let's recall that d = rt, namely distance = rate * time.
d = distance from one pier to another
c = speed of the current
b = speed of the boat
now, let's notice something, on the way over the boat travelled "d" kilometers in 4 hrs, and back the same "d" kilometers in 5 hours.
when going with the current, the boat is not really going at "b" km/s, is really going faster, at "b + c" km/s, because the current is adding to it.
now, when going against the current, the boat is not really going "b" fast, is really going slower, at "b - c", because the current is subtracting from it.
from the above, we can conclude that the 4hrs trip was with the current, since it took less time, and the 5hrs trip was against the current, and we also know that the boat does 70 km with the current in 3.5 hrs, ok hmmm let's put all that in a table.
[tex]\begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{km/h}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{on the way over}&d&b+c&4\\ \textit{on the way back}&d&b-c&5\\\cline{1-4} \textit{we also know}&70&b+c&3.5 \end{array}~\hfill \begin{cases} d=(b+c)4\\\\ d = (b-c)5 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{(b+c)4~~ = ~~(b-c)5}\implies 4b+4c=5b-5c \\\\\\ 4c=b-5c\implies \boxed{9c=b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{we know that}}{70~~ = ~~(b+c)3.5}\implies 70=(b+c)\cfrac{7}{2}\implies \stackrel{\textit{substituting "b"}}{70=(9c+c)\cfrac{7}{2}} \\\\\\ 70=10c\cdot \cfrac{7}{2}\implies 70=\cfrac{70c}{2}\implies 140=70c\implies \cfrac{140}{70}=c\implies \blacktriangleright 2=c \blacktriangleleft \\\\\\ \stackrel{\textit{the speed of the boat in still water is then}}{9c=b\implies 9(2)=b}\implies \blacktriangleright 18=b\blacktriangleleft[/tex]
The following box plot shows the class scores on a particular math test:
10
20
30
70
80
90
100
40 50 60
Percent
Which of the following data sets is represented in the box plot?
{40, 50, 50, 77, 77, 100)
{0.50, 60, 75, 85, 100)
{50, 60, 60, 75, 75, 85, 85, 100)
[60, 65, 70, 75, 85, 85, 85)
Answer:
maybe the third one and i would also like to see the box plot
Step-by-step explanation:
Help me please it’s algebra
Answer:
80 degrees
Step-by-step explanation:
To convert radians to degrees, multiply by 180π since a full circle is 360° or 2π radians. Cancel the common factor of π. Factor π π out of 4π 4 π.
hope this helps.
How can a cruise ship float despite its mass (This is science)
A cruise ships floats despites it mass because it is boyanty and experiences and upthrust
Achimedes Principle of FloationThis principle states that "When a body is partially or totally imersed in a fluid, it experiences an upward force (Upthrust) which is equal to the volume of the fluid displaced"
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Match the value to the correct image. Not all values will be used.
Find the approximate surface area of each right regular prism.
The approximate surface areas of corresponding prisms are listed below:
A = 108 units²A = 229 units²A = 454 units²How to match given surface areas with given figuresThe surface area of the each figure ([tex]A[/tex]), in square units, is equal to the sum of the surface area of the two bases ([tex]A_{b}[/tex]), in square units, and the surface areas of the lateral sides ([tex]A_{l}[/tex]), in square units. Since bases are regular polygons, base surface area can be determined by this expression:
[tex]A_{b} = \frac{l^{2}\cdot n }{4\cdot \tan \frac{180}{n} }[/tex] (1)
Where:
l - Side length, in unitsn - Number of sidesThe area of one lateral side is expressed by this expression:
[tex]A_{l} =h\cdot l[/tex] (2)
Where h is the height of the rectangle, in units.
The total surface area is defined by the following formula:
[tex]A = 2\cdot A_{b} + n\cdot A_{l}[/tex] (3)
Now we proceed to calculate each surface area:
Case I ([tex]l = 2[/tex], [tex]n = 6[/tex], [tex]h = 9[/tex])[tex]A = 2\cdot \left[\frac{2^{2}\cdot (6)}{4\cdot \tan \left(\frac{180}{6} \right)} \right]+6\cdot (2)\cdot (9)[/tex]
A = 108.136 units²
Case II ([tex]l = 4\sqrt{3}[/tex], [tex]n = 3[/tex], [tex]h = 9[/tex])[tex]A = 2\cdot \left[\frac{(4\sqrt{3})^{2}\cdot (3)}{4\cdot \tan \left(\frac{180}{3} \right)} \right]+3\cdot (4\sqrt{3})\cdot (9)[/tex]
A = 228.631 units²
Case III ([tex]l = 6[/tex], [tex]n = 5[/tex], [tex]h = 11[/tex])[tex]A = 2\cdot \left[\frac{6^{2}\cdot (5)}{4\cdot \tan \left(\frac{180}{5} \right)} \right]+5\cdot (6)\cdot (11)[/tex]
A = 453.874 units²
The approximate surface areas of corresponding prisms are listed below:
A = 108 units²A = 229 units²A = 454 units²To learn more on surface areas, we kindly invite to check this verified question: https://brainly.com/question/2835293
Answer:
Look at the picture
What is ED?
