Answer: speed of train = 94.53 km/h
Speed of car = 59.98 km/h
Step-by-step explanation:
Let x = speed of the train
Let y = speed of the car
The total distance travelled by the man is 600 km. It takes 8 hours 40 min if he travels 320km by train and rest by car. This means that the distance travelled by car is 600 - 320 = 280km
60 minutes = 1 hour
The total time of travel = 8 + (40/60) = 8.67 hours
Total time = total distance/total speed
8.67 = 320/x + 280/y
320/x = 8.67 - 280/y
320/x = (8.67y - 280)/y
Cross multiplying, it becomes
320y = x(8.67y - 280)
y = x(8.67y - 280)/320- - - - - - - - - - -1
it would take 30min more if he travels 200km by train and rest by car. The total time would be 8.67 + 0.5 = 9.17 hours
Distance covered by the car is 600 - 200 = 400 km
Therefore,
9.17 = 200/x + 400/y
200/x = 9.17 - 400/y
200/x = (9.17y - 400)/y
Cross multiplying, it becomes
200y = x(9.17y - 400)
y = x(9.17y - 400)/200 - - - - - - - 2
Equating equation 1 to equation 2, it becomes
x(8.67y - 280)/320 = x(9.17y - 400)/200
Dividing both sides by x, it becomes
(8.67y - 280)/320 = (9.17y - 400)/200
Cross multiplying, it becomes
200(8.67y - 280) = 320(9.17y - 400)
1734y - 56000 = 2934.4y - 128000
2934.4y - 1734y = - 56000 + 128000
1200.4y = 72000
y = 72000/1200.4
y = 59.98 km/h
Substituting y = 59.98 into equation 1, it becomes
59.98 = x(8.67 × 52.98 - 280)/320
52.98 × 320 = x(459.3366 - 280)
16953.36 = 179.3366x
x = 16953.36/179.3366
x = 94.53 km/h
What is the value of the expression. 3√216 NEED ANSWER RIGHT NOW
Answer:
18√6 or 44.1
Step-by-step explanation:
3√216= 3√4*9*6=3*2*3√6=18√6 = 44.1
given a force of 10 N and an acceleration of 5 m/s 2. What is the mass ?
Answer:
2 kg.
Step-by-step explanation:
F = m * a (Newton's Second Law of Motion).
10 = m * 5
The mass m = 10/5 = 2 kg.
Solution,
Here,
Given,
Force= 10N
Acceleration= 5m/s^2
Mass= ?
Therefore, as we know that
Force= Mass× Acceleration
10=M×5
10/5= M
Therefore, M= 5kg.
If it helped, please mark it as the brainliest answer :)What is the measure of angle B?
60 degrees, because it's an equilateral triangle, as you can tell because the sides are all the same length.
What is the solution to this equation?
X- 16 = 9
O A. x=-7
O B. x = 7
O C. x = -25
O D. x= 25
Answer:
d) x=25
Step-by-step explanation:
x-16=9
add 16 to both sides canceling out -16 and adding 9 and 16, making it positive 25
after moving 16 to the other side of the =, and adding it to 9 it should look like:
x=25
therefore making the answer x=25
pls help it’s due at 9am and i need the work too
Answer for 1. 72
Answer for 2.536
Answer for 3.195
In a six-question multiple-choice test, there are four possible answers for each question. For a person who guesses at each question, what is the expected number of correct answers?
Answer:
idk
Step-by-step explanation:
if not i would help sorry
Answer:
1 answer. (possibly 2)
Step-by-step explanation:
There's [tex]\frac{1}{4}[/tex] chance they get the correct answer for a question.
That means if they answer 4 questions, they can expect 1 answer to be correct. If they answer 6 questions, they can expect 1.5 answers to be correct but you can't have 0.5 of an answer so they can expect 1 question answered correctly.
Find solution r+9-6r=28
Answer:
hope this is correct
Find the area of the shaded region below.
All shapes in the figures are regular polygons.
PLSS HELP
Answer:
Step-by-step explanation:
We have 2 hexagons there, so we need to use the area formula for the large hexagon - the area of the small hexagon. As long as both of these are regular (and they are), we will use the formula
[tex]A=\frac{1}{2}ap[/tex]
where a is the apothem and p is the perimeter of the hexagon. We'll start with the large one first.
