Two trains start from Fort Worth traveling at the same speed. The trip for Train W takes 20 hours, while the trip for Train Z takes 25 hours. If the city Train Z is traveling to is 400 miles farther away than the city Train W is traveling to, how far will Train Z travel in total to reach its destination?

a) 1,200 miles
b) 480 miles
c) 2,400 miles
d) 2,000 miles
e) 1,600 miles

The number of days when there is only 3 g remaining is approximately 26 days.

To find the number of days when there is only 3 g remaining, we need to solve the equation m(t) = 3 for t.

The given equation is: m(t) = 15e^(-0.085t)

Setting m(t) equal to 3, we have: 3 = 15e^(-0.085t)

Dividing both sides by 15: e^(-0.085t) = 3/15

Simplifying the right side: e^(-0.085t) = 1/5

Taking the natural logarithm of both sides to remove the exponential: ln(e^(-0.085t)) = ln(1/5)

Using the property of logarithms: -0.085t ln(e) = ln(1/5)

Since ln(e) = 1, we have: -0.085t = ln(1/5)

Dividing both sides by -0.085: t = ln(1/5) / -0.085

Using a calculator to evaluate the right side, we find: t ≈ 26.07

Rounding to the nearest whole number, the number of days when there is only 3 g remaining is approximately 26 days.

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The perimeter of the triangle is inches 5x+12.

The perimeter is the distance around a shape's edge.

The distance encircling a shape's boundary is its perimeter.

The sides of the triangles are 4x+1, x+4 and 7 inches.

To find the perimeter of the triangle:

The formula for the perimeter of a triangle is the sum of the length of all the sides of a triangle.

That means,

the perimeter of the triangle = (4x+1) + (x+4) + 7

The perimeter of the triangle = 5x+ 12

Therefore, 5x+12 is the perimeter of the triangle is 5x+ 12.

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Answer:

\(5xyz\)

Step-by-step explanation:

\(\frac{15x^2y^3z}{3xy^2}\)

Step 1: Divide the numbers

\(\frac{15}{3}=5\\\\=\frac{5x^2y^3z}{xy^2}\)

Step 2: Simplify

\(\frac{x^2}{x}\\\\= x\\\\=\frac{5xy^3z}{y^2}\)

Step 3: Simplify

\(\frac{y^3}{y^2} = y\\\\=5xyz\)

Therefore, the simplified answer is \(=5xyz\)

Answer:

5x^3 y^5 z

Step-by-step explanation:

See the steps below:)

Answer:

False

Step-by-step explanation:

numbers are integers, the integers are negative, zero and positive, 

while natural numbers are only positive, 

therefore the statement is false

 . False. Integers comprise negative and positive numbers (...- 3, -2, -1, 0, 1, 2, 3 ...) and natural numbers only comprise positive integers (0, 1, 2, 3 ...)  

Answer:

h(t) = -5*t^2 + 20*t  + 2

Step-by-step explanation:

First, we know that the motion equation of the ball will be quadratic, so we write the equation:

h(t) = a*t^2 + b*t + c

Now we need to work with the data in the table.

h(1) = 17

h(3) = 17

h(1) = h(2) = 17

Then we have a symmetry around:

(3 - 1)/2 + 1 = 2

Remember that the symmetry is around the vertex of the parabola, then we can conclude that the vertex of the parabola is the point:

(2, h(2)) = (2, 22)

Remember that for a quadratic equation:

y = a*x^2 + b*x + c

with a vertex (h, k)

we can rewrite our function as:

y = a*(x - h)^2 + k

So in this case, we can rewrite our function as:

h(t) = a*(t - 2)^2 + 22

To find the value of a, notice the first point in the table:

(0, 2)

then we have:

h(0) = 2 = a*(0 - 2)^2 + 22

         = 2 = a*(-2)^2 + 22

            2 = a*(4) + 22

           2 - 22 = a*(4)

            -20/4 = -5 = a

Then our function is:

h(t) = -5*(t - 2)^2 + 22

Now we just expand it:

h(t) = -5*(t^2 - 4*t + 4) + 22

h(t) = -5*t^2 + 20*t  + 2

The correct option is the first one.

The estimate of ∫e^x dx using rectangles with heights given by right-hand endpoints and four subintervals (n = 4) can be determined by evaluating the function at those endpoints and multiplying by the width of each rectangle.

Among the given options, the correct representation of the estimate is:

∫e^x dx is approximately (0.5)e^0.5 + (0.5)e^1 + (0.5)e^1.5 + (0.5)e^2.

This is because we divide the interval [0,2] into four subintervals of equal width, each with a width of 0.5. For the right-hand endpoint approximation, we evaluate the function e^x at those endpoints.

The height of each rectangle is given by e^x evaluated at the right-hand endpoint of each subinterval. The width of each rectangle is 0.5.

By multiplying the height and width of each rectangle and summing them up, we obtain the estimate of the integral.

Therefore, the correct representation is (0.5)e^0.5 + (0.5)e^1 + (0.5)e^1.5 + (0.5)e^2 as an estimate of ∫e^x dx using rectangles with right-hand endpoints and four subintervals.

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Option (a) is correct. The value of sinθ will be \(-\frac{5\sqrt{41} }{41}\)

We are given the value of the cosθ  = \(\frac{4\sqrt{41} }{41}\) where, θ is in the IV Quadrant.

We know that cosine is the ratio of the adjacent side to the hypotenuse.  Also, we have
hypotenuse = h = 41, And Adjacent Side = b = \(4\sqrt{41}\)
So, for the value of the opposite side, we need to use the Pythagorean theorem which is stated as:\((Hypotenuse)^{2} = (opposite side)^{2} + (adjacentside)^{2}\)
\(h^{2} = a^{2} + b^{2}\)

\(a^{2} = h^{2} - b^{2}\)

a = \(\sqrt{41^{2} -(4\sqrt{41})^{2} }\) =  \(\sqrt{1681 - 656 }\) = \(\sqrt{1025}\) = \(5\sqrt{41}\)

The opposite side is  \(5\sqrt{41}\) , as sine is negative (-) in the IV quadrant so the value will be   \(-5\sqrt{41}\).

So we know that Sine is the ratio of the Opposite side to the hypotenuse, which can be written as:

sineθ = \(\frac{Opposite}{Hypotenuse}\)

sineθ =  \(-\frac{5\sqrt{41} }{41}\)

So, option (a) will be the right option.

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Your Question is incomplete, but most probably your full question was

Consider this equation. cosθ  = \(\frac{4\sqrt{41} }{41}\) if θ is an angle in quadrant IV, what is the value of sinθ?
(a)       \(-\frac{5\sqrt{41} }{41}\)

(b)   \(\frac{5\sqrt{41} }{41}\)

(c) \(-\frac{5}{4}\)

(d) \(\frac{5}{4}\)

Answer: c

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

If 2 gallons gets you 26 miles, then you get 13 miles per gallon. If you need to go 91 miles, you divide that by the 13 per gallon, and you get 7.

Number of homeowners planted exactly two of the three vegetables is 434

|P| = 240, |S| = 165, |G| = 142.

|P ∩ S ∩ G| = 36, |P ∩ S| = 0, |P ∩ G| = 0, |S ∩ G| = 0.

Where, P is the set of homeowners who planted peppers, S is the set of homeowners who planted spinach, and G is the set of homeowners who planted garlic

According to inclusion-exclusion

|P∪∪ G| = |P|+|S|+ |G|-|P ∩ S|-|P ∩ G|-|S ∩ G|+ |P∩S∩G|

= 240 + 165 + 142 - 0 - 0 - 0 + 36

= 583

|X| = |P ∩ S' ∩ G'| + |P' ∩ S ∩ G'| + |P' ∩ S' ∩ G|

Substitute the values

= 82 + 45 + 22

= 149

|Y| = 583 - 149

= 434

Therefore, there are 434 homeowners planted exactly two of the three vegetables

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Answer:

It is everything except for The outcome of events A and B are dependent on each other.

Step-by-step explanation:

Don't worry about it.

Answers:

A, B, C, E are the correct answers

Explanation:

I got it correct in my test :)

Given the trigonometry equation expressed as;

We are to simplify for the value(s) of 'x"

Recall from trigonometry identity that:

Substitute the result into the original equation to have:

Solve for the value of "x"

The general solution to the given trigonometry function is:

The probability that a random variable lies within 1.5 standard deviations of the mean is approximately 34% (or 0.340 when rounded to three decimal places).

