Matthew has a standard deck of cards. There are four suits with 13 cards in each from ace through to king.

He shuffles the deck and selects one card and then another. In its simplest form, what is the probability that he draws a pair of tens?

Answer:

Area of 27" 4:3 screen = 349.92 square inches

Area of 27" 16:9 screen ≅ 311.5 square inches

Traditional 4:3 screen is larger

Step-by-step explanation:

The Traditional TVs is  larger than  LCD tv screen

The diagonal of a rectangle is a line segment that joins any two of its non-adjacent vertices.

The length of diagonals of a rectangle can be calculated as:

Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]

According to the question

The screen size of a television is determined by the length of the diagonal of the rectangular screen.

Traditional TVs

Ratio of the length to width =  4:3

Let a be the constant for both length and width

therefore

Length of Traditional TVs = 4a

Width of Traditional TVs = 3a

The area of a 27-inch traditional tv screen

i.e

Diagonal of Traditional TVs =  27

Now applying formula of diagonal of rectangle

Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]

substituting the values

27 = [tex]\sqrt{(4a)^{2} + (3a)^{2} }[/tex]

27 = [tex]\sqrt{16a^{2} + 9a^{2} }[/tex]

27 = [tex]\sqrt{25a^{2} }[/tex]

27 = ± 5a

a cannot be -ve

a = 5.4

now,

Length of Traditional TVs = 4* 5.4 = 21.6 inches

Width of Traditional TVs = 3 * 5.4 = 16.2 inches

Area of Traditional TVs = Length * width

                                       = 21.6 * 16.2

                                       = 349.92 [tex]inches^{2}[/tex]

LCD TVs

Ratio of the length to width =  16:9

Let a be the constant for both length and width

therefore

Length of LCD TVs = 16a

Width of LCD TVs = 9a

The area of a 27-inch LCD TVs screen

i.e

Diagonal of LCD TVs=  27

Now applying formula of diagonal of rectangle

Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]

substituting the values

27 = [tex]\sqrt{(16a)^{2} + (9a)^{2} }[/tex]

27 = [tex]\sqrt{256a^{2} + 81a^{2} }[/tex]

27 = [tex]\sqrt{337a^{2} }[/tex]

27 = ± 18.357a

a cannot be -ve

a = 1.47

now,

Length of LCD TVs = 16*1.47 = 23.53

Width of LCD TVs = 9*1.47 = 13.23

Area of Traditional TVs = Length * width

                                       = 21.6 * 16.2

                                       = 311.30 [tex]inches^{2}[/tex]

Hence, the Traditional TVs is  larger than  LCD tv screen .

To know more about diagonal of rectangle here:

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Answer:

[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]

Required

Select equivalent expression

[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]

Factorize the numerator and denominator

[tex]\frac{x(2x^2+11x-21)}{x(x+3)}[/tex]

Divide by x/x

[tex]\frac{2x^2+11x-21}{x+3}[/tex]

Expand the numerator

[tex]\frac{2x^2+14x-3x-21}{x+3}[/tex]

Factorize the numerator

[tex]\frac{2x(x+7)-3(x+7)}{x+3}[/tex]

[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]

Hence, the equivalent expression is:

[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]

Answer:

See the proof below

Step-by-step explanation:

Given the following coordinates

P(2, −1)

Midpoint of PQ M(3, 0)

We can get the coordinate point Q using the midpoint formula;

M(X,Y) = (x1+x2/2, y1+y2/2)

X = x1+x2/2

3 = 2+x2/2

6 = 2+x2

x2 = 6-2

x2 = 4

Y = y1+y2/2

0 = -1+y2/2

0 = -1 + y2

y2 = 0+1

y2 = 1

Hence the coordinate of Q is (4, 1)

Next is to get the coordinate of R

Given the midpoint of QR to be N(5, 3)

(5,3) = (4+x2/2, 1+y2/2)

