If a barrel has the capacity to hold 75 gallons how many gallons does it contain when it is 3/5 full

Answer:

P ≈ 0,94

Step-by-step explanation:

The normal deck of cards consists of  52 cards, (with 4 kings )

If we take a king a deck will have 51 cards ( three kings )

The probability to get a non-king card is

Probability of non-king card (P)  = 1 - Probability of getting a king card (P₁)

Probability of getting a king card  P₁= 3/51 ≈ 0,059

Then P = 1 - 0,059

P ≈ 0,94

Answer:

  {30}

Step-by-step explanation:

The solution set can be written a couple of ways:

Roster: lists the elements of the set:

  x = {30}

Set builder notation: defines the elements of the set according to some rule or rules

  {x : x = 30}

The latter form can have variations that define the domain of x on the left, such as

  [tex]\{x\in\mathbb{Z}:x=30\}[/tex]

This is pronounced, "x is an element of the set of integers such that x is equal to 30." This sort of notation is more commonly used when the set is specified by an inequality or a functional relationship. You may see the colon (:) replaced by a vertical bar (|).

_____

Comment on the above notations

I don't like the notation x = {30} because the solution to the equation is a value, not a set of values. I prefer to write it as x ∈ {30}. "x is an element of the set containing 30." The "is an element of" symbol (∈) is not always available, so the equal sign is often used instead.

Answer:

corporate team-building event cost will cost $98

Step-by-step explanation:

A corporate team-building event costs $32, plus an additional $1 per attendee.

Let cost be C

The expression for the above statement

C($)= 32+n(1)

Where n is the number of attendees

So a situation where there are 66 attendees, the total cost will be

C($) = 32 +66(1)

C($) = 32+66

C($)= 98

Answer:

                              Twins in Family History           Twins not in Family History

Twins Born                          0.06                                            0.03

Single child born                 0.94                                            0.97

Answer: x - 5/x + 1

Step-by-step explanation:

This algebraic fraction

The task to be performed here is factorisation and simplification. Now going by the question,

x² + 4x - 45/x² + 10x + 9, the factorisation of

x² + 4x - 45 = x² + 9x - 5x - 45

= x(x + 9 ) - 5(x + 9 )

= ( x + 9 )(x - 5 ), don't forget this is the algebraic fraction's Numerator

The second part

x² + 10x + 9 = x² + x + 9x + 9

= x(x + 1) + 9( x + 1 )

= ( x + 9 )( x + 1 ), this is the algebraic denominator.

Now place the second expression which is the denominator under the first expression which is the numerator.

( x + 9 )( x - 5 )/( x + 9 )( x + 1 ).

You can see that, ( x + 9 )/( x + 9 ) divide each other , therefore therr then cancelled and left with

x - 5/x + 1

Answer:

1. $6.00 to 95 cents  = 6.32

2. 3 hours to 35 minutes  = 5.14

3. 42 inches to 2 feet = 1.75

Step-by-step explanation:

Given

$6.00 to 95 cents

3 hours to 35 minutes

42 inches to 2 feet

Required

Express in 2 decimal places

1. $6.00 to 95 cents

Express as ratio

[tex]\$6.00 : 95\ cents[/tex]

Convert dollars to cents

[tex]6.00 * 100\ cents: 95\ cents[/tex]

[tex]600\ cents: 95\ cents[/tex]

Convert ratio to division

[tex]\frac{600\ cents}{95\ cents}[/tex]

[tex]6.31578947368[/tex]

Approximate

[tex]6.32[/tex]

2. 3 hours to 35 minutes

Express as ratio

[tex]3\ hours : 35\ minutes[/tex]

Convert hours to minutes

[tex]3 * 60\ minutes: 35\ minutes[/tex]

[tex]180\ minutes: 35\ minutes[/tex]

Convert ratio to division

[tex]\frac{180\ minutes}{35\ minutes}[/tex]

[tex]5.14285714286[/tex]

Approximate

[tex]5.14[/tex]

3. 42 inches to 2 feet

Express as ratio

[tex]42\ inches: 2\ feet[/tex]

Convert feet to inches

[tex]42\ inches:2 * 12\ inches[/tex]

[tex]42\ inches : 24\ inches[/tex]

Convert ratio to division

[tex]\frac{42\ inches}{24\ inches}[/tex]

[tex]1.75[/tex]

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{(x - 7)(x - 6)}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ {x}^{2} - 13x + 42 }[/tex]

Here, we have to find the two numbers that adds to 13 and multiplies to 42.

