The speed of the raft if the speed of the motorboat in still water is 3 km/h
What is speed?
Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Let the speed of the raft (current) - r
Speed of motorboat - 12 km/h
The distance between villages - is 44 km
Let the time spent by Aniskin - t
The time the thief was in travel = 2 hr 40 min + t = 2 40/60 + t = 3/8 + t
The distance the thief traveled = 44 - 27 = 17 km
We have the following equations:
r(8/3 + t) = 17
(12 - r)t = 27
Simplify the equations:
r(8/3 + t) = 17 ⇒ rt + 8/3r = 17
(12 - r)t = 27 ⇒ 12t - rt = 27
Add up the equations and solve for r:
rt + 8/3r + 12t - rt = 44
8/3r + 12t = 44
r = 16.5 - 4.5t
Substitute r into the second equation:
(12 - 16.5 + 4.5t)t = 27
4.5t² - 4.5t = 27
9t² - 9t - 54 = 0
Solving we get
t = 3 h
Find r:
r = 16.5 - 4.5*3 = 3 km/h
Therefore the speed of the raft if the speed of the motorboat in still water is 3 km/h
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NO LINKS!! Write the equation of the trigonometric graph. Try fractional values or π for the box next to x.
Answer:
y = 1·cos(π/3·x) +3
Step-by-step explanation:
The general form of the trig equation will be ...
y = (amplitude)·cos(2π/(period)·x) +(midline shift)
__
midlineYou have already determined correctly that the midline shift is 3 units.
amplitudeThe amplitude is the difference between the peak value (4) and the midline, so is ...
amplitude = peak - midline = 4 -3 = 1
periodThe period is the horizontal distance between corresponding parts of the graph. Here, the distance between peak values is 6 units, so the period is 6. That means the argument of the cosine function is ...
(2π)/6·x = (π/3)·x
__
The function you are looking for is ...
[tex]y=1\cdot\cos\left(\dfrac{\pi}{3}x\right)+3[/tex]
Answer:
[tex]y=\boxed{1}\: \cos(\:\boxed{1}\:x)+\boxed{3}[/tex]
Step-by-step explanation:
General form of cos periodic function:
y = A cos(B(x + C)) + D
where:
A = Amplitude (height from the center line to the peak or trough)2π/B = Period (horizontal distance between one peak and the next)C = (horizontal) Phase ShiftD = Vertical ShiftParent function → y = cos(x)
The parent function y = cos(x) has a center line at y = 0.
The center line of the new function is at y = 3, so the parent function has been shifted vertically by 3 units. Therefore, D = 3:
⇒ y = A cos(B(x + C)) + 3
The amplitude of the parent function is 1.
The amplitude of the new function is also 1. Therefore, A = 1:
⇒ y = 1 cos(B(x + C)) + 3
The parent function has a peak at x = 0.
The new function has a peak at x = 0. Therefore there has been no horizontal phase shift, so C = 0:
⇒ y = 1 cos(B(x + 0)) + 3
⇒ y = 1 cos(Bx) + 3
Finally, from inspection of the curve, the period appears to be 2π (6.28)
2π/B = 2π so B = 1
⇒ y = 1 cos(1x) + 3
Please see attached graph for reference.
The parent function is shown in blue.The dotted line is shown in grey.The new function is shown in black.Show what you know: work out the problems below and submit a photo of your work to receive full credit.
The Florida A&M Rattlers are decorating campus for homecoming weekend. Students use 3 rolls of orange streamers for every 2 rolls of green streamers for every dorm they decorate.
Draw a model that represents the ratio of different colored streamers.
Draw a model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.
The model for representing the ratio of the number of orange and green rolls are [tex]\dfrac{3}{2}[/tex].
A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms will be 3O=2G
What is ratio?The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times to the other number.
A model that represents the ratio of different colored streamers.
[tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex]
A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.
D=3O and D=2G
3O=2G
Hence the models are [tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex] and 3O=2G.
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The price of a tv was decreased by 20% to £1440. What was the price before the decrease?
Answer:
€7200
Step-by-step explanation:
20%---------1440
100%----------y
y= 100×1440/20
y= 144000/20
y= €7200
price before decrease= €7200
r= 8.4 in
Calculate the diameter of the
circle.
Answer:
The diameter is 16.8
Step-by-step explanation:
The diameter is double the radius.
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[tex]\diamond\large\blue\textsf{\textbf{\underline{Question:-}}}[/tex]
r=8.4 in. What is the circle's diameter?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
Since the radius is exactly one-half of the diameter, we multiply the radius times 2 in order to find the diameter, which results in:-
d(diameter)=16.8 in
Good luck with your studies.-- - - - - - - - - - - - -- -- - - - - - - - - - - -- - -
Find the missing length.
✓ [?]
?
C=
C
2
11
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer:
11.18 is the missing length
) Evaluate
42+(9 divided by 3 x 2) - 4
Answer:
44
Step-by-step explanation:
Parenthesis
Exponents
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
42 + (9 ÷ 3 x 2) - 4 <== divide first (left to right)
42 + ((9 ÷ 3) x 2) - 4
42 + (3 x 2) - 4 <== multiply
42 + 6 - 4 <== add
48 - 4 <== subtract
44
Final answer: 44
Hope this helps!
5
5.2
4
Find the area of the parallelogram.
square units
Answer:
20 square units
Step-by-step explanation:
Area of a parallelogram is calculated with the following formula:
b*h (b: base, h: height)
5*4 = 20 square units
help me please i need it now
Answer:
1.75
Explanation:
Take two points: (0, -3), (4,4)
[tex]\sf rate \ of \ change: \dfrac{y_2- y_1}{x_2 - x_1} = \dfrac{rise}{run}[/tex]
Here rate of change:
[tex]\sf \rightarrow \dfrac{4-(-3)}{4-0}[/tex] (insert values)
[tex]\sf \rightarrow \dfrac{7}{4}[/tex] (in fraction)
[tex]\sf \rightarrow 1.75[/tex] (in decimals)
Answer:
1.75
Step-by-step explanation:
Rate of change = slope of the line
Taking two points (4,4) and (0, -3) :
slope (m) = 4 + 3 / 4 - 0slope (m) = 7/4slope (m) = 1.75PLS HELP!!!
The coast guard is out to sea and gets notification that two ships need help. One ship is directly west of the coast guard, and the other is directly south, as shown in the image below. The two ships are 6 miles from each other. Which ship is currently closer to the coast guard?
PLEASE INCLUDE EXPLANATION!!!! THANK YOU!!!
So
cos47=Base/Hypotenusecos47=y/6y=6cos47And
sin47=x/6x=6sin47sin47=0.73
cos47=0.68
So meanwhile sin is greater so 6sin is also greater
x is greatership 2 is closerAnswer:
Ship 2
Step-by-step explanation:
From inspection of the diagram, the problem has been modeled as a right triangle. Therefore, to find [tex]x[/tex] and [tex]y[/tex], use trigonometric ratios then compare to determine which distance is the smallest.
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)To find [tex]x[/tex] use the sine trig ratio:
[tex]\implies \sf \sin(\theta)=\dfrac{O}{H}[/tex]
[tex]\implies \sin(47^{\circ})=\dfrac{x}{6}[/tex]
[tex]\implies x=6 \sin(47^{\circ})[/tex]
[tex]\implies x=4.39 \: \sf miles \:(2\:dp)[/tex]
To find [tex]y[/tex] use the cosine trig ratio:
[tex]\implies \sf \cos(\theta)=\dfrac{A}{H}[/tex]
[tex]\implies \cos(47^{\circ})=\dfrac{y}{6}[/tex]
[tex]\implies y=6 \cos(47^{\circ})[/tex]
[tex]\implies y=4.09 \: \sf miles \: (2 \: dp)[/tex]
As 4.09 < 4.39, ship 2 is currently closer to the coast guard.
What are the phrase in a business cycle
How to multiply problem in photo?
_____
yStep-by-step explanation:
A PACK OF TOILET PAPER WAS ORIGINALLY $4.50 , IT COST $6.75. DID THE PRICE INCREASE OR DECREASE?
whats mean and median of 11, 18, 5, 20, 8, 124, 17?
Answer:
The mean would be 29 and the median would be 17
Step-by-step explanation:
Hope this helps! :)
What is the value of the expression
1/2 divided by 6
Answer:
here is 1/2 divided displayed mathematically
1/2 ÷ 6
1= numerator
2= denominator
3= whole number
to make it fraction from the answer you keep the
numerator by the whole number to make a new
denominator
___1___ = _1_
2×6 12
thus the answer to 1/2 divided by 6 on fraction form is
1/12 is the answer
Please help and thank you.
X=[?]
x = 6
Step-by-step explanation:Equilaterals are a type of triangle where all of the sides are congruent. The angles are also all equal.
Setting Up the Equation
As stated above, all of the sides are congruent. This means that the lines must be equal to which others. Since the sides are equal, we can set them equal to each other.
AB = ACNow, we can substitute the expressions in the equation.
22x - 33 = 7x +57Solving the Equation
After we set up the equation, we can solve for x using the properties of equality. There are different orders in which this can be solved. So if you prefer to work in a different order, the answer should still be the same.
First, rewrite the equation
22x - 33 = 7x +57Next, add 33 to both sides
22x = 7x + 90Then, subtract 7x from both sides
15x = 90Finally, divide both sides 15
x = 6This gives us our final answer of 6.
