What is the value of this expression.

one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. then the probability of all 5 questions prepared for appears is 2

Recall : nCr = n! ÷ (n-r)!r!

The total possible outcome ; 5 questions out of 10

10C5 = 10! ÷ 5!5! = (10*9*8*7*6)÷(5*4*3*2*1) = 252

Required outcome :

All 5 questions set being from the 9 questions covered and 0 from the 1

left uncovered

9C5 * 1C0

9C5 = 9! ÷ 4!5! = (9*8*7*6) ÷ (4*3*2*1) = 126

1C0 = 1! ÷ 1!0! = 1

Probability = required outcome / Total possible outcomes

P(All 5 questions prepared for appears) :

[9C5 * 1C0] ÷ 10C5

(126 * 1) / 252

= 126/ 252

=2

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Answer:4

Step-by-step explanation:

Answer:a) Given :

51 pounds of seed  can be planted in = 9 acre field.

Per pound of seed =

We can convert 9/51 in simplest fraction by dividing top and bottom by 3.

We get

Therefore, 3/17 of an acrs can be planted per pound of seed.

b) $10 amount = 16 pounds of sugar.

$1 amount = 16/10 = 1.6 pounds of sugar.

Therefore, 1.6 pounds of sugar she got per dollar.

Step-by-step explanation:

The last month's payment for White family can be algebraically expressed as;

⇒ 2665 - d - 11m.

What is an expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

Cost of a new pool table = $2,665

Down payment = d dollars

And, The monthly payment = m dollars.

Since, we have to given a duration of twelve months, we will have to subtract one month from 12 to give, 11 months.

Hence, We can formulate an algebraic equation as;

2665 - d - 11m.

Thus, The last month's payment for White family can be algebraically expressed as;

⇒ 2665 - d - 11m.

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Answer:

y = 4x+2

Step-by-step explanation:

To find an equation that runs through (-4,1) and (4,3) first find the difference between the two y numbers and x number to find the slope. between the two y numbers you go left or right 8 units, and difference between the two x numbers, which is 2. making the slope 4. looking at a graph and marking the two points, draw a line connecting the two given points, find the y intercept. the y intercept is at coordinates (0, 2) making the y intercept 2. making that into an equation is y = 4x + 2

For the function f(x) =[tex]\sqrt{8x+10}[/tex] the inverse function [tex]f^{-1}[/tex](x) = [tex]\frac{x^2-10}{8}[/tex] x≥ 0 as can be calculated through the inverse function's formula.

In mathematics, any kind of inverse is a function that serves to “undo” any other function. That is, if f(x) produces y, then while putting y into the inverse off it produces the output x.

To find the inverse of a function, write the function y as a function of x i.e., y = f(x) and then solve for x as a function of y.

Inverse operations are seen as opposite operations that provides undo to each other. For example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse operations.

Every one-to-one function f has an inverse; this inverse is denoted by f−1 and read aloud as 'f inverse'. A function and its inverse 'undo' each other: one function does something, the other undoes it.

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a.) The Assessed value is $43,830

b.) Annual Tax is $2,848.95

Define marked price

'Marked price' is the general price of the thing without any discount. 'discount' is a percentage of the marked price.

Given,

Assessment rate = 45%

Tax rate is $65 per $ 1000 of assessed value

Marked value = $97,400

a.)

To obtain assessed value,

calculate the 45% of $97,400 like that

45/100 = x/97,400

cross multiply the ratios

100x = 45 * 97,400

x = (45 * 97,400) / 100

x = 45 * 974

x = 43,830

Hence,the Assessed value is $43,830

b.)

Find yearly real estate tax,

Assessed value = $43,830

Tax rate is = 65 / 1000 of assessed value

                 = 0.065 * 43830

                 = 2,848.95

Hence, the  annual tax is $2,848.95

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48×35. By using standard algorithm we got 1680.

Given that,

48×35

We have to find the multiplication of the numbers by standard algorithm.

Standard algorithm is nothing but the words "Standard" and "Algorithm" make up the standard algorithm. Standard refers to the standard or standard way of doing anything, such as eating, bathing, or brushing one's teeth. Algorithms are nothing more than a task's sequential execution. As a result, solving a problem step by step is a common algorithm in mathematics. You will discover what a standard algorithm is in this article, along with the addition, subtraction, multiplication, and division standard algorithms.

If you don't use the standard algorithm , your answers will be incorrect.

48×35=1680

Therefore, By using standard algorithm we got 1680.

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Answer: [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]

Step-by-step explanation:

Using the vertex form, the equation is

[tex]y=a \left(x-\frac{1}{2} \right)^2 +1[/tex]

Substituting in the coordinates (2, -8) to solve for a,

[tex]-8=a \left(2-\frac{1}{2} \right)^2 +1\\\\-8=\frac{9}{4}a+1\\\\-9=\frac{9}{4}a\\\\a=-4[/tex]

So, the equation is [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]

The area of square is increasing with the rate of 144 cm/s2.

For physics, The term "thermal expansion" refers to a material's change in length, width, height, or volume when its temperature is raised or lowered. Solids exhibit particularly noticeable thermal expansion due to their closely packed atoms. There are numerous uses for thermal expansion of solids in daily life.

A solid's atoms vibrate more quickly around their fixed positions when it is heated. As a result, there is little relative growth in the size of solids during heating. In order to prevent buckling when exposed to heat from the sun, metal train tracks feature tiny gaps.

L = length of a side

A = L2

dA/dt = 2L dL/dt

dL/dt = 8 cm/s

A = 81 cm2 ⇒ L = √A = √81 cm = 9 cm

dA/dt = 2(9cm)(8 cm/s) = 144 cm/s2

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The side of square is 216 units and side of cube is 36 units.

According to question we have given that Sally has a cube of some length in units. Let the length of side of cube is S units .

As we know , Area of cube = 6 (side)²= 6S² square units.

Volume of cube = (side)³ = S³ cubic units

Then, as given area in square units of cube = 1/6 of volume of cube in cubic units . That is 6S²= 1/6 S³ => S = 36 units

Area of cube with side 36 units = 6×36²=46656 square units

Volume of cube with side 36 units = 36 ³ cubic units

So, the side of cube is 36 units.

Also, the number of square units in area of Square = number of cubic units in volume of cube

Area of square (S²) = 46656

Side of square = sqrt (46656 ) = 216 units

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The number of heartbeat in ten minutes is 420 beats

Unit rates are the rates of a quantity to one of another quantity

From the question, the given parameters are:

The number of heartbeats in these ten minutes is then calculated as

Total heartbeats = Number of heartbeats per minute x Number of minutes

Substitute the known values in the above equation

So, we have

Total heartbeats = 42 x 10

Evaluate

Total heartbeats = 420

Hence, the total heartbeat is 420 beats

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Answer:

1

Step-by-step explanation:

Given:

The given function is, f (x) = -4x + 5.

The objective is to reflect the graph across the y - axis and find the new function.

Explanation:

The general transformation formula for reflection over y-axis is,

To find f(-x):

The required transformation can be calculated as,

Hence, the new function is g(x) = 4x + 5.

Answer:

6/3=2

30/10=3

Step-by-step explanation:

For simple division like this, you can look and see how many times 3 can go into 6, and 10 into 30.

Total outcome is 50 [because the number produced by the machine is from 1 to 50]

Question a:

Multiple of 10 are 10, 20, 30, 40, 50

There are five possible outcomes for multiple of 10

P(Multiple of 10) = 5/50 = 1/10

Question b:

Number 1 to 50 will be all the outcomes that are not 100

There are 50 possible outcomes

P(not 100) = 50/50 = 1

Question c:

Multiple of 4 that are less than 50 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

There  are 12 possible outcomes for multiple of 4

We want 'not multiple of 4' so we need to do 50 - 12 = 38 outcomes

P(not a multiple of 4) = 38/50 = 19/25

Question d:

One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9

There are 9 possible outcomes

P(one-digit number) = 9/50

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[tex]\sqrt[3]{27x^6y^4}\implies \sqrt[3]{3^3 (x^2)^3 y^3 y^1}\implies 3x^2 y\sqrt[3]{y}[/tex]

the probability that a randomly selected student scored less than 82.

Then the value is  P( X< 82)=0.9192

From the question we are told that

The sample size is  n  =  24

The mean is    =75

The standard deviation is  =5

Generally the  probability that a randomly chosen student scored is less than 82 is mathematically represented as

P( X < 82) = P ( Z< 82-75/5)

                =P(Z <1.4)

                =0.9192

From the z table  the area under the normal curve corresponding to  1.4 is  0.9192

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Answer:

64°

Step-by-step explanation:

it's a right angle (90°) so u take away the other angle (26°) which gets you 64°

Answer:

Speed of northbound train = 66

Speed of southbound train = 54

Step-by-step explanation:

First, let's make the variables simpler:

Speed of southbound train = x

Thus:

Speed of northbound train = y = x + 12

Distance = speed · time

240 = 2 ( x + x + 12 ) = 2 ( 2x + 12 ) = 4x + 24

216 = 4x

x = 54

Now, plug in x to find the speed of the northbound train (y):

y = 54 + 12 = 66

Answer:

s:[-2,-3] is the answer

The set S:{ - 2 , - 3 } will make the inequality 2p - 8 < 5p + 4 true

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

The set S : { - 2 , - 3 , - 4 , - 5 }

The inequality relation is 2p - 8 < 5p + 4

Now , substituting the value from set S in the inequality , we get

When p = - 2 :

2p − 8 < 5p + 4

2(-2) − 8 < 5(-2) + 4

-4 − 8 < -10 + 4

-12 < -6  TRUE

When p = - 3

2p − 8 < 5p + 4

2(-3) − 8 < 5(-3) + 4

-6 − 8 < -15 + 4

-14 < -11  TRUE

When p = - 4

2p − 8 < 5p + 4

2(-4) − 8 < 5(-4) + 4

-8 − 8 < -20 + 4

-16 < -16  FALSE

When p = - 5

2p − 8 < 5p + 4

2(-5) − 8 < 5(-5) + 4

-10 − 8 < -25 + 4

-18 < -21  FALSE

Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation

Hence , the set S:{ -2,-3 } is the solution

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Answer: Your answer would be D

Step-by-step explanation: The reason why is because in the question it said he is already carrying a 20 pound chair. It then say he can carry some boxes that weigh 5 pounds each. The word each is your keyword. With that you can replace the x variable with some single digit numbers. But you also need to make sure your total is less than or equal to 60 pounds. You would pick the less than or equal to sign since he can only carry 60 pounds or less.

The expression, for example, x²- 49 may be factored as (x+7)(x-7).  can be factored in using the difference of squares identity.

The difference of the square's identity is shown below:

(a+b)(a-b) = a² -b²

When an expression can be seen as the difference of two perfect squares, i.e. a² -b², we can factor it as (a+b) (a-b).

For example, x²- 49 may be factored as (x+7)(x-7).

This approach is based on the pattern (a+b)(a-b) = a² -b², which may be validated by extending the parenthesis in (a+b)(a-b).

Thus, the expression, for example, x²- 49 may be factored as (x+7)(x-7).  can be factored in using the difference of squares identity.

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Answer:

  C) no: The packs of socks are marked up to $7 and then discounted to $4.20

Step-by-step explanation:

You want to know the price of a $5 pair of socks after markup by 40%, and again after that price is marked down 40%.

When the $5 cost is marked up by 40%, the resulting price is ...

  $5 + 0.40×5 = $5 +2 = $7.

The socks are marked up to $7.

When the $7 price is marked down by 40%, the resulting price is ...

  $7 - 0.40×7 = $7.00 -2.80 = $4.20

The socks are discounted to $4.20.

Answer:

348 ft

Step-by-step explanation:

First split the sidewalk into two rectangles. then multiply the LxWxH (length times width times height) of both rectangles. 8 times 6 times 6 = 288 ft. then 10 times 2 times 2 = 60. then add the two volumes of the rectangles to result in 348 cubic ft

Answer:

0.875 inches

Step-by-step explanation:

Pretty easy. Just divide how many inches thick the boards are by how many there are: inches-thick/amount

Now substitute 10.5/12 and find your answer

0.875 inches thick per board

Using substitution method, the best initial step in solving the equation is solve the first equation for x.

The equation can be solved by substitution method as follows:

2x + 3y = -12

6x + y = 18

Hence, let's make y the subject of the formula in equation(ii)

6x + y = 18

y = -6x + 18

We have to substitute the value of y in equation(i)

2x + 3y = -12

2x + 3(-6x + 18) = -12

2x - 18x + 54 = -12

- 16x + 54 = -12

-16x = - 12 - 54

- 16x = -66

x = 66 / 16

x = 33 / 8

Therefore,

6(33 / 8) + y = 18

99 / 4 + y = 18

y = 18 - 99 / 4

y = - 27 / 4

From the solving above the best step to solve the equation is solving the first equation for x.

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Answer:39.2 40.2 444.96

Step-by-step explanation:

The law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.

Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.

It is given that:

The statement is:

If you have a cat, then it will chase mice.

As we know, from the definition of the Law of Syllogism, the legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.

Your cat will chase mice.

The Law of syllogism makes this argument true.

Thus, the law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.

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The example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because it will not occur.

The probability is the branch of mathematics that shows the occurrence of the random event. The value of the probability varies from 0 to 1.

The equation of the probability is

Probability = Number of favorable outcomes / Total number of outcomes

The probability of getting number number 7 when you throw a die once is zero. Because when you throw a die the possible outcomes are 1, 2, 3, 4, 5 and 6. We wont get number 7. Therefore the probability is zero

Hence, the example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because  it will not occur.

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Answer:

Use this relation

Im^2 = 10000cm^2

Answer:

multiply m² by 10000

Step-by-step explanation:

1 m = 100 cm

1 m² = 100² = 10000 cm²

then to change m² to cm² , multiply m² by 10000