Note that a hexagon has 6 central angles that are all equivalent in degree. 360 / 6 = 60 degrees. Each of those 6 triangles has a vertex angle of 60. If we extract one of those triangles and then cut it in half by dropping an altitude from the vertex angle to the base of the triangle, we get a right triangle. The vertex angle is 30, one base angle is 90 and the other is 60. The height of this right triangle is the apothem, for which we want to solve. Using right triangle trig,
[tex]tan(60)=\frac{a}{7}[/tex] The 7 comes from the fact that when we split the triangle in half by dropping an altitude, we not only split the vertex angle in half, we also split the base length in half...from 14 to 7. Continuing,
7 tan(6) = a and
a = 12.124
Filling in the area now for the large hexagon:
[tex]A=\frac{1}{2}(12.124)(84)[/tex] {the perimeter is 6 sides times a length of 4 per side} and
A = 509.208
Now for the small hexagon. We'll do the same thing...extract a triangle and cut it in half by dropping an altitude and solving for a which is the height of the triangle. This half triangle has a base of 3 (half of 6).
3 tan(60) = a and
a = 5.196
Filling in the area now for the small hexagon:
[tex]A=\frac{1}{2}(5.196)(36)[/tex] and
A = 93.528
Now subtract the smaller area from the larger:
509.208 - 93.528 = 415.68
Mukuunda bought 20 dozen of pencilsat Rs. 100. At what rate should a pencil be sold so that the profit may be Rs. 20
LAST ONE
Find the range of the data.
16, 55, 61, 92, 31
range =
Answer:
76
Step-by-step explanation:
arrange the data set from least to greatest:
16, 31, 55, 61, 92
Range = Highest value - Lowest value = answer
Range = 92 - 16 = 76
A company is hosting a charity meal 800 people work for the company it is estimated 70% of the employees will attend it is expected that if an employee attends they will bring a partner the cost of attending the meal is £5 how much money will there is for charity?
Answer:
5600 pounds
Step-by-step explanation:
first find the number of workers attending:
70%of 800 = 560
Next find the number of people attending:
560 x 2 = 1120
Now, Calculate the money raised:
5 X 1120 = 5600
Hope this helps
Good Luck
1 + 1 =
long method pls
I can’t get this one
Answer:
36/40
Step-by-step explanation:
Hope you understand this
HAVE A GOOD DAY!
What is the slope of the line that passes through (2, 1), (0, 0)?
The answer is 1/2
please see the attached picture for full solution
hope it helps
Good luck on your assignment
Find the surface area of the cylinder. Round to the nearest hundredth.
Answer:
The surface area of the cylinder is 276.32m²
Step-by-step explanation:
To solve this problem we have to calculate the circle area and the lateral area
To calculate the area of the circle we use the following formula
a = area
r = radius = 2m
π = 3.14
a = π * r²
we replace with the known values
a = 3.14 * (2m)²
a = 3.14 * 4m²
a = 12.56m²
The area of the circle is 12.56m²
To calculate the lateral area of the cylinder we use the following formula
a = area =
h = heighti = 20m
r = radius = 2m
π = 3.14
a = 2 * π * r * h
we replace with the known values
a = 2 * 3.14 * 2m * 20m
a = 6.28 * 40m²
a = 251.2m²
The lateral area of the cylinder is 251.2m²
Now we add the lateral area of the cylinder with 2 times the area of the circle and obtain the area of the cylinder
251.2m² + (2 * 12.56m²) = 276.32m²
The surface area of the cylinder is 276.32m²
Need help ASAP! Which is the simplified form of the expression StartFraction (6 Superscript negative 4 Baseline) Superscript negative 9 Baseline Over 6 Superscript 6 Baseline EndFraction? StartFraction 1 Over 6 Superscript 42 Baseline EndFraction StartFraction 1 Over 6 Superscript 19 Baseline EndFraction 6 Superscript 6 6 Superscript 30
Answer: D. [tex]6^{30}[/tex]
Step-by-step explanation:
Using exponent rules an exponent to the power of a number will multiply by each other.
So the -4 and -9 will multiply.
The 6 in the numerator will now have a positive exponent of 36.
[tex]\frac{6^{36}}{6^6}[/tex]
Now we can divide and when we do so the exponents will subtract from each other.
