Two planes, which are 3950 miles apart. fly toward each other. Their speeds differ by 40 mph. If they pass each other in 5 hours, what is the speedof each?Answer How to enter your answer (opens in new window) 3 PointsKeypad
Answers
Given the word problem, we can deduce the following information:
1. The two planes are 3950 miles apart.
2. Their speeds differ by 40 mph.
3. Time =5 hours
To determine the speed of each plane, we first let:
x= speed of the fist plane
x+40 =speed of the second plane
Based on the above information, the combined speed is 2x+40. Our equation would be:
\(2x+40=\frac{3950}{5}\)Next, we find the value of x:
\(\begin{gathered} 2x+40=\frac{3950}{5} \\ \text{Simplify and rearrange} \\ 2x+40=790 \\ 2x=790-40 \\ 2x=750 \\ x=\frac{750}{2} \\ \text{Calculate} \\ x=375 \end{gathered}\)Hence,
x= speed of the fist plane=375 mph
x+40 =speed of the second plane=375+40= 415 mph
Related Questions
As sample of 105 sanitation workers for the city of Euonymus, Texas, earns an average of $24,375 per year. The average salary for all Euonymus city workers is $24,230, with a standard deviation of $523. Are the sanitation workers overpaid? Conduct both one- and two-tailed tests.
Answers
The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
We have:
Average x = 24375
u = 24230
SD = 523
n = 105
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is overpaid.
u > 24230
Assume significance level = 0.05
From the Z-table:
Z(critical) = 1.645
Now,
Z = (x-u)/(SD/√n)
Z = (24375-24230)/(523/√105)
Z = 2.84
Z > Z(critical)
So, reject the null hypothesis.
The average salary of sanitation workers in the city of Euonymus is overpaid.
Now, from the two-tail test:
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is 24230
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is not 24230
u ≠ 24230
Assume significance level = 0.05
From the Z-table for the two-tail test:
Z(critical) = ±1.96
Now,
Z = 2.84
Z > z(critical)
∴ The average salary of sanitation workers in the city of Euonymus is not 24230.
Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
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What is the effective annual rate of an account that pays interest at the nominal rate of
7% per year, compounded daily? Compounded hourly?
Answers
Answer:
To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:
EAR = (1 + r/n)^n - 1
where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.
For daily compounding, n = 365 (since there are 365 days in a year), so we have:
EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%
To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:
EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%
Therefore, the effective annual rate for hourly compounding is approximately 7.27%.
It is expected that 30% of the criminals in our prisons are violent offenders, 65% are nonviolent, and 5% are actually innocent. A sample of 300 inmates showed that 90 were violent offenders, 200 were nonviolent, and 10 were innocent. At the .05 significance level, can we conclude that the observed frequencies are different than the expected frequencies?
Answers
Help plssssssssssssssss
Answers
take I don't know it's right or wrong I just guessing and saying to u .
78
Write the following expression using the fewest possible terms. (−4x − 15) + (17 + 7x)
Answers
Answer:
3x +2
Step-by-step explanation:
Write the following expression using the fewest possible terms.
(−4x − 15) + (17 + 7x) =
-4x -15 + 17 + 7x=
3x +2
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is
95% salt. She wants to obtain 60 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?
Answers
we know A is 45% salt, so the amount of salt in A is (45/100)*A or 0.45A.
likewise we know that B is 95% salt, so the salt amount in it is (95/100)*B or 0.95B.
\(\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.45&0.45x\\ B&y&0.95&0.95y\\ \cline{2-4}&\\ mixture&60&0.85&51 \end{array}~\hfill \begin{cases} x+y=60\\ 0.45x+0.95y=51\\[-0.5em] \hrulefill\\ y = 60 -x \end{cases}\)
\(\stackrel{\textit{substituting on the 2nd equation}}{0.45x+0.95(60-x) = 51}\implies 0.45x+57-0.95x=51 \\\\\\ 0.45x-0.95x=-6\implies -0.5x=-6\implies x = \cfrac{-6}{-0.5} \\\\\\ \boxed{x = 12}~\hfill \stackrel{\textit{we know that}}{y = 60 -x}\implies \boxed{y=48}\)
How do i solve this one
Answers
Answer:
900π
Step-by-step explanation:
Hello!
RadiusThe radius is represented by the function \(r(t) = 15\sqrt{t +2}\).
The radius of the ripple can be found when \(t=2\)
Solve:
\(r(t) = 15\sqrt{t + 2\)\(r(2) = 15\sqrt{2 +2}\)\(r(2) = 15\sqrt4\)\(r(2) = 15*2\)\(r(2) = 30\)The radius of the ripple is 30 inches
AreaThe area of a circle is calculated by the formula \(A = \pi r ^2\)
Given the radius is 30, we can find the area of the circle.