5 = 4+x2/2

10 = 4+x2

x2 = 10-4

x2 = 6

1+y2/2 = 3

1+y2 = 6

y2 = 6-1

y2 = 5

Hence the coordinate of R is (6,5)

Given the coordinates M(3, 0) and N(5, 3)

Slope is expressed as:

m = y2-y1/x2-x1

m = 3-0/5-3

m = 3/2

Slope of MN = 3/2

Get the slope of PR

Given the coordinates P(2, −1) and R (6,5)

Slope of PR = 5-(-1)/6-2

Slope of PR = 5+1/4

Slope of PR = 6/4 = 3/2

Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR

To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:

For MN with coordinates  M(3, 0) and N(5, 3)

MN = √(x2-x1)²+(y2-y1)²

MN = √(5-3)²+(3-0)²

MN = √2²+3²

MN = √13

Get the length of PR where P(2, −1) and R (6,5)

PR = √(6-2)²+(5+1)²

PR = √4²+6²

PR = √16+36

PR = √52

PR = √4*13

PR = √4*√13

PR = 2√13

Since MN = √13

PR = 2MN

Divide both sides by 2

PR/2 = 2MN/2

PR/2 = MN

Hence MN = 1/2 PR (Proved!)

Answer:

1. fraction=51/94

decimal= 51/94 a decimal is approximate: 0.54255 (Rounded to fifth decimal place)

2. fraction= 2/8

decimal= 2/8 as a decimal is 0.25.

3. fraction= 75/5

decimal= 75/5 as a decimal is 15.

Answer:

sorry i could only answer the first one hope it helps as a decimal 0.54255

Step-by-step explanation:

aswdqr4f 4crd

Answer:

uuuuuuuuuuuuuummmmmmmmmmmmm what

Step-by-step explanation:

Answer:

Therefore, n is smaller than 26 (n < 26).

Step-by-step explanation:

First, you have to form an inequality. With the given informations, the inequality will be :

[tex]n - 6 < 20[/tex]

Next, you have to solve it, by adding 6 to both sides :

[tex]n - 6 < 20[/tex]

[tex]n - 6 + 6 < 20 + 6[/tex]

[tex]n < 26[/tex]

Answer:

N-6≤20 N≤26

Step-by-step explanation:

n-6≤20

n-6=20

  +6 +6

n≤26

Answer:

0.41 and 0.5 are both greater than .40 and less than .65

Step-by-step explanation:

9514 1404 393

Answer:

  120.8%

Step-by-step explanation:

Maybe you want to find $42,900 as a percentage of $35,500.

That is ...

  42900/35500 × 100% = 120.8%

__

Comment on the question

The question is easier to read if you don't shuffle the phrases. Copying and pasting often requires a check and edit step afterward.

Answer:

15

Step-by-step explanation:

3 2/4+ 2 3/4+ 2 3/4+ 2 1/4+ 1 1/4+ 1

first add the whole numbers so 3+2+2+2+1+2=12

then we are left with the fractions. 11/4 divides into 2 with a remainder of three so we add it to the top.

From here we have 2/4+3/4+3/4+1/4+3/4

add them together and we get 12/4=3. Then add back our whole numbes to get 12+3=15

Answer:

Yes, it is a function.

Step-by-step explanation:

As long as there are no more than one point in a single x-value, it is considered a function.

Answer:

the number of minutes of call when the two cost plans would be equivalent to each other is 175 minutes

Step-by-step explanation:

The computation of the number of minutes of call when the two cost plans would be equivalent to each other is shown below:

Let us assume the number of minutes be x

Now the equation is

$9 + 0.13x = $16 + $0.09x

0.13x - 0.09x = $16 - $9

0.04x = $7

x = $7 ÷ 0.04

= 175 minutes

Hence, the number of minutes of call when the two cost plans would be equivalent to each other is 175 minutes

Answer:

$41.69

Step-by-step explanation:

The computation of the selling price of the each pair of slacks is as follows:

