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]
There are 7 red counters in a bag.
The rest of the counters in the bag are blue,
There are more blue counters than red counters in the bag.
Two counters are to be taken at random from the bag.
The probability that there will be one counter of each colour is
7/15.
Work out the total number of counters in the bag before any counters are taken from the bag.
Let x be the number of counters in the bag.
Pr(red counter) is drawn first = 7/x
Pr(blue counter) is drawn first = (x-7)/x
Pr(counters will be same) = 8/15
solution:with replacement:
P^req= 7/7+x × x/7+x= 7/15
so, the total number of counters in the bag before any counters are taken from the bag are 7/15.
The change in the x-coordinates of any two points on a line in the xyplane is
the
O A. slope
B. rise
C. run
D. angle
SUBMIT
Answer: The change in the x-coordinates of any two points on a line in the XY plane is the:RUN
Step-by-step explanation:
NEED HELP ASAP!!! GIVING BRAINLIEST+20 POINTS TO B4ST ANSWER FOR THESE 2 QUESTIONS!! YOU CAN DO IT! :D
1. Solve two thirds times two thirds.
1.two ninths
2.two sixths
3.four ninths
4.four over one
2. Matt is painting a mural on a 1-square meter section of a wall. He has completed a rectangular part of the mural that is four sixths of a meter wide and two fifths of a meter tall. What part of the mural has been completed?
1. four fifths
2. eight sixths
3. six elevenths
4. eight thirtieths
Answer:
See below ↓↓
Step-by-step explanation:
1.
2/3 x 2/3Numerator (N) = 2 x 2 = 4Denominator (D) = 3 x 3 = 9Fraction = N/D = 4/9⇒ 3. four ninths2.
Area completed = 4/6 x 2/5Numerator (N) = 4 x 2 = 8Denominator (D) = 6 x 5 = 30Fraction = N/D = 8/30 ⇒ 4. eight thirtiethsExplanation:
[tex]\bold{two \ third \ refers \ to }\ \ \boxed{\sf \frac{2}{3}}[/tex]
[tex]\hookrightarrow \sf \dfrac{2}{3} *\dfrac{2}{3}[/tex]
[tex]\hookrightarrow \sf \dfrac{2*2}{3*3}[/tex]
[tex]\hookrightarrow \sf \dfrac{4}{9}[/tex]
answer: four ninths
2nd
area of the finished part:
Length * Width
[tex]\hookrightarrow \sf \dfrac{4}{6} * \dfrac{2}{5}[/tex]
[tex]\hookrightarrow \sf \dfrac{4*2}{6*5}[/tex]
[tex]\hookrightarrow \sf \dfrac{8}{30}[/tex]
answer: eight thirtieths
Q. Find the volume
10
8
12
3
2
answer choices
A. 128
B. 180
C. 124
D. 182
Answer:
A.128
Step-by-step explanation:
First you break the prism apart so that you have one 7x4x2 rectangular prism and one 12x3x2 prism. Find the volume of both, then add them together.
Volume of 12x3x2:
12 x 3 = 36. 36 x 2 = 72.
Volume of 7x4x2:
7 x 4 = 28. 28 x 2=56.
Then add both volumes: 72 + 56 = 128.
8th grade mathe help8th grademath heelp
Answer:So for number 35 you will put the qwestion in a calculator... now you have your answer so put that ansor to the side, and solve all of the ones in the answer choices and see which one has a common answer from the one in the problem
Step-by-step explanation:
The length of a rectangle is twice its width, The perimeter of the rectangle is 36ft. what are the length and width of the rectangle?
Answer:
length is 12 feet and the width is 6 feet
Step-by-step explanation:
w=width l=length
l=2w
2l+2w=36ft
4w+2w=36ft
6w=36ft
w=6ft
l=2*6=12ft
The probability that the sample will accurately represent the target group within the margin of error is called the Group of answer choices confidence level. polling bias. margin of error. random sample.
Answer:
What is the probability of a sample mean?
The Probability of a Sample Mean The Probability of a Sample Mean We saw in the previous section that if we take samples, the distribution of the sample means will be approximately normal. This will hold true even when the underlying population is not normally distributed, provided we take samples of n=30 or greater.p-by-step
Order -3,5, 16, and -10 from least to greatest.
Then order the same numbers from closest to
zero to farthest from zero. Describe how your
lists are similar.
Using the function f(x) = 32 * (3/4)z, evaluate the following mentally.
f(3) =
Answer:
I also need help with this I'm new to this app so id
The air quality index, or aqi, measures how polluted the air is in your city and assigns a number based on the quality of the air. over 100 is "unhealthy". the number of days the aqi exceeds 100 in a given year is modeled by the following quadratic regression equation: n = 1.76 t squared minus 13.32 t 41.00 let n represent the number of days the aqi exceeds 100 in a given year. approximately how many days did the aqi exceed 100 in the year 1988? round to the nearest whole day. (let t represent the number of years since 1990. therefore, t = 0 corresponds to the year 1990.) a. 60 days b. 75 days c. 61 days d. 21 days
The number of days in which the air quality index exceed 100 in the year 1988 is 75 days. Then the correct option is B.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The air quality index (AQI) is given by the function.
