Question 4 This question has two parts. First, answer Part A. Then, answer Part B. Part A Fill in the blank question. COLLEGE LIVING The total number of students T who attend a college consist of two groups: students who live in dorm rooms on campus D and students who live in apartments off campus A. The number (in hundreds) of students who live in dorm rooms and the total number of students enrolled in the college can be modeled by the following equations, where n is the number of years since 2001. T=17n+23 D=11n+8 Write an equation that models the number of students who live in apartments. A= n+ Predict the number of students who will live in apartments in 2020. Part B What do you need to assume in order to predict the number of students who will live on campus in 2020? Multiple choice question. A) The total number of students does not include students who commute. B) Students do not share dorm rooms. C) The number of students enrolled in the college remains the same. D) Many students live at home during the summer.

Answer:

factoring

Step-by-step explanation:

Answer:

the first one is 240

the second one is 280

the third one is 200

The answers that would be discarded would be 220, 360 and 500

Step-by-step explanation:

Hey There!

So for this problem all we have to do is plug in the hours worked and drones sold into the expression 10h+40d

For the first one we just plug in 8 for hours (because he worked 8 hours) and 4 for drones ( because he sold 4 drones )

so we would have 10(8) + 40(4)

10x8=80

40x4=160

160+80=240 So 240 would go with the first one

For the second one we plug in 4 for hours ( because he worked 4 hours) and 6 for drones ( because he sold 6 drones)

so we would have 10(4)+40(6)

10x4=40

40x6=240

240+40=280

So 280 would go with the second one

For the third one we plug in 12 for hours ( because he worked 12 hours) and 2 for drones ( because he sold 2 drones)

so we would have

12(10)+2(40)

12x10=120

2x40=80

120+80=200

so 200 would go with the third one

hope this helps :)

The value for p is 30.

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The simplified expression of \((\frac{3^{\frac{1}{2} }}{4^{ \frac{1}{5} }} )^{\frac{5}{6} }\) is determined as \(\frac{3^{\frac{5}{12} }}{4^{ \frac{1}{6} }} }\).

option C.

To simplify an expression means to write an equivalent expression which contains no similar terms. This means that we will rewrite the expression with the fewest terms possible.

The given expression;

\((\frac{3^{\frac{1}{2} }}{4^{ \frac{1}{5} }} )^{\frac{5}{6} }\)

The given expression is simplified as follows;

The power '5/6" will be used to multiply every power in the bracket as follows;

1/2 x 5/6 = 5/12

1/5 x 5/6 = 1/6

We will replace the powers in the bracket with simplified form as follows;

= \(\frac{3^{\frac{5}{12} }}{4^{ \frac{1}{6} }} }\)

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Answer: y=x+4

Step-by-step explanation:

y=-x+5

Slope: -1

Perpendicular slope: -1*(-1/1)

-1*(-1/1)=-1*(-1)=1

y=x+b

2=-2+b

b=4

y=x+4

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Step-by-step explanation:

Let's give each person a variable:

A for Alfred

C for Clarissa

B for Benji

Now, we can take what the question is saying and convert them into equations:

Alfred has 10 more tokens than Clarissa can look like this:

A = C + 10

Since Alfred has 10 more coins than Clarissa we can take C and add 10 to find how many tokens Alfred has.

Clarissa has twice as many tokens as Benji looks like this:

C = 2B

Since Clarissa has twice as many tokens as Benji we can multiply B (how many tokens Benji has) by 2.

Lastly, they have 85 tokens all together:

A + B + C = 85

We have these 3 equations:

A = C + 10

C = 2B

A + B + C = 85

Now, we can substitute some variables:

A = (2B) + 10    Since C is equal to 2B we can substitute 2B in for C in the first equation.

We have found what A equals, we can plug that in to the last equation:

(2B) + 10 + B + C = 85

We can also substitute the second equation into the third equation:

(2B) + 10 + B + 2B = 85

Combine like terms:

5B + 10 = 85

Solve

5B = 75

B = 15

This means that Benji has 15 tokens. Now we can find how much the other children have:

C = 2(15) = 30

Clarissa has 30 tokens

A = 30 + 10

A = 40

Alfred has 40 tokens.

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Checking the Answer

A + B + C = 85

40 + 15 + 30 = 85

85 = 85

I hope this helps!!

- Kay :)

The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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A representative sample based on the hospital scenario is option A

A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.

Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.

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Given A room is half as long again as it is broad

Let the breadth of the room x m

length of the room x + x/2 = 3x/2m

Area of the room , x × 3x/2 = 3x²/2m

Given , cost of carpeting the room at Rs. 3.25m⁻²

So , total cost , 3x²/2 × 3.25

But , Total cost of carpeting is given as 175.50 so ,

let the height of the room H m

Area of the four wall = 2(L+ b)× h 2(6+9)× H

= 30H m²

Area of the of the one door and two window is 8m²

8m² Area to be prepared = Area of four wall - area of two window and 1 door = (30H - 8) m²

Given cost of preparing wall is Rs. 1.40m²

total cost of preparing wall is (30H - 8) × 1.40

Total cost of preparing wall is given as 240.80

comparing , (30H - 8 ) × 1.40 = 240.80

Hence, Dimensions of the room are lengths 9m , breadth 6m and height 6m

The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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Step-by-step explanation:

Area=b×h

= (x+5)×(x+6)

=x^2+6x+5x+30

=x^2+11x+30

If u simplify u will get (x+5)(x+6) as answer.

Keep smiling and hope u are satisfied with my answer.Have a good day :)

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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Answer:

B.

Step-by-step explanation:

Explanation:

1 hat = 45 dollars

6 hats = 6*45 = 270 dollars

1 phone = 40 dollars

4 phones = 4*40 = 160 dollars

total = $270 + $160 = $430

Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430

In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.

Answer:

10y+6

See diagram below

Explanation:

Given expressions One and Two below:

• Expression One: y+10

• Expression Two: 9y-4

The completed table showing the addition of the expressions is given below:

Therefore:

The sum is 10y+6.

Based on the amount of gasoline Mario bought in gallons, the amount in liters would be 5.8 liters.

A single gallon is equivalent to 3.875 liters.

If Mario bought 1.5 gallons of gasoline, the amount he bought in liters would be:

= Gasoline in gallons x Number of liters per gallon

= 1.5 x 3.875

= 5.8125

= 5.8 liters

In conclusion, Mario bought 5.8 liters of gasoline.

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If an object is traveling at a constant speed, its velocity and acceleration vectors are orthogonal.

To prove that the velocity and acceleration vectors of an object traveling at a constant speed are orthogonal, we need to show that their dot product is zero. Let's consider a particle moving in a straight line.

The velocity vector, v, represents the rate of change of displacement with respect to time. Since the object is moving at a constant speed, the magnitude of the velocity vector remains constant. Therefore, the derivative of the velocity vector with respect to time is zero, resulting in a constant velocity vector.

The acceleration vector, a, represents the rate of change of velocity with respect to time. Since the speed is constant, the direction of the velocity vector remains constant, and there is no change in direction. As a result, the acceleration vector is perpendicular (orthogonal) to the velocity vector.

We can express the dot product of the velocity and acceleration vectors as v ⋅ a = |v| |a| cos θ, where θ is the angle between the vectors. Since the speed is constant, |v| is constant. If the angle between the velocity and acceleration vectors is 90 degrees (cos θ = 0), the dot product will be zero.The velocity and acceleration vectors are orthogonal when the object is traveling at a constant speed.

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Answer:

x = 2

Step-by-step explanation:

-4x + 136 + 52 = 180             {supplementary  angles}

        -4x + 188 = 180

Subtract 188 from both sides

                -4x = 180 - 188

                -4x = -8

Divide both sides by (-4)

          x = -8/-4

x = 2

The gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

To find the gradient of the function \(\( f(x, y) = e^{3x} \sin(4y) \)\) at the point \(\((-1, -3)\)\), we need to compute the partial derivatives with respect to \(\(x\) and \(y\)\) and evaluate them at that point.

The gradient of a function is given by:

\(\[\nabla f(x, y) = \left(\frac{{\partial f}}{{\partial x}}, \frac{{\partial f}}{{\partial y}}\right)\]\)

Let's calculate the partial derivatives:

\(\[\frac{{\partial f}}{{\partial x}} = \frac{{\partial}}{{\partial x}}\left(e^{3x} \sin(4y)\right) = 3e^{3x} \sin(4y)\]\)

\(\[\frac{{\partial f}}{{\partial y}} = \frac{{\partial}}{{\partial y}}\left(e^{3x} \sin(4y)\right) = 4e^{3x} \cos(4y)\]\)

Now, we can evaluate these derivatives at the point \(\((-1, -3)\):\)

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{3(-1)} \sin(4(-3)) = 3e^{-3} \sin(-12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{3(-1)} \cos(4(-3)) = 4e^{-3} \cos(-12)\]\)

Simplifying further:

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{-3} \sin(-12) = -3e^{-3} \sin(12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{-3} \cos(-12) = 4e^{-3} \cos(12)\]\)

Therefore, the gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

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Answer:

A slope of 2/3

Step-by-step explanation:

if you look at the line, starting at the y axis, then just count up 2 and over three, in other graphed lines, just start at the y axis and try to find where the line crosses a specific point, then calculate the rise/run.

The coordinates of point A are A(-1, 3l) and the coordinates of point B are B(k, 3), where k = 3l - (3/2).

