Two cargo trains each leave their respective stations at 1:00 p.m. and approach each other, one traveling west at 6 miles per hour and the other on separate tracks traveling east at 14 miles per hour. The stations are 40 miles apart. Find the time when the trains meet and determine how far the eastbound train has traveled.
A). 3 p.m, 28 mi
B). 12 p.m., 20 mi
C). 2 p.m., 18 mi.
D). 1 p.m., 15 mi
let x = hours
6x + 14x = 40
20x=40
x = 40/20 = 2 hours
1 pm + 2 hours = 3 pm
eastbound trains is going 14 miles per hour, 14 mph x 2 hours = 28 miles
Answer is A. 3 pm and 28 miles
The eastbound train has traveled 28 miles and they met at 3:00 pm
Speed is the ratio of total distance to total time taken. It is given by:
Speed = distance / time
Let both cargo trains meet each other at time t.
For the train traveling west:
6 = d₁ / t
d₁ = 6t
For the train traveling east:
14 = d₂ / t
d₂ = 14t
Since both trains are 40 miles apart, hence:
d₁ + d₂ = 40
6t + 14t = 40
20t = 40
t = 2 hours
t = 3:00 pm (1:00 pm + 2 hours)
Distance travel by east bound train = d₂ = 14t = 14(2) = 28 miles
The eastbound train has traveled 28 miles and they met at 3:00 pm
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If p(a) = 0.62, p(b) = 0.47, and p(a or
b.= 0.88, then p(a and
b.= _____
Probabilities are used to determine the chances of an event
The value of P(a and b) is 0.21
The given parameters are:
P(a) = 0.62
P(b) = 0.47
P(a or b) = 0.88
P(a and b) is calculated using the following formula
P(a and b) = P(a) + P(b) - P(a or b)
So, we have:
P(a and b) = 0.62 + 0.47 - 0.88
P(a and b) = 0.21
Hence, the value of P(a and b) is 0.21
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Let n be a natural number such that the remainder of the division of 4294 by n is 10, and the remainder of the division of 3521 by n is 11. what is n?
simplify the fraction 48 over 75
48/75
both numbers are divisible by 3
so it simplifies to 16/25
A major stadium has 45,000 seats. If baseball fans have bought 5/8 of the seats for the next game, how many seats are available?
if 5/8 were bought then 3/8 are still available ( 5/8 +3/8 = 1)
45000 * 3/8 = 135000/8 = 16,875 seats are still available
mrs. ellis wants to tile a rectangular room that is 16 feet long and 12 feet wide with square tiles. each square floor is 2 feet. the tiles cost $0.84 per tile. what is the cost to tile the room not including labor?
Mrs. Ellis would need 48 tiles to cover the area of her room. The cost of a single tile is $0.84, so the total cost to tile the room not including labor would be $40.32.
Explanation:To determine the cost to tile the room, we first need to figure out how many tiles Mrs.Ellis needs. We know that each tile covers an area of 2ft * 2ft, which is 4 square feet. Now, we must find out the area of the room by multiplying the length by the width (16ft * 12ft), resulting in 192 square feet. To find out how many tiles are needed, we can divide the total area of the room by the area of one tile (192ft² / 4ft² = 48). Therefore, Mrs. Ellis needs 48 tiles to cover the entire room. Since each tile costs $0.84, the total cost would be 48 * $0.84 = $40.32. Thus, the cost to tile the room excluding labor charges is $40.32.
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Baruka has gallon of milk left in the 1/2 fridge. How many 5/64 gallon (10-ounce) servings of milk does she have left? Show your work
Baruka has [tex]\( \frac{32}{64} \)[/tex] gallons left. [tex]\( \frac{32}{5} \) servings of \( \frac{5}{64} \)[/tex] gallons; she has 6 servings.
To find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk Baruka has left, we need to first convert the amount of milk she has in gallons to the same unit as [tex]\( \frac{5}{64} \)[/tex] gallons.
Since [tex]\( 1 \)[/tex] gallon is equivalent to [tex]\( \frac{64}{64} \)[/tex] gallons, and she has [tex]\( \frac{1}{2} \)[/tex] gallon left, she has [tex]\( \frac{1}{2} \times \frac{64}{64} = \frac{32}{64} \)[/tex] gallons left.
Now, we can find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings are in [tex]\( \frac{32}{64} \)[/tex] gallons:
[tex]\[ \frac{\frac{32}{64}}{\frac{5}{64}} = \frac{32}{5} \][/tex]
Now, we divide [tex]\( 32 \) by \( 5 \)[/tex] to find the number of servings:
[tex]\[ \frac{32}{5} = 6.4 \][/tex]
So, Baruka has [tex]\( 6.4 \)[/tex] servings of [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk left. However, since she can't have a fraction of a serving, she has [tex]\( 6 \)[/tex] servings left.
forty more than twice malia's age is 64
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current
The measure of the third outgoing current will be 0.5 amperes.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.
Then the measure of the third outgoing current will be
We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.
Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆. Then we have
I₁ + I₂ + I₃ = I₄ + I₅ + I₆
0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆
1.85 = 1.35 + I₆
I₆ = 0.5
Thus, the measure of the third outgoing current will be 0.5 amperes.
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find factors of 5x^3+10x^2+35x
Use the inequality -4t - 8 ≤ 12 to fill in the missing numbers.
a) t ≥ ?
b) t + 4 ≥ ?
c) t - ? ≥ 0
d) t + 10 ≥ ?
e) 3t ≥ ?
f) t/? ≥ -5
So here's the question
"Melissa knitted a scarf with 9 1/5
yards of red yarn. She used another 3 11/25 yards of blue yarn to finish knitting. How much more red than blue yarn did Melissa use?"
I need help solving it, and it is subtraction, right?
you work for a dress maker and your boss sends you to the fabric store to buy blue fabric she tells you to buy the best deal what's is the best deal
20 yards for $30.00
40 yards for $45.00
50 yards for $70.00
65 yards for $85.00
draw or write to explain why 1 hundred 4 tens and 14 tens name the same amount
Tony buys a CD that is priced at $13.59. He has a coupon for $1.85 off. He pays with a $20 bill. Which is the best whole number estimate of how much change he gets? $8
a light bulb consumes 3600 Watts hours per day. how long does it take to consume 12600 Watts hours?
it would take 84 hours,or 3.5 days,hope this helps
What is the simplified form of the expression k^3(K^7/5)^-5
What percentage is 1022.40 of 1420 and how do i solve
James has 875 feet of rope. There are 13 teams of hikers. If James gives an equal amount of rope to each team how much rope will each team receive
Answer:
67.307 feet of rope per team
Step-by-step explanation:
60 bricklayers began a 16-day project to build a castle. After five days, five of the bricklayers quit the job. If they work the same amount each day, how many extra day(s) (beyond the original estimate of 16) will the remaining bricklayers need?
Find a basis for the row space and column space of a matrix and the rank .
Final answer:
To identify a basis for the row and column spaces of a matrix and determine its rank, one uses row reduction to reach REF or RREF. The non-zero rows of the RREF are the basis for the row space, the corresponding columns in the original matrix form the basis for the column space, and the rank is the number of these basis vectors. In statistics, the degrees of freedom for the Test of Independence is calculated as (number of columns - 1)(number of rows - 1).
Explanation:
To find a basis for the row space and column space of a matrix as well as the rank, you follow specific procedures. First, perform row reduction on the matrix to bring it to row echelon form (REF) or reduced row echelon form (RREF). The non-zero rows of the RREF correspond to a basis for the row space. The columns in the original matrix that correspond to the leading 1s in the RREF form a basis for the column space. The rank of the matrix is equal to the number of leading 1s in the RREF form, which is also the number of basis vectors for either the row space or column space since they have the same dimension.
The Test of Independence in statistics uses a contingency table to determine if two categorical variables are independent. The number of degrees of freedom for the test is given by the formula: (number of columns - 1)(number of rows - 1). This is critical when referencing the chi-squared distribution table to determine the p-value for the hypothesis test.
Which rows represent when (p ∧ q) ∨ (p ∧ r) is true?\
Answer:
The answer is B. A, B, and C
Step-by-step explanation:
Just took the test on edg
Mr. Yu applies 1/2 ounce of fertilizer to every 5/8 square meter of his lawn. How many ounces of fertilizer does Mr. Yu use per square meter for his lawn? Enter your answer in the box as a fraction in simplest form.
Answer:
[tex]\frac{4}{5} [/tex] ounce
Step-by-step explanation:
We can use rule of three to answer this problem.
The data we have is the following:
fertilizer (ounces) area(m^2)
1/2 ⇒ 5/8
x ⇒ 1
the x represents the unknown quantity of fertilizer that is used in one square meter.
Now we multiply the cross quantities and divide by the remaining value.
[tex]x=\frac{1}{2}*1[/tex] ÷ [tex]\frac{5}{8}[/tex]
[tex]x=\frac{1*8}{2*5} =\frac{8}{10} =\frac{4}{5}[/tex]
He will use 4/5 ounces of fertilizer per square meter.
Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function that best represents Samantha's account and how much does she have in savings after 5 years? Round your answer to the nearest dollar. Hint: Use the formula, f(x) = P(1 + r)x. (5 points)
Answer: The answer is y = 500(1.04) x
Step-by-step explanation: The formula is y = P (1 + r) x
So, given that P which is the initial value 500(1+0.4) x
f(x)=500(1.04) x
The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick whats the inside diameter
please help im really dumb lol
Taylor bought 200 shares of stock for $18.12 per share last year. He paid his broker a fl at fee of $30. He sold the stock this morning for $21 per share, and paid his broker 0.5% commission. a. What were Taylor's net proceeds?
Final answer:
Taylor's net proceeds from the stock transaction are $525, after accounting for the initial purchase cost and broker's commissions on both the buying and selling of the stock.
Explanation:
Taylor bought 200 shares of stock at $18.12 per share and paid a flat brokerage fee of $30. To find the initial cost, we multiply the number of shares by the purchase price and then add the fee:
200 shares × $18.12/share + $30 = $3,654
When Taylor sold his shares at $21 per share, his gross proceeds were:
200 shares × $21/share = $4,200
The broker commission of 0.5% on the selling price is calculated as:
$4,200 × 0.005 = $21
To find Taylor's net proceeds, we subtract both the initial cost and the selling commission from the gross proceeds:
$4,200 - $3,654 - $21 = $525
Therefore, Taylor's net proceeds from the stock transaction are $525.
Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = x3 + x − 9, [0, 2]
you have a standard deck of 52 cards. you pick one card from the deck and then , without putting the first card back , pick a second card . what is the probability that both cards will be 9s??
there are 4 9's in a deck
so first pick = 4/52 reduces to 1/13
second pick there would be 3 9's left and 51 cards so it would be 3/51 reduces to 1/17
probability of both happening = 1/13 * 1/17 = 1/221 (fraction form)
if you need it in decimal it = 1/221 = 0.00452, rounded to 0.005
Jan has a 12 ounce milkshake four ounces in the milkshake are vanilla and the rest is chocolate what are two equivalent fraction of the milkshake is vanilla
Answer:
In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6...
hope it helps