A committee is formed consisting of one representative from each of the 4 departments (CS-IS-IT-SW) in the computer science college, where the representative from a department is either the president or one of the two representatives from that department. How many ways are there to form this committee?

Answer:

w = 22 in, h = 8 in.

Step-by-step explanation:

Reading the problem, I immediately see two equations. This hints me towards a system of equations problem.

Statement 1 is The width of a triangle is six more than twice the height.

The width (w) of a triangle is (=) six (6) more (+) than twice (2) the height (h).

Equation 1: w = 6 + 2h

Statement 2 is The area of the triangle is 88 in2.

The formula for the area of a triangle is [tex]\frac{wh}{2}[/tex]. So, we get our second equation.

Equation 2: wh/2 = 88

We see that we have the same number of equations as unknowns, two. This is important as it lets us know that we can find two unknowns in the two equations. If there are more unknowns than equations, then we cannot find the values of all the variables. Look for another equation in the problem. However, if the # equations greater than or equal to number of unknowns, then we are ready to start solving!  So, we can now move to solving.

Equation 1 isolates one of the unknowns (w). So, we can replace w in the second equation with the right side of eq 1. Then, we simplify for h.

[tex]\frac{wh}{2} = 88[/tex]

[tex]\frac{(6 + 2h)h}{2} = 88[/tex]

[tex]\frac{6h + 2h^2}{2} = 88[/tex]

[tex]6h + 2h^2 = 176[/tex]

[tex]2h^2 + 6h - 176 = 0[/tex]

[tex]h = -11, 8[/tex] (assuming you know how to solve quadratics)

Since we know that heights of triangles cannot be negative, we find that [tex]h = 8[/tex] in.

For the final step, we plug [tex]h[/tex] into our first equation to find [tex]w[/tex].

[tex]w = 6 + 2h[/tex]

[tex]w = 6 + 2(8)[/tex]

[tex]w = 6 + 16[/tex]

[tex]w = 22[/tex]

So, the answer is w = 22 in, h = 8 in.

To check if we were right, we can plug the values into both equations to see if they are equal. I will skip equation 1 since we used that equation "as-is" to find w.

[tex]\frac{wh}{2} = 88[/tex]

[tex]\frac{22 * 8}{2} = 88[/tex]

[tex]11 * 8 = 88[/tex]

[tex]88 = 88[/tex]

The solution checks out!

Answer:

Sure

Step-by-step explanation:

First you need to ____

Next you need to ____

Last, put nothing

That's what you did, so I helped you out.

Is dis good

i- I think you forgot to put the picture.

Answer:

Mean = 8

Variance = 22

Standard deviation = 4.6904

Step-by-step explanation:

To find out Mean the formula is : total sum of data set / number of values

(11 + 11 + 3 + 1 + 11 + 11) / 6 = 48 / 6 = 8

Mean = 8

Now for variance we will form a table

x                  11     11     3      1      11      11

(x - Mean)    3     3    -5     -7      3      3  

(x - Mean)²   9     9    25    49    9      9

Now we the formula of variance =

Variance = (9+9+25+49+9+9)/(6-1) = 110/5 = 22

Variance = 22

Now we know Standard deviation = √(variance)

Therefore standard deviation = √22 = 4.6904

Hope this helps!<3

Answer: Mean = 8

Step-by-step explanation:

Using the binomial distribution, it is found that there is a:

a) 0.3526 = 35.26% probability of rejecting a lot that is 3% defective.

b) 0.4295 = 42.95% probability of accepting a lot that is 4% defective.

For each device, there are only two possible outcomes, either it is defective, or it is not. The probability of a device being defective is independent of any other device, hence the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the sample has 100 units, hence [tex]n = 100[/tex].

Item a:

3% of the pieces are defective, hence [tex]p = 0.03[/tex].

The probability is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{100,0}.(0.03)^{0}.(0.97)^{100} = 0.0476[/tex]

[tex]P(X = 1) = C_{100,1}.(0.03)^{1}.(0.97)^{99} = 0.1471[/tex]

[tex]P(X = 2) = C_{100,2}.(0.03)^{2}.(0.97)^{98} = 0.2252[/tex]

[tex]P(X = 3) = C_{100,3}.(0.03)^{3}.(0.97)^{97} = 0.2275[/tex]

Then:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0476 + 0.1471 + 0.2252 + 0.2275 = 0.6474[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6474 = 0.3526[/tex]

0.3526 = 35.26% probability of rejecting a lot that is 3% defective.

