Answer:
The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.
The cruise ship's will need 2.425 hours for its upstream journey.
Step-by-step explanation:
The total time of the cruise ([tex]t[/tex]), in hours, is the sum of the times for the upstream ([tex]t_{u}[/tex]) and downstream journeys ([tex]t_{d}[/tex]), in hours. Let suppose that both river and cruise ship travel at constant velocity, the cruise ship travels against the current in its upstream journey, whereas it is in favor of the current in the downstream journey, meaning that:
[tex]t = t_{u} + t_{d}[/tex]
[tex]t = \frac{x}{v_{S/C} - v_{C}} + \frac{x}{v_{S/C} + v_{C}}[/tex] (1)
Where:
[tex]v_{C}[/tex] - Speed of the current, in kilometers per hour.
[tex]v_{S/C}[/tex] - Speed of the cruise ship relative to the current, in kilometers per hour.
If we know that [tex]t = 4\,h[/tex], [tex]x = 18\,km[/tex] and [tex]v_{C} = 2\,\frac{km}{h}[/tex], then we have the following expression:
[tex]4\,h = (18\,km)\cdot \left(\frac{1}{v_{S/C} - 2\,\frac{km}{h} } + \frac{1}{v_{S/C}+2\,\frac{km}{h} }\right)[/tex]
[tex]\frac{2}{9} = \frac{1}{v_{S/C}-2} + \frac{1}{v_{S/C}+2}[/tex]
[tex]\frac{2}{9} = \frac{2\cdot v_{S/C}}{v_{S/C}^{2}-4}[/tex]
[tex]2\cdot v_{S/C}^{2} - 8 = 18\cdot v_{S/C}[/tex]
[tex]2\cdot v_{S/C}^{2}-18\cdot v_{S/C}-8 = 0[/tex]
The roots of the second order polynomial are, respectively:
[tex]v_{S/C,1} \approx 9.424\,\frac{km}{h}[/tex], [tex]v_{S/C,2} \approx -0.424\,\frac{km}{h}[/tex]. Since the speed is the magnitude of the velocity, a realistic solution must be a positive quantity and the solution is:
[tex]v_{S/C} \approx 9.424\,\frac{km}{h}[/tex]
The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.
And the time needed for the upstream journey is:
[tex]t_{u} = \frac{x}{v_{S/C}- v_{C}}[/tex] (2)
If we know that [tex]x = 18\,km[/tex], [tex]v_{S/C} \approx 9.424\,\frac{km}{h}[/tex] and [tex]v_{C} = 2\,\frac{km}{h}[/tex], then time for the upstream journey is:
[tex]t_{u} = \frac{18\,km}{9.424\,\frac{km}{h}-2\,\frac{km}{h} }[/tex]
[tex]t_{u} = 2.425\,h[/tex]
The cruise ship's will need 2.425 hours for its upstream journey.
After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service
department randomly selects 50 cars on the dealership lot, examines them, and finds that 11 cars have damage.
They want to construct a 99% confidence interval for the true proportion of cars with damage from the storm. Are
the conditions for inference met?
O Yes, the conditions for inference are met.
O No, the 10% condition is not met.
No, the randomness condition is not met.
No, the Large Counts Condition is not met.
Answer:
A, yes the conditions for inference are met
Step-by-step explanation:
I got the question right so it's right
2) What is the volume of a basketball that has a diameter of 15 inches?
22. Using the graph, state the approximate
x-intercept of the function?
a. (0, -1)
b. (0.5, 0)
C. (-1,-1.75)
d. (1, 2)
Answer:
I believe Awnser B.. (0.5, 0)
Step-by-step explanation:
PLEASE HELP
Which expression defines the arithmetic series 1 + 5 + 9 + ... for seven terms?
