Final answer:
The freight and passenger trains will meet 120 miles from Boston at 2 PM, which is 2 hours after the passenger train departs.
Explanation:
To solve this problem, we need to figure out when the two trains will meet, given their different start times and speeds. Since the freight train leaves at 9 AM and the passenger train leaves at noon, there is a 3-hour difference between their departure times.
In those 3 hours, the freight train will cover a distance of 3 hours imes 24 miles/hour = 72 miles.
Both trains are now heading towards each other, with the passenger train moving faster. We need to find out how long it will take for the passenger train to catch up to the freight train, starting from the 72-mile head start.
Let's call the time it takes for the passenger train to catch up 't' hours. In 't' hours, the passenger train will cover 60t miles and the freight train will cover 24t miles.
Since the passenger train is trying to cover the lead that the freight train has plus the distance both are covering after noon, we can set up an equation: 60t = 72 + 24t. Solving for 't' gives us 't' = 72 / (60 - 24) = 2 hours. So, in 2 hours after noon, which is at 2 PM, the two trains will meet.
Now we find out how far from Boston they will meet by calculating the distance the passenger train travels in those 2 hours: Distance = 60 miles/hour imes 2 hours = 120 miles from Boston.
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a man owned 75 shares of stock worth $50 each the corporation declared a dividend of 8% payable in stock how many shares did he then own
After receiving an 8% stock dividend on his initial 75 shares, the man will own a total of 81 shares.
Explanation:The question is asking how many shares the man will own after a corporation where he holds stock declared a dividend payable in stock. The man initially owned 75 shares of stock, each worth $50, and the corporation declared an 8% dividend. To find out how many additional shares he receives as a dividend, we calculate 8% of his 75 shares:
Additional shares = 8% of 75 = 0.08 × 75 = 6 shares.
The man will then own his original 75 shares plus the 6 additional shares, for a total of:
Total shares owned = 75 + 6 = 81 shares.
You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What is the balance of the savings account by the end of the third year?
$4,618.81
$2,910.63
$5,722.23
$3,910.02
Algebraically determine if the relation y=10x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry
A.) y-axis
B.)no symmetry
C.)the origin
D.)x-axis
What is the area, in cm2, of the circle shown above? Round your answer to the nearest tenth.
hey can you please help me posted picture of question
hello can you please help me posted picture of question
The diameter of a circle is 8 inches.What is the area?
A.8 inches
B.16 inches
C.32 inches
D.64 inches
The required correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.
The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. Since the given information provides the diameter (twice the radius), we need to first find the radius by dividing the diameter by 2.
Given: Diameter = 8 inches
Radius = Diameter / 2 = 8 inches / 2 = 4 inches
Now we can calculate the area using the formula:
= πr² = π * (4 inches)²
≈ 3.14 * 16 square inches
≈ 50.24 square inches
Therefore, the correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.
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Final answer:
The area of a circle with an 8-inch diameter is calculated using the formula A = πr². The correct area is around 50.27 square inches, not one of the provided options.
Explanation:
The question asks for the area of a circle with a diameter of 8 inches. To find the area, we use the formula A = πr², where π is approximately 3.14159, and r is the radius of the circle. Since the diameter is 8 inches, the radius (r) is half of that, which is 4 inches.
To calculate the area:
Divide the diameter by 2 to find the radius: 8 inches / 2 = 4 inches.Square the radius: 4 inches ² = 16 square inches.Multiply by π (pi): π × 16 square inches ≈ 50.26548 square inches.The area of the circle is approximately 50.27 square inches, which means none of the given options A, B, C, or D is correct.
is 0.003km greater than, less than, or equal to 3 m
Find the feet of c and d
your drawer contains 6 black socks and 8 white socks. what is the probability that both socks are black
[tex] \displaystyle
|\Omega|=\binom{14}{2}=\dfrac{14!}{2!12!}=\dfrac{13\cdot14}{2}=91\\
|A|=\binom{6}{2}=\dfrac{6!}{2!4!}=\dfrac{5\cdot6}{2}=15\\\\
P(A)=\dfrac{15}{91}\approx16\% [/tex]
A line passes through the (1, -6) and has a slope of 5. write an equation for this line
Hey can you please help me posted picture of question
The ratio of the length to the width of a map is 8 to 5. The map is exactly 32 inches in length. What is the width of the map? A. 13 inches B. 20 inches C. 24 inches D. 32 inches
Answer:
B. 20 inches
Step-by-step explanation:
Remember that when dealing with ratios or unit rates you just have to do simple rules of three to calcuate what they are asking you, in this case you have that in the map for every 8 units in the length there will be 5 in the width, so how many will there be when the map is 32 inches in length?
[tex]\frac{8}{5}= \frac{32}{x}\\x=\frac{32*5}{8}\\ x=20[/tex]
So the width of a map with a length of 32 inches and a ratio of 8:5 will be 20 inches.
Michael bought a new soccer Jersey that was $24.99. after taxes the total cost was $28.99. What is the percent if increase
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?
What are the different ways you can solve a system of linear equations in two variables? What is the process for solving a system using each method?
please help with 23 and show how to work it out
Refer to narrative 14-1. a house is selling for $150,000. a deposit of $20,000 was made when the sales contract was signed. the down payment is 30% and the balance will be financed with a 25-year mortgage at 11% and 4 discount points. if the sellers are responsible for the broker's commission (6% of the purchase price); $1,300 in other closing costs; and the existing mortgage, with a balance of $40,000; what proceeds will they receive on the sale of the property?
-4 log8 x - 2 = 6
Round to the nearest ten - thousandth
(a) find the slope m of the tangent to the curve y = 5 + 5x2 − 2x3 at the point where x =
a. m = (b) find equations of the tangent lines at the points (1, 8) and (2, 9). y(x) = (at the point (1, 8)) y(x) = (at the point (2, 9))
The slope of the tangent will be "[tex]10a-6a^2[/tex]". The equation at point (1, 8) is "[tex]y = 4x+4[/tex]" and at point (2,9) is "[tex]y = -4x+17[/tex]".
Given equation is:
[tex]y = 5+5x^2-2x^3[/tex](a)
The slope of the tangent to the curve point where [tex]x = a[/tex] is:
→ [tex]\frac{dy}{dx} = m = 10x-6x^2[/tex]
→ [tex]= 10a-6a^2[/tex]
(b)
The equation of tangent at point (1,8) will be:
→ Slope, [tex]m = 10-6[/tex]
[tex]= 4[/tex]
→ [tex]y-8=4(x-1)[/tex]
[tex]y = 4x-4+8[/tex]
[tex]y = 4x+4[/tex]
and,
The equation of tangent at point (2,9) will be:
→ Slope, [tex]m = 10\times 2-6\times 2^2[/tex]
[tex]= 20-24[/tex]
[tex]= -4[/tex]
→ [tex]y-9=-4(x-2)[/tex]
[tex]y-9=-4x+8[/tex]
[tex]y = -4x+17[/tex]
Thus the above answer is right.
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Evaluate Cot0 if sin0= square root of 6/5
one day a store sold 12 sweatshirts white one cost $9.95 and yellow ones cost $12.50. In all 147.45 worth of sweatshirts were sold how many of each color were sold?
What is the quotient of -19/2 divided by 38/ 7
Which statements is true
A: all rectangles are squares
B: some trapezoids are parallelogram
C: all square are rhombues
D: no rhombuses are rectangles
Can someone please help me with this problem. I need help solving a and b
There is a game at the carnival that costs $20 to play. There are two outcomes: either you win $100 , or you lose. To play you roll a die. If a six appears you win; all other rolls you lose. if 1000 people played this game during one afternoon what would you expect to be the outcome?
A. the game earns $3330
B. the game earns $1660
C. the game loses $3330
D. the game loses $1660
Correct answer is Option(A) . The game earns $3330
Carnival Game Expected Outcome
To determine the expected outcome, we first need to calculate the expected value of playing this game once.
The cost to play is $20. If a six is rolled, the player wins $100; otherwise, they lose their $20.
Calculations:
Probability of rolling a six = 1/6Probability of not rolling a six (1, 2, 3, 4, or 5) = 5/6Expected value (EV) for one game:
EV = (1/6 x ($100 - $20)) + (5/6 x (-$20))EV = (1/6 x $80) + (5/6 x -$20)EV = $80/6 - $100/6EV = -$20/6EV ≈ -$3.33This means that on average, each player loses approximately $3.33 per game.
Outcome for 1000 Players
If 1000 people play the game, the total expected loss for the players will be:
Total Expected Loss = 1000 x EVTotal Expected Loss ≈ 1000 x (-$3.33) = -$3330Therefore, the game earns approximately $3330.
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What is the formula for finding a break-even point?
Answer:
break even point=(0.01)(# of points)(P)/monthly savings
Step-by-step explanation:
ap3x
Assuming boys and girls are equally likely, find the probability of a couple having a baby boy boy when their fourth fourth child is born, given that the first three three children were all boys all boys.
A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply.
Answer:
A,B,D,E
Step-by-step explanation:
did it on edge
Determine if the function is an even function, an odd function or neither. y=-5x^(2)-2x+6
Answer:
C
Step-by-step explanation: