Answer:
He traveled at 72km/hr during the rain
Step-by-step explanation:
Question is not well formatted. See comment
Given
[tex]d=400km[/tex] --- distance
[tex]t = 11hrs[/tex] --- total time
Let his speed from city A till the rain starts on his return trip be [tex]s_1[/tex]
Let his speed from city during the rain be [tex]s_2[/tex]
So:
[tex]s_2 = s_1 -20[/tex]
Required
Calculate [tex]s_2[/tex]
From the question, we understand that; he drives the whole 400 km and 2/5 of 400 km at [tex]s_1[/tex]
The distance covered during this period is:
[tex]d_1 = 400 + \frac{2}{5} * 400[/tex]
[tex]d_1 = 400 + 160[/tex]
[tex]d_1 = 560[/tex]
And the time during this period is:
[tex]t_1 = \frac{2}{5} * 11[/tex]
[tex]t_1 = 4.4[/tex]
So, the distance during the rain is:
[tex]d_2 = 2 * 400 - d_1[/tex]
[tex]d_2 = 2 * 400 - 560[/tex]
[tex]d_2 = 800 - 560[/tex]
[tex]d_2 = 240[/tex]
And the time during the rain is:
[tex]t_2 = 11 - t_1[/tex]
[tex]t_2 = 11 - 4.4[/tex]
[tex]t_2 = 6.6[/tex]
So, we have:
[tex]d_1 = 560[/tex] --- distance covered before the rain
[tex]d_2 = 240[/tex] --- distance covered when raining
[tex]s_2 = s_1 -20[/tex]
[tex]t_1 = 4.4[/tex] ---- time spent before the rain
[tex]t_2 = 6.6[/tex] --- time spent in the rain
Speed is calculated as:
[tex]Speed = \frac{distance}{time}[/tex]
Make distance the subject
[tex]distance = speed * time[/tex]
So:
[tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex]
Recall that:
[tex]s_2 = s_1 -20[/tex]
Make [tex]s_1[/tex] the subject
[tex]s_1 = s_2 + 20[/tex]
The expression [tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex] becomes:
[tex]560 + 240 = (s_2 + 20) * 4.4 + s_2 * 6.6[/tex]
[tex]800 = 4.4s_2 + 88+ 6.6s_2[/tex]
Collect like terms
[tex]6.6s_2 + 4.4s_2 = 880 - 88[/tex]
[tex]11s_2 = 792[/tex]
Solve for [tex]s_2[/tex]
[tex]s_2= \frac{792}{11}[/tex]
[tex]s_2=72km/h[/tex]
The distance and time 400 km and 11 hours as well as the speed
reduction gives the speed during the rainy part as 60 km/h.
Which method can be used to find the speed in the rain?Based on the comment in the question, we have;
Given:
Distance between City A and City B = 400 km
Distance travelled at the same speed on his way back = [tex]\mathbf{\frac{2}{5}}[/tex] of the distance
Amount by by which his speed is reduced in the remaining [tex]\frac{3}{5}[/tex] of the distance because of rain = 20 km/h
The duration of the trip = 11 hours
Required:
How fast Mr. Jones was driving during the rainy part of his trip from City
B to City A?
Solution:
Let v represent the constant speed, we have;
[tex]Time = \mathbf{ \dfrac{Distance}{Speed}}[/tex]
The distance for which his speed is v = ([tex]\frac{2}{5}[/tex] + 1) × 400 km = 560 km
Total distance of the round trip = 400 km + 400 km = 800 km
The distance for which the speed = v - 20 = 800 km - 560 km = 240 km
Therefore, we have;
[tex]\mathbf{\dfrac{560}{v} + \dfrac{240}{v - 20}}= 11[/tex]
Which gives;
[tex]\mathbf{\dfrac{560 \times (v - 20) + 240 \cdot v}{v\times (v - 20) } } = 11[/tex]
11 × (v² - 20·v) = 560·v - 20 × 560 + 240·v
11·v² - 220·v - 560·v - 240·v + 11200
11·v² - 1020·v + 11,200 = 0
Using the quadratic formula, to solve the above quadratic equation we have;
[tex]v = \dfrac{1020 \pm\sqrt{(-1020)^2 - 4 \times 11 \times 11200} }{2 \times 11} = \dfrac{1020 \pm740 }{22} = \mathbf{ \dfrac{1020 \pm740 }{22}}[/tex]
v = 80 or v = [tex]12 . \overline{72}[/tex]
The possible value for the constant speed is therefore;
v = 80 km/h
The speed during the rain = v - 20, which gives;
The speed during the rain = 80 km/h - 20 km/h = 60 km/hLearn more about quadratic formula here;
https://brainly.com/question/283838
There are 25 black cars, 15 blue cars, 21 red cars and 30 white cars what is the probability of getting a red car
Any help? Algebra I
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Answer:
2p +3d = 18.25; 4p +2d = 27.50popcorn: $5.75; drink: $2.25Step-by-step explanation:
a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.
