total amount of money that would be spent on Matinee tickets is mathematically evaluated as
[tex]t = 4 n + 4 j[/tex]
substituting values
[tex]t = 4 * 9 + 4* 4[/tex]
[tex]t = 52[/tex]
Now the total amount of money that would be spent on Evening ticket is mathematically evaluated as
[tex]T = 6n + 8j[/tex]
substituting values
[tex]T = 6(9) + 8(4)[/tex]
[tex]T = 86[/tex]
This implies that it is possible to take 9 children and 4 adults to both shows
given that
[tex]t \le m[/tex]
i.e $56 [tex]\le[/tex]$ 80
and
[tex]T \le e[/tex]
i.e $ 86 [tex]\le[/tex] $ 100
can anyone help me with this?
Answer: 16y² - x²
Step-by-step explanation: The - sign means a difference, so the choices with + signs are eliminated (though 64x² and 9 are squares)
10 is not a square so that one is eliminated (though the y² and the 4x² are squares)
16 is the square of 4, y² is the square of y, and x² is the square. That expression shows a difference of squares.
Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colors of 204 Scandinavian men and their female partners. The table below summarizes the results (rows represent male eye color while columns represent female eye color). For simplicity, we only include heterosexual relationships in this exercise.
(please round any numerical answers to 4 decimal places)
Blue Brown Green Total
Blue 78 23 13 114
Brown 19 23 12 54
Green 11 9 16 36
Total 108 55 41 204
a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?
b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?
c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?
d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?
e) Does it appear that the eye colors of male respondents and their partners are independent? Explain.
Answer:
a) P(male=blue or female=blue) = 0.71
b) P(female=blue | male=blue) = 0.68
c) P(female=blue | male=brown) = 0.35
d) P(female=blue | male=green) = 0.31
e) We can conclude that the eye colors of male respondents and their partners are not independent.
Step-by-step explanation:
We are given following information about eye colors of 204 Scandinavian men and their female partners.
Blue Brown Green Total
Blue 78 23 13 114
Brown 19 23 12 54
Green 11 9 16 36
Total 108 55 41 204
a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?
Using the addition rule of probability,
∵ P(A or B) = P(A) + P(B) - P(A and B)
For the given case,
P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)
P(male=blue or female=blue) = 114/204 + 108/204 − 78/204
P(male=blue or female=blue) = 0.71
b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?
As per the rule of conditional probability,
P(female=blue | male=blue) = 78/114
P(female=blue | male=blue) = 0.68
c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?
As per the rule of conditional probability,
P(female=blue | male=brown) = 19/54
P(female=blue | male=brown) = 0.35
d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?
As per the rule of conditional probability,
P(female=blue | male=green) = 11/36
P(female=blue | male=green) = 0.31
e) Does it appear that the eye colors of male respondents and their partners are independent? Explain
If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.
∵ P(B | A) = P(B)
P(female=blue | male=brown) = P(female=blue)
or alternatively, you can also test
P(female=blue | male=green) = P(female=blue)
P(female=blue | male=blue) = P(female=blue)
But
P(female=blue | male=brown) ≠ P(female=blue)
19/54 ≠ 108/204
0.35 ≠ 0.53
Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.
The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. For a 0.01 level of significance, what is the critical value for the rejection region? a. 7.173 b. 2.33 c. 6.635 d. 7.106
Answer:
Critical value: b. 2.33
As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
The significance level is 0.01.
The sample 1 (women), of size n1=150 has a proportion of p1=0.62.
The sample 2 (men), of size n2=200 has a proportion of p2=0.24.
The difference between proportions is (p1-p2)=0.38.
[tex]p_d=p_1-p_2=0.62-0.24=0.38[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{93+48}{150+200}=\dfrac{141}{350}=0.403[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.403*0.597}{150}+\dfrac{0.403*0.597}{200}}\\\\\\s_{p1-p2}=\sqrt{0.001604+0.001203}=\sqrt{0.002807}=0.053[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.38-0}{0.053}=\dfrac{0.38}{0.053}=7.17[/tex]
The critical value for a right-tailed test with a signficance level of 0.01 is zc=2.33 (see picture attached).
As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
Jason has bought a new pool and has already measured some of the sides. Using the figure below and your knowledge of quadrilaterals, solve for x and y.
Answer:
x = 12
y = 12
Step-by-step explanation:
Each triangle is a right angle triangle
5² + x² = 13²
x² = 169 - 25
x = √144
x = 12
The shape is a parallelogram
Therefore
x = y
y = 12
Below are the times (in days) it takes for a sample of 17 customers from Andrew's computer store to pay their invoices.
19.15, 43, 39, 35, 31, 27, 34, 34, 30, 30, 26, 26, 26, 21, 21, 17
Draw the histogram for these data using an initial class boundary of 14.5, an ending class boundary of 49.5, and 5 classes of equal width. Note that you can add
or remove classes from the figure. Label each class with its endpoints.
Frequency
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Answer:
Step-by-step explanation:
Hello!
The variable of interest is X: time it takes a customer from Andrew's computer store to pay his invoices.
You have the information of a sample of n= 17 customers
19, 15, 43, 39, 35, 31, 27, 34, 34, 30, 30, 26, 26, 26, 21, 21, 17
To determine the class width of the intervals for the divide the difference between the ending and initial class boundaries by the number of intervals that you want to determine:
Class width: (49.5-14.5)/5= 7
Then, starting from the initial class boundary, you have to add the class width to determine the next boundary, and so on until the ending class boundary:
Initial class boundary: 14.5
14.5 + 5.6= 20.1
1st interval: [14.5; 21.5]
and so on:
[21.5; 28.5]
[28.5; 35.5]
[35.5; 42.5]
[42.5; 49.5]
Once you determined all class intervals, you have to order the values of the data set from least to greatest and then count how many observations correspond to each interval and arrange it in a frequency table.
15, 17, 19, 21, 21, 26, 26, 26, 27, 30, 30, 31, 34, 34, 35, 39, 43
[14.5; 21.5] ⇒ 5
[21.5; 28.5] ⇒ 4
[28.5; 35.5] ⇒ 6
[35.5; 42.5] ⇒ 1
[42.5; 49.5] ⇒ 1
Once you have the data set organized in the table, you can proceed to draw the histogram.
(See attachment)
I hope this helps!
Mario and tabitha are calculating the probability of getting a 4 and a 2 if they roll a die twice. Who is correct?
Answer:
[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
4 = [tex]\frac{1}{12}[/tex]
2 = [tex]\frac{1}{12}[/tex]
[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]
Which of the following functions is graphed below?
Answer:
C
Step-by-step explanation:
C is the solution
Answer:
Option C
Step-by-step explanation:
The graph is a horizontal translation 4 units left and a vertical translation 2 units down ⇒ y= |x+4|-2
PLS HELP (pic included)
hope it helps uh.......
WHO CAN HELP ME WITH MY ACCOUNTING HOMEWORK???
Duran Manufacturing uses a process costing system and manufactures its product in three departments. Which of the following is NOT a way in which Duran can use the cost per unit of each process?
A) Duran can look for ways to cut the costs when actual process costs are more than planned process costs.
B) Duran needs to set the selling price to cover the costs of making the product and provide a profit.
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
D) Duran needs to know the ending balances in the following accounts: Work-In-Process Inventory, Finished Goods Inventory, and Cost of Goods Sold.
Answer:
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
Step-by-step explanation:
Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.
Find the value of x that will make a||b help ?
Answer:
x=30
Step-by-step explanation:
Find the value of x that will make A and B parallel
For A & B to be parallel, the interior angles must be supplementary, i.e.
4x+2x = 180
6x=180
x=30
When x=30, the interior angles are 120 and 60 which are supplementary.
Andrea and Helen participated in a donut eating contest. Andrea ate six more than four times the number of donuts that Helen ate. Let d represents the number of donuts Helen ate. Write the expression that gives the number of donuts that Andrea ate.
Answer:
4d + 6
Step-by-step explanation:
Helen ate d donuts.
Andrea ate 6 more than 4 times d.
4d + 6
The equation x2 − 6x − 27 = 0 when solved is:
Answer:
-3 , 9
Step-by-step explanation:
Sum = - 6
Product = -27
Factors = 3, -9
x² - 6x-27 = 0
x² + 3x - 9x - 9*3 = 0
x(x + 3) - 9(x + 3) = 0
(x + 3) (x - 9) = 0
x +3 = 0 ; x - 9 = 0
x = - 3 ; x = 9
Solution: x = -3 , 9
. A box contains four red, three yellow, and seven green balls. Three balls are randomly selected from the box without replacement. (a) What is the probability that all three balls are the same colo
Answer:
10/91
Step-by-step explanation:
Number of Red balls = 4
Number of Yellow balls = 3
Number of green balls=7
Total=4+3+7=14
If we pick three balls of the same color, there are three possibilities: (All Red, All Green Or all Yellow).
Therefore:
The probability that all three balls are the same color (note that the selections are without replacement)
=P(RRR)+P(GGG)+P(YYY)
[tex]=(\frac{4}{14} \times \frac{3}{13} \times \frac{2}{12})+(\frac{3}{14} \times \frac{2}{13} \times \frac{1}{12})+(\frac{7}{14} \times \frac{6}{13} \times \frac{5}{12})\\\\=\frac{1}{91} + \frac{1}{364}+ \frac{5}{52}\\\\=\frac{10}{91}[/tex]
The probability that all three balls are the same color is 10/91.
Overall Assessment Progress
Basic Office Skills
Question 5 of 47
1/4 + 7/8 = ?
Answer:
1 1/8
Step-by-step explanation:
1/4 + 7/8
Make denominators equal.
2/8 + 7/8
Add the fractions.
9/8
Convert to a mixed fraction.
1 1/8
Answer:
1 1/8
Step-by-step explanation:
1/4 + 7/8
Get a common denominator
1/4 * 2/2 + 7/8
2/8 + 7/8
9/8
Change to a mixed number
8/8+ 1/8
1 1/8
Write an equation that expresses the following relationship. w varies directly with u and inversely with d In your equation, use k as the constant of proportionality.
Step-by-step explanation:
solution.
if variable d increases then w reduces
w=k.u ×1/d
=ku/d
therefore w=k.u/d
Toby cuts a pizza into 6 equal slices. He eats half a slice. What fraction of the pizza has he eaten?
The pizza is cut into 6 slices so each slice would be 1/6 of the pizza.
He at 1/2 of a slice:
1/6 x 1/2 = 1/12 of the pizza
3.
A passenger jet can fly 1,290 mil
in 3 hours with a tailwind bi
1,230 miles in 3 hours
headwind. Find the speed
the Jet in Still air and the
of the wind.
Answer:
Jet= 420 mph Wind = 10mph
Step-by-step explanation:
The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.
The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.
This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.
So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.