The speed of current is [tex]\rm 2 \:km/h[/tex].
What is the relation between distance,speed and time?The relationship between distance, time and speed can be presented as:
[tex]\begin{aligned} \rm Distance &= Speed \times Time\\\\Speed &= \dfrac{\rm Distance}{Time} \\\\\rm Time &= \dfrac{\rm Distance}{\rm Speed} \end[/tex]
Calculations:
Given:
[tex]\begin{aligned} \rm Distance\: traveled\: on\: motorboat &= 25\:km\\\rm Speed\:of\:motorboat\:in\:still\:water &= 12\:km/h \end[/tex]
Let the speed of the current be [tex]\rm x[/tex]
The speed of the boat traveling against the current is [tex]{(12 -\rm x) km/h}[/tex]
Time spent on motorboat is 10 hours less than time spent on raft.
Therefore:
[tex]\rm \dfrac{25km}{x\:km/h} - \dfrac{25km}{(12 - x)km/h} = 10[/tex]
The equation obtained will be:
[tex]\dfrac{25}{\rm x} - \dfrac{25}{(12-\rm x)} - = 10[/tex]
Multiplying both sides of the equation by [tex]\rm x(12 - x )[/tex]
[tex]\begin{aligned} \rm 25(12 - x) - 25x &= 10\times \rm x(12 - x)\\\\300 - 25x - 25x &= 120x - 10x^2\\\\300 - 50x &= 120x - 10x^2\\\\10x^2 - 120x - 50x + 300 &= 0\\\\10x^2 - 170x +300 &= 0\end[/tex]
Dividing the equation by 10
[tex]\rm x^2 - 17x + 30 = 0[/tex]
On factoring the equation,
[tex]\rm =x^2 - 2x -15x + 30 = 0\\\\=x(x - 2) -15(x - 2)\\\\=(x - 2)(x - 15)[/tex]
The values of x is 2 and 15.
Since speed of current i.e [tex](12 -\rm x)km/h[/tex] cannot be negative, [tex]\rm x = 2[/tex] is the only acceptable value.
Therefore the speed of current is 2 km/h.
Learn more about the topic here:
https://brainly.com/question/2292310
Select all the expressions that could represent the volume of a box, which is a third degree polynomial in variables x and y.
A. 3 x y − 3 x y^2
B 2y-xy^3+7
C.3x^3y^2-3x^2y+10y^2-10y
D. 3x^2y+5xy
E. 3y^3+3x^3y^4
Answer:
A and D
Step-by-step explanation:
Third degree polynomials refers to polynomials that has 3 as the greatest power of the variable.
A. 3 x y − 3 x y^2
Degree = 1 + 2 = 3
This option is correct
B 2y - xy^3 + 7
Degree = 1 + 3 = 4
This option is wrong
C. 3x^3y^2 -3x^2y + 10y^2 - 10y
Degree = 3 + 2 = 5
This option is wrong
D. 3x^2y+5xy
Degree = 2 + 1 = 3
This option is correct
E. 3y^3 + 3x^3 y^4
Degree = 3 + 4 = 7
This option is wrong
Helpppppppppppppppppppppppppppppppp
Answer:
2/9 in the simplist form
Step-by-step explanation:
you multiply both the fractions for the area
then simplify
What’s the answer to this
12cm and 8 cm find the ratio and reduce them in term of lowest term
Answer:
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Step-by-step explanation:
Pierre found a new store where he hopes to save
money on his supplies. He bought 4 brushes and 7
tubes of paint for $32. He has another order for 6
brushes and 8 tubes of paint that will cost $43.
What is the cost of one brush? What is the cost of
one tube of paint?
Miguel ran 15 yards. What distance is that in feet? HELPPPP
Answer: 45 feet 1 yard= 3 feet so 3 feet times 15 is 45 feet
Step-by-step explanation:
Answer:
45 ft
Step-by-step explanation:
1 yd = 3 ft
15 yd = 3(15) ft
15 yd = 45 ft
There are 20 girls
and 12 boys in a class.
What would be the probability of
randomly selecting a girl? (Decimals please)
Answer:
0.625
Step-by-step explanation:
20+12=32 . ( amount of total pupils)
20/32=0.625
Probability is usually a percentage
please help i'm really stuck
how will apply the lesson i have learned in real life scenari
I just need help cause if I don’t I don’t know what imma do
Answer:
[tex]P(32) = \frac{1}{90}[/tex]
[tex]P(Odd) = \frac{1}{2}[/tex]
[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]
Step-by-step explanation:
Given
Sample Space = 10 to 99
First, we calculate the sample size (n)
[tex]n = 99 - 10 + 1[/tex]
[tex]n = 90[/tex]
Solving (a): P(32)
In 10 to 99, there is only 1 32.
So,
[tex]P(32) = \frac{n(32)}{n}[/tex]
[tex]P(32) = \frac{1}{90}[/tex]
Solving (b): P(Odd)
There are 45 odd numbers between 10 and 99
i.e.
[tex]n(Odd) = 45[/tex]
So:
[tex]P(Odd) = \frac{n(Odd)}{n}[/tex]
[tex]P(Odd) = \frac{45}{90}[/tex]
[tex]P(Odd) = \frac{1}{2}[/tex]
Solving (c): P(Multiple of 5)
There are 18 multiples of 5 between 10 and 99
i.e
[tex]P(Multiples\ 5) = \frac{18}{90}[/tex]
[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]
10 marbles 3 red,5 blue,2green what is the probability of not getting a green marble
Answer:
18/20 chance
Step-by-step explanation:
if you have 20 total marbles and two are green you have to subtract two because we are finding out the probability of NOT getting a green marble
100 - 50 + 4
HELP PLS PLS PLSSSSS
Answer:
54
Step-by-step explanation:
100-50+4=50+4
=54
.....