So 36 - 6 = 30
And the base of 6 does not change.
The simplified form is [tex]6^{30}[/tex]
Answer: D.
Step-by-step explanation:
Using exponent rules an exponent to the power of a number will multiply by each other.
So the -4 and -9 will multiply.
The 6 in the numerator will now have a positive exponent of 36.
Now we can divide and when we do so the exponents will subtract from each other.
So 36 - 6 = 30
And the base of 6 does not change.
The simplified form is
[tex]6^{30}[/tex]
Does anyone know this ??
Answer:
A
Step-by-step explanation:
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]
Rationalise the denominator by multiplying numerator/ denominator by [tex]\sqrt{34}[/tex]
sin x = [tex]\frac{3}{\sqrt{34} }[/tex] × [tex]\frac{\sqrt{34} }{\sqrt{34} }[/tex] = [tex]\frac{3\sqrt{34} }{34}[/tex] → A
Please tell me the answer for
Factorise 15p square - 7q square
Answer:
I do not think you can simplify it any further
Step-by-step explanation:
If you mean 15p squared - 7 q squared
Because they have different variables; p and q cannot be combined unless it is multiplication or division.
what is 2 times one over 10??
Answer:
20
Step-by-step explanation:
A jewelry store received 16 inches long, 10 inches wide, 12 inches high. The package contains 1-inch cube that each hold one ring. How many rings did the jewelry store receive? Explain how you found your answer.
Answer:
1920 rings
Step-by-step explanation:
We need to simply find the volume of the package and the volume of the cube and then divide the volume of the package by the volume of the cube.
The package is a rectangular prism. The volume of a rectangular prism is:
V = L * W * H
where L = length
W = width
H = height
The volume of the package is:
16 * 10 * 12 = 1920 [tex]in^3[/tex]
The volume of a cube is:
V = L^3
where L = length of side
The volume of the cube is:
V= 1^3 = 1 [tex]in^3[/tex]
The number of rings the jewelry store received is:
1920 / 1 = 1920 rings
Simplify, using the distributive property and then combining like terms.
5(3a+b)−2(3a+b)
The answer is 9a+3b
please see the attached picture for full solution
Hope it helps...
Good luck on your assignment...
Answer:
3(3a+b)
Step-by-step explanation:
use the distributive property:
15a+5b-6a-2b
combine like terms:
9a+3b:
if you need you can factor:
3(3a+b)
Amy read 42 pages from her 137 page magazine. She will spend 10 days reading the same number of pages each day until she finishes. Estimate how many pages Amy will need to read each day.
Answer:
Amy will need to read 1 page each day.
Step-by-step explanation:
Total number of page of the magazine = 137 pages
Read pages of the magazine = 42 pages
Remaining pages to be read = 137 pages - 42 pages = 95 pages
She spends 10 days reading the same number of pages each day until she finishes.
The number of pages read in each of the 10 days = 95 pages / 10 days
= 9.5 pages
In 10 days Amy reads 9.5 pages
In a day she reads ?
10 days -----------> 9.5 pages
1 day ----------------> ?
= 0.95 page
approximately 1 page per day
Thus, Amy will need to read 1 page each day.
Please answer quickly!!!
Answer:
3.5 min
Step-by-step explanation:
Please please help!!!! According to the probability distribution below, what is the expected value of X? X 0 1 2 3 4 5 P(X) 0.3 0.2 0.16 0.2 0.04 0.1 A.) The expected value is 0.1 B.) The expected value is 5 C.) The expected value is 2.5 D.) The expected value is 1.78
Answer:
D.) The expected value is 1.78
Step-by-step explanation:
The expected value of a probability distribution is evaluated using the formula.
Expected Value, [tex]E(X)=\sum^{n}_{i=1}x_iP(x_i)[/tex]
Therefore, from the given probability distribution, we have:
E(X)=(0*0.3)+(1*0.2)+(2*0.16)+(3*0.2)+(4*0.04)+(5*0.1)
E(X)=1.78
The Expected value of X is 1.78.
The correct option is D.
Answer:
D.) The expected value is 1.78
Step-by-step explanation:
i took the test
Jose is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4 people. Jose reserved twice as many small rooms as large rooms, which altogether can accommodate 70 guests. Write a system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved. Define the variables that you use to write the system.