To determine the coordinates of points A (-1, 3l) and B (k, 3) that lie on a line parallel to the line with the equation 2y + 3x = 9, we need to find the value of k for point B.

Given that the lines are parallel, they have the same slope. The equation 2y + 3x = 9 can be rewritten in slope-intercept form as y = -(3/2)x + 9/2, where the coefficient of x (-3/2) represents the slope of the line.

Since the lines are parallel, the slope of the line passing through points A and B should also be -3/2. Now we can find the value of k by substituting the coordinates of point A into the equation.

3l = -(3/2)(-1) + b

3l = (3/2) + b

3l - (3/2) = b

b = 3l - (3/2)

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The equation representing this function is y = tan(x)

The equation which represents a tangent function with a domain of all real numbers such that x is not equal to pi over 4 plus pi over 2 times n comma where n is an integer is:y = tan(x)The tangent function is one of the six trigonometric functions, which is abbreviated as tan. The inverse of the cotangent function is the tangent function. It is also referred to as the inverse tangent, arctan, or tan^-1.

It is defined by the ratio of the opposite side to the adjacent side of a right triangle. The tangent function is a periodic function with a period of π radians or 180°. Its value alternates between negative and positive infinity over each period.The tangent function is not defined at odd multiples of π/2, that is, (2n+1)π/2 for all integers n. This is because the denominator in the tangent function becomes zero, causing a vertical asymptote.
For example, the values of the tangent function for π/2, 3π/2, 5π/2, etc. are undefined. Therefore, the domain of the tangent function is all real numbers except for odd multiples of π/2. The notation for the domain is (-∞, -π/2) U (-π/2, π/2) U (π/2, 3π/2) U (3π/2, ∞).However, in this case, the domain is all real numbers except π/4 + nπ/2, where n is any integer.

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Answer:

infinity zeros are there

Step-by-step explanation:

please make me brainlsit answer

a. The solution to the equation 1/3(5x - 9) = 2(1/3x + 6) is x = 15.

b. The solution to the 4(3x + 5) - 3 = 9x - 7 is x = -8.

c. The solution to the equation 5(x + 7) - 3(x - 4) = 7x + 2 is 9

a. Give the equation 1/3(5x - 9) = 2(1/3x + 6)

We want to find the value of x

5/3x - 3 = 2/3x + 13

x - 3 = 12

Collect the like terms

x = 12 + 3

x = 15

b. 4(3x + 5) - 3 = 9x - 7

12x + 20 - 3 = 9x - 7

Collect the like terms

3x + 17 = -7

3x = -24

Divide

x = -24 / 3

x = -8

c. 5(x + 7) - 3(x - 4) = 7x + 2

5x + 35 - 3x + 12 = 7x + 2

2x + 47 = 7x + 2

Collect the like terms

5x = 45.

Divide.

x = 45 / 5

x = 9

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Answer:

True.

Step-by-step explanation:

In this true or false question, the answer is true.

Hope this helps!

Answer:

False

Step-by-step explanation:

Not every function in a rectangular plane will be a function in every plane. Hope this helps

Chen did not earn a bonus for his journey because his fuel efficiency was below the required threshold of 2.8 kilometers per liter.

To determine whether Chen earned a bonus for his journey, we need to calculate his fuel efficiency in kilometers per liter. Fuel efficiency can be calculated by dividing the total distance traveled by the amount of fuel used.

First, let's calculate the total distance traveled. We can do this by multiplying the average speed by the journey time:

Total distance = Average speed * Journey time = 61 km/hr * 4.5 hours = 274.5 km

Next, we divide the total distance by the fuel used to calculate the fuel efficiency:

Fuel efficiency = Total distance / Fuel used = 274.5 km / 96 liters ≈ 2.86 km/l

The calculated fuel efficiency is approximately 2.86 kilometers per liter. Since this value is above the required threshold of 2.8 kilometers per liter, Chen did not earn a bonus for his journey.

Therefore, based on the given information, Chen did not earn a bonus for his journey because his fuel efficiency was below the required threshold of 2.8 kilometers per liter.

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Step-by-step explanation:

. In Figure 5.144, of ΔABC, where

m(∠C) = 30, m(∠ABD) = 5x,

m(∠A) = 4x. Find m(∠ABC) in

degrees.

Answer:

-3y+4x+4

Step-by-step explanation:

if you need the step-by-step explanation I can work it out for you just let me know

the total number of votes in favor is 324 and the total number of votes against is 111.

In favor: 324

Against: 111

There are 435 members of the House of Representatives. 89 more members voted in favor than against, so there were 89 more members who voted in favor than against. To determine the total number of votes in favor, we add 89 to the number of votes against. Therefore, the total number of votes in favor is 324 and the total number of votes against is 111.

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