What is the answer? A, B, C, or D
Regina read his novel three nights in a row. Each night, he read for 3/4 of an hour. How many hours did regina read his novel altogether?
Answer:
Regina read for 2 1/4 hours or 2 hours and 15 minutes
Step-by-step explanation:
The Gable Construction Corporation has placed bids for installing electronic message boards on two different highways.
Because of competition from other companies, Gable Construction Corporation officials estimate that the probability that
they will be awarded the Macon Expressway contract is 0.65 and the probability that they will be awarded the Seaview
Expressway contract is 0.43. Furthermore, the probability that they will be awarded both contracts is 0.22. What is the
probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway
Answer:
0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway
Step-by-step explanation:
We solve this question using these events as Venn sets.
I am going to say that:
Event A: Awarded the Macon Expressway.
Event B: Awarded the Seaview Expressway.
Probability that they will be awarded the Macon Expressway contract is 0.65
This means that [tex]P(A) = 0.65[/tex]
The probability that they will be awarded the Seaview Expressway contract is 0.43.
This means that [tex]P(B) = 0.43[/tex]
Furthermore, the probability that they will be awarded both contracts is 0.22.
This means that [tex]P(A \cap B) = 0.22[/tex]
What is the
Probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway?
Only A:
[tex]P(A) - P(A \cap B) = 0.65 - 0.22 = 0.43[/tex]
Only B:
[tex]P(B) - P(A \cap B) = 0.43 - 0.22 = 0.21[/tex]
Either
0.43 + 0.21 = 0.64
0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway
A certain town never has two sunny days in a row. Each day is classified as being either sunny, cloudy (but dry), or rainy. If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is 60% of chance that it will be the same the next day, and if it changes then it is equally likely to be either of the other two possibilities. In the long run, how frequent are we observing a day for which it is rainy and the next two days are also rainy
Answer:
In the long run if one day is rainy there is frequency of 2/5 that other two days will also be rainy.
Step-by-step explanation:
A matrix is formed to classify the weather conditions. It is given that if one day is sunny then there is likely chance that the next day will be cloudy, but if one day is rainy then there is 60% chance that next day will be same. To identify the possibility of next two days we create probability matrix;
Probability (P) = [tex]\left[\begin{array}{ccc}0&\frac{1}{2} &\frac{1}{2} \\\frac{1}{4} &\frac{1}{2} &\frac{1}{4} \\\frac{1}{4} &\frac{1}{4} &\frac{1}{2} \end{array}\right][/tex]
After solving for probability we get a fraction of 2/5
If you buy 4 turkey subs that in total costs 26 dollars how much would 5 turkey subs cost.
Answer:
33/32.5
Step-by-step explanation:
26 divided by 4 equals 6.5
then 6.5 times 5 equals 32.5
Can someone write down the answers pls!!!!!!!!!!
Step-by-step explanation:
6b x>=1
6c y>7
7a x>3
7b -2<=2x<6
-1<=x<3
answer:-1,0,1,2,3
PLEASE HELP
what is the slope of the line?
Answer these correctly I’ll give brainalist + 10 points
3.663 rounded to the nearest tenth of an ounce
Answer:
the answere is 3.7
Step-by-step explanation:
Answer 1 and 2 for brainliest
What is the answer?
A)44
B)42
C)45
D)48
Answer:
44
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
because you take 3 pulse 2
2 1/3 x 3 5/6 please answer
Answer:
8 17/18
Step-by-step explanation:
I used an online calculator (calculator soup)
Answer:
8 17/18
Step-by-step explanation:
7/3 * 23/6
7*23
3*6
161/18
8 17/18
17 × 5/8 mixed solution
Answer:
10 5/8
Step-by-step explanation:
17/1 x 5/8. Multiply numerators together and denominators you will get 85/8. Then you convert the improper fraction.
Answer:
10 5/8
Step-by-step explanation:
17 × 5/8 = 85/8
Simplify, sub-step b: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
85 ÷ 8 = 10 remainder 5
85/8 = 10 5/8
6+x=23 what is x in the equation
What is the equation of the line in the slope intercept form?
Answer:
y = mx+b is the equation for slope-intercept form
Step-by-step explanation:
m=slope
x=independent variable
y= y-intercept
Answer:
y=-2x
Step-by-step explanation:
−2 2/21 +(−0.25÷(− 1/4 )−1.5÷(− 3/16 ))÷(−4 1/11 )
pls answer this is a hundred point question
The answer is -4.29523809524 . (The second period is NOT another point. It’s just marking the end of a sentence. Yes, I’m a grammar & math freak)
Answer:
-4.29523809524
Step-by-step explanation:
heyy i need help on me hw
Answer:
the answer is b
Step-by-step explanation:
brainliest pleasee?
ill so you the picture of it
Answer:
Of WhaT?
Thanks for the free points btw
The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per
year. Which function shows the company's profit as a function of time in years?
a. f(t) = 100,000 0.012^t
b. f(t) = 100,000(1 + 1.2)^t
c. f(t) = 100,000(1 + 0.012)^t
d. f(t) = 100,000 - 1.2^t
Given:
Initial profit = $100,000
Increasing rate of profit = 1.2%
To find:
The function that shows the company's profit as a function of time in years.
Solution:
The exponential growth model is defined as:
[tex]f(t)=a(1+r)^t[/tex]
Where, a is the initial value, b is the growth rate and t is the time period.
Putting a=100,000 and r=0.012, we get
[tex]f(t)=100,000(1+0.012)^t[/tex]
Where, t is the number of years.
Therefore, the correct option is c.