Enter your answer in the box.
units
Answer:
x=4
Step-by-step explanation:
There
SHADOWS A rectangular billboard casts a shadow on the ground in the shape of a parallelogram. What is the area of the ground covered by the shadow? Round your answer to the nearest tenth.
Answer:
Its still a rectangle, just move the triangles, you get 450
Step-by-step explanation:
If you think of it like a triangle, you can use the base, the 90 degree angle, and the hypotenuse to get the area, do it twice since there are two, and your result is 225 for one triangle, 450 for both.
I guessed Supplementary, but I think I'm just not understanding, help
What is the volume of this container?
Answer:
1,253 in³
Step-by-step explanation:
The container can be split into two rectangular prisms. Adding their volumes together will give us the volume of the container.
The formula for the volume of a rectangular prism is length×width×height or base×height
Let's substitute!
(l×w×h)+(l×w×h)
=(7×5×5)+(11×14×7)
=175+1078
=1,253 in³
Hope this helps!
questions in the picture below
Answer:
Answer is
a) 50%
b) 20%
c) 40%
Step-by-step explanation:
The cost of a flat of strawberries to a grocery store is $7.60 and the store marks the strawberries
up 125%. Find the selling price
Answer:
7.60+9.50 = 17.10
Step-by-step explanation:
7.60 * 125% = 9.50
9.50+7.60 = 17.10
The group thought there was enough food for all 5 group members to
complete the trip, with each person getting the required 5600 calories per
day. However, they discover that they are missing 28,800 calories.
Using the map, create a plan a for the rest of the trip that includes taking as
many group members as possible to the South Pole, while sending the rest of
the group members directly back to base camp. Remember that each person
must have 5600 calories of food per day until he or she gets back to base
camp.
Be sure to explain how you came up with your plan. Include all work
necessary to support your answer.
To create a work plan for the food intake of each person in the group, there needs to be the required 5600 calories and there needs to be a replacement for the caloric deficit.
What is a Work Plan?This refers to the formal roadmap that is created for a project for the purposes of streamlining it.
Based on the fact that a map was not provided, there is insufficient data to solve the problem, so a general overview will be given about a work plan.
Because the group is 28,800 calories short and needs to complete the trip with their five members, then they need to ration their supplies.
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Tell whether each number is rational or irrational.0.121121112....
Please help me with this please and thank you
Answer:
L bozo
Step-by-step explanation:
bc ur an L. ur whole life is an L
given data 4,x,9,5,2,7 find x if the mode is 4
Answer:
x = 4
Step-by-step explanation:
This is because the definition of mode is the number that appears the most or is the popular of the numbers in the data set.
This could be any number since each number is listed once, but the requirements/directions say the mode is 4 so you need another 4 in order to have a mode of 4.
Each passenger on an airplane can take two suitcases, and each suitcase can
weigh no more than 50 pounds. If there are 120 passengers and each passenger
takes the maximum weight of luggage allowed, how many tons of luggage will
there be on the plane?
Answer:
6 tons
Step-by-step explanation:
So we know there are 120 passengers. If they all take the limit, which is 50 pounds each, we can multiply the 2 figures to get 120*50=6000 pounds. Since the question is asking us to answer in tons, we must convert 6000 pounds into tons. We can do this by using the convertion factor of 2000 lbs = 1 ton. With this logic, 6000 pounds equals 3 tons. But remember, each passenger can take 2 luggages. So just multiply by 2 to get 6 tons!
I hope this helped!
Please mark brainliest! I really need it. It would be very much appreciated.
help me if you can please?? and thanks! :)))
Answer:
0.0095
Step-by-step explanation:
= 0.009455 ( as they are bigger than 4 )
= 0.0095
Which decimal is the best approximation of √26?
5.1
5.5
5.9
I don't know.
Answer:
5.1
Step-by-step explanation:
√26 = 5.099
5.099 is approximately 5.1
Answer:
5.1
Step-by-step explanation:
k12 quiz :)
what is the total price of a $20,000 car plus 8.5% sales tax ?
You ran 4 1/2 times around a quarter-mile track how far did you run
Answer:
1,809 meters. (1 & 1/8 of a mile)
Step-by-step explanation:
quarter of a mile = 402 meters
402 * 4.5 = 1,809 meters = 1 1/8 mile
What is the area of the composite figure? (6π 4) cm2 (6π 16) cm2 (12π 4) cm2 (12π 16) cm2
The area of the considered composite figure is given by: Option: 6π + 16 cm²
How to calculate the surface area of a composite figure?Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
Thus, we have:
[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]
That ∑ sign shows "sum"
For this case, the missing image is attached below.
As visible, the area of the figure = Sum of area of those 3 semi circles + Area of that square(its square because it has 4 equal sides in which adjacent sides are perpendicular) in between.
