1 Suppose another student says he spends $29 each
week on entertainment. Will the mean and median
increase or decrease?
decreas
2 What is the new mean when the value from problem 1
is included in the data set?
Show your work. For elementary kids

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

8,16,24,32,40,48,56,64,72,80

12, 24, 36, 48, 60, 72, 84, 96, 108, 120,

Step-by-step explanation:

LCM of 8 and 12 is 24.

a) The percentile rank of 321.8 is 64%.

ii. The percentile rank of 296.3 is 36%.

b) The score that is in the 75th percentile is 263.1.

ii. The score that is in the 95th percentile is 223.4.

In Mathematics, the percentile rank of a data can be calculated by using the following formula:

Percentile rank = L/N × 100

Where:

Part a.

Next, we would determine percentile rank of 321.8 as follows;

i. L = 9 and N = 14

Percentile rank = L/N × 100

Percentile rank = 9/14 × 100

Percentile rank = 64.28 ≈ 64%.

ii. L = 5 and N = 14

Percentile rank = L/N × 100

Percentile rank = 5/14 × 100

Percentile rank = 35.71 ≈ 36%.

Part b.

We would determine which score is in each of the given percentile as follows;

i. 75th percentile

Percentile rank = L/N × 100

75 = L/14 × 100

L = 1050/100

L = 10.5 ≈ 11.

Therefore, rank 11 on the table is 263.1.

ii. 95th percentile

Percentile rank = L/N × 100

95 = L/14 × 100

L = 1330/100

L = 13.3 ≈ 13.

Therefore, rank 13 on the table is 223.4.

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Answer:

its 2 1/6 (B)

Step-by-step explanation:

Answer:

because everything is relative to each other.

Step-by-step explanation: Graphing ordered pairs is only the beginning of the story. Once you know how to place points on a grid, you can use them to make sense of all kinds of mathematical relationships. A linear relationship is a relationship between variables such that when plotted on a coordinate plane, the points lie on a line. Let’s start by looking at a series of points in Quadrant I on the coordinate plane. Look at the five ordered pairs (and their x– and y-coordinates) below.

Answer:

Graphing ordered pairs is only the beginning of the story. Once you know how to place points on a grid, you can use them to make sense of all kinds of mathematical relationships. A linear relationship is a relationship between variables such that when plotted on a coordinate plane, the points lie on a line. Let’s start by looking at a series of points in Quadrant I on the coordinate plane. Look at the five ordered pairs (and their x– and y-coordinates) below.

Brainliest?!?!??!?

I need one more .

Functions f(x) = x² + 1 and g(x) = x – 4, the value equivalent  to f(g(10)) is, 37

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

f(x) = x² + 1

g(x) = x – 4

f(g(10)) = ?

f(g(x))  =  (x - 4)² + 1

           =  x² - 8x + 16 +1

           =   x² - 8x + 17

f(g(10)) =  10² - 8×10 + 17

            = 100 - 80 + 17

            = 37

The value of  f(g(10)) is 37

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Answer:

Step-by-step explanation:

To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.

Let's apply the Luhn algorithm to the given credit card number:

Step 1: Starting from the rightmost digit, double every second digit

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|

Step 2: If the doubled value is greater than 9, add the digits of the result

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |

Step 3: Add up all the digits in the credit card number, including the check digit

5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61

Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.

61 is not divisible by 10, therefore the given credit card number is invalid.

Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.

Answer:

52

Step-by-step explanation:

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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Answer:

add my sc = bmic ava, no spaces

or add my discord = XoXo_ava

Step-by-step explanation:

have a good day bro

Answer:

Option (a) \(\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}\)

Step-by-step explanation:

The given expression is :

\(\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....\)

We need to rewrite the sum using sigma notation.

The numerator is 3 in all terms.

At denominator, in first term (1)(2), in second term (2)(3) and so on.

A general term for the denominator is k(k+1).

Sigma notation is :

\(\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}\)

Hence, the correct option is (A).