Mohamed's purchase is ...
2p +3d = 18.25
Miguel's purchase is ...
4p +2d = 27.50
__
b) We can subtract half the second equation from the first to get an equation for the cost of a drink.
(2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)
2d = 4.50 . . . . . . simplify
d = 2.25 . . . . . . divide by 2
4p +2(2.25) = 27.50 . . . . substitute for d in the second equation
4p = 23.00 . . . . . . . . . subtract 4.50
p = 5.75 . . . . . . . . . divide by 4
The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.
No step by step answers or links
Answer:
1. k = 15
2. d = 20
3. n = 3
A cylindrical water tower has a volume of
10007 ft.
If the tower is 10 ft tall, what is the radius of the tower?
Answer:
r≈17.85
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
Answer:
r=17.85
Step-by-step explanation:
i just got it and did the math
which geometric figures are shown in the diagram
Answer:
A circle to start off, encompassing almost the entire figure, then a triangle, with D, A and C as its vertices, then a fan (a sector of a circle), with C, E and B as its vertices. Next, a chord (DA) which serves as a line segment at the same time, and finally three rays, starting from C and ending in A, B and E respectively. In total, six geometric figures.
Step-by-step explanation:
Hope this helped!
Use the exact values of the ratios and find the value of tan 45° + sin 30°
Answer:
1.5
tan45=1
sin30=1/2
so 1+1/2=1.5 or 3/2
The police measured the skid marks made by a car that crashed into a tree. The formula used to approximate the distance in feet that it takes to stop a car after the brakes are applied for a car traveling at a rate of r miles per hour is d= 0.045 r^2 + 1.1 r . If the measurement gave a braking distance of 250 ft, was the driver exceeding the legal speed limit of 55 mi/h? Find the speed of the car before the brakes were applied.
Replace r in the equation with 55 mph and solve for d.
D = 0.045(55)^r + 1.1(55)
Simplify:
D = 0.045(3025) + 60.5
D = 136.125 + 60.5
D = 196.625
At the speed limit of 55 mph the skid mark would be 196.625 feet long.
Because the skid mark was greater than that it was going faster than 55 mph.
To find the speed the car was going replace d with 250 and solve for r:
250 = 0.045r^2 + 1.1r
Multiply both sides by 1000 to remove decimals:
250000 + 45r^2 + 1100r
Subtract 250000 from both sides
45r^2 + 1100 -250000 = 0
Use the quadratic formula to solve:
R = -1100 + sqrt(1100^2 14x45(-250000) /(2 x45)
R = 63.308 miles per hour
The speed of the car was 63.3 miles per hour
The 12th term of GP whose
1
first term is 1/8 and second
term is 1/2is
Answer:
jjanation:jdgjdjgdjgjkdkidjgjghdjjghhkd
Please help so urgent
Answer:
Option E. None of the above.
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
Recall:
When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e
f(x) × f¯¹(x) = 1
With the above information, we can determine the inverse of function given above as follow:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
f(x) × f¯¹(x) = 1
(x – 5)/(2x + 3) × f¯¹(x) = 1
f¯¹(x)(x – 5) / (2x + 3) = 1
Cross multiply
f¯¹(x)(x – 5) = (2x + 3)
Divide both side by (x – 5)
f¯¹(x) = (2x + 3) / (x – 5)
Thus, the inverse of the function is (2x + 3) / (x – 5).
Option E gives the correct answer to the question.
Assuming p: she is beautiful,q :she is clever,the verbal form of ~p^ (~q) is she is beautiful but not clever. she is beautiful and clever she is not beautiful and not clever.she is beautiful or not clever.
Answer:
C. she is not beautiful and not clever.
Step-by-step explanation:
A. she is beautiful but not clever. B. she is beautiful and clever
C. she is not beautiful and not clever.
D. she is beautiful or not clever.
p: she is beautiful
q :she is clever
~p^ (~q) in verbal form
~p = she is not beautiful
~q = she is not clever
~p^ (~q) = she is not beautiful and not clever.
C. she is not beautiful and not clever.
HELP FAST PLS
Factor x2 - 7x + 8.
O (X + 8)(x - 1)
O Prime
O (x - 3)(x - 1)
O (X + 8)(x + 1)
si franco comió 8/3 de pizza y Fabián comió 5/6 de la misma pizza. ¿quien comió más ? si quedó 4/9 de pizza.
Answer:
Franco comió 8/3 de pizza.
Fabián comió 5/6 de pizza.
Queremos saber quien comió más.
Entonces básicamente queremos ver cuál número es más grande, 8/3 o 5/6,
Podemos reescribir el primero como:
8/3 = (2 + 3 + 3)/3 = 2/3 + 3/3 + 3/3 = 2/3 + 1 + 1
= 2 + 2/3
En cambio, para el número 5/6, el numerador es menor que el denominador, entonces sabemos que:
5/6 < 1
Claramente podemos ver que 8/3 > 5/6
Entonces podemos concluir que Franco comió más.
Will Mark Brainlest help please
Answer:
g(-1 )=-1 and g(2)+g(1)=7
Step-by-step explanation:
If g(x) = x^3+x^2-x-2 find g(-1)
if we find g(-1)
we substitute all the x's in the function with -1
-1^3+-1^2-(-1)-2
-1^3 = -1
-1^2 = 1
-1+1+1-2
(two minuses make a plus)
-1+1 = 0
0+1 = 1
1-2 = -1
if x=-1, g(-1) is -1
g(2)+g(1)
substitute the x's in the function with 2 and 1 and add your results
2^3+2^2-2-2
2^3 = 8, 2^2 = 4
8+4-2-2
8+4= 12, 12-2 = 10, 10-2 = 8
g(2)=8
g(1) now
1^3 + 1^2-1-2
1^3=1, 1^2 = 1
1+1-1-2
1+1 = 2, 2-1 = 1, 1-2 = -1
g(3) = -1
g(2) (which equals 8) + g(3) (which equals -1) =
8+(-1) = 7
g(2)+g(3)=7
if the ratio of the volume of two cubes is 1 : 8 , then find the ratio of the total surface area of the two cubes
Answer:
V = L^3 where v is volume and L the length of one side
A = 6 * L^2 total area of cube with side L
A = 6 * V^2/3 area of cube expressed in V
A2 / A1 = (V2 / V1)^2/3 6 cancels
A2 / A1 = 8^2/3 = 4 ratio of areas
What the cubic inches…
Step-by-step explanation:
The radius r is 5 in (r = D/2). so the volume V of the beach ball is
[tex]V= \dfrac{4 \pi}{3}r^3 = \dfrac{4 \pi}{3}(5\:\text{in})^3[/tex]
[tex]\:\:\:\:\:= 523.6\:\text{in}^3[/tex]
Which expression is equivalent to a^7
Answer:
here is your answer
Step-by-step explanation:
here is your answer
simplification please
Answer:
5
Step-by-step explanation:
WHen we raise a power to a power, we multiply them, in this case 5 is the base so we can just ignore it for now and replace it with x.
(X^1/3)^3
Multiply 1/3 by 3 and we get 1
So:
X^1
Which does nothing, so we can simplify to just:\
X
Remember x is 5 so the answer is:
5
Here is a table of values for y = f(x).
Х
-2 -1 0 1 2 3
4.
5
6
f(x) 5
6 7 8 9 10 11 12 13
Mark the statements that are true.
Step-by-step explanation:
the true answers are:
A. f(-1)=6
D. the domain for f(x) is the set
{-2,-1,0,1,2,3,4,5,6}
-5(-3x+1)= 45 solve for x
Answer:
x=[tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Hi there!
We are given the equation -5(-3x+1)=45 and we need to solve for x
we do this by isolating x by itself on one side of the equation; the numbers (the value of x) is on the other side
First, do the distributive property and distribute -5 on -3x and 1 on the left side (multiply both -3x and 1 by -5)
15x-5=45
add 5 to both sides (-5+5=0)
15-5=45
+5 +5
_________
15x=50
divide both sides by 15 (15÷15=1)
15x=50
÷15 ÷15
________
x=[tex]\frac{50}{15}[/tex]
we can simplify this fraction by factoring five out of 50 and 15
x=[tex]\frac{10*5}{3*5}[/tex]
cancel 5 out of the numerator and denominator
x=[tex]\frac{10}{3}[/tex]
The answer can be left as an improper fraction
Hope this helps! :)
Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.
Given right triangle GYK, what is the value of tan(G)?
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
StartRoot 3 EndRoot
Answer:
The answer is A
Step-by-step explanation:
just took it on egde
If someone can pls give the answer with steps that would be greatly appreciated :)
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The measures of [tex]x[/tex] and [tex]y[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\: 210°\:and\:\:y\:=\: -30°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
An exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
[tex] 40° = 70° + y[/tex]
[tex]➪ \: y= 40° - 70°[/tex]
[tex]➪ \: y = - 30°[/tex]
Also,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
[tex]y[/tex] + [tex]x[/tex] = [tex]180°[/tex]
[tex]➪ \: -30° + x= 180°[/tex]
[tex]➪ \:x = 180° + 30°[/tex]
[tex]➪ \:x = 210°[/tex]
[tex]\sf\purple{Therefore,\:the\:measures \:of\:the\:unknown\:angles\:are\:"x=210°"\:and\:"y=-30°.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
In the figure below net of cube is show
Find the surface area of cube.
