let's recall that d = rt, distance = rate * time.
a = speed of the airplane in still air.
w = speed of the wind
the distance travelled with the wind is 960 miles, so the return trip is pretty much just that, 960 miles.
when the airplane is going with with wind, the airplane is really not going as fast as "a" mph, is really going faster due to the wind, so the speed of the plane is "a + w", because the wind is adding its speed to it.
when the airplane is going against the wind is not really going "a" mph fast either, is really going slower at "a - w" mph, because the wind is subtracting speed from it, so
[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{with the wind}&960&a+w&5\\ \textit{against the wind}&960&a-w&6 \end{array}~\hfill \begin{cases} 960=(a+w)(5)\\\\ 960=(a-w)(6) \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{960=(a+w)(5)}\implies \cfrac{960}{5}= a + w\implies 192=a+w\implies \boxed{192-w=a}[/tex]
[tex]\stackrel{\textit{substituting on the 2nd equation}}{960=(\underline{192-w}~~ - ~~w)(6)}\implies \cfrac{960}{6}=192-w-w\implies 160=192-2w \\\\\\ 2w+160=192\implies 2w=32\implies w=\cfrac{32}{2}\implies \blacktriangleright w=16 \blacktriangleleft ~\hfill \blacktriangleright \stackrel{192 - 16}{176=a} \blacktriangleleft[/tex]
1. Tom rides his bike 6_1/4 miles round trip to work. He works 2 days each
week. How far will Tom ride his bike to and from work in 5 weeks?
⚫️31_1/4 miles
⚫️62_1/2 miles
⚫️12_1/2 miles
⚫️62 miles
Answer:
B. 62 1/2
Step-by-step explanation:
The coldest temperature recorded on the surface of a planet was - 248 Celsius is the warmest temperature recorded on the surface of the planet was 108 Celsius what are the correspondence temperatures in degrees Fahrenheit
Answer:
-414.4 F° and 226.4 F°
hope it helps
Gabrielle’s age is two time Mikhaïl’s age. The sum of their ages is 27. What is Mikhail’s age?
Mikhail is 9
Step-by-step explanation:
Divide 27 by 3 because G is 2 times than Mik. So G=2 Mik=1. and 27 divided 3 is 9
How do I solve it the problem completely
Answer:
42 in²
Step-by-step explanation:
Total: Shape 1 + Shape 2
Area of a square: l x w, where l is the length and w is the width.
= 6 x 5
= 30
Area of a triangle: 1/2 x b x h, where b is the base and h is the height.
= 1/2 x 4 x 6
= 1/2 x 24
= 12
Total = 30 + 12
= 42 in²
Answer:
Step-by-step explanation:
This figure is trapezium
a and b are the parallel lines.
a = 5 +4 = 9 in & b = 5 in and h = 6 in
[tex]\boxed{\text{Area of trapezium =$\dfrac{(a+b)*h}{2}$}}[/tex]
[tex]\sf = \dfrac{(9+5)*6}{2}\\\\=\dfrac{14*6}{2}\\\\= 7*6\\\\= 42 \ in^{2}[/tex]
2. When an adult is physically active, suppose the amount of water they will consume is normally distributed with an average of 20 ounces of water with a standard deviation of 7 ounces. If 10 adults are physically active, what is the probability that the average water consumed by them is less than 18 ounces? (note that we are working with a sampling distribution in this question). Report to 5 decimal positions
Using the normal distribution and the central limit theorem, it is found that there is a 0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For the population, the mean and the standard deviation are, respectively, given by [tex]\mu = 20, \sigma = 7[/tex].
For samples of n = 10, the standard error is given by:
[tex]s = \frac{7}{\sqrt{10}} = 2.2136[/tex]
The probability that the average water consumed by them is less than 18 ounces is the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 20}{2.2136}[/tex]
Z = -0.9.
Z = -0.9 has a p-value of 0.18406.
0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Please Help ASAP (show work if you want its not needed i just need the answer)
[tex] \cos(60) = \frac{12}{x} \\ [/tex]
[tex] \frac{1}{2} = \frac{12}{x} \\ [/tex]
[tex]x = 24[/tex]
_____________________________________________
[tex] \sin(60) = \frac{y}{x} \\ [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{y}{24} \\ [/tex]
[tex]y = 12 \sqrt{3} [/tex]
4
Ms. Thorson bought a piece of lace that was 3 feet long. She cuts off as many pieces as possible that are 9 inches long. Will Ms. Thorson have any lace left over? Show and explain your work.
Answer:
No
Step-by-step explanation:
1 foot = 12 in.
3 feet = 36 in.
36 / 9 is 4
4 is an integer
Therefore, none will be left
Answer:
No , there will not be any piece left
Step-by-step explanation:
No of feet :- 3 feet which is 36 inches
If we cut of 36 inches in part each of 9 inch we will get 4 parts of 9 inch
36/9 :- 4
4 is complete no. , so there wouldn't be any piece left .
A relief worker needs to divide 1350 bottles of water and 144 cans of food into boxes that each contain the same number of items. Also, each box must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put in each box?
The largest number of relief supplies that can be put in each box is 75 bottles and 8 cans of food respectively.
How to find highest common factorThe factors of:
1350 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675 and 1350.
144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
The highest common factor of 1350 and 144 is 181350 bottles / 18
= 75 bottles per box
144 cans of food / 18
= 8 cans of food per box
So, there 18 boxes of items, each containing 75 bottles and 8 cans of food respectively.
Learn more about highest common factor:
https://brainly.com/question/120215
Find the value of the expression 1/2x+3 if x=12
Answer:
The answer is 9.
Step-by-step explanation:
1/2 * 12 = 6
6+3=9
Answer:
9
Step-by-step explanation:
x = 12
1/2 · 12 = 6
6 + 3 = 9
Ella rolls a die and then flips a coin. The sample space for this compound event is represented in the table (H is heads and T is tails). Complete the table and the sentence beneath it. Die 1 2 3 4 5 6 Coin heads H-1 H-2 H-3 H-5 H-6 tails T-1 T-3 T-4 T-5 The size of the sample space is .
The size of the sample space is { H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5 }
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Sample space is the set of all possible outcome the considered random experiment can result to.
Thus, suppose we toss a coin, then tossing a coin is a random experiment, and the sample space is {'head', 'tail'}.
We ignore other outcomes like slant coin, or standing coin by assuming that coin is very thin to stand and always falls down.
Ella rolls a die and then flips a coin.
The sample space for this compound event is represented in the table (H is heads and T is tails).
Die 1 2 3 4 5 6
Coin: heads H-1 H-2 H-3 H-5 H-6
tails T-1 T-3 T-4 T-5
Hence, the size of the sample space is { H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5 }
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ5
Answer:
hope this works for you
Step-by-step explanation:
* PLEASE HELP ME SOLVE THIS PROBLEM I WILL GIVE BRAINIEST*
2. Change from dog/cat to tails/heads.
DDC = ________
CDC= _________
DCD = ________
CCD = _________
DDD = _________
CCC = _________
DCC = _________
CDD = _________
please help :))
Answer:
Tails Tails Heads
Heads Tails Heads
Tails Heads Tails
Heads Heads Tails
Tails Tails Tails
Heads Heads Heads
Tails Tails heads
Heads Tails Tails
------------------------------------------------——------------------------------------------------------
Thanks!
Always keep more than 2 smiles so that you can share it to someone who doesn't have one. You happy! Me happy! EVERYONE HAPPY!!!!
Have a great day!
:D
Please help me i need help!!!
Answer:
sorry cant help with that
Step-by-step explanation:
What does using the degrees of freedom in a sample correct for? possible bias between the alternative and null hypotheses possible bias between the sample and the population possible bias between the standard deviation and variance possible bias between the standard deviation and the mean
In Statistics and mathematics, the degrees of freedom in a sample are used to correct: A. possible bias between the alternative and null hypotheses.
What is a null hypothesis?A null hypothesis ([tex]H_0[/tex]) can be defined as the opposite of an alternate hypothesis ([tex]H_a[/tex]), and it asserts that two (2) possibilities are the same.
In In Statistics and mathematics, the test statistics of a given sample is calculated with this formula:
[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the sample size.Also, the degrees of freedom in a sample are used to correct a possible bias that exists between the alternative and null hypotheses.
Read more on null hypothesis here: https://brainly.com/question/14913351
The function h(x) is a transformation of the square root parent function, f(x) = pi x. What function is h(x)?
Answer:
A
Step-by-step explanation:
you can see graph of f(x) changed one unit to the left, since it goes to the left, you should +1 in terms of x. so sqr x+1 is the solution. one way to think about that is you plus one for every x value, that means you get to a point previously for one unit. and turns out it looks like you moves to the left.
Hope that helps
Which is the inverse of the function f(x) = 4x − 9?
Step-by-step explanation:
x and y trade places.
f(x) = y = 4x - 9
y + 9 = 4x
x = (y + 9)/4
and to make it a true function notation, we need to rename x to y and vice versa and get
y = (x + 9)/4
A very slow man walks
20 cm.in 0.5 left, what his
velocity in meter per second?
Jessica sells 50.5 ounces of lemonade for a total of 20.20.
Find the unit price in dollars per ounce.
If necessary, round your answer to the nearest cent.
Answer:
2.5
Step-by-step explanation:
Answer: 2.5
Step-by-step explanation: do it yourself jk lol first you add then divide by 6.5
Solve for the b 4 ( b + 5 )- 2b = 100
4 ( b + 5 )- 2b = 100
____________________
B = 40
Answer:
[tex]\tt b=40[/tex]
Step-by-step explanation:
[tex]\tt 4 ( b + 5 )- 2b = 100[/tex]
[tex]\bf Expand\; (Apply\; Distributions\; Law) :-[/tex]
[tex]\tt 2b+20=100[/tex]
[tex]\tt 2b+20-20=100-20\;\; (Subtract \;20\; from\; both \;sides)[/tex]
[tex]\tt 2b=80[/tex] [tex]\tt (Simplify)[/tex]
[tex]\tt \cfrac{2b}{2}=\cfrac{80}{2}\;\;( Divide\; both \;sides\: by\; 2)[/tex]
[tex]\tt b=40[/tex]
~
I need the answer to this quick pls
Answer:
Option A
Step-by-step explanation:
The median of the trapezoid is the line connecting the midpoints of the legs.The median of the trapezoid can be caculated by the fromula,
[tex]\bf Median = \dfrac{a +b}{2}[/tex]
Here, a and b are the base (parallel sides)
a = 13 inches & b = 19 inches
[tex]\bf Median = \dfrac{13+19}{2}[/tex]
[tex]= \dfrac{32}{2}\\\\\\= 16 \ inches[/tex]
A car dealership sold 212 cars in 4 months. At what rate did the dealership sell cars in cars per month?
Answer: 59 cars per month
Step-by-step explanation:
These numbers are multiples of __________.
4, 8, 16, 24
A) 3
B) 4
C) 5
D) 6
Answer:
4
Step-by-step explanation:
All these numbers multiply by 4
Answer:
The answer is B.
Step-by-step explanation:
4÷4=1
8÷4=2
16÷4=4
24÷4=6
Which term best describes vthe figure shown below
Answer:
Line LM
Step-by-step explanation:
A ray has a point at one end, this figure does not.
A line goes out forever in both ends, this is shown by the two arrows. Line LM describes this figure.
Points LM are going to be two separate points, this figure does not have points.
Plane LM will have three points to show a plane, this is a single line.
Using these definitions and facts we know, we can figure out this is best described as Line LM.
Two red and two blue blocks are
placed into a bag. You randomly
take one block out of the bag. If
you replace the block each time,
how many red blocks would
you expect to take out if you try
8 times?
Answer:
1/3
Step-by-step explanation:
Probability of an Event = Number of Favorable Outcomes/Total Number of Possible Outcomes
If 12Kg of chicken feed cost 20 how much would 5kg cost?
and what is the unit rate? ( price per 1 kg)
Step-by-step explanation:
if you 12kg cost 20 what about 5kg that will be 5kg×20÷12kg= 8.33 when you round of to the nearest hundredth this is the price of 5kg
sorry but i dont think i know how to answer the other question i have done what i only know thankyou
in the figure d||m. what is the value of x?
Step-by-step explanation:
2X - 20 =86 ( Alternate angles are equal)
2X = 86 - 20
2X = 66
X = 33
[tex] \rm \int_{0}^2 \left( \sqrt[3]{ {x}^{2} + 2x} + \sqrt{1 + {x}^3 } \right )dx \\ [/tex]
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
[tex]\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx[/tex]
Let [tex]f(x) = \sqrt{1 + x^3}[/tex]. Compute the inverse:
[tex]f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}[/tex]
and we immediately notice that [tex]f^{-1}(x+1)=\sqrt[3]{x^2+2x}[/tex].
So, we can write the given integral as
[tex]\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx[/tex]
Splitting up terms and replacing [tex]x \to x-1[/tex] in the first integral, we get
[tex]\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}[/tex]
The equation is:
Answer: the number of labor was :
Answer:
equation: 1368 = 380 +52xlabor hours: 19Step-by-step explanation:
The desired equation will relate labor cost, parts cost, and total cost.
A.The total cost is the sum of the parts cost and the product of labor hours and labor rate. We're told to use x to represent labor hours.
total cost = part cost + (labor rate)(labor hours)
1368 = 380 + 52x
__
B.This equation can be solved in 2 steps:
988 = 52x . . . . . . . step 1, subtract 380 from both sides
19 = x . . . . . . . . . . step 2, divide both sides by the coefficient of x
The number of labor hours was 19.
Joey has completed a portion of his weekend chores. This portion is represented by the point on the number line below. What percentage is represented by the point on the number line?
A. 12.5%
B. 60%
C. 75%
D. 80%
Answer:
C - 75%
Step-by-step explanation:
6/8 = 75%
What is the product?
48+ 2 K-2
24 2+1
4
O2k+1
2
K-2
2
2641
2
R+2
Answer:
[tex]\frac{2}{k+2}[/tex]
Step-by-step explanation:
Simplify the expression and you will get this.
hope this helps
What is the area of the figure shown delow?
Answer:
160mm2 is the correct answer
Step-by-step explanation: