Johnny and his father go fishing at 5:00 AM. After motoring 6 km upstream, Johnny writes a letter to his friend, puts the letter in a bottle, and drops it into the river. The bottle floats in the current and reaches at 7:40 AM the point where Johnny and his father began their trip. If the speed of the boat in still water is 9 km/h, what is the speed of the river current?
Answer:9/2 km per hour
Step-by-step explanation:
equation,
6/9-x + 6/x=8/3
Upstream is flowing of the boat in the opposite direction of the stream. The speed of the river current is 4.5 km per hour.
Given-Johnny and his father go fishing at 5:00 AM.
Total traveled by the Johnny and his father in upstream is 6 km.
The speed of the boat is 9 km/h.
What is upstream?
Upstream is flowing of the boat in the opposite direction of the stream.
Let x be the speed of the river current.
Time taken by the Johnny and his father to travel 6 km in upstream is ,
[tex]=\dfrac{6}{9-x}[/tex]
The time taken by the bottle to floats in the current river is,
[tex]=\dfrac{6}{x}[/tex]
As Johnny and his father start from 5:00 AM and the bottle reached to the point where Johnny and his father began their trip at 7:40 AM. Thus the total time is,
[tex]=7:40-5:00[/tex]
[tex]=2:40[/tex]
In hours,
[tex]=2\dfrac{40}{60}[/tex]
[tex]=\dfrac{8}{3}[/tex]
As the total time is equal to the sum of the Time taken by the Johnny and his father to travel 6 km in upstream and The time taken by the bottle to floats in the current river. Thus,
[tex]\dfrac{6}{9-x}+\dfrac{6}{x}=\dfrac{8}{3}[/tex]
[tex]\dfrac{6x+54-6x}{9x-x^2}= \dfrac{8}{3}[/tex]
[tex]\dfrac{27}{9x-x^2}= \dfrac{4}{3}[/tex]
[tex]x^2-9x+\dfrac{81}{4}=0[/tex]
On solving the above quadratic equation we get the positive value of the x is 4.5.
Thus the speed of the river current is 4.5 km per hour.
Learn more about the upstream here;
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Henry's height is 3 inches more than one-half of Charlie's height. If Henry is 24 inches tall, how tall is Charlie?
Answer:
Charlie is 20.5 inches tall
Step-by-step explanation:
Henry: 24 inches
3 and 1/2 inches taller than Charlie
Charlie: 24 - 3.5 inches
20.5 inches
Answer:
9 inches
Step-by-step explanation:
henry = 3 inches more than 1/2 of charlie
24=henry
24/2= 12-3=9 inches hope this helps
somebody help me fast pleaseee 5 rate
Answer:
(7m+4m+8m)×219m×2=38mGiven: m∠B = 46°; m∠C = 45°; m∠R = 46°;
m∠T = 89°
Prove: △ABC ~ △TRS
Triangles A B C and T R S are shown. Angles A B C and T R S are 46 degrees. Angle B C A is 45 degrees. Angle R T S is 89 degrees.
Melissa believes that the AA similarity theorem can prove that the triangles are similar. Which fact would be necessary in the proof?
△ABC is an acute triangle.
△TRS is larger than △ABC.
The sum of the measures of the interior angles of a triangle is 180°.
The sum of the side lengths of two sides of a triangle is greater than the third side length
Answer:
85
Step-by-step explanation: multiply
Answer:
B: Triangle R S P is similar to triangle Z X Y
C: Triangle S R P is similar to triangle X Z Y
E: Triangle R P S is similar to triangle Z Y X
Step-by-step explanation:
1. The function f(x) = -0.05(x2 - 26x - 120) represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent? (1 point)
Answer:
f(x) represents the vertical height of the cannon
Step-by-step explanation:
The given function is presented as follows;
f(x) = -0.05·(x² - 26·x - 120)
Given that 'x' represent the horizontal path of the cannon and the function describes the path of the cannon, we have that the vertical height reached by the cannon as it moves along the horizontal path is given as the function f(x)
Therefore, we have;
f(0) = -0.05·(0² - 26×0 - 120) = -0.05 × -120 = 6
f(0) = 6
The starting height of the cannon = 6
The maximum height reached by the cannon is given as follows;
f'(x) = d(-0.05·(x² - 26·x - 120))/dx = -0.05·d(x² - 26·x - 120)/dx = -0.05×(2·x - 26)
f'(x) = -0.05×(2·x - 26)
f'(x) = 0 At maximum height, therefore, we have;
-0.05×(2·x - 26) = 0
(2·x - 26) = 0
2·x = 26
x = 26/2 = 13
x = 13
f(13) = -0.05·(13² - 26×13 - 120) = 14.45
The maximum height = 14.45
Therefore;
f(x) = The vertical height of the cannon
(x^7 + 3x^6 - x^2 + 4) + (3x^7 - x^4 + 3x^2 - 9) add
Answer:
4x^7 + 3x^6 - x^4 + 2x^2 - 5
1
Which is an equation of the line with slope 2 that contains the point (6,4)?
a.y= 22 - 8
1
y =
+1
b.