Checking the Answer
If you wanted to, you can check your answer by plugging 6 into the original equation.
22(6) - 33 = 7(6) + 57Then solve the equation
99 = 99Since both sides are equal, the answer must be correct.
If you reflect point B(- 2, 5) over the y- axis, what is the reflected point ?
Answer:
(2,5)
Step-by-step explanation:
Since it is reflected across the y-axis only the x point will change and vise-versa
PLEASE HELP ILL MARK BRAINLIEST kellys farm has 8 chickens for every 3 cows and 2 pigs for every 5 cows. if kellys farm has 30 pigs how many chickens are on the farm
Answer:
Step-by-step explanation:
Aaron is designing a party game in which he needs exactly 24 possible outcomes. Which sets of actions can he use to have a statistically fair game?
Toss a coin twice, then roll a 6-sided number cube with the digits 1 to 6.
Select a card from a set of cards with the letters A through D, then spin this once.
Randomly select a number from 1 to 16, then roll an 8-sided number cube with the digits 1 to 8.
Spin this and roll an 8-sided number cube with the digits 1 to 8.
Randomly select an odd digit {1, 3, 5, 7, 9}, then flip a coin twice.
Select a card from a set of cards with the letters A through N, then spin this once.
The set of actions that should be used is: toss a coin twice, then roll a 6-sided number cube
Which sets of actions can he use to have a statistically fair game?
We know tath the game has 24 possible outcomes. Then we need to find a set of actions that gives 24 different outcomes all with the same probability.
Of the given options, the only one that has a sample space of 24 elements is the first one.
Toss a coin twice and then roll a D6.
For each coin toss, the outcomes are 2 (tails and heads).
For the D6 there are 6 outcomes (1, 2, 3, 4, 5, 6)
Then the total number of outcomes for two tosses and rolling the number cube is given by the product between the numbers of outcomes for each individual part:
C = 2*2*6 = 4*6 = 24.
From this, we conclude that this is the correct option.
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Answer:
the correct ones are
2, Select a card from a set of cards with the letters A through D, then spin this once.
5,Toss a coin twice, then roll a 6-sided number cube with the digits 1 to 6.
6, spin this and roll an 8-sided number cube with the digits 1 to 8.
Step-by-step explanation:
so basically both the colored wheel answers and the one with the coin and cube
plato 2022
Answer the Volume Based Question. I will make uh Brainliest + 50 points
Step-by-step explanation:
(i) For cuboid shaped container:[tex]l = 3a\: cm,\: b = 3a\:cm,\: h = x\:cm[/tex] (Given)Container is filled with water so the volume of water can be given by the following formula:[tex]V_{water} = lbh[/tex]Plugging the values of l, b and h in the above formula, we find:[tex]V_{water} = (3a)(3a)(x)[/tex][tex]\huge{\red{\boxed{V_{water} = 9a^2x\:cm^3}}}[/tex](ii) For solid right circular cylinder:radius (r) = a cm, h = a cmFormula for volume of cylinder is given as:[tex]V_{cylinder} =\pi r^2 h[/tex][tex]V_{cylinder} =\pi (a)^2 (a)[/tex][tex]\huge{\purple{\boxed{V_{cylinder} =\pi a^3 \:cm^3}}}[/tex]The figure below shows three quadrilaterals on a coordinate grid: A coordinate grid is shown from positive 8 to negative 8 on the x axis and from positive 8 to negative 8 on the y axis. An image of a rectangle labeled M is shown on ordered pair negative 1, negative 1 and negative 3, negative 1 and negative 3, negative 2 and negative 1, negative 2. Another image of a rectangle labeled N is shown on ordered pair negative 2, negative 2 and negative 6, negative 2 and negative 6, negative 4 and negative 2, negative 4. Another image of a rectangle labeled O is shown on ordered pair 1, 1 and 1, 2, and 3 , 2 and 3, 1. Which of the following statements is true about the three quadrilaterals? N and O are similar and congruent. M and N are similar and congruent. M and O are similar but not congruent. M and N are similar but not congruent.
The quadrilateral A and quadrilateral B are similar but not congruent. Then the correct option is A.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in a series is called a quadrilateral.
If a polygon is four-sided (a quadrilateral), the sum of its angles is 360°
The figure below shows three quadrilaterals A, B, and C on a coordinate grid.
Then the quadrilateral A and quadrilateral C are similar and congruent too.
The quadrilateral A and quadrilateral B are similar but not congruent.
Similarly, the quadrilateral C and quadrilateral B are similar but not congruent.
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Tanisha's website had x visitors on Friday. On Saturday, it had 500 more visitors than it did on Friday. The total
number of visitors on Friday and
Saturday was twice the number on Sunday. In terms of x, how many visitors did Tanisha's website have on
Sunday?