To find the probability that a random variable lies within 1.5 standard deviations of the mean in a normal distribution, we can use the empirical rule (also known as the 68-95-99.7 rule). According to this rule, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% falls within 2 standard deviations, and approximately 99.7% falls within 3 standard deviations.

In this case, we are interested in the probability within 1.5 standard deviations. Since 1.5 is less than 2 (the second standard deviation), we can use the rule to estimate the probability.

The empirical rule tells us that approximately 68% of the data falls within 1 standard deviation. Therefore, approximately half of this percentage, or 34%, falls within half of the standard deviation.

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The vector in exact component form is \((x, y) = (12 \cdot \cos(210^{\circ}), 12 \cdot \sin(210^{\circ}))\).

To write a vector in exact component form, we need to express the vector in terms of its horizontal and vertical components. Given the angle \( \theta = 210^{\circ} \) and magnitude \( \text{mag} = 12 \), we can use trigonometric functions to find the components.

The horizontal component, denoted as \( x \), can be found using the formula \( x = \text{mag} \cdot \cos(\theta) \). Plugging in the values, we have \( x = 12 \cdot \cos(210^{\circ}) \).

The vertical component, denoted as \( y \), can be found using the formula \( y = \text{mag} \cdot \sin(\theta) \). Plugging in the values, we have \( y = 12 \cdot \sin(210^{\circ}) \).

Therefore, the vector in exact component form is \((x, y) = (12 \cdot \cos(210^{\circ}), 12 \cdot \sin(210^{\circ}))\).

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The statement that is true about the graph as it relates the unit rate is:

d. The unit rate is $22.50 per hour

Unit rate of a relationship between two variables, x and y, that are proportionally related can be found using k = y/x, where k is the unit rate.

Given that:

x = hours he worked

y = his total earnings

We are told that (4, 90) is a point on the graph.

Using the point, (4, 90), we can find the unit rate as shown below:

k = y/x = 90/4

k = 22.5

Therefore, the statement that is true about the graph as it relates the unit rate is:

d. The unit rate is $22.50 per hour

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

To model the roof line of Terry's house, we can use the concept of absolute value. The equation for an absolute value function can be written as:

y = |x - h| + k

where (h, k) represents the vertex of the absolute value graph.

In this case, the peak of the roof line is at 24 feet. Since the width of the house is 32 feet, the vertex of the absolute value graph will be at the midpoint of the width, which is 16 feet. Therefore, h = 16.

Since the peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

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Answer:

John had drove 162 miles is what you need to say.

Step-by-step explanation:

lets say miles = x         20.95 +  .72x = 137. 59     = step 1 ) eliminate base fee both sides through opposite subtraction  = 20.95  - 20.95 +  .72x = 137. 59  -20.95 =  .72x = 137. 59  -20.95 =  .72x = 116.64  = step 2) eliminate cost per mile through division to both sides to find full mileage =  116. 64/ .72 = 162 miles and x = 162  as proved in reverse  162 * .72 = 116 64 charges of total found earlier therefore John had drove 162 miles is what you need to say.

Answer:

it is true

Step-by-step explanation:

The equation describing Line B in the form Y=mX+b, where m is the slope of the line and b is a constant term, is Y = X + 0.

In this equation, the slope (m) is 1, which means that for every increase of 1 in the X-coordinate, there is an increase of 1 in the Y-coordinate. The constant term (b) is 0, which means that the line intersects the Y-axis at the point (0,0).

To understand this equation better, let's take a look at a few points on Line B.

When X = 0, substituting this value into the equation gives Y = 0 + 0, which means that the point (0,0) lies on the line.

When X = 1, substituting this value into the equation gives Y = 1 + 0, which means that the point (1,1) lies on the line.

When X = -1, substituting this value into the equation gives Y = -1 + 0, which means that the point (-1,-1) lies on the line.

These points confirm that the equation Y = X + 0 represents Line B, where the slope (m) is 1 and the constant term (b) is 0.

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The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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Amanda's answer correct is not correct. The correct answer is 4 R2, because she might have incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead

Amanda's answer, 3 R10, is not correct.

When we divide 34 by 8, we want to know how many times 8 goes into 34, and what is left over. We start by dividing 8 into the first digit of 34, which is 3. 8 cannot go into 3, so we move on to the next digit, which is 34.