Answer:
No. of large rooms = 7
No. of small rooms = 14
Set of equations
4x + 3y = 70
y = 2x
Variable definitions
No. of large rooms is x
No. of small rooms is y
Step-by-step explanation:
capacity of large rooms = 4 people
let the no. of large rooms be x
thus, total no of people which can be accommodated in x rooms = 4*x = 4x
capacity of small rooms = 3 people
let the no. of small rooms be y
thus, total no of people which can be accommodated in y rooms = 3*y = 3y
total no. of people which can be accommodated in x large room and y small room will be = 4x + 3y
It is given that total small room and large room can accommodate 70 guests
thus,
4x + 3y = 70 _________equation 1
_________________
It is also given that Jose reserved twice as many small rooms as large rooms,
so, if no. of large rooms is x and no. of small rooms is y
then
y = 2x _________equation 2
substituting value of y in equation 1 we have
4x + 3(2x) = 70
=>4x + 6x = 70
=> 10x = 70
=> x = 70/10 = 7
No. of large rooms = 7
No. of small rooms = y= 2x = 2*7 = 14
Set of equations
4x + 3y = 70
y = 2x
Variable definitions
No. of large rooms is x
No. of small rooms is y
The number of the small rooms is 14.
The number of large rooms is 7.
Assuming that the number of the large rooms is x,
So, the number of small rooms is 2x
According to the question:
[tex]3[/tex] × [tex]2x[/tex] [tex]+ 4[/tex] × [tex]x = 70[/tex]
[tex]6x+4x=70\\10x=70\\x=7[/tex]
So, 2x = 2(7) = 14
Therefore, the number of the small rooms is 14 and the number of large rooms is 7.
For more information:
https://brainly.com/question/22971109
O proprietário de uma lanchonete descobriu que na produção do hambúrguer comum gasta R$ 1,25 de material em cada unidade, além disso, tem um gasto fixo de R$ 97,00 por conta de gás e outros materiais. Qual a função que representa o custo (C) total na produção dos hambúrgueres em função da quantidade produzida (x)
Answer:
C(x) = 97 + 1,25x
Step-by-step explanation:
A função (C) que representa o custo total em função do número de hambúrgueres produzidos (x) contém duas partes: uma constante referente ao custo fixo de R$ 97,00, e uma variável referente ao custo de R$ 1,25 por hambúrguer para "x" hambúrgueres. A função C(x) é:
[tex]C(x) = 97 + 1,25x[/tex]
Hellllppp
Examine the rotation. Which best describes point D?
angle of rotation
center of rotation
image
pre-image
Answer:
center of rotation
Answer:
Center of rotation.
Step-by-step explanation:
The center of rotation is the point at which an image turns.
Point D is described as the center of rotation.
A store is having a 20%-off sale on all merchandise.
a) If Mai buys one item and saves $13, what was the original price of her purchase? and explain
A square tile measures 20cm by 20cm. A rectangular tile is 3cm long and 2cm narrower than the square tile what is the difference in area between the two tiles
Answer:
346 cm²
Step-by-step explanation:
Area of square:
Area = [tex]Length*Length[/tex]
A = 20*20
A = 400 cm²
Area of rectangle:
Length = 3 cm
Width = 20-2 = 18 cm
Now, The Area:
Area = [tex]Length * Width[/tex]
Area = 3 * 18
Area = 54 cm²
Now, The difference in their areas:
=> 400-54
=> 346 cm²
Answer:
hiya 13 more points
Step-by-step explanation:
In triangle ABC points M and N lie on sides AB and BC, respectively such that MN∥ AC . Segments AN and CM intersect at point K and AK = KC. Prove that △ABC is isosceles.
Answer:
Step-by-step explanation:
An isosceles triangle has two equal sides and two equal base angles.
Given that : AK = KC and MN∥ AC
ΔMNB is similar to ΔACB (congruence property)
ΔANB = ΔANC (SAS congruence property)
ΔCMB = ΔCMA (SAS congruence property)
[tex]\frac{AB}{BN}[/tex] = [tex]\frac{AC}{CN}[/tex] (Angle bisector theorem)
So that:
<BAC = <ACB (base angle property of an isosceles triangle)
/AB/ = /BC/ (side property of an isosceles triangle)
Therefore, ΔABC is an isosceles triangle.