If the number of visitors on Friday, Saturday, and Sunday is x, x + 500, and x + 250. Then the total number of visitors will be 3x + 750.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Tanisha's website had x visitors on Friday.
On Saturday, it had 500 more visitors than it did on Friday. That is x + 500
The total number of visitors on Friday and Saturday was twice the number on Sunday. That is (2x + 500)/2
Then the total number of the visitors will be
→ Friday + Saturday + Sunday
Then we have
[tex]\rm \rightarrow x + x + 500 + \dfrac{2x + 500}{2}\\\\\rightarrow 2x + 500 + x + 250\\\\\rightarrow 3x + 750[/tex]
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The table describes a probability distribution for a certain
event. Find the mean, u, for the probability distribution.
X
P(x)
10
0.534
20
0.193
30
0.140
40
0.085
50
0.048
This value is exact.
===============================================================
Explanation:
Use your favorite spreadsheet app to form a third column of values. This new column will be the result of multiplying the original two columns.
For instance, we have x*P(x) = 10*0.534 = 5.34 as the first entry of the new column. The other rows are treated in a similar manner. Refer to the screenshot below..
After getting that third column set up, add up those results. The sum is the expected value (aka the mean mu, which is the symbol [tex]\mu[/tex])
5.34 + 3.86 + 4.2 + 3.4 + 2.4 = 19.2
whats the mean and median of 13, 1, 17, 6, 2, 111, 3?
Answer:
111
Step-by-step explanation:
Find the area of this semi-circle with diameter,
d
= 11cm.
Give your answer rounded to 2 DP.
Solve the system of equations graphically. Then classify
the system as consistent or inconsistent and the
equations as dependent or independent.
5x - y = 7
5x+6y= -7
Answer:
They are consistent and independent
Step-by-step explanation:
Consistency
If two lines have an intersection point, they are said to be consistent. For example, two parallel lines do not have an intersection and therefore they are inconsistent.
In the problem, the two lines intersect at (1, -2) so they have a unique solution and therefore consistent.
Dependency
Two lines are said to be independent if one of them cannot be written as an integer multiple of the other. Or, in other words, if the slope-intercept form of both equations have different slope and y intercept
Note: slope-intercept form of an equation is y = mx + c where m is the slope and c the y intercept
Line 1: 5x - y = 7 can be written as y = 5x - 7 which has slope +5 and y intercept -7
Line2 : 5x + 6y = -7 can be re-written as y = (-5/6)x - (7/6). This has slope -5/6 and y intercept -7/6
Since slope and intercepts of both lines are different they form a system of independent equations
A ball is hit from the ground. When the ball has traveled a horizontal distance of d meters, its height, h, in
meters, can be modeled by the function h (d) = -
1 d + d.
What is the horizontal distance from the point where the ball is hit to the point where the ball lands on the
ground?
nour in the snaca nrovided
Answer:
125 meters
Step-by-step explanation:
The ball will hit the ground when its height is zero. Use that value for h in the equation, and solve for d.
__
h(d) = -d²/125 +d . . . . the given equation
0 = d(-d/125 +1) . . . . . use h=0, and factor out d
This equation is satisfied by values of d that make the factors zero:
d = 0 ⇒ d = 0
-d/125 +1 = 0 ⇒ d = 125
The horizontal distance to the landing point is 125 meters.
What am I supposed to do here?
Answer:
here is your answer.
Step-by-step explanation:
total frequency is 24
i need help with 7th grade math please 30 points need help ASAP
Answer:
Area = 657 ft^2
Step-by-step explanation:
Heron's Formula: [tex]S=\frac{a+b+c}{2}[/tex] ,
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\frac{20+21+29}{2}=\frac{70}{2} =45 ft[/tex]
[tex]Area=\sqrt{45(45-20)(45-21)(45-29)}\\\\=\sqrt{45(25)(24)(16)}\\\\=\sqrt{432000}[/tex]
= 657.267069
Area = 657 ft^2
Answer:
210 ft²
Step-by-step explanation:
Take the base and height of the triangle.
Base = 21 ft.Height = 20 ft.Solving for area :
A = 1/2 x base x heightA = 1/2 x 21 x 20A = 10 x 21A = 210 ft²Can anyone please solve this for me right now?
The population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The population model, which describes the population of a country in millions t years after the 2003 is,
[tex]A=645.4 e^{0.001t}[/tex]
For the year 2003 the value of t will be 0 as no year is passed after 20036. Thus,
[tex]A=645.4 e^{0.001\times0}\\A=645.4 e^{0}\\A=645.4(1)\\A=645.4[/tex]
Thus, the population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.
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What is 16x^4-100y^4 factored completly
Answer:
16x^(4)-y^(4)
Step-by-step explanation: