what is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced?

The probabilities of picking an A, a B or a C is given as follows:

167/210.

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes in the context of a problem.

For each event, the probabilities in this problem are given as follows:

To find the or probability, we add the probabilities of the desired outcomes, hence:

P(A) + P(B) + P(C) = 1/5 + 3/7 + 1/6 = (42 + 90 + 35)/210 = 167/210.

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You can form 56,800 possible teams from a pool of 16 eligible engineers by selecting a total of 3 team members.

The total number of teams can be calculated using combination formula. The combination formula is nCr where n is the total number of items and r is the number of items you want to choose.

In this case, n = 16 and r = 3. Hence, the number of possible teams:

This means you can form 56,800 unique teams by choosing 3 engineers out of 16 eligible engineers. The combination formula helps in finding the number of possible combinations when the order does not matter, which is the case here as the order of engineers in a team does not matter.

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A student taking thirteen credit hours should plan for approximately 13-15 hours of work outside of class each week.

Generally, if a student is taking thirteen credit hours, they should plan for approximately 13-15 hours of work outside of class each week. This includes attending lectures, studying, and completing assignments. To calculate this, the student should take the total number of credit hours (13) and multiply it by the number of hours per credit (usually 3 hours). This would give the student 39 hours of work outside of class.

However, this number should not be taken as an exact number, as the amount of time needed to complete the course may vary based on the student's learning style, the difficulty of the course, and the amount of time required for each assignment. For example, if a student is taking a particularly difficult course, they may want to plan for more hours than the calculation suggests.

In order to ensure success, students should plan ahead, create a schedule, and stick to it. This will help them stay on track and complete their coursework in a timely manner.

A student taking thirteen credit hours should plan for approximately 13-15 hours of work outside of class each week.

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Yes, the equation y = 5x represents a proportional relationship

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=5x.

In a proportional relationship, the ratio of y to x is constant.

In the given equation the variable x and y has a proportional relationship.

The equation is in the form of y=mx+b

the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.

Hence,  Yes, the equation y = 5x represents a proportional relationship

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Here's the completed table of values for y = 2x^2 + x

7,1,9

To find the value of y for each x, substitute x into the equation and simplify:

For [tex]x = -2: y = 2(-2)^2 + (-2) = 7[/tex]

For[tex]x = -2: y = 2(-2)^2 + (-2) = 7[/tex]

For[tex]x = 0: y = 2(0)^2 + 0 = 1[/tex]

For [tex]x = 1: y = 2(1)^2 + 1 = 4[/tex]

For[tex]x = 2: y = 2(2)^2 + 2 = 9[/tex]

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Answer:

The data points in Set 1 are more spread out than the points in set 2

he mean than the points in Set 2 because the mean absolute deviation is Larger

Step-by-step explanation:

The mean absolute deviations for two sets of data are shown.

A 2-column table with 2 rows. Column 1 is labeled Set with entries 1, 2. Column 2 is labeled M A D with entries 8.4, 0.2.

The data points in Set 1 are more_____

the mean than the points in Set 2 because the mean absolute deviation is_____

Answer:

2 6/13

Step-by-step explanation:

the surface area of the rectangular prism is 348 inches²

The surface area of a rectangular prism is given by: SA = 2 (lh +wh + lw ) Square units.

Given here: A rectangular prism with dimensions are 6 in.

We know the surface area of a prism is given by

2(wl+hl+hw)

where l is the length , w is width and h is the height.

Thus Surface area A=2(wl+hl+hw)

2·(8·6+9·6+9·8)=348

Thus the surface area of the rectangular prism is 348 inches²

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Answer:

i think its answer 2

As total = 4100

Insurance = 123/4100*100 = 3%

Housing = 574/4100*100 = 14%

Entertainment = 164/4100*100 = 4%

The solution of the system of equation is , x= -4 & y= -8.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

from the given graph we get,

one line is passing through the points (0,10) , ( 4,28)

so, the equation of the line can be,

4y= 18x + 40

and, second line is passing through the points (0,8) , (1,12)

so, the equation of the line can be,

y= 4x+8

solving the equations we get,

x= -4

y= -8

Hence, The solution of the system of equation is , x= -4 & y= -8.

