100 meter long Christmas train needs 30 seconds to cross a 400nmetrr long bridge assuming the train goes at a steady speed how fast is it

Answers

Answer 1

Since it's 100m long, to cross the front needs to go 500m. 500/30= (16+2/3)meters per second

Related Questions

6300 and 530
The value of 3 in ___is____times the value of 3 in ___.

Answers

Hope this helps you out :)
6300 Ana 530

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

A newspaper finds that the mean number of typographical errors per page is six. Find the probability that (a) exactly four typographical errors are found on a page, (b) at most four typographical errors are found on a page, and (c) more than four typographical errors are found on a page.

Answers

In this case, the Poisson distribution is the best one to use. The formula for Poisson distribution is given as:

P[x] = e^-m * m^x / x!

Where,

m = mean number of typographical errors = 6

x = sample value

A. The probability of exactly 4 errors are found on a page is:

P[4] = e^(-6) * 6^4/4!

P[4] = 0.1339

B. The probability that at most 4 errors will be the summation of x = 0 to 4:

P[0] = e^(-6) * 6^0/0! = 2.479 E -3

P[1] = e^(-6) * 6^1/1! = 0.01487

P[2] = e^(-6) * 6^2/2! = 0.04462

P[3] = e^(-6) * 6^3/3! = 0.08924

Therefore summing up all including the P[4] in A gives:

P[at most 4] = 0.2851

C. The probability that more than 4 would be the complement of answer in B.

P[more than 4] = 1 - P[at most 4]

P[more than 4] = 1 - 0.2851

P[more than 4] = 0.7149

The Henderson family and the Tran family each used their sprinklers last summer. The Henderson family's sprinkler was used for 15 hours. The Tran family's sprinkler was used for 40 hours. There was a combined total output of 1800L of water. What was the water output rate for each sprinkler if the sum of the two rates was 70L per hour?
Henderson family’s sprinkler: __ L per hour
Tran family’s sprinkler: __ L per hour

Answers

You have to create a system of equations in order to solve this, one based on total output and one based on output of each family's sprinkler. The first equation is based on the total output according to how many hours each sprinkler ran. Let's use H for the Henderson's and T for the Tran's. The equation for the total output is:
15H + 40T = 1800
That means that the Henderson's ran their sprinkler for 15 hours using H amount of water, and the Tran's ran their sprinkler for 40 hours using T amount of water, and that the total amount between the 2 families was 1800.
The next equation is based on each individual family's use of water per hour.
H + T = 70
That means that the Henderson's and the Trans together used 70 L per hour.
Solve the second equation for either variable (I picked H):
H = 70 - T
Now sub that value in for H in the second equation:
15(70 - T) + 40T = 1800
Now we will distribute the 15 into the parenthesis. The reason for that substitution is because we have 2 unknowns originally, an unknown H and an unknown T, and we can't solve an equation with 2 unknowns. The substitution gave us the equation in terms of T only.
1050 - 15T + 40T = 1800
1050 + 25T = 1800
25T = 750
T = 30
Now that we have a value for T, sub it in to the simple equation H + T = 70 to get H + 30 = 70, so H = 40

A line passes through the point (6−6) and has a slope of 3/2 . Write an equation in point-slope form for this line.

Answers

y= (3/2)x-15 is the equation

A triangle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?

Answers

you must first subrtact 4 -6 to get 42 then add 99

A fish is 5 feet below the surface of a lake. If its position can be recorded as −5 feet, what would the position of 0 represent?

Answers

Hey!

According to your question, we can see that if we got a negative number, that would represent that we are below sea level, that may mean being underwater. If we got a positive number, then that means we are above the sea level. The position of 0 would represent sea level.