The numbers are 7 and 6

[tex] \sf{ {x}^{2} - (7 + 6)x + 42}[/tex]

⇒[tex] \sf{ {x}^{2} - 7x - 6x + 42}[/tex]

Factor out x from the expression

⇒[tex] \sf{x(x - 7) - 6x + 42}[/tex]

Factor out 6 from the expression

⇒[tex] \sf{x(x - 7) - 6(x - 7)}[/tex]

Factor out x - 7 from the expression

⇒[tex] \sf{(x - 7)(x - 6)}[/tex]

Hope I helped!

Best regards!!

Answer:

x-7 For AP EX peeps

Step-by-step explanation:

Answer:

6.5

Step-by-step explanation:

The midpoint of the line is (-1,7). If you draw a line between that and (1.6), you’ll pass through the y-axis at 6.5.

Answer:

y-intercept =6.5

Step-by-step explanation:

First , lets find the slope

[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-3,\:8\right),\:\left(x_2,\:y_2\right)=\left(1,\:6\right)\\m=\frac{6-8}{1-\left(-3\right)}\\\\Refine\\m=-\frac{1}{2}[/tex]

[tex](-3,8) =(x_1,y_1)\\m =-\frac{1}{2} \\\\[/tex]

Plug in values point point slope form

[tex]y-y_1=m(x-x_1)\\\\y -8=-\frac{1}{2} (x-(-3))\\\\y - 8 =-\frac{1}{2} (x+3)\\\\y -8= -\frac{1}{2} x -\frac{3}{2} \\\\y =-\frac{1}{2} x - \frac{3}{2} +8\\\\y = -\frac{1}{2}x +\frac{13}{2} \\y =\:mx\:+\:b[/tex]

Where b = y-intercept

y-intercept =[tex]\frac{13}{2}[/tex]

Answer:

Rectangle: 27

Triangle: 39

Step-by-step explanation:

To find the perimeter of a rectangle use the expression P = 2(l + w)

Before substituting 4.5 for x simplify the equation

2((-3 + x) + 1/2(4x + 6)) = P

First simplify in the parenthesis

2(-3 + x + 2x + 3) = P

Now combine like terms, then multiply 2 and 3x

2(3x) = P

P = 6x

Lastly substitute 4.5 for x to find the perimeter

P = 6(4.5)

P = 27

Now do the same thing that we did with the rectangle but with a triangle

P = a + b + c

(3x - 4) + (3x - 4) + 2/3(6x + 3) = P

10x - 6 = P

10(4.5) - 6 = P

P = 39

Answer:

The north campus had [tex]800[/tex] while the south campus had [tex]200[/tex].

Step-by-step explanation:

The question stated that there are [tex]1000[/tex] students in the merged campus. That's the sum of the number of students in the north and the south campus before the merger.

Let [tex]x[/tex] denote the number of students in the north campus before the merger. The other [tex](1000 -x)[/tex] students would all belong to the south campus before the merger.

Before the merger, [tex]20\%[/tex] of the students of the north campus are of music majors. In terms of [tex]x[/tex], that's [tex](20\%)\cdot x = 0.20\,x[/tex] students.

On the other hand, [tex]70\%[/tex] of the students of the south campus are of music majors. That corresponds to [tex](70\%)\cdot (1000 - x) = 0.70\cdot (1000 - x) = 700 - 0.70\, x[/tex] students.

With a similar logic, the number of music students in the merged east campus will be [tex]30\% \times 1000 = 300[/tex].

The question implies that the sum of students in the two campuses should be equal to the number of music students in the east campus. That is:

[tex]0.20\, x+ (700 - 0.70\, x) = 300[/tex].

Solve for [tex]x[/tex]:

[tex]x = 800[/tex].

In other words, there are [tex]800[/tex] students in the north campus and [tex](1000 - 800) = 200[/tex] students in the south campus before the merger.

Answer:

A. (14 – 7)n – 55

Step-by-step explanation:

it cost $14 to make so $14 - $7 to make then you have to advertise it AFTER and it takes more money to advertise so, -55 so the answer would be:

(14 – 7)n – 55

Answer:

When added together, the sum of the given functions have a value of -6.