х
1
2
2 +4
C С.
1
y =
2
Question 2
Which is the equation of a line that passes through the point (5, 6) and has a slope of O?
a.y = 5
b.y=6
X cx=5
d. x = 6
Okoo
Answer:
Step-by-step explanation:
1. y - 4 = 2(x - 6)
y - 4 = 2x - 12
y = 2x - 8
2. y - 6 = 0(x - 5)
y - 6 = 0
y = 6
answer is b
Expand (- 3a - 5x) (- 2b - 4y).
Answer: −3a(−2b−4y).−5x(−2b−4y). to this
6ab+12ay+10bx+20xy
Step-by-step explanation: hope this helps :)
Answer:
( −3a − 5x ) ( −2b − 4y )
= ( −3a + − 5x ) ( −2b + −4y )
=( −3a ) ( −2b ) + ( −3a ) ( −4y ) + ( −5x ) ( − 2b ) + ( − 5x ) ( − 4y )
= 6ab + 12ay + 10bx + 20xy
Hope it helps
Please mark me as the brainliest
Thank you
A box with a base that had an area of 144 square inches. The box measured 9 inches high. What is the volume of the box?
Answer:
1152 in^3
Step-by-step explanation:
Given data
Area of the box= 144 in^2
Height = 9 in
Volume=??
We know that
volume= Area* Height
substitute
volume= 144*8
volume= 1152 in^3
Hence the volume will be 1152 in^3
express the product in the simplest form
7/4 x 12
i will mark u brainly and give u more points
Answer:
21
Step-by-step explanation:
Set it up as 7/4 x 12/1. Multiply the numerators and denominators. That equals 84/4 which simplifies to 21.
Find the value of x. Round to the nearest tenth. 9 4 x = [?]
Answer:
26.4° (nearest tenth)
Step-by-step explanation:
[tex]\boxed{sinθ = \frac{opp}{hyp} }[/tex]
[tex]sinx = \frac{4}{9} [/tex]
Taking the inverse of sine on both sides:
[tex]x = sin^{ - 1} ( \frac{4}{9} )[/tex]
x= 26.4° (nearest tenth)
what is the positive solution to this equation?
4x²+12x=135
Answer:
x = 4.5
Step-by-step explanation:
Solve for x by using the quadratic formula
x = -12 + or - [tex]\sqrt{144+2160}[/tex] / 8
so (-12 + 48) / 8 or (-12 - 48) / 8
so 36/8 or -60/8, they just want the positive solution so x = 4.5
At work, Mr. Grinnell receives 20 phone calls every 60 minutes. How many calls should he expect to receive in 180 minutes?
60
80
100
40
Answer:
Use a ratio.
20/60 = x/180
180/60 = 3, so 20*3 is 60.
The answer is 60.
Answer:
60
Step-by-step explanation:
Find out how many phone calls Mr. Grinnell receives in 1 minute.
60 mins = 20
1 min = 20 ÷ 60 = 0.333
180 mins = 0.333 x 180 = 59.94
59.94 rounded to the nearest whole number = 60
In a certain country the heights of adult men are normally distributed with a mean of 69 inches and a standard deviation of 2.2 inches. The country's military requires that men have heights between 64.6 inches and 73.4 inches.
Complete Question
In a certain country the heights of adult men are normally distributed with a mean of 69 inches and a standard deviation of 2.2 inches. The country's military requires that men have heights between 64.6 inches and 73.4 inches.
What percentage of this country's men are eligible for the military based on height?
Answer:
95.45 %
Step-by-step explanation:
We solve using z score formula
z-score iis z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 69
σ is the population standard deviation = 2.2
For x= 64.6 inches
z = 64.6 - 69/2.2
z = -2
Probability value from Z-Table:
P(x = 64.6) = 0.02275
For x= 73.4 inches
z = 73.4 - 69/2.2
z = 2
Probability value from Z-Table:
P(x<73.4) = 0.97725
The probability of this country's men are eligible for the military based on height is calculated as:
p(x = 73.4) - p( x = 64.6)
0.97725 - 0.02275
= 0.9545
Converting to Percentage is
= 0.9545 × 100
= 95.45 %
this is due in 15 minutes pls help me lol thx
Answer:
ITS A
Step-by-step explanation:
PLZ GIVE BRAINLEIST
Order the steps to solve the equation log(x2 - 15) = log(2x) form 1 to 5.
x² – 2x - 15=0
Potential solutions are -3 and 5
x² – 15 = 2x
X-5 = 0 or x + 3 = 0
(x - 5)(x + 3) = 0
Answer:
Took L for my gang keep working hard
Step-by-step explanation:
HURRY I NEED HELPPPPP !!!!
Write each expression as a single power of 10 .
A. 10^(−3) ⋅ 10^(−2)
B. 10^4 ⋅ 10^(−1)
C. 10^5/10^7
D. (10^(−4))^5
E. 10^(−3) ⋅ 10^2
F. 10^y / 10^5
Answer:
A. 10^(−3) ⋅ 10^(−2) = 10^-5
B. 10^4 ⋅ 10^(−1) = 10^3
C. 10^5/10^7 = 10^-2
D. (10^(−4))^5 = 10^-20
E. 10^(−3) ⋅ 10^2 = 10^-1
F. 10^y / 10^5 = 10^(y-5)
NEED HELP ASAP! TY IN ADVANCE <3 DO THE TABLE OF VALUES AS WELL!