Σ(27-1)
Σ(3n-4)
Σ(4n-3)
Σ(n-1)
Answer:
[tex]\sum\limits^7_{n=1}(4n - 3)[/tex]
Step-by-step explanation:
Given
[tex]1 + 5 + 9 + .....[/tex]
Required
Write a definition
First, we derive a formula for the series using:
[tex]T_n = a + (n - 1)d[/tex]
From the attached data;
[tex]a = 1[/tex]
[tex]d = 5 - 1 = 4[/tex]
So:
[tex]T_n = a + (n - 1)d[/tex]
[tex]T_n = 1 + (n - 1) * 4[/tex]
[tex]T_n = 1 + 4n - 4[/tex]
Collect like terms
[tex]T_n = 4n - 4+1[/tex]
[tex]T_n = 4n -3[/tex]
So, the definition for first 7 terms is:
[tex]\sum\limits^7_{n=1}(4n - 3)[/tex]
ABC and XYZ are similar find the missing side length
Answer:
5
Step-by-step explanation:
Since both triangles are similar, the ratio of their corresponding side lengths would be equal.
This implies that:
AB/40 = 8/64
Cross multiply
AB*64 = 40*8
AB*64 = 320
AB = 320/64
AB = 5
Answer:
Step-by-step explanation:
the Answer is 4
The average speed for a family trip at 62 mph which equation models the distance traveled day and time in hours T
D=T +62
D =T -62
D =T/62
D =62T
Step-by-step explanation:
Last one is the correct answer .
Give brainliest please.
One consequence of the popularity of the Internet is that it is thought to reduce television watching. Suppose that a random sample of 35 individuals who consider themselves to be avid Internet users results in a mean time of 1.99 hours watching television on a weekday.
Required:
Determine the likelihood of obtaining a sample mean of 1.99 hours or less from a population whose mean is presumed to be 2.45 hours.
Answer:
Step-by-step explanation:
What is the value of a in the right triangle shown below?
Answer:
Step-by-step explanation:
plsssss help me i’m confused
Answer:
c
Step-by-step explanation:
What is the volume of the prison below?
Answer:
3 1/2
Step-by-step explanation:
To find the volume of a rectangular prism, you multiply l*w*h.
We just have to multiply 1 3/4 by 2!
*This is because the 1 doesn't give you anything.*
That equals 3 1/2!
4. For his garden, Clay has a mixture of 12
white corn seeds, 24 yellow corn seeds, and
16 bicolor corn seeds. If he reaches for a
seed without looking, what is the probability
that Clay will plant a bicolor corn seed first?
Answer:
I believe about 30.8%
which of the following best defines alternate interior angles?
1) non-adjacent angles formed by the intersection of two lines
2) adjacent angles that form a right angle
3) adjacent angles that form a straight angle
4) angles on the same side of a transversal and in the same position related to parallel lines
Answer:
its a
Step-by-step explanation:
brainliest pls
PLEASE HELP!!
Suppose f(x)=4x - 2 and g(x)= -2x + 1
Find the value of f(-3)/g(-5)
Step-by-step explanation:
f(x)=4x-2
g(x)=-2x+1
f(-3)/g(-5)={4×(-3)-2}/{(-2)×(-5)+1}
=-14/-9
=14/9
a. 61
b. 30
c. 45
d. 41
Answer:
the answer is 61
we complete the degree to 180
so 119+x=180
x=61
Answer:
value of m=180-119
=61,,
Find the perimeter of a quadrilateral with vertices at C (-2, 1), D. (2, 4), E (5,0), and. F (1, -3)
12 units
O 16 units
O 20 units
O 24 units
What are the values for q that will make the equation true |4q+12|=4
Hi there! Solving the absolute value equation is like solving a quadratic equation.
[tex] \large{ |x| = a \longrightarrow x = \pm a}[/tex]
[tex] \large{ |x| = \begin{cases} x \: \: \: (x \geqslant 0) \\ - x \: \: \: (x < 0) \end{cases}}[/tex]
From the absolute equation:
[tex] \large{ |4q + 12| = 4}[/tex]
Cancel the absolute symbol and write plus-minus of 4.
[tex] \large{4q + 12 = \pm 4}[/tex]
Solve the equation for q-term.