The side of the square is of 2+2=4 cm( as half of its side is 2 cm), thus, Area of that square = 4² = 16 cm²
All those 3 semicircles has radius = 2 cm
Since radius is same, so area of those 3 semicircle is same = [tex]\dfrac{\pi r^2}{2} = \dfrac{\pi (2)^2}{2} = 2 \pi\: \rm cm^2[/tex]
Thus, we get:
Area of the composite figure = [tex]2 \pi +2 \pi +2 \pi + 16 \: \rm cm^2 = 6 \pi+ 16 \: \rm cm^2[/tex]
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graph the linear equation. find three points that solve the equation, then plot them on the graph. 5x-4y=-18
What is the area of the beach ball with a diameter of 14 in. ?
Answer:
The answer is 675.75 square Inches
Step-by-step explanation:
Given;Diameter (d) = 14 in.To Find;Area of beach ball = ?Formula;Area = 4πr²Now,
Radius (r) = diameter ÷ 2
r = 14/2 in.
r = 7 in.
Now,
A = 4πr²
A = 4 × 22/7 × (7)² in.
A = 4 × 22 × 7 in.
A = 615.75 square in.
Thus, The area of the beach ball with a diameter of 14 in. is 615.75 square in.
Answer:
615.8 in²
Step-by-step explanation:
The area of a sphere is given by the formula ...
A = 4πr² . . . . . sphere of radius r
In terms of diameter, the area is ...
A = 4π(d/2)² = πd²
__
For a diameter of 14 inches, the area of the beach ball is ...
A = π(14 in)² = 196π in² ≈ 615.8 in²
The area of the ball is about 615.8 square inches.
Ex. 1 Write an equation in slope-intercept form for the line that passes through (3, 8) and is
perpendicular to the line with equation y = -1/3x+8
Answer:
Step-by-step explanation:
The line perpendicual to a reference line will have a slope that is the negative inverse of the reference line. In this case, the reference line is y= -(1/3)X+8, with a slope of -(1/3). The negative inverse would be 3. So the new line would have the form:
y = 3x + b
To find b, the y-intercept, use the given point and solve for b:
y = 3x + b
or 8 = 3*3 + b for the point (3,8)
8=9+b
b= -1
Thje equation of the line perpendicualr to the reference line and going through point (3,8) is:
y = 3x - 1
See attached graph.
If 2x - 3y = 14 and -x + 2y = -8
what is the value of x+y?
answer = 4 does it is correct
Find the median of the data set without the outlier.
Then, find the median of the data set with the outlier.
Answer:
Median without the outlier: 9
Median with the outlier: 9
Step-by-step explanation:
The outlier here is 1, because it's smaller than most of the values in the data set.
Median: the middle value of a data set
Median without the outlier: 9
7, 8, 8, 9, 9, 10, 10, 10, 10
Median with the outlier: 9
1, 7, 8, 8, 9, 9, 10, 10, 10, 10
9 + 9 = 18
18/2 = 9
Hope this helps!
Answer:
the without the outlier 9
set with with the outlier 9
Step-by-step explanation:
What is the Evaluate 5^3+6x3
Answer:
33 Is your answer :)
Step-by-step explanation:
Always do P.E.M.D.A.S ( always go in order it gives you) parenthesis, exponets, multiply/divide, and add/subtract
5^3+6*3=
15+18= 33
Find the surface area (Leave your answer in terms of π) of a sphere with a radius of 12. Use 4πr² to solve.
76π
576π
48π
580π
Answer:
576π
Step-by-step explanation:
Surface Area of a Sphere
4πr²Given
r = 12Solving
S.A. = 4 x π x (12)²S.A. = 4 x 144 x πS.A. = 576πIn pensacola in june, high tide was at noon. the water level at high tide was 12 feet and 2 feet at low tide. assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in june for pensacola as a function of time (t). f(t) = 12 cospi over 2t 5 f(t) = 5 cospi over 2t 12 f(t) = 5 cospi over 6t 7 f(t) = 7 cospi over 6t 12
An equation for water level in june for pensacola as a function of time (t) is f(t) = 5 cos pi/6 t + 7.
Which equation of cos show period amplitude ?
The equation given below show aplitude and period
[tex]y = A cos bx + c[/tex]
where A = amplitude,
b = 2 pi/Period,
Period = 12 hrs,
c = midline,
x = t and y = f(t)
We have to find the amplitude
What is the formula for the amplitude?
[tex]A = 1/2 (Xmax - Xmin)[/tex]
[tex]12 - 2 / 2 = 10/2 = 5[/tex]
[tex]b = 2 pi / 12 = pi/6[/tex]
[tex]c = 1/2 (Xmax + Xmin)[/tex]
[tex]12+2/2 = 7[/tex]
Therefore, the an equation for water level in june for pensacola as a function of time (t)
[tex]f(t) = 5 cos pi/6 t + 7[/tex]
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Which is more, 662 feet or
1
8
of a mile?
Answer:
the answer is 662 feet
Step-by-step explanation:
becuase one eighth of a mile is 660 feet
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
mode = 1
Step-by-step explanation:
the mode is the value that occurs most often in the data set.
1 occurs 3 times and is therefore the mode