Step-by-step explanation:

When we see f(-2), it means that our value of x for the f(x) function is -2. When we see g(5), it means that our value of x for the g(x) function is 5. So, let's use this information and plug it into our equation.

f(-2) + f(5) = (3(-2) - 1) + (-(5) + 6)

Multiply 3 by -2 and distribute the negative to 5.

f(-2) + f(5) = (-6 - 1) + (-5 + 6)

Subtract 1 from -6 and add 6 to -5.

f(-2) + f(5) = (-7) + (1)

Add 1 to -7.

f(-2) + f(5) = -6

So, when added, the sum of the functions is -6.

Answer:21

Step-by-step explanation:

Answer:

5 - n^2

Step-by-step explanation:

Represent the unknown number by n.  Then the desired expression is:

5 - n^2

Expressing the problem as a mathematical equation, the required expression ls n² - 5

Let the number = n ;

The square of the number, n = n²

Subtracting 5 from the squared Value of the number n² ;

The expression becomes ; n² - 5

Therefore, the required expression which expresses 5 minus the square of a number is n² - 5

Learn more : https://brainly.com/question/15165519

Answer:

9m - 2

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

-5m - 2(1 - 7m)

Step 2: Distribute -2

-5m - 2 + 14m

Step 3: Combine like terms

9m - 2

Answer: 32.202

or 32.20

or 32.2



Answer:

The volume of the space between the balls and the rectangular box is [tex]4r^{3}(6 - \pi)[/tex]

Step-by-step explanation:

The attachment below shows the description of the rectangular bow and the three spherical balls.

From the description,  

This means the balls are tightly fitted into the rectangular box.

Each of the balls has a radius r

Hence, The volume of one of the balls is given by the volume of a sphere

[tex]Volume of a sphere = \frac{4}{3} \pi r^{3} \\[/tex]

The volume occupied by one of the balls is [tex]\frac{4}{3} \pi r^{3} \\[/tex]

∴ The volume occupied by the three spherical balls will be

3 × [tex]\frac{4}{3} \pi r^{3} \\[/tex]

= [tex]4\pi r^{3}[/tex]

The volume occupied by the three spherical balls [tex]4\pi r^{3}[/tex]

For the rectangular box,

The volume of a rectangular box = [tex]l w h[/tex]

Where [tex]l\\[/tex] is the length

[tex]w[/tex] is the width and

[tex]h[/tex] is the height

Since the balls are tightly packed,

The width of the rectangular box will be the diameter of the balls

diameter of the balls = 2r

∴ [tex]w[/tex] = 2r

The height of the rectangular box will also be the diameter of the balls

∴ [tex]h[/tex] = 2r

The length of the rectangular box will be 3 times the diameter of the balls

∴[tex]l[/tex] = 3 × 2r = 6r

Hence,

The volume of a rectangular box = 6r × 2r × 2r

= 24r³

The volume of the space between the balls and the rectangular box is given by

Volume of the space between the balls and the rectangular box =

volume of the rectangular box -  volume occupied by the three spherical balls

Volume of the space between the balls and the rectangular box= 24r³ - 4πr³

=  24r³ - 4πr³

= 4r³(6 - π)

Answer:

Following are the answer to the given choices:  

Step-by-step explanation:

In potion A:

The model, that will be formed can be defined as follows:

[tex]\widehat{W age} = \hat b_{0} + \hat b_{1} x Y_{rs} \epsilon done \\\\ \hat B_1 = \frac{\sum_{i=1}^{n} (W_{age}i - \widehat{W age} \times (Y_{rs} Edui - \widehat{Y_{rs}\epsilon})}{\int S_{yrs}\epsilon dre}\\[/tex]

[tex]\ the \ new \ W_{age} = 10^{-3} \times W_{age} \\\\\hat {B_{1 new}} = 10^{-3} \hat {B}\\\\ \hat{B_{0}} = \widehat{W age} -\hat {B_1} \bar{Y_{rs}\epsilon dus} \\\\\hat{B_{0 \ new}} = \widehat{W age} \times 10^{-3} - 10^{-3} \hat {B_1} Y_{rs}\epsilon dus \\[/tex]

           [tex]= 10^{-3} \hat {B_0}\\[/tex]

[tex]\hat B_{0 \ new} = 15 \times 10^{-3} \\\hat B_{1 \ new} = 0.28 \times 10^{-3} \\[/tex]

In potion B:

[tex]\ The \ new \ Y_{rs}\epsilon dus = \frac{Y_{rs} \epsilon dus}{7} \\\hat b_{1 \ new} = 7 \hat b_1\\\hat b_{ 0 \ new } = \widehat{W_{age}} - 7 \hat b_1 \times \frac{\bar Y_{rs}\epsilon dus}{7} \\\hat b_{0 \ new} = \hat B_{0}\\\hat b_{0} = 15.00 \\\hat b_{1} = 0.04 \\[/tex]