[tex]\rm n = 1.76t^2-13.32 +41[/tex]
Where n be the number of days the AQI exceeds 100 in a given year.
For [tex]\rm t = -2[/tex], then we have
[tex]\rm n = 1.76(-2)^2-13.32(-2) +41\\\\n = 7.04+26.64+41\\\\n = 74.68 \approx 75[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
HELPPPPPPPPPPPPPPPPPPPP
Answer:
I think the modes are: 20 ,18 and 19
Mr. Potter's class will take a test for 1\dfrac121 2 1 1, start fraction, 1, divided by, 2, end fraction hours. They need to finish by half past 111111 to get to lunch on time. What is the latest time the class can start the test to get to lunch on time?
Answer:
is it half past one or another no?
True or false.
If two figures are similar and one is bigger than the other, the scale factor of bigger to smaller will be the same as the scale factor of smaller to bigger.
don't guess
Answer:
true
Step-by-step explanation:
Fiona is studying how income taxes impact various families and their finances. She creates a table with various amounts of taxes owed and estimates that this represents 9% of each family’s gross income.
Using proportions, it is found that the values that complete the table, from top to bottom, are given by: $670, $920, $1500, $2100.
What is a proportion?A proportion is a fraction of a total amount.
Considering that the amounts in taxes correspond to 9% of the gross income, we have that for each family, we will find the incomes as follows:
Family 1:
0.09I = 60.30.
I = 60.30/0.09
I = $670.
Family 2:
0.09I = 82.80.
I = 82.80/0.09
I = $920.
Family 3:
0.09I = 135.00.
I = 135.00/0.09
I = $1500.
Family 4:
0.09I = 189.00.
I = 189.00/0.09
I = $2100.
More can be learned about proportions at https://brainly.com/question/24372153
Question 3 options: lily is building a picture frame. the larger rectangle represents the frame. the smaller rectangle represents the picture. the shaded area represents the 2-inch border around the picture. what is the area of the border, or the shaded region, of this figure in square inches?
The area of the shaded region of this figure which can be calculated by the difference of the larger region from the smaller region would be 104 in.²
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Area of a larger rectangle
= Length × Width
= 18 × 12
= 216 in.²
Area of the smaller rectangle
Length = 12 - 2 - 2 = 8 in.
Width = 18 - 2 - 2 = 14 in.
= Length × Width
= 8 × 14
= 112 in.²
Area of the shaded region = Area of a larger rectangle - Area of the smaller rectangle
= 216 - 112
= 104 in.²
Hence, the area of the shaded region of this figure is 104 in.²
Learn more about the area;
https://brainly.com/question/2289492
Write 2 In 6 + 3 In 4 - 5 In (1/3) as a single logarithm
Answer:
ln 559872
Step-by-step explanation:
2 In 6 + 3 In 4 - 5 In (1/3) = ln 6² + ln 4³ - ln (⅓)⁵
= ln 36 + ln 64 - ln 1/243
= ln [(36×64)/(1/243)]
= ln 559872
What is the multiplier for a 12% increase
Answer:
d
Step-by-step explanation:
d because 12% is = to 0.12
so D
write down
the largest 5 digit
and factorize it.
Answer:
99999
Five Digit Numbers
The smallest five-digit number is 10000 and the greatest five-digit number is 99999.
Step-by-step explanation:
The prism below has dimensions 2 inches by 3 inches by 4 inches. To the right of the prism, shade the number of prisms necessary, if stacked on top of each other as shown, to create a new prism with a surface area between 100 square inches and 130 square inches.
HELPPPPPPPPPPPP
The area of the stacked prism is the amount of space on it
To create a total area between 100 square inches and 130 square inches, 2 to 2.5 prisms
How to determine the number of prisms?
The dimension of the prism is given as:
2 inches by 3 inches by 4 inches
The surface area of the prism is calculated as:
A = 2 * (LW + WH + LH)
This gives
A = 2 * (2 * 3 + 3 * 4 + 2 * 4)
Evaluate the product
A = 52
When the prisims are stacked onto one another, the surface area is between 100 square inches and 130 square inches.
So, the number of prisms (n) needed is:
100/ 52 < n < 130/52
Evaluate the quotient
1.9 < n < 2.5
Approximate
2 < n < 2.5
Hence, 2 to 2.5 prisms are needed to create a total area between 100 square inches and 130 square inches.
Read more about areas at:
https://brainly.com/question/24487155
. Marcella leaves home at 8:00 AM and drives to school, arriving at 8:45 AM. If the distance she
traveled is 27 miles, what is Marcella's average rate of speed in miles per hour?
Step-by-step explanation:
the formula is distance/time
since it is miles per hour and the time is given in minutes. you divide 45minutes by 60(to convert it to hour) and then you divide 27 by the answer
I need help with this problem?