Answer:
Domain {-2, 0, 1, 6}
Range {13, 5, 7, 77}
Step-by-step explanation:
table of values
Domain {-2, 0, 1, 6}
Range {13, 5, 7, 77}
Answer:
Step-by-step explanation:
[tex]y_{1}[/tex] = 2( - 2 )² + 5 = 2(4) + 5 = 13
[tex]y_{2}[/tex] = 2( 0 )² + 5 = 5
[tex]y_{3}[/tex] = 2( 1 )² + 5 = 7
[tex]y_{4}[/tex] = 2( 6 )² + 5 = 77
Range: { 5, 7, 13, 77 }
are the triangles below similar? yes or no?
Answer:
Yes. They all have the same angle measurements making them similar.
One angle of an isosceles triangle measures 48°. Which other angles could be in that isosceles triangle? Choose all that apply.
Answer:
70° and 62° could be the other angles in that isosceles triangle
PLEASE HELP ME THANK YOU IF U DO
Answer: Acceleration
Step-by-step explanation:
b) Select all expressions that can be used to find 85% of 280.
A. O
8.5
10
280
B.
0.85
100
280
c. O
85
100
• 280
Answer:
238
Step-by-step explanation:
85%of 280 is 238 ok.......
help anyone giving 5 stars
Answer:
4,5 in
Step-by-step explanation:
Find The Volume (nearest integer):*
Answer:
3053.63 or to the nearest integer 3054
Step-by-step explanation:
Volume formula of a sphere
[tex]V=4/3\pi r^3\\V=4/3*\pi *9^3\\V= 3053.63 \\[/tex]
Rounded off = 3054
2/3x=-20 A -60 B -30 C -10 D 10
Answer:
B. -30
Step-by-step explanation:
[tex]x = -20\cdot \frac{3}{2} = -30[/tex]
in how many ways can a supermarket chain select 3 out of 12 possible sites for construction of a new supermarket?
Answer:
its 220
Step-by-step explanation:
There are 220 ways supermarket chains can select 3 out of 12 possible sites for the construction of a new supermarket.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Supermarket chains select 3 out of 12 possible sites for the construction of a new supermarket.
As we know,
[tex]\rm C(n, r) =\dfrac{n!}{( r! (n - r)! )}[/tex]
n = 12
r = 3
[tex]\rm C(12, 3) =\dfrac{12!}{( 3! (12 - 3)! )}[/tex]
C(12, 3) = 220
Thus, there are 220 ways supermarket chains can select 3 out of 12 possible sites for the construction of a new supermarket.
Learn more about permutation and combination here:
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What is the best measure of center for this data set?
{101, 2, 108, 104, 102, 107, 109, 102}
A.mean because there is an outlier
B.median because there is an outlier
C.mean or median because there is no outlier
D.mode because there is an outlier
Answer:
it is B the median hope this helps :)
Step-by-step explanation:
Answer:
A. Mean
Step-by-step explanation:
When there is an outlier, the mean is the best way to figure out the average. Median doesn't work because it determines the exact middle, and the outlier (that 2) would affect it greatly, and the mode doesnt work, because it is the value that apears most in the data set, but just because it appears most doesnt mean its the average. In this case the mode is 102, but that is not the average. I hope this helps :)
can someone help.. i’ll chose brainliest if best
Answer:week 3 and week 1
Step-by-step explanation:
Answer:
chicken
Step-by-step explanation:
Expand to write an equivalent expression: −14(8x+12y)
Factor to write an equivalent expression: 36a−6
Pls solve these quick
Answer:
-112x-168y, 6(6a-1).
Step-by-step explanation:
-14(8x+12y)
-112x-168y
-----------------
36a-6
6(6a-1)
Answer:
Step-by-step explanation:
yassssssss
Jack correctly wrote another expression, 100−2t 100 - 2 t , to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.
Complete question :
Kate had 50 tickets to use for rides at the fair. She lost some of them. Her dad doubled the tickets she had left. Kate wrote the expression 2(50−t) to find the number of tickets she has now, where t t is the number of tickets she lost. Jack correctly wrote another expression, 100−2t, to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.
Answer:
50 means Kate's initial number of tickets
t = number of tickets she lost
2 = multiple by which her dad gave ; two times the number of her remaining tickets.
100 = double the number of initial tickets
2t = two times the number of tickets lost
Step-by-step explanation:
Kate's expression :
2(50 - t)
50 means Kate's initial number of tickets
t = number of tickets she lost
2 = multiple by which her dad gave ; two times the number of her remaining tickets.
Jack's expression:
100 - 2t
Jack's expression is an expanded for of Kate's equation
100 = double the number of initial tickets
2t = two times the number of tickets lost
2(50 - t) :
(2 * 50) - (2 * t)
100 - 2t