In potion C:

[tex]\ Y_{rs}\epsilon dus \ new = \frac{Y_{rs} \epsilon dus}{180} \\\\\widehat{W_{age} new} = \widehat{W_{age}} \times 10^{-2} \\\\\hat b_{1 \ new} = \hat b_{1} \times 10^{-2} \times 180 = \hat b_1 \times 1.8 \\\\\ hat b_{ 0 \ new } = 10^{-2} \widehat{W_{age}} - \hat b_1 \times 1.8 \times \frac{\bar Y_{rs}\epsilon dus}{180} \\\\[/tex]

               [tex]= 10^{-2} \ \hat B_{0}\\[/tex]

[tex]\hat b_{0 \ new} = 0.15 \\\hat b_{1 \ new} = 0.504 \\[/tex]

Answer:

Step-by-step explanation:

Part A. The total length of a line segment is the sum of the lengths of its parts.

  AM +MB = AB

Substituting the given information, this equation becomes ...

  (7x +8) cm + (9x -8) cm = 128 cm

  16x = 128 . . . . . . . . . collect terms, divide by cm

  x = 128/16 . . . . . divide by the coefficient of x

  x = 8

__

Part B. Then the length of AM is ...

  AM = (7x +8) cm = (7(8) +8) cm = (56 +8) cm

  AM = 64 cm

__

Part C. The length of BM is ...

  BM = (9x -8) cm = (9(8) -8) cm = (72 -8) cm

  BM = 64 cm

__

Part D. AM = BM = 64 cm, so point M is the midpoint of AB. Point M divides the segment into two equal parts.

While the letter grade to numerical contribution for a single subject is ordinal, the moment you compute a grade point average you already treated it as interval at that moment (otherwise you have no basis on which to assert that A+C = B+B).

Answer:

General rule of thumb: if you can add it, it's quantitative. For example, a G.P.A. of 3.3 and a G.P.A. of 4.0 can be added together (3.3 + 4.0 = 7.3), so that means it's quantitative. While the letter grade to numerical contribution for a single subject is ordinal, the moment you compute a grade point average you already treated it as interval at that moment

Answer:

Space in inches= 22 inches

Step-by-step explanation:

bedroom wall is 138 inches inches inches wide.

want to hang two posters, each 36 inches inches across, with an equal space between each poster and the wall edges

Total space remaining= 138-(36*2)

Total space remaining=138-72

Total space remaining= 66

To hang the posters to have equal spacing from the egde and between each other, let's bear in mind that we have 3 partions..

Space in inches= 66/3

Space in inches= 22 inches

Answer:

Step-by-step explanation:

5/8

Answer:  5/8

Step-by-step explanation:

Well if 5  of the 8 students in total are boys then the fraction will be 5/8  because is the number of boys out of the total people.

This question is incomplete, the complete question is;

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis

Answer:

V = π (512/15)

Step-by-step explanation:

Given that;

region of rotation

y² = 2x, x = 2y

Region is rotated about y-axis as shown in the image

for the point of intersection,

y²/2 = 2y

y² - 4y = 0

y(y-4) = 0

∴ y = 0, y = 4

so the region lies in 0 ≤ y ≤ 4

Now cross section area of washer is

A(y) = π(outer radius)² = π(inner radius)²

A(y) = π(2y)² - π(y²/2)²

A(y) = π(4y²) - π(y⁴/4)

A(y) = π(4y² - (y⁴/4))

now volume of the solid of revolution is

V = ⁴∫₀ A(y) dy

V = ⁴∫₀ π(4y² - (y⁴/4))dy

V =  π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }

V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }

V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }

V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }

V = π { 256/3 - 1024/20 }

V = π { (5120 - 3072) / 60 }

V = π (512/15)

Answer:

2 dollars

Step-by-step explanation:

if 8 limes costs 2 dollars, then 4 limes cost 1 dollar

you purchased 12 limes so since you already know what 8 limes coms, you could subtract that

12-8=4

now you need to find out how much for 4 limes which would be half the price of 8 limes.. which should be 1 dollar

so $2.00+$1.00= $3.00

finally 5 dollars minus 3 would result in a change of 2 dollars

Answer:

  551/1

Step-by-step explanation:

  [tex]551 = \dfrac{551}{1}[/tex]

__

Any integer can be written as a rational number with a denominator of 1.