Answer:
Step-by-step explanation:
Volume of cylinder:
[tex]\boxed{\text{Volume of cylinder=$\pi r^{2}h$}}[/tex]
Bottom cylinder:
1 inch = 2.54 cm
diameter = 14 in
r = 14/2 = 7 in
r = 7 *2.54 = 17.78 cm
h = 4 in = 4*2.54 = 10.16 cm
Volume = 3* 17.78 * 17.78 * 10.16
= 9635.59 in³
Upper cylinder:
diameter = 12 in
r = 12/2 = 6in
r = 6*2.54 = 15.24 cm
h = 12 in = 12*2.54 = 30.48 cm
Volume = 3 * 15.24 *15.24 * 30.48
= 21237.63 in³
Volume of the object = 9635.59 + 21237.63
= 30873 cm³
Find the y-intercept and the slope of the line. y=-5/4x+3
Answer:
y intercept is (3,0) and slope is -5/4
Step-by-step explanation:
Look at the equation and know y=mx+b formula
Need help with angle solving
Step-by-step explanation:
corresponding angles (CA)
Alternative interior angles (AIA)
co interior angles (CIA)
question 1 angles =5 + 3 = 180 ( CIA)
83⁰ + 3 = 180
angle 3 = 180 - 83⁰
angle 3 = 97
angle 8 = angle 3.... CA
angle 8 = angle 16 ....CA
ANGLE 16 = ANGLE 12.....CA
angle 5 = angle 13 ....CA
ANGLE 3 = Angle 6......AIA
ANGLE 5 = ANGLE 4.......AIA
ANGLE 4 = ANGLE 7......CA
ANGLE 6 = ANGLE 1......CA
ANGLE 13 = ANGLE 9......CA
ANGLE 12 = ANGLE 14.....AIA
ANGLE 13 = ANGLE 11.....AIA
ANGLE 14 = ANGLE 10.......CA
ANGLE 11 = ANGLE 15
NOW JUST PUT THE VALUES GIVEN IN QUESTION AND AT THE TOP OF MY ANSWER IN EACH CASE AND UR DONE.....
QUESTION 2 :
ANGLE 1 = ANGLE 7 .......AIA
2X + 40 = 6X - 20
40 + 20 = 6X - 2X
60 = 4X
60/4 = X
15⁰ = X
SO, ANGLE 7 = 6× 15 -20 = 90 - 20 = 70⁰
AND, ANGLE 1 = 2 × 15 + 40 = 30 + 40 = 70⁰
ANGLE 7 = ANGLE 3 ......CA
ANGLE 3 = ANGLE 5 .....AIA
ANGLE 3 + ANGLE 6 = 180 .....CIA
70 + ANGLE 6 = 180⁰
ANGLE 6 = 180 - 70⁰ = 110⁰
angle 2 = Angle 6
ANGLE 2 = ANGLE 8.....AEA ALTERNATIVE EXTERIOR ANGLE
ANGLE 8 = ANGLE 4
NOW, JUST PUT THE VALUES I HAVE WRITTEN ABOVE ACCORDINGLY IN EACH CASE....
Did I really jst got 15 points for this (ノ｀Д´)ノ彡
HEHEEE JK:)
Solve the following inequality
Answer:
14<x<20
Step-by-step explanation:
14<x<20 is your required answer
Work out the equation of the line which has a gradient of 2 and
passes through the point (2, 5)
Answer:
y=2x+1
Step-by-step explanation:
You use the equation y=mx+b and substitute m for the slope/gradient. Then you use (2,5) to subtitue for y and x. Solve the equation for b. Then you have your slope and b, and you can make your equation from this.
i need answer please a 78 b 204 c 102 d 51
A’B’C’ is a reflection of ABC over the y_axis. What is the length of A’C’?
~Denki~
Answer:
the length of "AC" should be the same as it was before it was reflected over the y-axis.
(there is no picture so i cant get as specific as intended)
hope this helps :D
The following points lie on a certain line.
х, у
-2, -11
1. -5
4, 1
6, 5
What is the equation of the line?
Oy=-3x + 3
Oy - 2x - 3
Oy - 2X-7
o y = -4x + 2
[tex]y = 2x - 7[/tex]
should be it
A bale of hay in the shape of a rectangular prism has a length of 4 feet, a width of 2 feet, and a height of 2 feet. A cylindrical bale of hay has a diameter of 7 feet and a height of 6 feet. How many rectangular bales contain the same amount of hay as one cylindrical bale?
Answer:
14.424375 cubed feet (can round)
Sorry if this answer is not correct, if it is or is not, please tell me in the comments!
Step-by-step explanation:
First, find the volume of the rectangular prism which is 4 x 2 x 2 = 16 cubed feet.
Next, find the volume of the cylinder, and use this formula:
πrr (area of one circle) x the height
The r = the radius, but we only have the diameter. We need to divide the diameter by 2 to find the radius. (7 divided by 2 = 3.5 feet)
Now, we can plug all of the numbers in the previous formula:
π(3.5)(3.5) x the height (6 feet) = 230. 79 cubed feet
For the final step, we need to do 230. 79 divided by 16 to find how many rectangular prisms can fit in the cylinder.
So, the answer is 14.424375 cubed feet. (Add the label of "squared feet" and round the answer if you like!)
Select the correct answer. Which graph represents this equation? y − 4 = -3(x + 5) A. B. C. D.
