Train a And train b leave Central Station at the same time they travel the same speed but in opposite direction with a train a heading towards Station a and train b heading towards station b train a Reaches station after 2 1/2 hours train b reaching station be after four hours you station A and b Station are 585 miles apart what is the rate of the trains
Answer:
Both trains are traveling at 90 miles per hour.
Step-by-step explanation:
We are told that the rate is the same for both trains, and we know that the distance traveled by train a plus the distance traveled by train b equals 585 miles.
We will use [tex]Distance=Rate* Time[/tex] formula to solve this problem.
Train A: [tex]D_a=R*2.5[/tex] (Using 2.5 instead of 2 and 1/2)
Train B: [tex]D_b=R*4[/tex]
We can set an equation to solve for rate R of trains as:
[tex]D_a+D_b=585[/tex]
[tex]2.5R+4R=585[/tex]
[tex]6.5 R=585[/tex]
[tex]R=\frac{585}{6.5}[/tex]
[tex]R=90[/tex]
Therefore, rate of both train a and train b is 90 miles per hour.
The total distance between the two stations is
[tex]585 miles[/tex]
Let the distance between the Central Station and station b be x
This implies that the distance between the Central Station and station a is
[tex](585 - x) \: miles[/tex]
[tex]speed=\frac{distance}{time}[/tex]
so, let us write equations in terms of speed for the two trains and solve
For train a,
[tex]speed=\frac{585 - x}{4 } ....eqn \: 1[/tex]
For train b,
[tex]speed=\frac{x}{2 \frac{1}{2} } .....eqn \: 2[/tex]
We were told that both trains traveled with the same speed
This means that eqn 1 = eqn 2
[tex]\frac{585 - x}{4 }=\frac{x}{2.5} [/tex]
Cross multiplying
[tex]2.5(585 - x)=4(x) [/tex]
Expanding the brackets
[tex]1462.5 - 2.5x =4x[/tex]
Grouping like terms
[tex]1462.5= 4x + 2.5x[/tex]
[tex]6.5x = 1462.5 \\ x = \frac{1462.5}{6.5 } =225 \: miles[/tex]
The speed at which the trains were travelling is
[tex] \frac{225}{2.5}= 90 \: miles /hour[/tex]
Hence the rate of the trains is
[tex]=90\: miles /hour[/tex]
The length of a rectangle is 2 more than 5 times its width. Find the perimeter of the garden if the perimeter is 160m.
Take the breadth as x,as its the smallest value--(1)
Length is 2 more than 5 times the breadth--(2)
perimeter=160m
l=2+5x
b=x
Perimeter=2(l+b)
2(2+5x+x)
=2(2+6x)
Opening the brackets
=4+12x
4+12x=160
12x=160-4
x=156/12
=13
Therefore , by substituting the value of x
l=2+5*13=67m
b=13m
Solve with substitution, show your work.
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1
3x + 2y + z = 7 ⇒ z = 7 - 3x - 2y
*****************************************
5x + 5y + 4z = 3
= 5x + 5y + 4(7 - 3x - 2y) = 3
= 5x + 5y + 28 - 12x - 8y = 3
= -7x -3y + 28 = 3
= -7x - 3y = -25
*****************************************
3x + 2y + 3z = 1
= 3x + 2y + 3(7 - 3x - 2y) = 1
= 3x + 2y + 21 - 9x - 6y = 1
= -6x - 4y + 21 = 1
= -6x - 4y = -20
*****************************************
-7x - 3y = -25 ⇒ 4(-7x - 3y = -25) ⇒ -28x - 12y = -100
-6x - 4y = -20 ⇒ -3(-6x - 4y = -20) ⇒ 18x + 12y = 60
-10x = -40
x = 4
-7x - 3y = -25
-7(4) - 3y = -25
-28 - 3y = -25
-3y = 3
y = -1
z = 7 - 3x - 2y
= 7 - 3(4) - 2(-1)
= 7 - 12 + 2
= -3
Answer: x = 4, y = -1, z = -3
Complete the chart to find the mean, variance, and standard deviation. Remember to use commas and round numbers to the nearest tenth. Need help
Answer: The mean of the data is 433.75, variance of the data is 99667.19 and the standard deviation of the data is 315.7011.