Thanks
-TetraFish

Cosine law part 2 in need of help (ignore question 67)

Answers

the law of cosines applies if you have an angle and its sides making it up, so say, if you had angle B and sides "a" and "c", angle B is made by those two sides, and thus the law of cosines would apply to get a missing side or angle.

in this case, we have two angles, B and C and only one side, so.... no dice on the law of cosines then.

now... .let's check closely, B is 66° and C is 28°... wait just a second!, that means A is 180 - ( 66 + 28 ), or 86°.

so then

[tex]\bf \cfrac{sin(C)}{c}=\cfrac{sin(A)}{a}\implies \cfrac{sin(28^o)}{11.6}=\cfrac{sin(86^o)}{a}\implies a=\cfrac{11.6\cdot sin(86^o)}{sin(28^o)}[/tex]

make sure your calculator is in Degree mode.

but "a" is roughly 24.6484428

On two investments totaling $10,500, Brian lost 6% on one and earned 8% on the other. If his net annual receipts were $497, how much was each investment?

Answers

Let
x = the amount invested on the winner, then
10500-x = amount invested on the losing investment.

We know that the net profit is $497, so
0.08x - 0.06(10500-x) = 497
Solve for x:
0.14x = 497+630=1127
x=1127/0.14=8050

Therefore Brian invested $8050 on the investment that earned 8% and $2450 on the one that lost 6%.

The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S . Then use this equation to find the total cost to transport 19 tons of sugar.

Answers

Answer: Equation relating C to S : [tex]C=6500+250S[/tex]

The total cost to transport 19 tons of sugar is $11, 250.

Step-by-step explanation:

Given : It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.

Total cost = $6500 + $250 x (amount of sugar transported ( in tons))

Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.

Then, the equation relating C to S would be : [tex]C=6500+250S[/tex]

When S= 19 , we get

[tex]C=6500+250(19)=6500+4750= 11250[/tex]

Hence, the total cost to transport 19 tons of sugar would be $11, 250.

An equation that relates Cost to the amount of sugar S

C = 6500 + 250S

The total cost is $1120

The total cost of transporting 19 tons of sugar at 250 each

C = total cost

C = 6500 + 250(19)

Total cost = 6500 + 4750

= 11250

Therefore the total cost of transporting the 19 tons of sugar is $11250

Answers

lower box = x

upper box = y

x+y=137

x=137-y

12.50x + 10y=1502.50

12.50(137-y) + 10y=1502.50

1712.5-12.50y+10y=1502.50

1712.5-2.50y=1502.50

-2.5y=-210

y=-210/-2.50 = 84

y = 84

x=137-84=53

53 lower box tickets

84 upper box tickets

Differentiate
1/√x^2-1

Answers

the function is [tex]f(x)= \frac{1}{ \sqrt{ x^{2} -1}} [/tex]

write f again as [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex]

(the power -1 takes the expression to the denominator, and the power 1/2 is square root)

writing rational expressions as power expressions, generally makes differentiation more practical.

In [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex] we notice 2 functions:

the outer function [tex]u^{ -\frac{1}{2} } [/tex], where [tex]u=x^{2} -1[/tex], and the inner, u itself , which is a function of x.

So we differentiate by using the chain rule:

[tex]f'(x)= -\frac{1}{2}u^{- \frac{1}{2}-1 }*u'= -\frac{1}{2}u^{- \frac{3}{2} }*(2x)=- \frac{x}{ \sqrt{ u^{3} } } =- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]

Answer: [tex]- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]

a projectile is launched straight up from ground level with an initial velocity of 320 ft/sec when will it's height above ground be
1538 feet

Answers

Given: at time = 0, v0=+320 ft/s, [ assumed a=-g=-32.2 on earth ]

use kinematic equation for vertical projectiles,
Height,
H(t) = 1538 = v0(t)+(1/2)at^2=320t+(1/2)(32.2)t^2

Solve for t using the quadratic formula,
with A=16.1, B=320, C=-1538:
16.1t^2+320t-1538=0
t=8.14 or t=11.74

This means that at t=8.14, the projectile reaches 1538 feet (on its way up), and at t=11.74, the projectile falls back down and reaches also 1538 feet.

Final answer:

To calculate when the height of the projectile will be 1538 feet, use the kinematic equation and solve the quadratic equation for time.

