At noon, Train A is 40 miles due west of Train B. Train A is moving west at 20 miles per hour and Train B is sailing north at 20 miles per hour. How fast is the distance between the trains changing at 7 PM?

Answer:

Step-by-step explanation:

Use the distributive property.

Distributive property is a serving to distribute or allot or disperse.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

-10(1-9x)+6(x-10)

Expand.

-10(1-9x)

-10*1=-10

-10*9x=90x

\(\longrightarrow \sf{=-10+90x+6\left(x-10\right)}}\)

6(x-10)

6*x=6x

6*10=60

6x-60

Rewrite the problem down.

= -10+90x+6x-60

Combine like terms.

90x+6x-10-60

Add the numbers from left to right.

90x+6x=96x

96x-10-60

Finally, subtract the numbers from left to right.

-10-60=-70

\(\Longrightarrow \boxed{\sf{96x-70}}\)

Therefore, the final answer is 96x-70.

I hope this helps, let me know if you have any questions.

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Distributive Property :

\(-10(1-9x)+6(x - 10)\)

\(-10(-9x+1)+6(x - 10)\)

\(90x-10+6x-60\)

\(90x-70+6x\)

\(96x-70\)

\(answer : \boxed{\pink\star\tt{96x-70}}\)

━━━━━━━━━━━━━━━━━━━━━━━━

Common factor :

\(- 10(1 - 9x) + 6(x - 10)\)

\(96x - 70\)

\(2(48x - 35)\)

\( answer : \boxed{ \pink \star\tt{2(48x - 35)}}\)

Answer:

∡2 = 115°

Step-by-step explanation:

Therefore, Jeffrey Michael's gross earnings for the week are $1100.00.

Jeffrey Michael worked the schedule and earns $20.00 per hour.

Find his gross earnings by applying the labor laws regarding overtime. The labor law regarding overtime states that an employee is entitled to an overtime premium pay of 1.5 times their regular hourly rate for any hours worked over 40 hours in a week.

The schedule for Jeffrey Michael is as follows:

Monday: 8 hoursTuesday:

10 hoursWednesday: 8 hoursThursday: 9 hoursFriday: 8 hoursSaturday:

7 hoursTo find the gross earnings, we need to calculate the total number of hours worked in the week and apply the overtime pay rate for any hours over 40.

The total number of hours worked by Jeffrey Michael is:

8 + 10 + 8 + 9 + 8 + 7 = 50 hours

He worked 50 hours which means that he worked 10 hours of overtime (50 - 40 = 10)

Therefore, his gross earnings can be calculated as follows:For the first 40 hours:

$20.00/hour x 40 hours =

\($ < < 20*40=800 > > 800.00\)

For the 10 hours of overtime:

$30.00/hour x 10 hours

= \($ < < 20*1.5*10=300 > > 300.00\)

Total gross earnings:

$800.00 + $300.00 =

\($ < < 800+300=1100 > > 1100.00.\)

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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Answer:

131

Step-by-step explanation:

Using proportion,

If Out of 550 calculators = 6 are defective,

Then out of 12000 calculators = ? are defective

\(\frac{12000 calculators}{550calculators} * 6\)

= 21.8 * 6

= 130.8 ≈ 131

∴ Approximately 131 calculators are defective

Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

The cut sphere is called a hemisphere.

The surface area of a sphere is

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

Therefore, the total area of the hemisphere is,

The total surface area of a hemisphere is,

Therefore, the total surface area of the cut sphere is 461.8 square inches.

Answer:

the second

Step-by-step explanation:

The probability that the second card is a jack given that the first card was a 2 is 52/51.

To calculate the probability that the second card is a jack given that the first card was a 2, we need to consider the remaining cards in the deck after the first card is drawn.

When the first card is drawn and it is a 2, there are 51 cards remaining in the deck, out of which there are 4 jacks.

The probability of drawing a jack as the second card, given that the first card was a 2, can be calculated using conditional probability:

P(Second card is a jack | First card is a 2) = P(Second card is a jack and First card is a 2) / P(First card is a 2)

Since the first card is already known to be a 2, the probability of the second card being a jack and the first card being a 2 is simply the probability of drawing a jack from the remaining 51 cards, which is 4/51.

The probability of the first card being a 2 is simply the probability of drawing a 2 from the initial deck, which is 4/52.

