Mark had some money. He gave half of that to his brother and then he gave another $5 to his sister. He now has $20. How much money did Mark have in the beginning?

The standard deviation is 2.24 if the sum of squares for a sample containing 101 items equals 500 option (C) is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{n-1}[/tex]

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

∑(x(i) - X)² = 500

n = 101

SD = √(500/101-1)

SD = √5

SD = 2.236 ≈ 2.24

Thus, the standard deviation is 2.24 if the sum of squares for a sample containing 101 items equals 500 option (C) is correct.

Learn more about the standard deviation here:

brainly.com/question/12402189

#SPJ4

The radius of the Sphere that submerged in the water is 178.9 mm.

Volume of the Cuboid:

Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space.

The general form of the Volume of the Cuboid is,

Volume of a cuboid = l × b × h    [cubic units]

Where,

l = length

b = breadth

h = height

Given,

A water tank is a cuboid 45cm long, 30cm wide and 26cm high.

It contains water to a depth of 21cm.

A sphere is placed in the tank and is fully submerged. the water level rises by 1.8cm.

Here we need to find the radius of the Sphere and we have to use the Volume of the sphere as 4/3πr³.

First, we need to find the volume of the water,

For that, we have to take the measurement of it.

l = 45 cm

b = 30 cm

h = 21 cm

( here we have to find the volume of water, so we have take the water depth as its height)

Now, the volume of the water is,

V₁ = 45 x 30 x 21

V₁ = 28350 cm³

After placed the sphere on the tank the water level is increased as 1.8 cm,

So, the new height = 21 + 1.8 = 22.8

Now the new volume is,

V₂ = 45 x 30 x 22.8

V₂ = 30780 cm³

So, the Volume of the increased water level is,

=> 30780 - 28350

=> 2430 cm³

Now we have to consider this as the Volume of the Sphere and calculate the radius through it,

=>  4/3πr³ = 2430

=> r³ = 2430 x 3/4 x π

we know that the value of π = 22/7

So,

=> r³ = 2430 x 3/4 x 22/7

=> r³ = 5727.86

=> r = ∛5727.86

=> r = 17.89

Therefore, the radius of the sphere is 17.89 cm

Now we have to convert it into mm,

=> 1 cm = 10 mm

So,

=> 17.89 cm = 178.9 mm

Therefore, the radius of the sphere is 178.9 mm.

To know more about Volume of Cuboid here.

https://brainly.com/question/23118276

#SPJ4

The fraction of 1/2 of the number of liters of blue paint is 3/4 therefore 3/4 liters of blue paint must be used to draw that painting.

If we divide two numbers by each other then the upper word is called the numerator, a lower word is called the denominator, and the representation is known as the fraction.

Given that,

Maritza bought 1.5 liters of blue paint.

The given painting is going to be used 1/2 fraction of the total liters of blue paint.

1/2 of the blue paint ⇒

(1/2)1.5

⇒ (1/2)15/10

⇒ (1/2)3/2

⇒ 3/4 liters of blue paint.

Hence "The fraction of 1/2 of the number of liters of blue paint is 3/4 therefore 3/4 liters of blue paint must be used to draw that painting".

For more about fractions,

https://brainly.com/question/10354322

#SPJ1

The given question is in another language the translation in English is as follows;

Maritza bought 1.5 liters of blue paint. if I use 1/2 of the contents of that can to paint a mural

How many liters of blue paint do I use on this?

Answer:

-2

Step-by-step explanation:

[tex]Rule(s): a\frac{b}{c} = \frac{a \cdot c + b}{c}, \frac{-a}{b}=-\frac{a}{b}, \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c} \\2\frac{2}{3}=\frac{2\cdot 3+2}{3}\\=\frac{8}{3}\\=\frac{-\frac{8}{3}}{\frac{4}{3}}\\=-\frac{\frac{8}{3}}{\frac{4}{3}}\\=\frac{-8\cdot \:3}{3\cdot \:4}\\= \frac{-24}{12}\\= -2[/tex]

Answer:

x = 2b - a

Step-by-step explanation:

2(x + a) = 4b

2x + 2a = 4b

x + a = 2b

x = 2b - a

I think this question is incomplete

Answer:

7

Step-by-step explanation:

2+4+6+8+10+2

=42÷6(coz 6 multiples)

=7

Answer: x=6

Step-by-step explanation:

[tex]5x+4x-68=34-8x\\\\9x-68=34-8x\\\\9x-68+8x=34-8x+8x\\\\17x-68=34\\\\17x-68+68=34+68\\\\17x=102\\\\Divide \ both \ parts\ of\ the\ equation\ by\ 17:\\\\x=6\\[/tex]

Your friend should have added 68 to each side of the equation, but instead subtracted 68 from the right side.

[tex]17x=34-68\\17x=-34[/tex]

Divide both parts of the equation by 17:

[tex]x=-2[/tex]

Answer:

3/2

Step-by-step explanation:

xy= -2 X -3

= 6

z = 4

so xy/z is 6/4 which is 3/2.

Answer:

6.913339

Step-by-step explanation:

176/2^10 = 0.171875.

n=10, p=1/2, q=1/2

probability of student passes the quiz only if he answers 7 or more than 7 questions correctly and let it be x

P(x)=10C7(0.5)^7(0.5)^3 + 10C8(0.5)^8(0.5)^2 + 10C9(0.5)^9(0.5)^1

+ 10C10(0.5)^10(0.5)^0

=120 /1024 + 45/1024 + 10/1024 + 1/1024

P(x)=176 / 1024

For more information on probability click on the link below:

https://brainly.com/question/24756209

#SPJ4

The temperature at midnight is -8°C.

Let the initial temperature be x.

It should be noted that there are 7 hours between midnight and 7am.

Therefore, the equation will be:

x + (1.1 × 7) = -0.3

x + 7.7 = - 0.3

x = -0.3 - 7.7

x = -8

The temperature at midnight is -8°C.

Learn more about temperature on:

brainly.com/question/24746268

#SPJ1

Answer:

50

Step-by-step explanation:

Apply PEMDAS to this problem

8 × 5 = 40

Now you are left with: 40÷4×5

You then use PEMDAS from left to right from here

So 40 ÷ 4 would be 10, and now you are left with 10 × 5, which would be 50.

The marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

The marginal utility simply refers to the change or extra satisfaction derived from the change in consumption.

Hence, the marginal utility of the fifth apple equals :

Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)

= (250 - 220) = 30

Hence, marginal utility per dollar: Marginal utility/price per apple

Price per apple = $0.5

Marginal utility of 5th apple = 30

Marginal utility of 5th apple = 30 / 0.5

Marginal utility of 5th apple = 60

Therefore, the marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

Complete question :

If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:

a) 20

b) 30

c) 40

d) 60

Number of apples ____total utility

2__________________130

3__________________180

4__________________220

5__________________250

6__________________270

7__________________280

To know more about marginal utility follow

https://brainly.com/question/15050855

#SPJ4

Answer:

x = 23         y = 42

Step-by-step explanation:

y + 54 + 4x - 8 = 180

y + 4x = 180 - 46

y + 4x = 134

180 - (5x - 19) = 4x - 8

180 - 5x + 19 = 4x - 8

180 + 19 + 8 = 4x + 5x

207 = 9x

207/9 = x

x = 23

y + 4(23) = 134

y = 134 - 92

y = 42

The value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85

The expression is given as

(12 - 3/5√25)^2 + (2 - 4)^2

Evaluate the square root of 25

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3/5 * 5)^2 + (2 - 4)^2

Evaluate the product

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3)^2 + (2 - 4)^2

Evaluate the difference

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = 9^2 + (2 - 4)^2

Evaluate the exponent and the sum

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = 85

Hence, the value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85

Read more about expression at

https://brainly.com/question/723406

#SPJ1

Answer:

Step-by-step explanation:

the amount of garbage started to increase around 2005 or 2007

Just plot a point anywhere they graph is straight

Answer: Derivative of f(x) =3x+5=3

Step-by-step explanation:

By the Sum Rule, the derivative of 3x+5 with respect to x is d/dx[3x]+d/dx[5]

d/dx[3x]+d/dx[5]

evaluate:  d/dx[3x]

Since 3 is constant with respect to x, the derivative of 3x with respect to x is 3d/dx[x].

3d/dx[x]+d/dx[5]

Differentiate using the power rule

which states that d/dx[[tex]x^{n}[/tex]] is [tex]nx^{n-1}[/tex]    where n=1.

3⋅1+d/dx[5]

Multiply 3 by 1.

3+d/dx[5]

Differentiate using the Constant Rule.

Since 5 is constant with respect to x, the derivative of 5 with respect to x is 0.

3+0

Add 3 and 0 = 3

So, derivative of f(x) =3x+5=3

Learn more about area here https://brainly.in/question/1044252

#SPJ9

Answer: 144N

Step-by-step explanation:

A=acceleration. N=net force. M=mass

A=N/M

4.5=N/32

4.5*32=N

N=144N

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Net Force acting on a body can be determined by formula :

[tex]\qquad \sf  \dashrightarrow \: f = m \times a[/tex]

where,

[tex]\qquad \sf  \dashrightarrow \: f = 32 \times 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \: f = 144 \: \: N[/tex]

So, the net force acting on the body is 144 Newtons.

Answer:

16x² + 8x + 1

Step-by-step explanation:

(4x + 1)(4x + 1)

each term in the second factor is multiplied by each term in the first factor, that is

4x(4x + 1) + 1(4x + 1) ← distribute both parenthesis

= 16x² + 4x + 4x + 1 ← collect like terms

= 16x² + 8x + 1

Answer:

16 x 2 + 8x + 1

Step-by-step explanation:

Using the foil method we expanded the polynomial.

The linear combination of u and v = <3,-27>=5U+4V.

A linear combination of two or more vectors is the vector formed by multiplying two or more vectors (with distinct directions) by scalar values. The above equation demonstrates that the vector is produced by adding two vectors to three vectors.

The term "linear" has two independent meanings: geometric and algebraic. Because linear combinations essentially linear in the both senses, the expression is accurate.

Let u= <3,3> and v= <-3,3>

<3,-27> = x< 3,3> + y<-3,3> = <3x - 3y, 3x + 3y>

3x - 3y = 3 => x - y = 1

3x + 3y = -27 => x + y = -9

Adding both, we get

2x = -8 => x = -4

y = -5

So <3,-27> = -4< 3, 3 > + (-5) < -3 , 3 >

The linear combination of u and v = <3,-27>=5U+4V.

To know more about vectors visit:

https://brainly.com/question/1563531

#SPJ4

I understand that the question you are looking for is:

A sum of scalar multiples of two vectors (such as au + bv, where a and b are scalars) is called a linear combination of the vectors.

Let u= <3,3> and v= <-3,3>. Express <3,-27> as a linear combination of u and v.

Answer:

the coordinates of BB would be: B(8,1)

Answer:

2.667

Step-by-step explanation:

the thousandths place is the third place after the decimal point, going

0.123

1 is the tenths

2 is the hundredths

3 is the thousands

all you have to do is divide 4 by 15 to get 2.66666667

rounded to the thousands the answer is about 2.667

Answer:the answer is 8n hope that helps!

34.3 Km /h was her average velocity in km/h.

What is average velocity?

average velocity = Displacement / time taken

            V = d/ l

V = 10.3 Km/0.300m = 34.3Km

Learn more about average velocity

brainly.com/question/862972

#SPJ4

Answer: When students register online, the question appears in a pop-up window that must be answered in order to proceed with registering. If students register in person, make them answer the question before their registration is processed.

Step-by-step explanation:

Answer:

From top to the bottom:

Acute,

Right,

Straight

Step-by-step explanation:

An acute angle is formed when the measure of the angle is smaller than 90° which is provided in te first image.

A right angle is formed when the measure of an angle is precisely 90° which we can see in the second image.

A straight angle is formed when the measure of an angle is precisely 180° no less no more, which we can see in the last image.