Answer:
9
Step-by-step explanation:
A freight and passenger train share the same track. The average speed of the freight train is 45 mph, whereas that of the passenger train is 70 mph. The passenger train is scheduled to leave 20 minutes after the freight train departs from the same station. Determine the location where a siding would need to be provided to allow the passenger train to pass the freight train. Also determine the time it takes for the freight train to arrive at the siding. As a safety precaution, the separation headway between the two trains at the siding should be at least equal to 6 minutes.
Answer:
The first siding should be located at 30 miles
The time for the freight to arrive at the siding is 40 minutes
Step-by-step explanation:
From the given information:
Let [tex]T_f[/tex] represent the time for the freight train
Also, let [tex]T_P[/tex] represent the time at which the passenger train reach the location
Let Y represents the location where the location of the siding of the track needed to take place.
Thus, for freight time:
[tex]T_f = \dfrac{Y}{45} --- (1)[/tex]
The siding location is:
[tex]T_P = \dfrac{2}{6}+\dfrac{Y}{70}[/tex]
[tex]T_P =0.333+\dfrac{Y}{70} --- (2)[/tex]
To determine Y:
[tex]T_P -T_f = 0.1 --- (3)[/tex]
replacing the value of [tex]T_f[/tex] and [tex]T_P[/tex] in the above equation (3), we have:
[tex]0.333+\dfrac{Y}{70} - \dfrac{Y}{45} =0.1[/tex]
collecting like terms, we have:
[tex]\dfrac{Y}{70} - \dfrac{Y}{45} =0.1-0.333[/tex]
[tex]\dfrac{45Y- 70Y}{3150} =-0.233[/tex]
[tex]\dfrac{-25Y}{3150} =-0.233[/tex]
- 25Y = -0.233 × 3150
- 25Y = -733.95
Y = -733.95/-25
Y = 29.36 miles
Y [tex]\simeq[/tex] 30 miles to the nearest whole number
Thus, the first siding should be located at 30 miles
To estimate the time for the fight to arrive the siding, we replace 30 miles for [tex]T_f[/tex] in equation (1).
Then, we have:
[tex]T_f = \dfrac{Y}{45}[/tex]
[tex]T_f = \dfrac{30}{45}[/tex]
[tex]T_f =0.667\ hr[/tex]
[tex]T_f =(0.667 \times 60 )minutes[/tex]
[tex]T_f =40.2 \ minutes[/tex]
[tex]\mathsf{T_f \simeq 40 \ minutes}[/tex]
Thus, the time for the freight to arrive at the siding is 40 minutes
Find all excluded values for the expression. That is, find all values of x for which the expression is undefined.
x+6/x² - 6x-27
Answer:
The values of x for the expression is undefined is -3 or 9
Step-by-step explanation:
Given function,
[tex]f(x) = \frac{X +\ 6}{X^2 - 6X-27}[/tex]
The values of x for which the expression is undefined is obtained when the denominator is equal to zero, from the expression it is given by;
x² - 6x - 27 = 0
Factorize the equation
x² + 3x - 9x - 27 = 0
x (x + 3) -9(x + 3) = 0
(x + 3)(x - 9) = 0
x = -3 or x = 9
Therefore, the values of x for the expression is undefined is -3 or 9
1) Between which two integers does the square root of 48 lie? *
Answer:
6 and 7
Step-by-step explanation:
I think you mean 'the sq rt of 48 lies between what 2 integers.'
The answer is 6 and 7.
1 point
If one person can stand on a 4 square feet floor area, how many persons
can stand on 64 square foot floor area? Which proportion accurately solves
this problem? *
A) 1/4= X/64
B) 1/4= 64/x
C)1/64= 4/x
D)4/64= x/1
Answer:
A) 1/4=X/64
Step-by-step explanation:
It's 1 person every 4 square feet on the floor area so 1/4 would represent that and since we don't know the number of people that fit on 64 square feet on the floor area it would be x/64.
Hope that helps!
write 24.23 as a mixed number in simplest form
Answer:
24 23/100
Step-by-step explanation:
Which of the following statements are true for using proportions to solve for missing measures? Select three options.
Corresponding dimensions must be in different positions in the ratios.
Corresponding dimensions must be in the same position in the ratios.
D The two ratios in the proportion are equal.
The enlargement or reduction is proportional to the original figure.
D The scale factor will be different for each ratio.
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Mark this and return
Answer: C D B
Step-by-step explanation:
JUST TOOK THE TEST ON ENDEGENUITYYYYY
The correct statements for using proportions to solve for missing measures are:
Corresponding dimensions must be in the same position in the ratios.The two ratios in the proportion are equal.The enlargement or reduction is proportional to the original figure.What are ratios?Ratios are fractional values representing relations between two quantities.
What are proportions?When two ratios are equal, they are said to be in proportion.
What is a scale factor?The simplest form of a ratio, in a given proportion, is called the scale factor of the proportion.
How to solve the given question?In the question, we are asked to select the correct statements from the given set of statements for using proportions to solve for missing measures.
We analyze each statement:
Corresponding dimensions must be in different positions in the ratios: This is incorrect as the corresponding dimensions need to be in the same position for equality in the units of the ratio.Corresponding dimensions must be in the same position in the ratios: This is correct as the corresponding dimensions need to be in the same position for equality in the units of the ratio.The two ratios in the proportion are equal: This is correct, as it is the basis of proportions (equality of ratios).The enlargement or reduction is proportional to the original figure: This is correct, as the sides are always in proportion to each other in the process of enlargement or reduction.The scale factor will be different for each ratio: This is incorrect, as the scale factor is the simplest form which is always constant.∴ The correct statements for using proportions to solve for missing measures are:
Corresponding dimensions must be in the same position in the ratios.The two ratios in the proportion are equal.The enlargement or reduction is proportional to the original figure.Learn more about Proportions at
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The greatest payout for a personal injury was recorded at $163,882,660 in 1993. The car wreck actually occurred in the year 1987. If the guilty part paid in the year the wreck actually happened, what would have been the equivalent payout in 1987?
Answer:
$127,618,279.99
Step-by-step explanation:
Adjusted for inflation, $163,882,660.00 in 1993 is equal to $127,618,279.99 in 1987.
Annual inflation over this period was 4.26%.
Braden had 216 quarters. If it costs 8
quarters to buy a soda from the vending
machine, how many sodas can he buy?
Markel said he has 4 times
as many yellow cars as
blue cars. What is the ratio
for blue cars to yellow
cars?
Answer:
4:1
Step-by-step explanation:
Question 4: The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days.
76 61 74 62 73 63 73 64 72 64
72 65 72 66 71 66 71 67 70 67
70 68 69 68 68
Determine the (approx) value of the 53rd percentile Round answer to nearest integer:
Answer:
69
Step-by-step explanation:
Since there are 25 values, then n=25.
Now, calculate the index:
i=p/100n=53/100⋅25=53/4.
Since the index i is not an integer, round up: i=14
The percentile is at the position i=14. So, the percentile is 69.
A new computer is on sale for 1/5
off the original price. If the original price of the computer is $1495, what is the
sale price?
$1794
$1196
$1288
$299
Answer: $299
Step-by-step explanation:
divide the original price by 5
Sale price of the computer is equals to $299.
What is sale price?" Sale price is defined as the discounted price at which goods are sold."
According to the question,
Original price of the computer = $1495
Price decided on sale of a computer = [tex](\frac{1}{5})[/tex] Original price of the computer
Substitute the value to get the sale price of a computer we get,
Sale price of a computer = [tex]\frac{1}{5} (1495)[/tex]
= $299
Hence, sale price of the computer is equals to $299.
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Select all that apply.
Which of the following are linear factors of p(x) = x 3 - 2x 2 - 5x + 6 ?
x + 1
x + 2
x - 1
x - 3
100 POINTS!!! ASAP-- Pls show work too TY
Answer:
I will help you but is there any picture that can help me answer the question?
Answer:
[tex]\sin(\theta)=\frac{\sqrt{13}}{7}\approx0.5151[/tex]
Step-by-step explanation:
So we know that Θ is acute and that:
[tex]\cos(\theta)=6/7[/tex]
First, note that since Θ is acute, it is between 0 and 90 degrees, meaning that all of our trig ratios will be positive since the angle is in the Quadrant I.
The Pythagorean Identity is:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
We know that cosine is 6/7. Substitute:
[tex]\sin^2(\theta)+(\frac{6}{7})^2=1[/tex]
Square:
[tex]\sin^2(\theta)+\frac{36}{49}=1[/tex]
Subtract both sides by 36/49. Change the 1 to 49/49 to make a common denominator:
[tex]\sin^2(\theta)=\frac{49}{49}-\frac{36}{49}[/tex]
Subtract:
[tex]\sin^2(\theta)=\frac{13}{49}[/tex]
Take the square root of both sides:
[tex]\sin(\theta)=\pm\sqrt{\frac{13}{49}}[/tex]
Simplify:
[tex]\sin(\theta)=\pm\frac{\sqrt{13}}{7}[/tex]
As mentioned previously, since Θ is acute, all of the trig functions must be positive. So, we can ignore our negative answer:
[tex]\sin(\theta)=\frac{\sqrt{13}}{7}\approx0.5151[/tex]
and we're done!
State whether each system is consistent and independent, consistent and
dependent or inconsistent
y = 0.5x
2y = x + 4
consistent and independent
consistent and dependent
inconsistent
none of the above
Help?
Answer:
Step-by-step explanation:
C
The lines are have one solution and are consistent and Independent.
What is Consistent and Inconsistent?Gaining values for x and y allows us to determine whether the pair of linear equations is consistent or inconsistent. The system is consistent if x and y both have the same value. When there are no x and y values that fulfil both equations, the system becomes inconsistent.
Given:
y = 0.5x
2y = x + 4
Now solving the Above Equation
2(0.5x) = x+ 4
x = x+ 4
0 = 4
and, [tex]a_1= 0.5, b_1= -1, c_1= 0\\a_2= 1, b_2 = -2, c_ 2 = 4[/tex]
Now, [tex]a_1/ a_2 = b_1/ b_2\neq c_1/ c_2[/tex]
Then, the lines are have one solution and are consistent and Independent.
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If a person drives his car in the speed 50 miles per hour, how far can he cover the distance in 2.5 hours ?
Answer:
Hey there!
50 miles = 1 hour
x miles = 2.5 hours
50/1= x/2.5
x=2.5x50
x=125
The car can go 125 miles.
Hope this helps :)
Answer:
125miles
Step-by-step explanation
distance=speed *time
d=50*2.5
d=125m
Find 5.5x when x=7.5
Answer:
41.25
Step-by-step explanation:
if x=7.5 in order to find 5.5x you would multiply 5.5 by 7.5
=41.25
Answer:
41.25
Step-by-step explanation:
5.5(7.5) Stubstitue the varuable for the value
41.25 Multiply
BRAINLIEST PLEASE HELP Use the given conditions to write an equation in point-slope form. Keep parenthesis in point-slope form. passing through (3,5) and (8,15).
Answer:
Step-by-step explanation:
(15 -5)/(8 - 3)= 10/5= 2
y - 5 = 2(x - 3)
y - 5 = 2x - 6
y = 2x - 1
midpoint of (5, 8) (-1, -4)
Answer:
(2,2)
Step-by-step explanation:
mid point formula: x1+x2/2 y1+y2/2
5+(-1)=4/2=2
8+(-4)=4/2=2
(2,2)
Como se ecribe 8 de 10
en decimale
which unit represents 0.01 liters
Answer:1 centiliter
Step-by-step explanation:1 centiliter equals 0.01 liters
Which of the following is equivalent to 15.45 + ( − 98.25 ) 15.45+(-98.25)
Answer:
-82.8
Step-by-step explanation:
15.45 + ( − 98.25)
15.45 - 98.25
= -82.8
Since the two terms are of opposite signs, you have to subtract and use the sign of the greater term (positive or negative)
-3/7(x-52) given x=10
Answer:
18
Step-by-step explanation:
-3/7 * ( x-52)
Let x = 10
-3/7 ( 10-52)
-3/7 * -42
-3 * -42/7
-3 * -6
18
Which of the following statements are true and which are false? Give reasons for your answers.(i) Only one line can pass through a single point.(ii) There are an infinite number of lines which pass through two distinct points.(iii) A line can be produced indefinitely on both sides.(iv) If two circles are equal, then their radii are equal.(v) if AB=PQ and PQ=XY, then AB=XY.
Complete Question
Which of the following statements are true and which are false? Give reasons for your answers.
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A line can be produced indefinitely on both sides.
(iv) If two circles are equal, then their radii are equal.
(v) if AB=PQ and PQ=XY, then AB=XY.
A (i),(ii) - True
(iii),(iv),(v)-False
B(i),(ii),(iii) -True
(iv),(v)-False
C (i),(ii) -False
(iii),(iv),(v)-True
D (i),(ii),(iii) -False
(iv),(v)-True
Answer:
The correct option is C
Step-by-step explanation:
i is false because several lines can pass through a single point
ii is false because only one line can pass through two distinct points
iii is true because you can extend a line from both points (start and end points )
iv is true because when two equal circle are placed together and radius is trace we will discover that they are equal
v is true because from Euclid's First Axiom , if a= c and c = d the a = d
The area of a square garden is A= 121ft2 how long is each side of the garden?
Answer:
11ft.
Step-by-step explanation:
121 is the square root of 11, but that's not important. basically, you just find out what multiplies to be 121, since it's just side * side. long division can help if you're not allowed to use a calculator. I hope I was at least somewhat helpful. I feel like this wasn't the best explanation out there.
solve it............
Answer:
7
Step-by-step explanation:
1) for '8'; '3'; and '10':
8/2+3+3=10
2) for '2'; '5' and '11':
2/1+5+5=11
3) for '6'; '2' and '?':
6/2+2+2=7
Look at the photo HELPPPP I NEED IT RNN!!!
Answer:
-150
Step-by-step explanation:
Which of the following math statements contains variables check all that apply A.3+6=x B.3+6=9 C. X+___=9 D.3+__=9
Answers
B.
D.
Use the slope formula to find the missing coordinate.
m= 3, P(3, 2) and Q(8,_)
O-1
1
05
Let the missing value = x
Slope is the change in y over the change in x:
3 = (x-2)/ (8-3)
3 = (x-2) / 5
Multiply both sides by 5:
15 = x-2
Add 2 to both sides:
X = 17
The missing coordinate is 17
Find the straight time pay if you earn $7.90 per hour and worked 37 hours.
Answer: $292.30
Step-by-step explanation:
I need help please helpp
Answer:
I believe it's B.Let me know if it's right,if it not,i'm so sorry
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The other statements incorrectly describe the transformations. C is facing a different direction and so without involving rotations it can not be the reflection of any of the other triangles.