We can see that 8 goes into 34 four times, because 8 x 4 = 32. This means that the whole number part of the answer is 4.

But there is still a remainder left over. To find the remainder, we subtract 32 from 34, which gives us 2.

Therefore, the correct answer is 4 R2.

Amanda's mistake may have been to incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead.

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Answer:

y=2x+1   SLOPE is  2

Step-by-step explanation:

(0,0)

(1,2)

Formula- y2-y1/x2-x1

2-0/1-0= 2/1

rise over run method :) hope this helps

Answer:

1. \(m=2\)

2. \(y=2x\)

Step-by-step explanation:

1. To find the slope we will use the slope formula \(\frac{y_{2}-y_{1} }{x_{2}-x_{2} }\).

We have two points located at (0,0) and (1,2)

Use these points and plug it into the slope formula.

\(\frac{2-0}{1-0}\)

\(\frac{2}{1}\)

\(2\)

Our slope in this case is 2. So, \(m=2\).

2. To write the equation, we must use \(y=mx+b\)

We found out that m=2. So we will use that in our equation.

b is usually the y-intercept, but since our y-intercept is 0, we do not need to write it.

So, your answer is \(y=2x\)

Step-by-step explanation:

13-9=6x

4-6x

This is the coefficient

Answer:

g=7

Step-by-step explanation:

5.1 times 7 is 35.7

Answer:

Step-by-step explanation:

5.1g = 35.7

g = 35.7 / 5.1

= 7.

Answer:

What is the question?

Step-by-step explanation:

Comment it

Answer:

same i feel you bru

Step-by-step explanation:

i'm actually, uh, procrastinating on brainly. can i vent? actually i will anyways so here: i have an science quiz on space and the moon phrases and i barely payed attention in class so i don't even know how to solve half of the problems. i normally always do ok on quizzes but i feel like this one is different and i'm going to fail. it's due by today at midnight and i'm procrastinating on brainly to take my mind away from reality. i know i'm being a total coward by trying to avoid what is my own consequences but... here i am haha ;-; it would be better if i at least started studying now even if it's short  to get my grade up just a little but i'm scared to even look at the quiz. i also have a lot of homework and an essay that's due tomorrow that i haven't started on yet... and yet i procrastinate. i don't understand myself and sometimes i want to cry because i don't know why i'm like this. i feel like the more homework i get, the more i procrastinate. i'm miserable really.

The percent error of Dewey's balance is found as δ = 0.22 %.

The given values.

Original mass of object (Va) = 35 grams

Mass by Dewey's balance (Ve) = 34.92 grams

δ = (Va - Ve) ÷ Va × 100%

δ = ( 35 - 34.92 ) ÷ 35  × 100%

δ = 0.22 %

Thus, the percent error of Dewey's balance is found as δ = 0.22 %.

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\(cos^2(x) = cos^2(x)\).

This equation is true for all values of x, so the solution is:
x ∈ ℝ (x is any real number).

To solve the equation\(cos^2(x)\)= (power reducing formula),

we need to replace \(cos^2(x)\) with the power reducing formula.

The power reducing formula for \(cos^2(x)\) is:
\(cos^2(x) = (1 + cos(2x)) / 2\)
Now, let's solve the equation:
\((1 + cos(2x)) / 2 = cos^2(x)\)
We want to find x when this equation is true.

Since the left side is the power reducing formula for \(cos^2(x)\),

we can simply write:
\(cos^2(x) = cos^2(x)\).

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

\(cos^2(x) = (1 + cos(2x))/2\)

The power reducing formula for sine is:

\(sin^2(x) = (1 - cos(2x))/2\)

These formulas can be derived using the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1.\)

By solving for either \(sin^2(x) or cos^2(x)\) in terms of the other, and then using the double angle formula for cosine \((cos(2x) = cos^2(x) - sin^2(x)),\)we can arrive at the power reducing formulas.

The power reducing formulas can be used to simplify trigonometric expressions and make them easier to work with.

For example, if you have an expression such as \(sin^4(x)\), you can use the power reducing formula for sine to express \(sin^4(x)\) in terms of \(sin^2(x),\)and then use the power reducing formula for cosine to express \(sin^2(x)\)in terms of cos(2x).

This can make the expression simpler and easier to integrate or differentiate.

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