Explanation:
The given data is 900, 35, 500 and 300.
The number of observation is 4.
Formula of mean is,
[tex]\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
[tex]\bar{X}=\frac{900+35+50+300}{4} =433.75[/tex]
The formula of variance is given below,
[tex]\sigma^2=\frac{1}{n}\sum{(X-\bar{X})^2}[/tex]
[tex]\sigma^2=\frac{398668.75}{4}[/tex]
[tex]\sigma^2=99667.19[/tex]
The variance of the data is 99667.19
[tex]\sigma=\sqrt{99667.19}[/tex]
[tex]\sigma=315.7011[/tex]
The standard deviation of the data is 315.7011.
The other information or values of given chart is shown in the attached table.
Answer:
i. mean of the data is 402.5
ii. variance of the data is 77556.25
iii. standard deviation of the data is 278.49
Step-by-step explanation: (x - ⁻x)²
from the chart given to me, the observation are: 45, 340, 400, 825
i. mean is the summation of the observation divided by number of observation. ∈x÷n =( 45 + 340 + 400 + 825)÷ 4 = 402.5
ii. variance is the square of the difference between the observation and mean divided by the number of observation.
variance = (45-402.5)²+(340-402.5)²+(400-402.5)²+(825-402.5)²÷4=77556.5
In a sale of game boys were reduced by 2/5 what is the sale price if the original price was 50.00
Final answer:
To calculate the sale price of the Game Boy with an original price of $50.00 and a discount of 2/5, you multiply the original price by the discount to find the amount reduced ($20), then subtract that from the original price to find the sale price ($30).
Explanation:
The question involves calculating the sale price of an item after a discount. Initially, the original price of the Game Boy is $50.00. The discount is given as 2/5 of the original price. To find the amount of discount, we multiply the original price by 2/5:
Discount = Original Price × Fraction of discount
Discount = $50 × 2/5
Discount = $20
Now, we subtract this discount from the original price to find the sale price:
Sale Price = Original Price - Discount
Sale Price = $50 - $20
Sale Price = $30
Therefore, the sale price of the Game Boy after the discount is $30.
The county fair charges $2.50 per ticket for the rides. Henry bought 15 tickets for the rides and spent a total of $55.50 at the fair. Henry spent his money only on ride tickets and far admission. The price of the fair admission is the same for everyone. Use x to represent the number of tide tickets and y to represent the total cost.
(A) Find the cost of admission to the fair. Explain how you found the cost of admission.
(B) Write a linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission.
(C) Explain what the coefficient on x and the constant of your linear equation represent.
To find the cost of admission to the fair, subtract the cost of the ride tickets from the total spent. The linear equation 2.50x + y = 55.50 can be used to calculate the cost for anyone. The coefficient on x represents the cost per ride ticket, while the constant represents the total amount spent on ride tickets and admission.
Explanation:(A) To find the cost of admission to the fair, we need to subtract the cost of the ride tickets from the total spent. Since Henry bought 15 tickets and spent a total of $55.50, we can use the equation 2.50x + y = 55.50, where x represents the number of ride tickets. Substituting x = 15, we can solve for y to find the cost of admission.
(B) The linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission is 2.50x + y = 55.50, where x represents the number of ride tickets and y represents the cost of admission.
(C) In the linear equation, the coefficient on x (2.50) represents the cost per ride ticket. The constant (55.50) represents the total amount spent on ride tickets and admission.
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The high temperatures for each day last week increased by one degree each day: 65°, 66°, 67°, 68°, 69°, 70°, 71°. What was the mean temperature for the week?
Answer:67.8 is the answer
Step-by-step explanation:
i hope it helps
Question 7
Solve the following system of equations by using the elimination method.
-4x – 2y = -12
4x + 8y = -24
(5, 3)
(-6, -6)
(3, 1)
(6, -6)
To solve this problem you must apply the proccedure shown below:
1. You have the following system of equation:
[tex]\left \{ {{-4x-2y=-12} \atop {4x+8y=-24}} \right.[/tex]
2. As you can see, you can cancel out the variable [tex]x[/tex], because it has equal coefficient with different signs at both equations. Then, if you add both equations, you obtain:
[tex]6y=-36\\y=-6[/tex]
3. Let's substitute the value obtained into the second equation to calculate the other variable:
[tex]4x+8(-6)=-24\\4x-48=-24\\x=6[/tex]
The answer is: (6,-6).
What is the sum of the hundreds in this equation? 357 + 421
357+421 = 778
Hope this helps :)
For a student fundraiser Ronna needs to sell 56 boxes of cookies so far she has sold 13 boxes of lemon cookies to her aunt 14 boxes of chocolate cookies to her mother and three boxes of oatmeal cookies to her neighbor how many more boxes of cookies does Ronna need to sell
PLEASE HELP ME I DONT UNDERSTAND.
width = 7cm
Length= 41cm
width=x
length=3x+20
96=3x+20+3x+20+x+x
96=8x+40
56=8x
x=8
Rectangle has 4 sides
You have the 2 side lengths (l) and the 2 side widths (w)
"The length is 20 centimeters more than triple the width" in math terms is
l = 20 + 3w
The perimeter is 96 centimeters, which is all the sides added up
2l + 2w = 96
2(20 + 3w) + 2w = 96
40 + 6w + 2w = 96
40 + 8w = 96
8w = 56
w = 7
now plug in w = 7 to get length in
l = 20 + 3w
Which expression can be used to find the difference of the polynomials? (10m – 6) – (7m – 4)
Answer choices
[10m + (–7m)] + [(–6) + 4](10m + 7m) + [(–6) + (–4)][(–10m) + (–7m)] + (6 + 4)[10m + (–7m)] + [6 + (–4)]
(10m – 6) – (7m – 4)
= 10m - 6 - 7m + 4
= 3m - 2
So
[10m + (–7m)] + [(–6) + 4]
= 3m + (-2)
= 3m - 2 ..............matching answer.
Answer
[10m + (–7m)] + [(–6) + 4]
To add or subtract any algebraic expression, variables add or subtract with variables and constant term add or subtract with constant terms in the expression.
To solve given expression, we use [10m + (–7m)] + [(–6) + 4] expression.
Given expression is,
(10m – 6) – (7m – 4)
Now, variables add or subtract with variables and constant term add or subtract with constant terms in the above expression.
10m - 6 - 7m + 4
(10m - 7m) + (-6 + 4)
[10m + (–7m)] + [(–6) + 4]
So, first option is correct.
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-5.3 ≥ 6.7 + 4.3 + q
Please help and show work!!
Simplify both sides of the inequality.
−5.3≥q+11
Flip the equation.
q+11≤−5.3
Subtract 11 from both sides.
q+11−11≤−5.3−11
ANSWER: q≤−16.3
Your name is included in a list of 6 names. One name is selected at random. Write the probability, as a decimal, that it is your name.
Answer:
The probability of my name being chosen is 1/6. As a decimal, that's 0.16666...
Step-by-step explanation:
As a decimal, that's 0.16666...
If an acute angle of an isosceles right triangle measures (2x-15), What is the value of x?
The value of x in the isosceles right triangle is 52.5.
Explanation:The measure of the acute angle in an isosceles right triangle can be determined by setting the expression equal to 90 degrees:
(2x - 15) = 90
Simplifying the equation, we get:
2x = 90 + 15
2x = 105
x = 105/2
x = 52.5
Therefore, the value of x is 52.5.
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21) on the first day of his cross-country trip, mike drove 100 miles in 2 hours before stopping for lunch. After lunch, he drove 420 miles in 6 hours. What was average speed in miles per hour for his 8 hours of driving?
Answer:
Average speed = 65 miles per hour
Step-by-step explanation:
Mike drove 100 miles in 2hrs
He stopped to take lunch then;
drove 420 miles in 6hrs
Total distance covered = 100 + 420 miles = 520 miles
Total time taken = 2 + 6 hrs = 8hrs
Average speed = Total distance ÷ total time = 520/8 = 65 miles per hour
Match the reasons with the statements. GIVEN: x2 + 6x + 2x + 12 = 0 TO PROVE: x = -6 or x = -2 1. x2 + 6x + 2x + 12 = 0 Subtraction property of equality 2. x2 + 8x + 12 = 0 Distributive Postulate 3. (x + 6)(x + 2) = 0 Combining like terms 4. x + 6 = 0 or x + 2 = 0 Zero product postulate 5. x = -6 or x = -2
Given: [tex]x^2 + 6x + 2x + 12 = 0.[/tex]
1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):
[tex]x^2+(6x+2x)+12=0,\\\\x^2+8x+12=0.[/tex]
2. Distributive postulate:
[tex]x^2+8x+12=(x+6)(x+2).[/tex]
The equation is
[tex](x+6)(x+2)=0.[/tex]
3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):
[tex]x+6=0 \text{ or } x+2=0.[/tex]
4. Subtraction property of equality:
a) subtract 6 from the first equation:
[tex]x+6=0\Rightarrow x+6-6=-6, \ x=-6.[/tex]
b) subtract 2 from the second equation:
[tex]x+2=0\Rightarrow x+2-2=-2, \ x=-2.[/tex]
Answer:
1. x2 + 6x + 2x + 12 = 0 1. Given
2. x2 + 8x + 12 = 0 2. Combining like terms
3. (x + 6)(x + 2) = 0 3. Distributive Postulate
4. x + 6 = 0 or x + 2 = 0 4. Zero product postulate
5. x = -6 or x = -2 5 Subtraction property of equality
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Solve the equation.
x^2 + 10x + 24 = 0
A) -12 and 2
B) 12 and -2
C) -4 and -6
D) 4 and 6
Answer:
Option C
Step-by-step explanation:
Given a quadratic equation
x^2+10x+24 =0
We can use either formula or factorization method to solve this equation.
The last term is 24, it is a product of 6 and 4. Sum =6+4 =10
Hence factoring can be done easier
Split the middle term as 6x +4x
x^2+6x+4x+24 =0
x(x+6)+4(x+6)=0
(x+4)(x+6)=0
Either x+4 =0 or x+6 =0
x=-6 or x =-4
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!
A basket holds at most 14 pounds of apples and oranges. There are at least 3 pounds of apples in the basket. This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges. Which point represents a viable solution?
I took it last time it D. YOu welcome
The point that represents a viable solution is (4, 3)
Which point represents a viable solution?From the question, we have the following parameters that can be used in our computation:
The graph
This is given as an attachment
From the graph, we have solution to the system to be the shaded region
This means that all coordinates in the shaded region are the solutions to the system
One of the coordinates in the solution to the systems of inequalities graphically is (4, 3)
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What is the radius of a sphere with a surface area of 144πcm2?
I believe the radius would be 3.39
Hope this helps! Good luck! :)
144(π)cm² = 4(π)r² Divide by π on both sides
144cm² = 4r² Divide by 4 on both sides
36 = r² Find the square root of both sides
√36 = √r²
6 = rCole and his sister chloe are cleaning their house. The house has nine rooms in it. If it take one person about 18 minutes to clean one room, how long will it take cole and chloe, working together to clean the whole house?
Answer: Cole and his sister Chloe will take 81 minutes to clean the whole house.
Step-by-step explanation:
Total rooms in the house = 9
Total persons to clean the house = 2 (Cole and his sister Chloe)
Time taken by 1 person to clean one=18 minutes
Time taken by 2 persons to clean one room together=18 divided by 2 = 9 minutes
Time taken by 2 persons to clean 9 rooms (which is the total number of rooms in the house)=9 multiply 9 = 81 minutes
therefore, they will take 81 minutes to clean the whole house.
How many more year can a 75 year old person expect to live
Answer:
A 75-year-old person can expect to live 11.7 more years.
Step-by-step explanation:
edmentum/plato
Julianne opens a dance studio. Her start up costs for the building, advertising, and supplies total $52,000. Each day, she spends $680 on operating costs (like utilities and wages). she earns $960 per day from her students' lesson fees.
Part A: Write an equation or inequality to represent this situation. let d be the number of days.
Part B: When will Julianne begin making profit? Show all the work you did to arrive at your answer.
For this case we have:
Initial costs = $ 52,000 Operating costs = $ 680 per day Earnings = $ 960 per dayPart A:
Since d is the variable that represents the number of days, we can represent an inequality for the gains given by:
[tex]680d + 52000 <960d\\[/tex]
Part B:
We want to know the moment from which Julianne obtains earnings, for that we clear d of the previous inequality:
[tex]52000 <960d-680d\\\\52000 <280d\\\\\frac{52000}{280}<d\\[/tex]
[tex]185.7 <d\\\\d> 186 days\\[/tex]
To start making a profit, Julianne must work more than 186 days.
Answer:
[tex]680d + 52000 <960d\\\\d> 186 days\\\\[/tex]
What value of k makes the equation true?
k – 26.7 = 12.8
A.
13.9
B.
38.5
C.
39.5
D.
39.9
All you have to do is just add 26.7 with 12.8, with the result being 39.5
A reasonable estimate for 697 times 82 is
A reasonable estimate for 697 times 82 would be 56,000
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility. Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We could round both numbers to make estimation easier to find.
So let's consider that 82 is 80 and 697 is 700.
As we know that 8 x 7 is 56, then the product of them will be;
80 x 700 = 56,000.
Therefore, This is a great way to estimate of big numbers easily.
Hence, A reasonable estimate for 697 times 82 would be 56,000
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If c ⊥ b, what is m∠2?
A =98
B =82
C =not enough information
D =90
Answer:
C
Step-by-step explanation:
I would say not enough information. You cannot tell from the givens how A,B and m<2 are related to each other.
Answer C
Answer:
c
Step-by-step explanation:
The cafe where you work just ran out of coffee, and you are at the store to buy 112 pounds of coffee. You have put a can with 34 pound of coffee into your shopping cart. How many more pounds of coffee do you need?
The student needs 78 more pounds of coffee to reach the total of 112 pounds required.
The student's question:
The total amount of coffee needed is 112 pounds. You have already put 34 pounds into your cart. To find out how many more pounds you need, you subtract the amount you have from the total needed.
Sarah was trying to save up $475. At her job she made $12 an hour and she worked 28 hours a week after paying for her food and other expenditures she ended up saving 1/6 of her weeks earning how much money did she save up each week?
$56 a week
earnings = $12 × 28 = $336
saved = [tex]\frac{1}{6}[/tex] x $336 = [tex]\frac{336}{6}[/tex] = $56
Plz help!!!you are purchasing four items and want to calculate the tax. The itemscost $2.50, $8.75, $3.00, and $10.25. The tax rate is 6%. How much is the tax? you exercised 24 hours each month for a year. How many hours did youexercise by the end of the year? You may be able to do the math mentally thanksto expanded notation and the distributive property. find the value of this integer expression: -2( 3+ -4 +-8+ 7)find the value of this fraction computation: 6( 1/2 + 2/3 + 3/4)find the perimeter of a rectangular area with a length of 13 inches anda width of 7 inches. give an original example of a situation in which the distributive property could beused.( calculate with and without the distributive property for all and i will put good things on your profile and mark you the brainlyest answer.)
1. The cost of items are= $2.50, $8.75, $3.00, $10.25
Total cost = $ 24.50
Tax rate = 6%
Hence tax amount is = [tex]\frac{6}{100} *24.50[/tex] = $ 1.47
2. Time involved in exercise in 1 month = 24 hours
Hence, total time involved in exercising for a year = [tex]24*12=288[/tex] hours
3. find the value of this integer expression: -2( 3+ -4 +-8+ 7)
Value is obtained by [tex]-2(3+(-4-8)+7)[/tex]
= [tex]-2(3-12+7)=-2(-2)=4[/tex]
4. find the value of this fraction computation: 6( 1/2 + 2/3 + 3/4)
[tex]6(\frac{1}{2}+\frac{2}{3}+\frac{3}{4})[/tex]
=[tex]6(\frac{6+8+9}{12})[/tex]
=[tex]6(\frac{23}{12}) = \frac{23}{2}[/tex]
5. find the perimeter of a rectangular area with a length of 13 inches and width of 7 inches.
Perimeter of a rectangle = 2(length + width)
perimeter = [tex]2(13+7)[/tex]
=[tex]2(20)=40[/tex] inches
6. a situation in which the distributive property could be used is the perimeter of a rectangle.
2(length + width) = 2length + 2width
example- suppose the length of the rectangle is 10 cm and width is 4 cm
so, perimeter is 2(10+4)
= 2(10) + 2(4) = 20+8 =28cm ..... with distributive property
or
2(10+4) = 2(14) =28cm ........ without distributive property
Which equation has the following characteristics?