Item b:

4% of the pieces are defective, hence [tex]p = 0.04[/tex].

Lot is accepted if less than 4 units are defective, hence:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]

[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]

[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]

[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]

Then:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0169 + 0.0703 + 0.1450 + 0.1973 = 0.4295[/tex]

0.4295 = 42.95% probability of accepting a lot that is 4% defective.

A similar problem is given at https://brainly.com/question/24863377

Answer:

I did this question for my little brother. and the answer is A. I think.

Answer:

7feet I hope this help you.

Answer

f= 1

step by step explanation

Hello, hope you are having a splendiferous day.

Here are the numbers you can make with these 4 digits:

2596

6952

2965

5629

And so on.

However, the largest number we can make using these digits is

9652

Hope it helps. Glad to help.

Ask me if you have any queries.

Carry On Learning

~An emotional teen who helps others with joy

Good luck.

x=1 becuase when 1x is it

Answer:

  -9

Step-by-step explanation:

  2.6×10^-2 = (5.2×10^7)/(2×10^n) = (5.2/2)×10^(7-n)

  2.6×10^-2 = 2.6×10^(7-n)

The mantissas are equal, so we can equate the exponents:

  -2 = 7 -n

  n = 7 +2 = 9 . . . . . . add n+2

The value of n in the equation is 9.

Answer:

24 x 40% = 9.6

Step-by-step explanation:

the answer is Lil Debbie™ 9.6 cup used.

Answer:

x=25

Step-by-step explanation:

5x-5+  2x+10 =180

2x-5x = 10+5

3x= 15

x=5

5(5)-5+ 2(5) +10 =180

Step-by-step explanation:

,

[tex] \frac{7}{8} = \frac{49}{x} \\ 7x = 392 \\ x = \frac{392}{7} \\ x = 56[/tex]

Answer:

x = 56

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    7/8-(49/x)=0

Step by Step solution:

Step 1:

Simplify 49/x

Equation at the end of step 1:

7/8 - 49/x = 0

Step 2:

Simplify 7/8

Equation at the end of step 2:

7/8 - 49/x = 0

Step 3:

Calculating the Least Common Multiple :

Find the Least Common Multiple

     The left denominator is :       8  

     The right denominator is :       x  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 3 0 3

Product of all  

Prime Factors  8 1 8

                 Number of times each Algebraic Factor

           appears in the factorization of:

   Algebraic    

   Factor      Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

x  0 1 1

     Least Common Multiple:

     8x  

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

    Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

Left_M = L.C.M / L_Deno = x

 Right_M = L.C.M / R_Deno = 8

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      7 • x

  ——————————————————  =   —————

        L.C.M              8x  

  R. Mult. • R. Num.      49 • 8

  ——————————————————  =   ——————

        L.C.M               8x  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

7 • x - (49 • 8)     7x - 392

————————————————  =  ————————

       8x               8x    

STEP

4

:

Pulling out like terms :

4.1     Pull out like factors :

  7x - 392  =   7 • (x - 56)  

Equation at the end of step

4

:

 7 • (x - 56)

 ————————————  = 0  

      8x      

STEP

5

:

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 7•(x-56)

 ———————— • 8x = 0 • 8x

    8x    

Now, on the left hand side, the  8x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  7  •  (x-56)  = 0

Equations which are never true:

5.2      Solve :    7   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.3      Solve  :    x-56 = 0  

Add  56  to both sides of the equation :  

                     x = 56

One solution was found :

x = 56

The statement is true: the area under the graph line made with the x-axis

represents the change in position of the object on a velocity versus time

graph.

Reasons:

[tex]\displaystyle Velocity = \frac{Dislacement}{Time}[/tex]

The area under the velocity time graph is given by the integration of the function for the velocity over the time interval.

A constant velocity is an horizontal line and the integration of a constant with time, gives the product of time and the constant, which is area under the rectangular graph.

Therefore, the area under the graph line made with the x-axis represents the change in position of the object on a velocity versus time graph.