P(Second card is a jack | First card is a 2) = (4/51) / (4/52)

Simplifying the expression:

P(Second card is a jack | First card is a 2) = (4/51) * (52/4)

P(Second card is a jack | First card is a 2) = 52/51

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Answer:

2/^7-2+1=57

Step-by-step explanation:

Answer:

Dimensions are:

Length = 4 ; width = 10

or

Length = 10 ; width = 4

Step-by-step explanation:

let the length = L

let the width = W

we are given the following:

area of rectangle = L × W = 40 m² - - - - - - ( 1 )

perimeter of a rectangle = 2L + 2W = 28 m - - - - - ( 2 )

from equation (2)

2L + 2W = 28

2L = 28 - 2W

dividing both sides by 2

(2L = 28 - 2W) ÷ 2

L = 14 - W  - - - - - - (3)

Next, let us replace the value of L in equation 1 with equation 3

L × W = 40 - - - - (1)

where L = 14 - W

(14 - W) × W = 40

14W - W²  = 40

0 = W² - 14W + 40

solving the quadratic equation

using completing the squares method

W² - 14W + 40

W² [-4W - 10W] + 40 =  0

(W² - 4W) - (10W + 40) = 0

W(W - 4) - 10(W - 4) = 0

W - 10 = 0; ∴ W = 10

or

W - 4 = 0 ;  ∴ W = 4

putting the values of W into equation (3)

L = 14 - W

where W = 10 or 4

L = 14 - 10 = 4

or L = 14 - 4 = 10

∴ Dimensions are:

Length = 4 ; width = 10

or

Length = 10 ; width = 4

We would expect the size of the population to increase by 12 individuals.

Here are the terms we'll be using:
- Initial population size: 100 individuals
- Per capita birth rate: 0.25
- Per capita death rate: 0.13
To find the expected increase in population size, follow these steps:
Calculate the net per capita growth rate by subtracting the per capita death rate from the per capita birth rate:
Net per capita growth rate = Per capita birth rate - Per capita death rate
Net per capita growth rate = 0.25 - 0.13
Net per capita growth rate = 0.12.

Multiply the net per capita growth rate by the initial population size to find the expected increase in the number of individuals:
Expected increase = Net per capita growth rate × Initial population size
Expected increase = 0.12 × 100
Expected increase = 12 individuals.

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The expected population in Adamsville, assuming uninhibited exponential growth, is approximately 20470 in an additional 5 years.

To estimate the expected population in an additional 5 years, assuming uninhibited exponential growth, we can use the exponential growth formula:

P(t) = P₀ * \(e^{(r * t)\),

where:

P(t) is the population at time t,

P₀ is the initial population,

e is the base of the natural logarithm (approximately 2.71828),

r is the growth rate,

t is the time interval.

Given that the population of Adamsville grew from 8000 to 14000 in 6 years, we can calculate the growth rate (r):

r = ln(P(t) / P₀) / t

  = ln(14000 / 8000) / 6

  ≈ 0.229

Now, we can use this growth rate to estimate the expected population in an additional 5 years (t = 5):

P(5) = P₀ * \(e^{(r * t)\)

     = 8000 *\(e^{(0.229 * 5)\)

     ≈ 20470

Therefore, the expected population in an additional 5 years would be approximately 20470.

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Answer:

You are correct! But note the syntax:

the computer wants you to type in the box

2/3 x - 2

because "y =" is already written!

Step-by-step explanation:

The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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The question asks us to compute the expected value (e[x]) of a random variable with a given density function. To do this, we integrate the product of the variable and the density function over its possible values. In this case, the density function is given as 5x^2, if x > 5. However, since the integral diverges at infinity, we can conclude that the expected value of x does not exist in this case.

To compute the expected value (e[x]) of a random variable with a density function, we integrate the product of the variable and the density function over its possible values. In this case, we have:

e[x] = ∫x * f(x) dx, for x > 5

where f(x) is the density function given as 5x^2, if x > 5.

Substituting f(x), we get:

e[x] = ∫x * 5x^2 dx, for x > 5

e[x] = 5 ∫x^3 dx, for x > 5

Integrating, we get:

e[x] = 5 * (x^4/4) + C, for x > 5

Since we are interested in values of x greater than 5, we can evaluate the definite integral as follows:

e[x] = 5 * [(x^4/4) - (5^4/4)], from x = 5 to infinity

e[x] = 5 * [(∞^4/4) - (5^4/4)]

However, since the integral diverges at infinity, we cannot evaluate it directly. This means that the expected value of x does not exist in this case.