Solve:
\(A = \pi r^2\)\(A = \pi (30^2)\)\(A = 900\pi\\\)help quick please hw i needa A pls
Answers
16:4 = 9: X
Then we know
46 = X/9
Multiplying both sides by 9 cancels on the right
9 × (4/16) = (X/9) × 9
9 × (4/16) = X
Then solving for X
X = 9 × (4/16)
X = 2.25
Therefore
16:4 = 9: 2.25
Since
4:1 = 12: X
A little less criticism from you,
and Hayley will be just fine
Then we know
1/4 = X/12
Multiplying both sides by 12 cancels on the right
12 × (1/4) = (X/12) × 12
12 × (1/4) = X
Then solving for X
X = 12 × (1/4)
X = 3
Therefore
4:1 = 12:3
Since
4:7 = 133 : X
Then we know
714 = X/133
[Multiplying both sides by 133 cancels on the right
133 × (714) = (X/133) × 133
133 × (714) = X
Then solving for X
X = 133 × (7/4)
X = 232.75
Therefore
4:7 = 133:232.75
My Cours
Course H
Decide if the events A and B are mutually exclusive or not mutually exclusive. A person is selected at random.
A: Their birthday is in the fall.
B: Their birthday is in October.
Homewo
Answers
Answer: not mutually exclusive
Step-by-step explanation:
What is the circumference of a circle with a radius of 14 feet use 22/7 for pi
2,464?” Feet
616 feet
88 feet
44 feet
Answers
The circumference of a circle with a radius of 14 feet is 88 feet.
What precisely is a circle?Every point in the surface of a circle, which is a circular, two-dimensional object, is evenly separated from the centre. All lines that cross the circle join together to produce the line of reflected symmetry. Each angle has axis of symmetry around the centre, in addition. Monitoring a linear interpolation in a surface while keeping a fixed distance from some other point will result in the closed shape of a circle. The English term circle derives from the Greek word curriculum provides students, which also means hoop or ring.
When we find the circumference, we obtain:
The circumference( C) of a circle is 2πr.
C=2πr
⇒C=2×\(\frac{22}{7}\)×14=88 feet.
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The graphs below have the same shape. What is the equation of the red
graph?
G(x)=?
F(x) = x^3
A. G(X) = x^3 - 1
B. G(X) = (x - 1)^3
C. G(X) = x^2 + 1
D. G(x) = (x + 1)^3
Answers
B and D are wrong because they are transformations that slide left and right.
and C is wrong because the shift will cause you to up 1.
Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
Answers
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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1. Use a straightedge to construct a line that goes
through points A and B. Label the line l.
2. Which axis is parallel to line l?
10
Which axis is perpendicular to line l?
3
Plot two more points on line l. Name them Cand D.
51
4. Give the coordinates of each point below.
B.
A:
B:
С.
D:
0
5
10
5. Give the coordinates of another point that falls on line l with a y-coordinate greater than 20.
My
Answers
Answer: A
2". 1. 0 a. Put a square box at the origin of the number line. b. Plot point C so it is located at 2 ... d. Plot a point at the midpoint of C and E. Label it H. Lesson 2. 1. Name the ... 2. Line & passes through point H and is parallel to the y-axis. Construct line l.
Step-by-step explanation:
Step-by-step explanation:
A boy drops his toy car from the top floor of his house. The time it takes for the toy to fall from a height of 13 feet is given by the equation
h=94−16t^2, where t is the time in seconds. Determine the time it takes the toy to fall to the bottom floor.
Answers
It takes the toy car 2.43 seconds to fall to the bottom floor, answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.
Describe Equation?An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).
For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.
Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.
Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.
Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.
We have the equation \(h = 94 - 16t^2\), where h is the height of the toy car in feet and t is the time in seconds.
When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:
\(0 = 94 - 16t^216t^2 = 94t^2 = 94/16\)
\(t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds\) (rounded to two decimal places)
Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.
The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.
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what is 7/8 - 1/2 = in simplest form
Answers
Answer:
\( \frac{7}{8} - \frac{1}{2} = \frac{7 - 4}{8} = \frac{3}{8} \)
Step-by-step explanation:
I hope I helped you! :)
A car advertisement states that a certain car can accelerate from rest to 72 km/h in 12.5 seconds.
Initially the car is at rest, so the initial velocity is ______
m/s.
The car speeds up to 72 km/h which is equivalent to _______
m/s. Find the car’s average acceleration.
The acceleration of the car is _______
m/s2
Answers
The initial velocity is 0 m/sec
The car speed up to 72km/h which is equivalent to 36m/sec
The acceleration of the car is 2.88 m/sec².
What is acceleration?Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken
Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:
Initial Velocity = 0 m/sec
Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec
Time taken = 12.5 second
Now, the car’s acceleration in m/s can be written as,
Acceleration = (Final Velocity - Initial Velocity)/ Time taken
(36 m/sec - 0 m/sec)/12.5 seconds
= 2.88 m/sec²
Hence, the car’s acceleration in m/s is 2.88 m/sec².
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One month Lamar rented 12 movies and 2 video games for a total of $43. The next month he rented 3 movies and 5 video games for a total of $40. Find the rental cost for each movie and each video game.
Answers
Answer:
the answer is $53
Step-by-step explanation:
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answers
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = \(\frac{sum}{count}\)
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = \(\frac{168}{7}\) = 24
15= x/6-1 help me with this im just using it to study so show step by step because i forgot
Answers
The value of x after solving the expression, 15 = (x/6)-1, step by step is 96.
