How many different committees can be formed from 7 teachers and 41 students if the committee consists of 2 teachers and 2 ​students?

The question is incomplete hence, I gave you a similar question that will enable you to understand how to treat Linear Equations with Decimals.

This is best exemplified by the example below:

\(\left\{ \begin{array}{cl}0.2x-0.3y = 1.3 \\0.5x + 0.2y= 2.3\end{array} \right.\)
e

Solution

Step 1 - Remove all decimals by multiplying equation 1 and 2 by 10. This gives us:

\(\left\{ \begin{array}{cl}2x-3y = 13 \\5x + 2y= 23\end{array} \right.\)


Now we have an equation without decimals.

Step 2 - we proceed to solve by elimination.

Assuming:

2x - 3y = 13 ............is  Equation 3; and

5x -2y = 23 ............. is Equation  4;

Lets multiply equation 3 by 2; and equation 4 by 3. This gives us

⇒ 4x - 6y = 26 ...............5

   15 x + 6y = 69..............6


step 3 - Add equation 5 and 6 to eliminate y.

4x - 6y = 26

15 x + 6y = 69
19x = 95

solving for x

= 95/19

x = 5


Step 4 - Substitute x into any of the equations to find the value of Y


Using equation 5, we have:

4x - 6y = 26

⇒ 4(5) - 6y = 26

⇒ 20 - 6y = 26
⇒ -6y = 26-20
⇒ y = 6/-6

∴ y = -1

In summary, x = 5; y = -1


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The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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Answer:

155

Step-by-step explanation:

∠QOR= 25

∠POQ = x

here sum of both angles is 180 ( by linear pair)

therefore,

∠QOR + ∠POQ =180

25 + x = 180

x=180-25

x=155

hence, ∠POQ= 155

Answer:

a = -3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

a−2=

3+6a

3

a+−2=2a+1(Distribute)

a−2=2a+1

Step 2: Subtract 2a from both sides.

a−2−2a=2a+1−2a

−a−2=1

Step 3: Add 2 to both sides.

−a−2+2=1+2

−a=3

Listen go to Mathpapa it helps and shows step by step

Answer:

a = -3

Step-by-step explanation:

a - 2 = (3 + 6a)/3

Divide 3 + 6a by 3.

a - 2 = 1 + 2a

Subtract 2a from both sides.

-a - 2 = 1

Add 2 to both sides.

-a = 3

Multiply the equation by -1.

a = -3.

Proof:

a - 2 = (3 + 6a)/3

Substitute variable.

-3 - 2 = (3 + 6(-3))/3

Multiply inside parenthesis.

-3 - 2 = (3 + 18)/3

Add inside parenthesis.

-3 - 2 = (-15)/3

Divide.

-3 - 2 = -5

Subtract.

-5 = -5

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Nikki can use modern portfolio theory to assess the risk and return behaviors associated with different combinations of assets X and Y.

Modern portfolio theory involves calculating the expected return and risk of a portfolio of assets by analyzing the correlations between the assets. It also looks at the diversification benefits of combining different assets and the impact of adding riskier assets to a portfolio. By quantifying the risk and return behaviors of different portfolios, Nikki can make informed decisions about which portfolios are most suitable for her.Modern portfolio theory is used to assess the risk and return behaviors of different combinations of assets X and Y. It considers correlations between the assets, the diversification benefits of combining them, and the impact of adding riskier assets. By quantifying the risk and return behaviors, Nikki can make informed decisions about which portfolios are most suitable for her.

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Answer:

2/4? i think....

idrk sry :(

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

We know that Mia's frog only jumped \(\frac{4}{5}\) the distance of Chloe's frog - which means that Mia's frog must be behind Chloe's frog. Therefore, Mia's frog must also not be in first place.  

We also know that Tony's frog jumped \(1\frac{1}{4}\) the distance of Chloe's frog - meaning that Tony's frog jumped further than Chloe's frog, since it is above 1. So, Tony's frog is ahead of Chloe's frog. Therefore, Chloe's frog cannot be in first place either.

Let's look at the clues gathered so far:

Using logic, the only option that meets these requirements would be option A. Tony would be ahead of Chloe, Mia would be behind Chloe, and neither of the girls' frogs would be in first place. You could also use the process of elimination to get rid of the other answers.

Answer:

1564.42 mph

Step-by-step explanation:

Let a = Object A's speed

     b = Object B's speed

a = b + 1500

a/85000 = b/3500

Let's make subtract 1500 from both sides of the first equation

a = b + 1500

- 1500  - 1500

b = a - 1500

Cross multiply the second equation

3500a = 85000b

Plug in the new b into this new equation

3500a = 85000(a - 1500)

3500a = 85000a - 127500000

Subtract 3500a and 127500000 from both sides

3500a = 85000a - 127500000

- 3500a  - 3500a

0 = 81500a - 127500000

+ 127500000    + 127500000

127500000 = 81500a

Divide both sides by 81500

127500000/81500 = 81500a/81500

a = 1564.4171779141104

Answer: 9/14

Step-by-step explanation:

hope this helps!