Explanation:

To calculate when the height of the projectile will be 1538 feet, we can use the kinematic equation for free-falling objects. The equation is: h = [tex]h0 + v0*t - 16*t^2,[/tex] where h is the height above ground, h0 is the initial height (0 in this case), v0 is the initial velocity (320 ft/sec in this case), and t is the time.

Substituting the given values into the equation, we have: 1538 = 0 + 320*t - 16*t^2. Rearranging this equation, we get: [tex]16*t^2[/tex]- 320*t + 1538 = 0.

Now we can solve this quadratic equation for t by using the quadratic formula: t = (-b ± sqrt([tex]b^2[/tex] - 4ac)) / (2a), where a = 16, b = -320, and c = 1538. Plugging in these values, we can calculate the values of t.

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FInd the approximations to at least two decimal places for the coordinates of Point Z in the figure below. The angle theta or Q is -80 degrees and the radius is 11.

Z = ?

Also if you can explain to me, that would be great.

Answers

check the picture below.

thus the rectangular coordinates are [ 11cos(-80°), 11sin(-80°) ].

make sure your calculator is in Degree mode.

Final answer:

Point Z's polar coordinates can be found by using the formulas x = r*cos(θ) and y = r*sin(θ), converting the angle from degrees to radians first. Use r = 11 and θ = -80 degrees.

Explanation:

This question deals with the concept of polar coordinates, coordinates given by a distance from the origin (radius) and an angle from the positive x-axis (-80 degrees in this case). Point Z's coordinates can be found using the formulas: x = r*cos(θ) and y = r*sin(θ). Here r (the radius) is 11 and θ is -80 degrees, but remember we need to convert this angle to radians because the trigonometric functions in most calculators use radians. That can be done using the formula: Radians = Degrees * (π / 180). Hence calculate x and y to find Point Z.

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Manuel rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 87 cents for each mile driven. Manuel had to pay $248.98 when he returned the truck. For how many miles did he drive the truck?

Answers

Final answer:

After calculations, it is determined that Manuel drove approximately 269 miles.

Explanation:

Manuel rented a truck which had a base fee of $14.95 and an additional charge of 87 cents per mile. To find the number of miles driven, we need to subtract the base fee from the total amount paid and then divide by the cost per mile.

First, subtract the base fee from the total cost:

Total amount paid = $248.98

Base fee = $14.95

Amount paid for miles = $248.98 - $14.95 = $234.03

Next, divide the amount paid for miles by the cost per mile:

Cost per mile = 87 cents = $0.87

Number of miles driven = $234.03 / $0.87 = 269 miles (approximately)

Therefore, Manuel drove approximately 269 miles with the rented truck.

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Answers

inequation 1:

[tex] \frac{2}{3}x-3 \geq y[/tex]

to plot the pairs (x, y) for which the inequation holds, draw the line [tex]y=\frac{2}{3}x-3[/tex]

then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.

we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.

inequation 2:

[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]

[tex]y\ \textless \ - \frac{2}{3} x+ 4 [/tex]

draw the lines

i) [tex]y=\frac{2}{3}x-3[/tex] use points (0, -3), (3, -1)

ii)[tex]y=- \frac{2}{3} x+ 4 [/tex] use points ( 0, 4), (3, 2)

let's use the point P(3, 3) to see what region of the lines need to be coloured:

[tex]\frac{2}{3}x-3 \geq y[/tex] ;
[tex]\frac{2}{3}(3)-3 \geq 3[/tex]
[tex]2-3 \geq 3[/tex], not true so we color the region not containing this point

[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex](3)+ \frac{2}{3}(3)\ \textless \ 4 [/tex]
[tex]3+ 5\ \textless \ 4 [/tex] not true, so we color the region not containing the point (3, 3)

The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.

Answer:

in other words b

Step-by-step explanation:

if f(x) = 3x - 2 then f (8) - f(-5)=

Answers

f(8) = 3(8) - 2 = 22
f(-5) = 3(-5) - 2 = -17
so....
f(8) - f(-5) = 22 - -17 = 39

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Answers

Final answer:

The probability is approximately 0.267.