Answer:

2x^2-5x-12

Step-by-step explanation:

(2x+3)(x-4) can be simplified using the acronym FOIL, which stands for "first, outer, inner, last." This means that you multiply the first terms in each group, the the outer terms, then the inner terms, and lastly the last terms in  each group.

2x*x=2x^2

2x*-4=-8x

3*x=3x

3*-4=-12

Combine those and you get 2x^2-8x+3x-12. Combine like terms, and your final answer is 2x^2-5x-12

Answer:

x = 32

y = 16sqrt(5)

z = 8sqrt(5)

Step-by-step explanation:

x/16 = 16/8

x/16 = 2

x = 32

y^2 = 16^2 + 32^2

y^2 = 1280

y = 16sqrt(5)

z^2 = 8^2 + 16^2

z^2 = 320

z = 8sqrt(5)

Other answer formats are possible.

===========================================================

Explanation:

Let's say we want to solve the equation h = 54 + 10a for the variable 'a'. This is relevant to the problem at hand don't worry.

What we'd do is two things

So the steps look like this

h = 54 + 10a

h-54 = 10a

(h-54)/10 = a

a = (h-54)/10

Now let's say we wanted to solve this equation: h = 54 + ca, where c is a constant and can stand in place of any number. The steps would be pretty much identical. Instead of dividing both sides by 10, we divide both sides by c. We can do this as long as c isn't zero of course.

That means the equation h = 54+ca solves to a = (h-54)/c

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

Why did I do those examples? To build up to the equation your teacher gave you.

Let's replace c with 0.5t^2

This is because 1/2 = 0.5

The 1/2at^2 is the same as (1/2t^2)a

So instead of a = (h-54)/c, we'd get a = (h-54)/(0.5t^2)

As a last optional and encouraged step, we can multiply every term by 2 to get rid of that decimal value.

Doing so makes a = (h-54)/(0.5t^2) turn into a = (2h-108)/(t^2)

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

Here's another way to solve:

h = 54 + (1/2)at^2

h-54 = (1/2)at^2

2(h-54) = at^2

2h-108 = at^2

(2h-108)/(t^2) = a

a = (2h-108)/(t^2)

In the second step, I subtracted 54 from both sides. Immediately afterward, I multiplied both sides by 2 so I could clear out the fraction. Then I divided both sides by t^2 to fully isolated the variable 'a'.

Answer:

b(side length) = 15 centimeters

Step-by-step explanation:

Given an assumed regular rectangular prism which has a height of 18, and volume of 4050 cubic centimeters.

We are also given the formula b = (v/18)^1/2 which is said to find the side length of the rectangular prism. Therefore, it is implied that b must be the side length. Since we know everything except the side length we can substitute the volume since we are already given the height in the formula derived from the problem.

b = (4050/18)^1/2

b = (225)^1/2

b = 15

___________

We should also know that the volume of a rectangular prism is defined as V = l × w × h, with l as the length, w as the width, and h as the height, given that b is the side length which is multiplied by the width and height to get 4050, the base must be a square. Since 4050 = 15 × w × 18

4050 = 270 × w

4050/270 = w

15 = w

w = 15.

A square base is when the length and width are equal. Therefore this value has to be true.

As 15 × 15 × 18 = 4050.

( 1 - cos²x ) secx

=> sin²x . secx

Here the rule ( rule 1 ) is the first trigonometric identity [ sin²A + cos²A = 1 ] by simplifying we have , [ 1 - cos²A = sin² ] . So here we substituted 1 - cos²x = sin²x .

=> sin²x [ 1/cosx ]

Here the rule ( rule 2 ) is secx = 1/cosx . So here we substituted secx = 1/cosx .

=> sinx [ sinx/cosx ]

Here the rule ( rule 3 ) is sin²x can be written as sinx . sinx , so we get sinx . sinx [ 1/cosx ] next by simplifying , sinx [ sinx/cosx ].

=> sinx tanx

Here the rule ( rule 4 ) is , in the above we got sinx/cosx and here we know that , sinx/cosx = tanx . So we have tan x .

The proof of the identity that justifies that ( 1 - cos²x ) secx equals sinx(tanx) has been described below with statements and rules.

Statement 1; ( 1 - cos²x ) secx

This is given

Statement 2; sin²x · secx

Rule 1;  From trigonometric identities, we know that;

sin²x + cos²x = 1,

Thus; cos²x = 1 - sin²x

Thus; ( 1 - cos²x ) secx = sin²x · secx

Statement 3; sin²x (1/cosx)

Rule 2;  The rule here according to trigionometric identities is that; secx = 1/cosx. Thus; secx = 1/cosx .

Statement 4; sinx (sinx/cosx )

Rule 3;  The rule here is that sin²x can be expressed as (sinx * sinx)

Thus, we have; sinx . sinx (1/cosx) = sinx (sinx/cosx ).

Statement 5; sinx(tanx)

Rule 4;  The rule here is that; sinx/cosx = tanx.

Thus;  sinx (sinx/cosx ) gives us sinx(tanx)

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We are given the following expression

Where the values of a and b are also given

a = 1/3

b = 9

Let us substitute these values into the given expression and then simplify the expression

Therefore, the expression is simplified to 78

Answer:

If I were to be honest I think you did it perfectly

Answer: 20 meters

Step-by-step explanation:

A= w l

A= A /w = 600/30 = 20m

L= 20 m

Answer:

the 34 yrs Is wrong it will be 4yrs only.

Step-by-step explanation:

Let my present age=x years

After 12 years my age=x+12 years

4 years ago my age =x−4 years

According to the question,

x+12=3(x−4)

⇒x+12=3x−12

⇒3x−x=12+12

⇒2x=24

or x= 24/2 =12 years.

∴ my present age is 12 years.

hope this helps you.

lim x → 0 (2/x - 2/|x|) does not exist.

We need to find lim x → 0 (2/x - 2/|x|)

lim x → 0 (2/x - 2/|x|) = lim x → 0 (2|x| - 2x / x |x|)

Consider the left hand limit.

lim x → 0^- [(2|x| - 2x) / x |x|]

As the x values approach 0  from the left, the function values decrease without bound.

i.e., the function approaches -∞

Consider the right hand limit.

lim x → 0^+ [(2|x| - 2x) / x |x|]

Consider a table to see the behavior of the function as x approaches 0 from the right.

   x             f(x)

  0.1            0

 0.01           0

 0.01           0

As the x values approach 0 from right, the function values approach 0.

Thus, the limit of  [(2|x| - 2x) / x |x|] as x approaches 0 from the right is 0.

Since the left sided and right sided limits are not equal, the limit does not exist.

Therefore,  lim x → 0 (2/x - 2/|x|) does not exist.

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Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

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The value of the expected value of payout is $1.75.

In probability theory, the idea of expected value denotes the typical result of a random event when the event is repeated a lot of times. It is determined by multiplying each potential result by its likelihood before adding together all of these numbers. The anticipated value can shed light on the possible risks and benefits associated with various options or scenarios, making it frequently used to estimate the long-term average of a random process or to make decisions under uncertainty.

To get the payout we need to determine the probability of winning each prize.

For first prize = 1/400

Second prize = 1/400.

Third prize = 1/400.

Fourth prize = 1/400.

The expected value is calculated as:

(1/400) * $350 + (1/400) * $200 + (1/400) * $100 + (1/400) * $50

= $0.875 + $0.50 + $0.25 + $0.125

= $1.75

Hence, the value of the expected value of payout is $1.75.

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Answer:

THE ANSWER IS C

Step-by-step explanation:

just add it it and find it 0.007

Answer:

  647

Step-by-step explanation:

The divisibility rule for 9 can be used to find the unknown number.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The number 3D8 will be divisible by 9 when 3 + D + 8 = <multiple of 9>. Since D is a single digit, we must have ...

  11 +D = 18

  D = 7 . . . . . . . subtract 11

The number 3D8 is 378.

Now we know that the difference is ...

  ABC -3D8 = ABC -378 = 269

  ABC = 269 +378 = 647

ABC represents the number 647.