What a scale drawing a tree is 4 inches tall the scale factor is 1:24. Find the actual height

There are [tex]\binom{52}4[/tex] ways of drawing a 4-card hand, where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient.

There are 13 different card values, of which we want the hand to represent 4 values, so there are [tex]\binom{13}4[/tex] ways of meeting this requirement.

For each card value, there are 4 choices of suit, of which we only pick 1, so there are [tex]\binom41[/tex] ways of picking a card of any given value. We draw 4 cards from the deck, so there are [tex]\binom41^4[/tex] possible hands in which each card has a different value.

Then there are [tex]\binom{13}4 \binom41^4[/tex] total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is

[tex]\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761[/tex]

the awnser is B x-2                    

Answer:

y = 3/2x + 7/2

Step-by-step explanation:

Slope-intercept form is when y is the subject. So we make y the subject:

Add 3x to both sides :

2y = 3x + 7

Now we divide both sides by 2 :

y = 3/2x + 7/2

This is our final answer.

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We are asked to write the equation -3x+2y=7 in slope-intercept form.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So let's write this equation, -3x+2y=7, in slope-intercept form...

///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\///\\\////\\\///\\\///\\\////\\\\////\\\\

First, we add -3x to both sides of the equal sign:

[tex]\large\pmb{2y=7+3x}[/tex]

We can switch the order of the terms:

[tex]\large\pmb{2y=3x+7}[/tex]

This is starting to look like the slope-intercept equation. In fact, all we have to do is divide both sides by 2:

[tex]\large\pmb{y=(3x+7)\div2}[/tex]

Which simplifies to...

[tex]\large\pmb{y=\cfrac{3}{2}x+\cfrac{7}{2}}[/tex]

That's the equation in slope-intercept form.

Hope this helps you out! :D

Ask in comments if any queries arise.

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An equation is formed of two equal expressions. The number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let c represent the cost of a phone plan, m represent the number of months, and g represent the number of gigabytes of data used each month.

Equation1: C = 40m + 3.5mg = (40+3.5g)m

Equation2: C = 75m + 0.5mg = (75+0.5g)m

Equating C,

(40+3.5g)m = (75+0.5g)m

40 + 3.5g = 75 + 0.5g

3g = 35

g = 11.6667 gigabyte of data per month

Hence, the number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.

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Answer: 10

Step-by-step explanation:

By definition, the point at which a median intersects the side of the triangle opposite from the vertex from which it is drawn is the midpoint of that side.

Answer:

h = 19

Step-by-step explanation:

The are is given so we can use the area to find the height because the area of a trapezoid is calculated by the following formula:

1/2 * (a+b)*h (a: base, b: base, h: height)

We already know the bases; 37 and 51

1/2*(37+51)*h = 836 first multiply both sides by 2

(37+51)*h = 1672 now divide both sides by 88 (sum of bases)

h = 19

Answer:

12 or 7??

Step-by-step explanation:

it depends if they are being spinned at the same time because then you can get for eg. 'A,1' 'A2' etc.

Answer:

As a fraction:

x | y

________

|

7/3 | 2

3 | 4

11/3 | 6

13/3 | 8

As a mixed fraction:

x | y

________

|

2 ⅓ | 2

3 | 4

3 ⅔ | 6

4 ⅓ | 8

As a decimal:

x | y

___________

|

2.33.. | 2

3 | 4

3.66.. | 6

4.33.. | 8

You should start with x values since the y values will be easier to plot. x's will not be easy to represent.

For example:

x | y

________

|

0 | -5

1 | -2

2 | 1

3 | 4

4 | 7

5 | 10

Answer:

49,64

Step-by-step explanation:

Every time the number changes there is an addition of two. for instance, from 4 to 9 the was an addition of 5 and from 9 to 16 there was an addition of 7. Thats how it works

Answer:

step1:add 3y to both sides

step2:add 4 to both sides

step3:multiply both sides by(1/5)

14/15

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

You didn't include the choices but here is a solution

tan 68 = opp/adj = height / 13

13 Tan 68  = height of pole

Supplementary Angles:

[tex]\boxed{100°} and \boxed{80°}[/tex]

Arithmetically speaking, the closest 2 supplementary angles can get (in 3 and 2 digits respectively) is the upwritten.

Complementary Angles:

[tex]\boxed{45°} and \boxed{45°}[/tex]

Simply, in this case, for angles to be numerically as close as possible - make both the angles 45°.

Circumference = diameter x PI

Circumference = 8 in x Pi

Circumference = 8PI in. (Exact)

Or as a decimal answer: 25.12 in.