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Reduced form of given fraction is (2 + n)/7

An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

Given expression

(2x + nx - 2y - ny)/(7x - 7y)

It can be written as

[(2x - 2y) + (nx - ny)]/(7x - 7y)

Factoring out common factors

[2(x - y) + n(x - y)]/7(x - y)

Again factoring out common factor

(x - y)(2 + n)/7(x - y)

(2 + n)/7

Hence (2 + n)/7 is reduced form of the given expression.

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The distance of the parking lot from the first campsite is 3.14 miles.

The scale of the map is 1/24,000, which means that for every 1 inch on the map, it is equal to 24,000 inches in reality. To calculate the distance of the parking lot from the first campsite, we need to first convert the 8.3 inches on the map into inches in reality. To do this, we use the formula:

Actual distance = Map distance x (Map scale)

Actual distance = 8.3 inches x 24,000 inches

Actual distance = 199,200 inches

Now, to convert inches to miles, we can use the formula:

Miles = Inches / 63360

Miles = 199,200 inches / 63360

Miles = 3.14 miles

Therefore, the distance of the parking lot from the first campsite is 3.14 miles.

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The inequality is x<10, which is true when `x=4`.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a< b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

here, we have,

Given Data,

`x=4

so, from the given inequality, we get,

The inequality is x<10, which is true when `x=4`.

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Answer:

Below

Step-by-step explanation:

This is a two-stage problem

  for the first 12 years use cont compounding formula

        FV = PV e^(rt)     Future value  Presnt value   r = decimal int   t = years

         = 2000 e^(.05 * 12) = 3644.24    use this amount for the second stage

     Fv = pv e^(rt)  = 3644.24 ( e^(.08*8) ) = $ 6911.23

The central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

The formula for the area of a sector of a circle is [tex]A = (θ/360) * π * r^2,[/tex] where θ is the central angle in degrees, π is 3.14, and r is the radius of the circle.

Given the area of a sector of a circle is [tex]56 cm^2[/tex] and the radius is 10 cm, we can solve for θ:

[tex]56 cm^2 = (θ/360) * 3.14 * 10^2\\56 cm^2 = (θ/360) * 314\\θ = (56 * 360) / 314\\θ = 63.6[/tex]

Therefore, the central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

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The value of the expression is 18.

The value of the expression is calculated by applying the principle of order of operation as shown below.

The given expression y ÷ 4 • 3 – 6 ÷ x + 8

re-write the expression as follows;

= y/4 × 3 - 6/x + 8

where;

The value of the expression is calculated as;

= ( 16 / 4 ) x 3  -   6 / 3  + 8

= ( 4 x 3 ) - ( 2) + 8

= ( 12 ) - 2 + 8

= 12 - 2 + 8

= 18

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The complete question is below:

Given the values x = 3 and y = 16, find the value of this expression,  y ÷ 4 • 3 – 6 ÷ x + 8

Answer:

89.28

Step-by-step explanation:

First lets find 7% of 96

96 x 0.07 = 6.72

then subtract 6.72 from 96

96-6.72=89.28

The requried, a number that is 7% smaller than 96 is approximately 89.28.

To find a number that is 7% smaller than 96, we need to calculate 7% of 96 and then subtract that value from 96.

Calculate 7% of 96.

7% of 96 = (7/100) * 96 = 0.07 * 96 = 6.72

To get a number that is 7% smaller than 96, we need to subtract the value we found in Step 1 from 96. subtract the calculated value from 96.

Number = 96 - 6.72 = 89.28

Therefore, a number that is 7% smaller than 96 is approximately 89.28.

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There are 2,118,760 possible ways to select 6 cards from a deck of 52 cards if the spade ace must be selected.

If at all you must select the spade ace, you have 51 cards remaining from which to choose 5 more cards. The number of ways to choose 5 cards from 51 is 51C5, where C represents the number of combinations.

Using the formula for combinations, we have:

51C5 = 51! / (5! * (51 - 5)!) = 51! / (5! * 46!)