According to the question,
We have the following expression:
15 = (x/6)-1
Now, we can change the sides because it will not make any difference to the overall answer.
(x/6)-1 = 15
Now, we will move 1 from the left hand side to the right hand side. So, the sign will change from minus to plus.
x/6 = 15+1
x/6 = 16
Now, we will move 6 from the left hand side to right hand side. 6 is in the division on the left hand side then it will be in multiplication on the right hand side.
x = 16*6
x = 96
Hence, the value of x after solving the expression step by step is 96.
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Write an equivalent expression for y(6 + y) and (6 x y) + (6 x 7)
Answers
Answer:
For the first one: 6y + y^2
2nd one: 6y + 42
NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17 8(x + 1) = 24 5(x - 2) = 20 34 - 7x = 20 31 - x = 29 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
Answers
Given
The equations,
4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.
To find the solution to each equations.
Explanation:
It is given that,
The equations,
4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.
That implies,
1)
\(\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}\)Hence, the solution is x=5.
2)
\(\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1 \\ x=2 \end{gathered}\)Hence, the solution is x=2.
3)
\(\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2 \\ x=6 \end{gathered}\)Hence, the solution is x=6.
4)
\(\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 7x=14 \\ x=\frac{14}{7} \\ x=2 \end{gathered}\)Hence, the solution is x=2.
5)
\(\begin{gathered} 31-x=29 \\ 31-29=x \\ x=2 \end{gathered}\)Hence, the solution is x=2.
6)
\(\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}\)Hence, the solution is x=5.
What’s the graph to t/3 - 1 > -3
Answers
Answer: The answer is C
Step-by-step explanation: This is because the equation has a greater than or equal to sign (≥). This mean that there will be a closed dot. Also, when it comes to inequalities, the sign points to where the line will be drawn, (greater than is to the right and less than is to the left), which indicates that the answer is C
Find the volume of the irregular figure. 3 cm 3 cm [?] cm 9 cm 7 cm 3 cm 3cm 12 c
No links for answers
![Find the volume of the irregular figure. 3 cm 3 cm [?] cm 9 cm 7 cm 3 cm 3cm 12 cNo links for answers](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/qs1dufOUXY9ZwfNnyCgRtVNDnThgq3eD.jpeg)
Answers
Answer:
\(144cm^{3}\)
Step-by-step explanation:
Hope this helps!
![Find the volume of the irregular figure. 3 cm 3 cm [?] cm 9 cm 7 cm 3 cm 3cm 12 cNo links for answers](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/E60e6Ig9uoyf5Pi2JD8DFnRSMvp1s8rb.png)
Use Pythagoras' theorem to calculate the length of FG. Give your answer in centimetres (cm) to 1 d.p. 8 cm H 13 cm G
Answers
The length of FG is approximately 15.3 cm.
To calculate the length of FG using Pythagoras' theorem, we need to find the length of the hypotenuse (FG) of a right triangle. Let's denote the length of FG as x.
According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have:
\(FG^2 = GH^2 + FH^2\)
Given that GH = 8 cm and FH = 13 cm, we can substitute these values into the equation:
\(x^2 = 8^2 + 13^2\)
\(x^2 = 64 + 169\)
\(x^2\) = 233
To find x, we take the square root of both sides:
x = √233 ≈ 15.26 cm (rounded to 1 decimal place)
Therefore, the length of FG is approximately 15.3 cm.
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Select the correct answer from each drop-down menu.
What type of risk applies to an investment in Treasury bonds?
The risk that the value of the Treasury bond will diminish over time if the value of the dollar decreases, or buys less than it used to, is
called
government to repay the bond.
v risk. Treasury bonds are seen to have no
vrisk because theyre backed by the promise of the US
Answers
Answer:
The first drop down is Inflationary and the second drop down is Credit.
Step-by-step explanation:
Which graph represents 12 = 3x + 4y line a, line b, line c
Answers
Answer:
green line or "b"
Step-by-step explanation:
we can set this up into the slope intercept form
y=mx+b
where m is the slope and b is y intercept
12=3x+4y
-3x -3x
-3x+12=4y
/4. /4. /4
-3/4x+3=y
we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"
hopes this helps please mark rainliest
The store buys easels for 10.20 each he marks up the cost by 75% to get the selling price what is the selling price of each easel? show your work
Answers
what is the most effluence first step to isolate the variable term on one side of this equation -9x=-4x+5
Answers
rs + 2r210rs5s2Find the binomial factors
Answers
Rs+2r^2-10rs-5s^2
Combine like terms
2r^2-9rs-5s^2
i need help asap i have to finish
Answers
Answer: (D) 12 to 4
Step-by-step explanation:
First, we will find the number of people waiting in line for each activity.
➜ Bumper cars is 12
➜ Slingshot is 4
Next, we will create our ratio. This is asking for Bumper cars to Slingshot, so Bumper cars is first with Slingshot second.
➜ 12 to 4