[tex] \large{4q = \begin{cases} 4 - 12 \\ - 4 - 12 \end{cases}} \\ \large{4q = \begin{cases} - 8 \\ - 16 \end{cases}} \\ \large{q = \begin{cases} - \frac{8}{4} \\ - \frac{16}{4} \end{cases}} \\ \large{q = \begin{cases} - 2 \\ - 4 \end{cases}}[/tex]
Hence, the value of q are -2,-4
Answer
q = -2,-4A plane flies 35 km in the direction N 30° W, then flies 60 km in the direction N 60° E.
A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs ` 45 per litre, how much money is due to the vendor per day?
Answer:
4500
Step-by-step explanation:
Evaluate each series.
50 points and brainless!
Answer:
Sum of n terms of a GP:
Sₙ = a₁(rⁿ - 1)/(r - 1)#1
a₁ = 5r = 2n = 9S₉ = 5(2⁹ - 1)/(2 - 1) = 5(511) = 2555Correct choice is C
-----------------------------
#2
a₁ = 12r = 1/2n = 5S₅ = 12(1 - (1/2)⁵)/(1 - 1/2) = 12(31/32)/(1/2) = 23.25Correct choice is A
what is the area of the figure 26.8square meters 38.8square meters 43.2square meters 50.8square meters
Answer:
Choise B..... 38.8
Step-by-step explanation:
trust
What should be done to solve the following equation? d - 5 = 3
Answer:
d=8
Step-by-step explanation:
Firstly you need to get d by itself. To get d by itself you need to get 5 onto the other side. To do that you need to add 5 to 3 (because adding is the opposite of addition). Therefore you will get 8! So d = 8
Answer:
add 5 both sides making it
d=5+3
solve 5+3
=8
d=8!!!16x ___=192 i need help ill give brainiest to person n who gets it right
Answer:
12
Step-by-step explanation:
16 x 12 = 192
Annie walks at a rate of two miles per forty minutes. How many minutes does it take her to walk one mile?
Answer: 20 minutes
2 miles = 40 minutes
1 mile = 20 minutes
in an inverse variation, x=2 when y=-4. what is the value of y when x=16
Answer:
y = -1/2
Step-by-step explanation:
Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]
Plug in 2 as x and -4 as y, then solve for k:
y = [tex]\frac{k}{x}[/tex]
-4 = [tex]\frac{k}{2}[/tex]
-8 = k
So, the equation is y = [tex]\frac{-8}{x}[/tex]
Plug in 16 as x and solve for y:
y = [tex]\frac{-8}{x}[/tex]
y = [tex]\frac{-8}{16}[/tex]
y = -1/2
So, when x = 16, y = -1/2
Tell whether the triangle with each set of side lengths is a right triangle.
(See picture)
Answer:
Right Triangles:
(5.1, 6.8, 8.5) and (12.5, 30, 32.5)
Not Right Triangles:
(2.2, 4.5, 6.7) and (4.7, 8.6, 10.7)
Step-by-step explanation:
I solved by using the pythagorean theorem (a^2+b^2=c^2)
Plug the side lengths in, the largest side length is always c. If the equation comes out true, it is a right triangle.
120 de metri plus 125 de metri
Answer:
245
Step-by-step explanation:
120+125=245
PLEASE HELP!!!
You buy a car thats $11,800. The expected depreciation of the car is 35% per year.
Part A- what is the car worth each year it depreciates from the previous year?
Part B - Find the depreciated value of the car after 6 years.
YOU CAN ANSWER EITHER. BOTH WOULD BE NICE. PLEASE HELP.
Answer:
Part a- after one year of depreciation the car would value $7475
part b: the car would be worth $-12650
Step-by-step explanation:
not sure if its correct but that's what I got
Pls help I am falling
Answer:
152.98 square m but u can round off and write 153 square m
Step-by-step explanation:
2-1 whats the answer
Answer:
2-1=1hope it helps you have a great day keep smiling be happy stay safeAnswer:
2-1 is 1
Step-by-step explanation:
hope that it is helpful yo you
PLEASE HELP ASAP!!!!
Answer:
17=x
Step-by-step explanation:
Put in y and minus 4
