A plane flew for 4 hours heading south and for 6 hours heading east. If the total distance traveled was 3,370 miles, and the plane traveled 45 miles per hour faster heading south, at what speed was the plane traveling east?
The plane was traveling at 319 miles per hour heading east. This was determined by setting up equations for the distances covered in both directions, considering the speed difference, and solving for the eastward speed.
To find the speed at which the plane was traveling east, we need to set up two equations based on the given information.
Let's denote the speed of the plane heading east [tex]v_e[/tex] and the speed of the plane heading south [tex]v_s[/tex]. According to the problem, [tex]v_s[/tex] = [tex]v_e[/tex] + 45 mph. We also know that the plane flew south for 4 hours and east for 6 hours, covering a total distance of 3,370 miles.
To represent the sum of distances covered in both directions, we use the equation:
4[tex]v_s[/tex] + 6[tex]v_e[/tex] = 3,370
Substituting [tex]v_s[/tex] with [tex]v_e[/tex] + 45 in the equation yields:
4([tex]v_e[/tex] + 45) + 6[tex]v_e[/tex] = 3,370
By simplifying and solving for [tex]v_e[/tex], we find the speed of the plane traveling east. Let's solve it step by step:
4[tex]v_e[/tex] + 180 + 6[tex]v_e[/tex] = 3,370
10[tex]v_e[/tex] + 180 = 3,370
10[tex]v_e[/tex] = 3,190
[tex]v_e[/tex] = 319 mph
Therefore, the plane was traveling at 319 miles per hour heading east.
Identify each statement as true or false, show how you would rewrite it to make it a statement.
A salesperson earns a base salary of $36,000 plus 2 1/2% commission on sales. His total sales for one year was $500,000. Find the salesperson's total pay for that year.
To calculate the salesperson's total annual pay, we add the commission earned from the total sales to the base salary. The commission is $12,500, and the base salary is $36,000, resulting in a total pay of $48,500.
Explanation:The question asks us to determine the total pay for a salesperson with a base salary and a commission percentage on total sales. To find the salesperson's total pay for a year, we calculate the commission earned from total sales and add it to the base salary. The salesperson's commission is 2 1/2% of $500,000, which can also be written as 0.025. We calculate the commission by multiplying 0.025 by $500,000, which equals $12,500. Therefore, the total pay for the salesperson for that year is the sum of the base salary of $36,000 plus the commission of $12,500, which gives us $48,500.
Add or subtract the following mixed numbers using the first method. Be sure your answers are in mixed number format and reduced to lowest terms. 3 3/8 + 2 1/6 =
24x2+25x−47=(−8x−3)(ax−2)−53
jane drinks 3 1/2 pints of milk a day. how much is this in cups?
How to factor 4(x+5)^3(x-1)^2-(x+5)^4 • 2 (x-1) by grouping?
Reducing the original price of an item is often called
Answer:
Price reduction.Step-by-step explanation:
The act of reducing the selling price of products in order to attract costumers is called Price Reduction. This comprehends a marketing strategy.
Find the area of the shaded segment. Round your answer to the nearest square centimeter. Will make brainliest answer if correct :)
car rental in Thailand cost $35 per day when booked in advance. If rented locally you would be charged 1800 bahts per day. If the exchange rate is 40 bahts equals $1 how much cheaper is it to book in advance
Answer:
advance booking is cheaper by 400 bahts or $10.
Step-by-step explanation:
Car rental cost in advanced booking = $35 per day
and
when the rented locally it is charged = 1800 bahts per day
it is given that,
$1 is equal to 40 bahts.
now,
Car rental cost in advanced booking = 35 × 40
= 1400 bahts
hence, when booking is done advance
the cost is cheaper by 1800 - 1400 = 400 bahts
hence, advance booking is cheaper by 400 bahts or $10.
Which of the following nonlinear inequalities is graphed below? Picture included below!! PLEASE HELP ASAP!
Answer:
The correct option is A.
Step-by-step explanation:
The general form of an ellipse is
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Where, (0,0) is the center of ellipse, (±a,0) are x-intercepts and (0,±b) are y-intercepts.
From the given graph it is clear that the center of ellipse is (0,0), (±2,0) are x-intercepts and (0,±4) are y-intercepts. So, the equation of ellipse is
[tex]\frac{x^2}{(2)^2}+\frac{y^2}{(4)^2}=1[/tex]
[tex]\frac{x^2}{4}+\frac{y^2}{16}=1[/tex]
The shaded region is inside the ellipse, (0,0) lie in the solution set and the points lie on the ellipse are included in the solution set, therefore the sign of inequality is ≤.
[tex]\frac{(0)^2}{4}+\frac{(0)^2}{16}\leq 1[/tex]
[tex]0\leq 1[/tex]
This statement is true. The required inequality is
[tex]\frac{x^2}{4}+\frac{y^2}{16}\leq 1[/tex]
Therefore, the correct option is A.
A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time/4347395/f56da09a?utm_source=registration
Look at the quadratic equation below. x2 - 10x + 16 = -5 What is this quadratic equation written in standard form? A.5x2 + 10x - 16 = 0 B.5x2 - 10x + 16 = 0 C.x2 - 10x + 11 = 0 D.x2 - 10x + 21 = 0
Sixty dash fivesixty-five percent of households say they would feel secure if they had? $50,000 in savings. you randomly select 88 households and ask them if they would feel secure if they had? $50,000 in savings. find the probability that the number that say they would feel secure is? (a) exactly? five, (b) more than? five, and? (c) at most five.
To solve the following problems, we use the binomial probability equation:
P (r) = [n!/(n-r)! r!] p^r q^(n-r)
where,
n = total number of households = 8
r = number of sample
p = probability of success = 65% = 0.65
q = probability of failure = 0.35
A. r = 5
P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3
P (r=5) = 0.28
B. r >5
P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2
P (r=6) = 0.26
P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1
P (r=7) = 0.14
P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0
P (r=8) = 0.03
Therefore total is:
P (r>5) = 0.26 + 0.14 + 0.03 = 0.43
C. r ≤ 5
P (r ≤ 5) = 1 - P (r>5)
P (r ≤ 5) = 1 – 0.43
P (r ≤ 5) = 0.57
Identify the domain of the exponential function shown in the following graph: (2 points) Exponential graph starting at point 0, 30000 and approaching the x axis as it moves left to right. Select one: a. all real numbers b. x ≥ 0 c. 0 ≤ x ≤ 30,000 d. 7 ≤ x ≤ 30,000
Answer: b. [tex]x\geq 0[/tex] , where x is the positive real numbers.
Step-by-step explanation:
We Know that, The Set of all Possible values of independent variable is called Domain of the function.
Since, Exponential graph starting at point (0, 30000),
Thus, the initial value of value of independent variable is 0.
Also, The given exponential function is approaching the x axis as it moves left to right.
Therefore, The Domain must contain the all positive real numbers.
Thus, the Domain of the given function is [tex]x\geq 0[/tex] , where x is the positive real numbers.
Therefore, Option b is correct.
Use the direct variation equation y=x/4 to solve for x when y =60
Draw a quadrilateral with the given description
A rhombus with 6-centimeter sides and two 80 degree angles
Answer:
Step-by-step explanation:
By definition, a quadrilateral is a general term for a parallelogram and a rhombus. They are both 4-sided two-dimensional shapes with two sets of parallel sides. However, a rhombus is a special case. It has equal sides. Consequently, all its angles are equal. Therefore, the resultant drawing is alike to what's in the attached picture. But technically, all its sides are equal to 6 cm and all its angles are equal to 80°.
You place a cup of 200 degrees F coffee on a table in a room that is 67 degrees F, and 10 minutes later, it is 195 degrees F. Approximately how long will it be before the coffee is 180 degrees F? Use Newton's law of cooling: T(t)=T[a]+(T[o]-T[a])e^-kt A. 40 minutes B. 15 minutes C. 1 hour D. 35 minutes
In a study of blood donors, 200 were classified as group O and 250 had a classification other than group O. What is the probability that a person will have group O blood? (Enter your answer as a fraction.)
if 3×1=34 2×3=65 6×1=67 5×4=209 then 6×3=
Answer:
189 is the answer
Step-by-step explanation:
Traveling at 65 miles/hour, how many feet can you travel in 22 minutes? How do you know?
What are the domain and range of f(x)=1/5x
A total of 634 tickets were sold for the school play. They were either adult tickets or student tickets. There were 66 fewer students tickets sold than adult tickets. Him many adult tickets were sold?
For his long long distance phone service Chris pays a $6 monthly fee plus 8 cents per minute. Last month, Chris's long distance bill was $11.52. For how many minutes was Chris billed
total bill would be X=6.00 +0.08m
where m = minutes
X = total bill
so 11.52 = 6.00+0.08m
subtract 6 from each side
5.52 = 0.08m
now divide both sides by 0.08
5.52/0.08 = 69
he was billed for 69 minutes.
Find the quotient of 3 1/8 and 1 2/7 .
find the sum
5^71+5^72+5^73=?
this figure is a regular 12 sided polygon and measure of a angle is 4
You have $36,948.61 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until your account totals $280,000. you expect to earn 11% annually on the account. how many years will it take to reach your goal? round your answer to two decimal places at the end of the calculations.
Which system is equivalent to
y= 9x^2
x+y=5
?
Answer : Option A
Explanation:
we can clearly see that from x+ y=5 we can substitute y = 5-x in y = 9x^2
Option B is clearly incorrect x can not be y -5
Option C is incorrect because y can not be 5 +x
Option D is incorrect because its y = 9x^2 not y^2 =9x^2 so y can not be 3x
if its y^2 = 9x^2 then only implies y = 3x
Answer:
Option 1st is correct
[tex]5-x= 9x^2[/tex]
[tex]y = 5-x[/tex]
Step-by-step explanation:
Given the equations:
[tex]y = 9x^2[/tex] .....[1]
[tex]x+y = 5[/tex] .....[2]
We can write equation [2] as:
[tex]y = 5-x[/tex]
Now, substitute this y value in [1] we have;
[tex]5-x= 9x^2[/tex]
Therefore, the system which is equivalent to the given system equation is,
[tex]5-x= 9x^2[/tex]
[tex]y = 5-x[/tex]
4^2(2^3-3)^1+8(2-1)^10