Explanation:

To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:

Z = (x - μ) / (σ / sqrt(n))

where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).

We calculate the Z-score as follows:

Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617

We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.

Choose the polynomial written in standard form. (5 points)

xy2 + 4x4y + 10x2

x4y2 + 4x3y + 10x

x4y2 + 4x3y5 + 10x2

x6y2 + 4x3y8 + 10x

Answers

The polynomial in standard form from the given options is [tex]x^4y^2 + 4x^3y + 10x[/tex], as it orders the terms by degree in descending order, first by the degree of x and then y.

The term standard form in mathematics, especially in relation to polynomials, refers to a way of writing the polynomial so that the terms are ordered by their degree in descending order. More specifically, for a polynomial in two variables, x and y, the standard form would have the terms arranged first by the degree of x, then y, from highest to lowest.

Looking at the options provided in the question, the polynomial that is written in standard form would have the highest degree term first, and so on. The polynomial [tex]x^4y^2 + 4x^3y + 10x[/tex] follows this convention, with the terms ordered by decreasing powers of x first and y second. Therefore, this is the polynomial written in standard form.

Note that while the other options are all polynomials, they do not follow the standard form convention as closely as the correct option provided.

Find the value of x, rounded to the nearest tenth. Please help me!!

Answers

When two secant lines intersect each other outside a circle, the products of their segments are equal.

5(x+5) = 7(15+7)
5x + 25 = 7 * 22
5x + 25 = 154
5x = 154 - 25
5x = 129
x = 129/5
x = 25.8

The value of x for the circle is 25.8. The correct option from the following is (D).

Simple closed shapes include circles. It is the collection of all points in a plane that are a certain distance from the center. A segment is a section of a straight line that has every point on the line that lies in its middle and is enclosed by two clearly defined endpoints.

The products of two secant lines that cross one another outside of a circle are equal.

The value of x is:

5(x+5) = 7(15+7)

5x + 25 = 7 × 22

5x + 25 = 154

5x = 154 - 25

5x = 129

x = 129/5

x = 25.8

Hence, the value of x is 25.8.

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which is greater 2 or -13?

Answers

2, you can already tell -13 is less because it's a negative, and 2 is a positive.

2 is greater than -13.

If a number is negative, that means it's lower than 0.

what is 46 2/3 of 28

Answers

[tex]\bf 46\frac{2}{3}\implies \cfrac{46\cdot 3+2}{3}\implies \cfrac{140}{3}\qquad thus \\\\\\ \cfrac{140}{3}\cdot 28\implies \cfrac{3920}{3}\implies 1306\frac{2}{3}[/tex]

Translate to an algebraic expression. 5 INCREASED BY y

Answers

easy............5 + y

solve the equation 14x+7y=24 for x

Answers

You want to isolate the variable on one side of the equation so that you can see what it's value is with respect to the other terms

Which expression is equivalent to the following complex fraction? (2/x)-(4/y)/(-5/y)+(3/x)

Answers

See answer attached.

Final answer:

To find the equivalent expression, multiply the first fraction by y and the second fraction by x. Simplify the expression by combining like terms.

Explanation:

To find the expression equivalent to the given complex fraction, we can simplify it step by step. First, multiply the numerator and denominator of the first fraction (2/x) by y, and multiply the numerator and denominator of the second fraction (-5/y) by x. This gives us (2y)/(xy) - (4x)/(-5x). Next, simplify the expression by combining like terms. The final equivalent expression is (2y - 4x)/(xy + 5x).

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A collection of quarters and nickels is worth $3.75. There are 27 coins in all. Find how many of each there are.

Answers

Q +N =27

Q=27-N

0.25Q + 0.05N =3.75

0.25(27-N) + 0.05 =3.75

6.75-0.25N+0.05N=3.75

6.75-0.2N=3.75

-0.2N=-3

N=-3/-0.2 = 15

15 nickels

27-15 = 12

12 quarters

15x0.05 = 0.75

12 x 0.25 = 3.00

3.00 + 0.75 = 3.75

12 quarters & 15 nickels

You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in the 4% account?

Answers

Let x = amount invested in the 1st account
y = amount invested in the 2nd account
z = amount invested in the 3rd account

Because the total investment is $100,000, therefore
x + y + z = 100,000 (1)
Interest earned in one year from the accounts is $3,650, therefore
0.04x + 0.03y + 0.02z = 3,650
or
4x + 3y + 2z = 365,000 (2)

Because x = 5y, therefore obtain these 2 equations:
5y +y +z = 100,000
or
6y + z = 100,000 (3)
4*(5y) +3y + 2z = 365,000
or
23y + 2z = 365,000 (4)

Substitute z=1000,000 - 6y from (3) into (4).
23y + 2(100,000 - 6y) = 365,000
23y + 200,000 - 12y = 365,000
11y = 165,000
y = $15,000
Therefore
x = 5y = $75,000
z = 100,000 - 6y = $10,000

Answer:
The amounts invested are
1st account: $75,000
2nd account: $15,000
3rd account: $10,000

Assume the Poisson distribution applies. Use the given mean to find the indicated probability.

Find P(4) when μ = 8.

Answers

For given Poisson distribution, μ=8.

P(k)=μ^k*e^(-μ)/k!
so
P(4)=8^4*e^(-8)/4!=0.05725 approx.

Final answer:

Using the Poisson distribution formula, substitute the given mean and the number of occurrences into the formula to find the probability. Hence P(4; 8)= e^-8 * 8^4 / 4!. The answer will be in decimal form, signifying the probability.

Explanation:

The probability in a Poisson distribution that an event happens exactly k times when the mean occurrence rate (μ or Lambda) is given is determined using the following formula:

P(k; μ) = (e^-μ * μ^k) / k!

Where e is Euler's number (approximately equal to 2.71828), k is the number of occurrences (in this case, it is 4) and μ is the mean number of occurrences (in this case, it is 8).

Applying the values into the formula, we have:

P(4;8) = (e^-8 * 8^4) / 4!

You can calculate the above expression using a calculator to find the probability. Remember, the answer will be in decimal form, representing the probability of the event occurring 4 times when the average rate of occurrence is 8.

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Perform the indicated operation. (5 - 2i 2) 2

Answers

[tex]\bf (5-2i^2)^2\qquad \textit{now recall }i^2=\sqrt{-1}\cdot \sqrt{-1}=\sqrt{(-1)^2}=-1 \\\\\\ (5-2(-1))^2\implies (5+2)^2\implies 7^2\implies 49[/tex]

ANSWER

[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]

EXPLANATION

The given expression is

[tex](5 - 2 {i}^{2} ) ^{2} [/tex]

This is an expression containing a complex number.

Recall that in complex numbers,

[tex] {i}^{2} = - 1[/tex]

The expression now becomes,

[tex](5 - 2 {i}^{2} ) ^{2} = (5 - 2 ( - 1) ) ^{2} [/tex]

This implies that,

[tex](5 - 2 {i}^{2} ) ^{2} = (5 + 2 ) ^{2} [/tex]

This will simplify to,

[tex](5 - 2 {i}^{2} ) ^{2} = {7}^{2} [/tex]

This eventually gives us,

[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]

y=-x y=2x+3 graph the equation to solve the system

Answers

If Y=-x y=2x+3 was graphed it would be (-1,1)

Well to solve by graphing, you would graph both equations and then see where the two lines intersect. This graphical intersection is the point where both equations are equal to each other.

To solve using math :P

If a solution exists, (x,y)=(x,y) so we can say y=y and then we can say:

2x+3=-x add x to both sides

3x+3=0

3(x+1)=0

So x=-1, and since y=-x

y=1

So the solution to the system of equations, and the graphical intersection, is the point (-1, 1)

A total of 804 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

The student ticket number is 429 and adult is 375.

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