Using the factorial we can simplify this expression to:

51C5 = 51 * 50 * 49 * 48 * 47 / (5 * 4 * 3 * 2 * 1) = 2,118,760

Therefore, there are 2,118,760 possible ways to select 6 cards from a deck of 52 cards, if the spade ace must be selected.

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The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

y = 2x² + 4x

now, for, x= 0 , y = 0

for, x= 1, y = 6

for, x= 2, y = 16

Hence, The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

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The equivalent interest rate will be 0.5 % and it will be compounded 24 times

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

Compound interest is calculated by calculating the Amount

A = P( 1+r/n)^ ntp

A = amount

P is the principal

t is the time elapsed

since the interest rate is 6 % , the. monthly compounded interest will be 6/12, since there is 12 months in a year.

= 0.5 %

the number of times it will be compounded will be 12 × 2 = 24 times

therefore the equivalent interest rate is 0.5% per month and it will be compounded 24 times in the space of 2 years.

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Answer:

So if there were -4+20 the answer would be 16. When you add things, it goes to the right of the number line. When you subtract stuff it goes to the left. Simple but there are more rules like when this happens: 6--4 the two minuses turn into a plus 6+4—and other stuff. So -8 you have 8 negative signs and 20 positive signs. When a positive and a negative are added together they cancel each other out so now you have 12. This is modeled on the attachment. Hope this helped!

Step-by-step explanation:

After solving the given equation, the value of variable x is 7/2 so x+5 is not the factor of given equation.

Equation: f(x)=x3-4x*2+3x+7

Here we have equation or algebric expression to solve to check whether the given condition is correct or not.

Give:

x3-4*2+3x+7= 0

Multiply the monomials

3x- 8x+3x+7= 0

Combine like terms

-2x+7= 0

Rearrange variables to the left side of the equation

-2x= -7

Divide both sides of the equation by the coefficient of variable

x= [tex]-7/-2[/tex]

Determine the sign for multiplication or division

x= [tex]7/2[/tex]

The value of x is  [tex]7/2[/tex].

So x+5 is not a factor of f(x)=x3-4x*2+3x+7.

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The function with the greater initial value is (a) the function A

The complete question is added as an attachment

The initial value of a function is calculated when

x = 0

From the table of values, we have

y = 8 when x = 0

For the other function, we have

y = 4x + 3

So, the initial value is

y = 4(0) + 3

Evaluate

y = 3

8 is greater than 3

Hence, the function with the greater initial value is the table of values

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The amplitude, period, and zero value of the function y = 3cos(x+5) are (A) 3, 2π, later.

Option D is correct.

The amplitude of a cosine function is described  as half the difference between the maximum and minimum values of the function.

In the question given, the maximum value of the function y = 3cos(x+5) is 3 and the minimum value is -3, hence amplitude is:

A = (3 - (-3)) / 2 = 3

For a cosine function with a period of 2π, the maximum or minimum values repeat every 2π units along the x-axis.

In the question above, the period of the function y = 3cos(x+5) is:

P = 2π

in conclusion, the phase shift of a cosine function is the horizontal shift of the graph of the function along the x-axis, which is represented by the constant term (x+5) in this case.

Phase shift = later

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The system of inequalities is y >= 3x and y > 3 - x

From the question, we have the following parameters that can be used in our computation:

The graph

The inequalities on the graph are linear inequalites

So, we first write out their equations as follows:

y = 3x --- red line

y = 3 - x -- blue line

For the red line, we have

Thick line and the upper region is shaded

This is represented as y >= 3x

For the red line, we have

Dotted line and upper region is shaded

This is represented as y > 3 - x

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This model must be completed to represent 377 ÷ 12 as follows;

      30     1___

12 | 360  | 17 | 5.

In order to divide the given numbers by using the box method, we would write an expression to represent the number of times in which the number (377) can be divided by the number (12), while including the remainder (17) as follows;

377 ÷ 12 = (360 + 17) ÷ 12

377 ÷ 12 = (360 ÷ 12) + (17 ÷ 12)

377 ÷ 12 = 30 + (17 ÷ 12)

Note: 12 would divide 17 to give an output of one (1) remainder five (5).

In this context, the above mathematical expression would be re-written as follows;

377 ÷ 12 = 30 + 1 R 5.

Where:

The variable R represents remainder.

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