Learn more here:

https://brainly.com/question/18910091

Answer: True

Step-by-step explanation:

Answer:

To get least possible number of cubes, first find the HCF of 6, 12 and 15

HCF of 6, 12 and 15 = 3

Least possible number of cubes = (6/3)×(12/3)×(15/3)

=2 × 4 ×5

= 40

Answer:

proportion of ratio will be used

Answer:

C. 1 4/10 + 9/10 + 6/10

got it right

Answer:

2/3

Step-by-step explanation:

-5/3 + 2 1/3 =

= 2 1/3 - 5/3

= 2 1/3 - 1 2/3

= 1 4/3 - 1 2/3

= 2/3

Answer:

2/3

Step-by-step explanation:

First, change 2 1/3 into an improper fraction.

2 1/3 --> 7/3

Substitute that value back into the equation

-5/3 + 7/3

At this point, you can rewrite the equation into:

7/3 - 5/3

Since they have the same denominator, just subtract the numerator's values.

2/3

The perimeter of a square is the length of one side multiplied by 4 ( the number of sides)

3 ft x 4 sides = 12 ft.

Perimeter = 12 ft.

The weekly cost per worker is: $800

Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.

Recall:

Unit rate is calculated using: [tex]\mathbf{\frac{y_2 - y_1}{x_2 - x_1} }[/tex]

Unit rate represents the amount of a quantity compared to its unit of measure.

Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.

Since the relationship between number of workers and weekly cost is proportional, we would apply [tex]\mathbf{\frac{y_2 - y_1}{x_2 - x_1} }[/tex] in determining the weekly cost per worker using the points, ​(6​, 4800​) and ​(15​, 12000​):

Unit rate/weekly cost per worker = [tex]\frac{12,000 - 4,800}{15 - 6} = \frac{7,200}{9} = 800[/tex]

Unit rate/weekly cost per worker = $800

In summary, the weekly cost per worker is: $800

Unit rate can be used for calculating expenses, calculating cost of multiple units, or calculating expenses.

Learn more here:

https://brainly.com/question/19154956

Answer:

The answer is 10!

Step-by-step explanation:

Answer:

182.91

Step-by-step explanation:

First multiply the cost of the meal by the sales tax percentage as a decimal (.14)

[tex]136.50*.14=19.11[/tex]

Then multiply the cost of the meal before sales tax by the tip percentage

[tex]136.50*.2=27.30[/tex]

Then add the tip and the sales tax on top of the cost of the meal to calculate the total cost

[tex]136.5+19.11+27.3=182.91[/tex]

Answer:

35 degrees celsius

Answer:

this question

Step-by-step explanation:

Answer:

The first question was this: https://brainly.com/question/420 ur welcome :)

Step-by-step explanation:

Answer:

D or answer choice 4

Step-by-step explanation:

Answer:

maybe 3xz + 4yz + 4x + 2y

Step-by-step explanation:

I tried my best!

Answer:

we need 6 cups of cranberry juice for 12 gallons of punch

Answer:

remainder = 21

Step-by-step explanation:

If f(x) is divided by (x - h) then the remainder is f(h)

Here f(x) is divided by (x - 2) with h = 2 , then remainder is

f(2) = 4(2) + 3(2)² + 1 = 8 + 3(4) + 1 = 8 + 12 + 1 = 21

Answer:

Part A: f(x) = 1.50x/g(x) = 0.01(3)^x-1

Part B: Option A:  $9 

Part C: Option B:  $1,771.47

Part D: The eighth bushel picked is when the exponential function exceeds the linear function.

Step-by-step explanation:

Part A: Write a function to model each option.

Option A:  f(x) = 1.50x, where x is the number of bushels of apples picked

Option B: g(x) = 0.01(3)^x-1, where x is the number of bushels of apples picked.

--------------------------------------------------------------------------------------------------------------

Part B: If Rachel picks six bushels of apples, which option should she choose?  

Option A:  $9    Option B:  $2.43   

Option A is better since what the number is would be higher.

1.50x6 = 9. If I were to do the same for option b, option a would end up higher.

--------------------------------------------------------------------------------------------------------------

Part C: If Rachel picks twelve bushels of apples, which option should she choose?  

Option A:  $18 Option B:  $1,771.47

After calculating both of them by multiplying by 12 for each, option B ends up to be much better.

--------------------------------------------------------------------------------------------------------------

Part D: How many bushels of apples does Lucy pick to make option B better for her than option A?

The eighth bushel picked is when the exponential function exceeds the linear function.