Answer:

25.1 in (nearest tenth)

Step-by-step explanation:

Formula

Circumference = πd  (where d is the diameter)

From inspection of the diagram:

⇒ Circumference = 8π

                             = 25.1 in (nearest tenth)

Answer:

Given:

Cylinder: height = 16 cm ; radius = 5 cm

cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³

Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³ 

Answer:

d

Step-by-step explanation:

the length is how many units greater than twice the width ?

you skipped that information from us.

so, all we can say

length = 2×width + x

the perimeter is

2×length + 2×width

with width = w we get by using the first equating in the second :

2×(2×w + x) + 2×w = 4w +2x + 2w = 6w + 2x

so the right answer must be d.

it is the only option with "6w".

it means that 2x = 5 and x = 2.5.

so it was that the length is 2.5 units greater than twice the width

Answer:

  (b)  domain: {-2, 0, 2}, range: {-1, 0, 1}

Step-by-step explanation:

For the function defined by the table ...

  [tex]\begin{array}{|cccc|}\cline{1-4}x&-2&0&2\\\cline{1-4}y&-1&0&1\\\cline{1-4}\end{array}[/tex]

we want the function's domain and range.

__

The domain is the list of x-values for which the function is defined. Here, that list is ...

  domain = {-2, 0, 2}

__

The range is the list of y-values the function produces. Here, that list is ...

  range = {-1, 0, 1}

_____

The domain and range sets are most conveniently listed in order, with duplicates removed.

Answer:

Add and Divide.

Mean = 84

Step-by-step explanation:

Mean ( math word) and average (common usage word) tell us to ADD up the numbers in the list of data and DIVIDE by the number of pieces of data.

Here we add:

(80 + 84 + 88)

then divide by 3, because there's 3 numbers in this list.

(80 + 84 + 88)/3

= 252/3

= 84

The mean, or average is 84.

The summation notation is ∑ [tex](4^{n} -1)\\[/tex]/2.

The common ratio multiplied here to each term to get the next term is a non-zero number.

Given:  1/2+2+8+32+128

Using,

[tex]a_n= a_1r^{n-1}[/tex]

We have,

a1 =1/2 and r= 4

notation is : An= ∑ [tex](4^{n} -1)\\[/tex]/2

Hence, the notation is  An= ∑ [tex](4^{n} -1)\\[/tex]/2.

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A fraction is a way to describe a part of a whole. The quotient of the fraction is 1/(t+4)².

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The quotient of  [tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}[/tex] can be found by factorizing the denominator of the fraction. Therefore, the factors of the denominator are,

t² + 7t + 12

= t² + 4t + 3t + 12

= t(t+4) +3(t+4)

= (t+4)(t+3)

Now, quotient will be,

[tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\\\\\\=\dfrac{\dfrac{t+3}{t+4}}{(t+4)(t+3)}\\\\\\=\dfrac{(t+3)}{(t+4)(t+3)(t+4)}\\\\\\= \dfrac1{(t+4)^2}[/tex]

Hence, the quotient of the fraction is 1/(t+4)².

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Answer:

x = 10/3

x = -3

Step-by-step explanation:

3x² - x = 30

3x² - x - 30 = 0

multiply 3 and -30 which =

-90

what are 2 numbers that when multiplied make

-90

and that when added make

-1

(-1 is the number in -x in the equation)

they are the numbers 9 and 10

namely -10 and +9

3(x-10/3)(x+9/3)=0

divide both sides by 3

(x-10/3)(x+9/3)=0

then split factors being multiplied

(x-10/3)=0

(x+9/3)=0

x = 10/3

x = - 9/3 = -3

Answer:

-∞ < y ∞

The range is all real numbers.

to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]

[tex]a\cdot a^2+b\cdot a+c=a^3+ab+c[/tex]

Answer:

AB=CD and BC=AD because both of them are visually paired with the same longitude.

Answer:

AB = CD, BC = AD

Step-by-step explanation:

According to parallelogram properties,

Angle A = 180-Angle B; False
AB!=BC; False

AC==BD is only true when AB = BC, False
AB ==CD, BC == AD; True

Answer: rectangle

Step-by-step explanation:

The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.

To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.

[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]

So, the most specific classification is a rectangle

The correct answer is option C which is  [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.

The multiplication of the matrix will be calculated as:-

M = [tex]\dfrac{1}{2}\left[\begin{array}{cc}12&64&\\78&30&\\\end{array}\right][/tex]

M  =    [tex]\left[\begin{array}{cc}\dfrac{12}{2}&\dfrac{64}{2}&\\\dfrac{78}{2}&\dfrac{30}{2}&\\\end{array}\right][/tex]

M =     [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

Therefore the correct answer is option C which is  [tex]\left[\begin{array}{cc}8&32\\39&15&\\\end{array}\right][/tex].

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-3}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-3x+6\implies y=-3x+10[/tex]

[tex]-4(4x-6)=3(-7x-1)[/tex]

[tex]-16x+24=3\left(-7x-1\right) [/tex]

[tex]-16x+24=-21x-3 [/tex]

[tex]-16x+24+21x=-3 [/tex]

[tex]5x+24=-3 [/tex]

[tex]5x=-3-24 [/tex]

[tex]5x=-27 [/tex]

[tex]x=\frac{-27}{5} [/tex]

[tex]x=-\frac{27}{5} [/tex]

Explanation:

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