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The linear equality for the given graph is x > 0.

Option (B) is correct.

What is linear equality?

In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

The hollow circle in the linear equality shows that the point should be excluded and the line is going towards the positive x-axis.

So we can prepare the linear equality as

                       x > 0

Hence, the linear equality for the given graph is x > 0.

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Answer:

Answer C uwu

Step-by-step explanation:

Hope this helps

Answer:

2-30,42

3-15,21

5-5,7

7-1,7

-1,1

LCM of 30 and 42 is 210

Answer:

210

Step-by-step explanation:

30*42 by HCF of 30,42

1260 by 6 =210

Let's take the subspace (X,T) of (Y,T*), where (Y,T*) is a subspace of (Z,T**). Here, we are required to show that (X,T) is also a subspace of (Z,T**). Let's start our proof.

To show that (X,T) is a subspace of (Z,T**), we must show that (X,T) satisfies the subspace axioms. The subspace axioms that must be satisfied are:

1. The zero vector, 0, is in (X,T).

2. If u and v are in (X,T), then u + v is also in (X,T).

3. If u is in (X,T) and a is a scalar, then au is also in (X,T).

So, let's prove each axiom for (X,T) to be a subspace of (Z,T**):

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The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

Substituting the parameters, we have the following:

y - y₁ = m(x - x₁)

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

Answer:

Step-by-step explanation:

factored form of x^2 - 12x + 36

(x - 6)(x - 6) or (x - 6)^2

answer is D

The magnitude of the vertical force applied to the horizontal leg in the equivalent force system.

To determine the magnitude of the vertical force applied to the horizontal leg, we need to find the vertical component of the given force system. Looking at the diagram, we observe that the force system consists of a vertical force at point A and a horizontal force at point B. We can use trigonometry to find the vertical component of the force at point A.

Let's denote the magnitude of the force at point A as F_A and the angle it makes with the horizontal leg as θ. The vertical component of the force can be calculated using the formula: Vertical component = F_A * sin(θ).

Since the vertical component of the force should be equal to the force we are trying to find, we can set up the equation: Vertical component = F_vertical.

Now, we can substitute the given values into the equation and solve for F_vertical. Once we have the value, we can round it off to the nearest whole number, as instructed.

Please note that without specific values or angles provided in the problem statement or accompanying diagram, it is not possible to provide a precise numerical answer.

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The graph of Y > -2x + 4 can be drawn by plotting points on a coordinate plane and connecting them with a dashed line. The dashed line should be above the line Y=-2x+4.

A sample graph is shown below:

[Graph of Y > -2x + 4]

(0,4), (1,1), (2,-2), (3,-5), (4,-8)

To graph Y > -2x + 4, you need to plot points on a coordinate plane. Start by finding the intersection point of the line Y=-2x+4 and the x-axis, which will be (0,4). From there, you can calculate the coordinates of the other points by substituting x values into the equation and solving for y. For example, when x=1, y=-2x+4=-2+4=2, so the point (1,2) would be plotted. Then, plot the other points (2,-2), (3,-5), and (4,-8). Finally, connect the points with a dashed line to represent Y > -2x+4.

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Answer: B. 3

Step-by-step explanation:

4^2 + b^2 =5^2

16 + b^2= 25

-16            -16

b^2 = 9

\(\sqrt{9} =3\)  

For Part A,

Population is USA.

Sample are the readers.

Sample statistics is unknown.

Population parameters is unknown.

For Part B,

Population is Astronomers.

Sample is Galaxy.

Sample statistics is measuring distance within few stars.

Population parameter is mean of distance.

Answer:

I do not understand this either lolll lolll

but I guess eq 1 = D

EQ 2 = B

EQ 3 = A

EQ 4= C

Answer:

150 lies between 12 and 13

Step-by-step explanation:

Answer:

Answer

Correct option is

D

all of the above

For any two rational numbers a and b,  

(a+b),(a−b),(b−a) & (a×b) are all rational numbers.

Thus, rational numbers are closed under addition, subtraction and multiplication. (for the first one)

Answer:

The sum of x and y is a rational number

Step-by-step explanation:

X+Y or 5+7=12

A rational number is any number that can be divided without going on and on forever. (for the 2nd one )