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

9 1/8 ribbon would be remaining

answer:

y = -2/5x + 4

Answer:

55-15= 40

55,000-10,000=45,000

45000/55=819

it is 819?

Step-by-step explanation:

Answer:

55-15= 40

55,000-10,000=45,000

45000/55=819

it is 819?

Step-by-step explanation:

Answer:

Equation to find radius = Diameter divided by 2

Area is 1319.585

Step-by-step explanation:

Diameter = 41 cm

Radius = 41÷2 = 20.5cm

Area = πr^2

Area = 3.14×(20.5)^2

Area = 3.14×420.25

Area = 1319.585cm^2

Answer:

\(\displaystyle 3x - 2y = 13\:or\:y = 1\frac{1}{2}x - 6\frac{1}{2} \\ [0, -6\frac{1}{2}] \\ 1\frac{1}{2} = m\)

Step-by-step explanation:

First, figure the rate of change [slope] out:

\(\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-1 + 16}{-5 + 15} = \frac{15}{10} = 1\frac{1}{2} \\ \boxed{1\frac{1}{2} = m}\)

Now locate the initial value [y-intercept] by plugging an ordered pair into the slope-intercept formula. It does not matter which ordered pair you use:

_______________________________________________

\(\displaystyle y = mx + b\)

16 = 1½[15] + b >> \(\displaystyle 16 = 22\frac{1}{2} + b; -6\frac{1}{2} = b\)

OR

1 = 1½[5] + b >> \(\displaystyle 1 = 7\frac{1}{2} + b; -6\frac{1}{2} = b\)

\(\displaystyle [0, -6\frac{1}{2}]\)

_______________________________________________

You now have your initial value. All that is left is to write the equation of this line, which can be written two ways:

> Slope-Intercept Form

\(\displaystyle y = 1\frac{1}{2}x - 6\frac{1}{2}\)

> Standard Form \(\displaystyle [Ax + By = C]\)

y = 1½x - 6½

- 1½x - 1½x

___________

–1½x + y = –6½ [We CANNOT leave the equation this way, so multiply by –2 to eradicate the fraction\denominatour (if you wrote the equation as mixed numbers\if you wrote the equation as improper fractions).]

–2[–1½x + y = –6½]

\(\displaystyle 3x - 2y = 13\)

With that, you have defined all the information.

\(\displaystyle -3x + 2y = -13\)

*About this equation, INSTEAD of multiplying by –2, you multiply by its oppocite, 2. Now, you can leave it like this, but UNIVERSALLY, the A-term is positive, so you must multiply the negative out as well.

I am joyous to assist you at any time.

Given the following question:

Using the formula:

Answer:

Can I see the sign?

Step-by-step explanation:

Here are the steps to simplify the expression \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x} \\\):

1. Combine like terms that have the same radical term \(\sf\:\sqrt{3x} \\\):

\(\sf\:(5x - 2x - x)\sqrt{3x} \\\)

2. Simplify the coefficients:

\(\sf\:2x\sqrt{3x} \\\)

Therefore, \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x}\) simplifies to \(\sf 2x\sqrt{3x} \\\).

A rotation can be  transformation which turns a figure. It changes its position

what is rotation ?

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, and is used to describe the movement of objects in space.

In the given question,

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, A rotation can be  transformation which  turns a figure. It changes its position

when their is rotations it turns around its axis and their will be change in its position

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Answer:

1531 pesos

Step-by-step explanation:

The profit when x=10 is calculated as follows:

P(10) = 10^3 + 5(10^2) + 3(10) + 1 = 1000 + 500 + 30 + 1 = 1531 pesos.

The correct option is B.

The period of y = cos x is

or 360 degrees

Answer:

i. she got 9/10 multiple choice questions

ii. she got 24 true/false questions

Step-by-step explanation:

i. it is mentioned in the question that she got 9/10 multiple choice questions right

ii. the question says she got 4/5 out of 30 true/false questions.

therefore

4/5×30= 24 questions

if this helped pls give brainliest

Answer:

\(368.54 = 3*100 + 6.8*10 +5*1/10 + 4*100\)

Step-by-step explanation:

Given

\(368.54 = ( [\ ] * 100) + ( [\ ] * 10) + ( [\ ] * 1/10) + ( [\ ] * 1/100)\)

Required

Fill in the gap

The number can be expressed as:

\(368.54 = 300 + 60 + 8 +0.5 + 0.04\)

Factorize:

\(368.54 = 3*100 + 6*10 + 0.8*10 +5*1/10 + 4*100\)

Factor out 10 in 6 * 10 + 0.8 * 10

\(368.54 = 3*100 + [6 + 0.8]*10 +5*1/10 + 4*100\)

\(368.54 = 3*100 + 6.8*10 +5*1/10 + 4*100\)

Solved

Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

250

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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