3 in
Answer:
Surface Area = 54 in^2
Step-by-step explanation:
SA = [tex]6a^{2}[/tex]
SA = [tex]6(3)^2[/tex] Solve for the exponents first
SA = 6(9) Then multiply
SA = 54 square inches
Suppose that y varies inversely with x. Write a function that models the inverse function x=7 when y=3
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Answer:
y = 21/x
Step-by-step explanation:
The inverse variation relation means ...
y = k/x
For the given values, we can determine the constant k:
3 = k/7
3×7 = k = 21
Then the function is ...
y = 21/x
What are the solutions to x2 -8x =13
Answer:
See image below for answer:)
Step-by-step explanation:
Using the diagram below, which of the following parts of the triangles are
congruent?
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Answer:
B. ∠A ≅ ∠E
Step-by-step explanation:
The similarity statement tells you the corresponding angles are ...
ΔCAB ~ ΔCED
∠C ≅ ∠C . . . . listed first in the similarity statement
∠A ≅ ∠E . . . . listed second in the similarity statement
∠B ≅ ∠D . . . . listed third in the similarity statement
The relationship between angles A and E is properly shown in answer choice B.
25 points!!!!!!!!
Solve the system of equations.
4x + 3y + 5z = 6
6x + 8y + 62 = 4
4x + 2y + 62 = 8
please select the best answer from me the choices provided
a. (x = 1, y = - 1,2 = 1)
b. (x = 3, y = -3, z = 3)
(x = 0, y = 0, z = 2)
d. (x = 2, y = -2, z = 0)
Answer:
A is your answer, my guy
Step-by-step explanation:
4x1=4
3x-1=-3
5x1=5
4+(-3)+5=6
6x1=6
8x-1=-8
6x1=6
6+(-8)+6=4
4x1=4
2x-1=-2
6x1=6
4+(-2)+6=8
Waiting on the platform, a commuter hears an announcement that the train is running five minutes late. He assumes the arrival time may be modeled by the random variable T, such that
f(T = t) = {3/5 (5/t)^4 , t ≥ 5
0, otherwise
If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?
А. 62%
B. 73%
C. 88%
D. 91%
E. 96%
Answer:
D. 91%
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Less than 15 minutes.
Event B: Less than 10 minutes.
We are given the following probability distribution:
[tex]f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5[/tex]
Simplifying:
[tex]f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}[/tex]
Probability of arriving in less than 15 minutes:
Integral of the distribution from 5 to 15. So
[tex]P(A) = \int_{5}^{15} = \frac{375}{t^4}[/tex]
Integral of [tex]\frac{1}{t^4} = t^{-4}[/tex] is [tex]\frac{t^{-3}}{-3} = -\frac{1}{3t^3}[/tex]
Then
[tex]\int \frac{375}{t^4} dt = -\frac{125}{t^3}[/tex]
Applying the limits, by the Fundamental Theorem of Calculus:
At [tex]t = 15[/tex], [tex]f(15) = -\frac{125}{15^3} = -\frac{1}{27}[/tex]
At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]
Then
[tex]P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}[/tex]
Probability of arriving in less than 15 minutes and less than 10 minutes.
The intersection of these events is less than 10 minutes, so:
[tex]P(B) = \int_{5}^{10} = \frac{375}{t^4}[/tex]
We already have the integral, so just apply the limits:
At [tex]t = 10[/tex], [tex]f(10) = -\frac{125}{10^3} = -\frac{1}{8}[/tex]
At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]
Then
[tex]P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}[/tex]
If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087[/tex]
Thus 90.87%, approximately 91%, and the correct answer is given by option D.
Select the correct answer. Using synthetic division, find (2x4 + 4x3 + 2x2 + 8x + 8) ÷ (x + 2). A. B. C. D.
Step-by-step explanation:
If you use synthetic division, you get,
[tex]2x {}^{3} + 2x + 4 + \frac{0}{x + 2} [/tex]
Which is,
[tex]2x {}^{3} + 2x + 4[/tex]
Answered by GAUTHMATH
Answer:
The correct answer is:
2x^3+2x+4
Step-by-step explanation:
I got it right on the Plato test.
What equation is always true?
Answer: 4)
Step-by-step explanation: angles 2 and 3 equal 7 because they are both missing angle 4 to make it either 180 degrees or 360 degrees respectively.
tiệm cận ngang của đồ thị y= 2-x/x+3
tiệm cận ngang của đồ thị 3/x+3