Given that

Cost = $19.36 per pair  

Markup = $22.33

As we know that  

Markup = Sell Price - Cost

So,  

Sell Price = Cost + Markup

= $19.36 + $22.33

= $41.69

Hence, the selling price is $41.69

Using the decay constant on the exponential function, the mass of the sample that will be left in 2013 is 35g

An exponential function is a function that can be expressed in the form     f(x) = b^x, where b is a positive real number and x is a real number. The graph of an exponential function is a curve that increases or decreases rapidly as x increases or decreases.

here, we have,

In the exponential decay, the decay function can be given as;

y = ae⁻ⁿˣ

a = initial mass of sample

n = disintegration constant

x = time

The disintegration constant is also know as the rate of decay and we can calculate it as;

260 = 470e⁻ⁿ⁽³⁾

n = 0.197

n = 0.2

The disintegration constant is 0.2

The amount left in 2013 will be;

y = 470e⁻⁽⁰.²⁾⁽¹³⁾

y = 34.90

The mass in 2013 is 35g

Learn more on exponential function here;

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complete question:

A sample of a radioactive isotope had an initial mass of 470 mg in the year 2000 and decays exponentially over time. A measurement in the year 2003 found that the sample's mass had decayed to 260 mg. What would be the expected mass of the sample in the year 2013, to the nearest whole number?

Answer:

x^2 = 9^2-6^2 = 81-36 = 45

x = √45

UW = √45 ft

Answer:

It is 49

Step-by-step explanation:

multiply 12.25 by 4  since 1 inch is 12.25 and 4 inches times 12.25 is 49

Answer:

option 1

Step-by-step explanation:

because i am confident

Answer:

$6.76

Step-by-step explanation:

Answer:

3/16 pound

Step-by-step explanation:

hope it helps the picture show how its done

Answer:

132 degrees

Step-by-step explanation:

answer : 48 degrees

method

1. opposite angles are the same , so CFG os the same as GAC - these two added up are 132 + 132 = 264

2. angles add up to 360 in a quadrilateral , so the sum of the two remaining angles is 360 - 264 = 96

3. because the two remaining angles , ACF and FGA , are opposite , those are equal too. so u just half to get one of them : 96 / 2 = 48

Answer:

You have to answer to other question before answering this one, just in case anyone was confused

Step-by-step explanation:

Answer: 38  think

Step-by-step explanation:

Answer:

ok so

Step-by-step explanation:

874÷23=38

yw:)

Answer:

10 / 16

Step-by-step explanation:

10/16

5 x 2 = 10

8 x 2 = 16

Answer:

58% of 250 is 145.

Step-by-step explanation:

145 * 100/58

= 250

Answer:

250

Step-by-step explanation:

Answer: The system consists of parallel lines

Step-by-step explanation:

Given system of lines :

[tex]y=\dfrac13x-4[/tex]

[tex]3y-x=-7[/tex]

Substitute [tex]y=\dfrac13x-4[/tex] in [tex]3y-x=-7[/tex],  we get

[tex]3(\dfrac13x-4)-x=-7\\\\\Rightarrow\ x-12-x=-7\\\\\Rightarrow\ -12=-7[/tex] , which is not true.

That means , system has no solution.

i.e. they are representing parallel lines. [Parallel lines do not intersect and hence they do not have solution.]

Answer:

2 1/2 or 2 and a half

Step-by-step explanation:

if you divide it it will come out to be that (I hope its right but i don't know if it is

Answer to this question: "A kangaroo hops 2 kilometers in 3 minutes at this rate how far does the kangaroo travel in 2 minutes"

2.50

Answer: F is 11m.

Step-by-step explanation: Because H,I,G are all increasing their numbers like plus 3, plus 2, and the last one has to be plus 1.

Answer:

z(s) =  - 2,15 We accept H₀

Step-by-step explanation:

Assume Normal Distribution.

Sample size                  n = 290

Sample mean               μ = 7,6

Sample standard deviation   s = 0,8

Level of significance  0,02   ( CI = 98 % )

population mean  μ₀ = 7,5

α = 0,02       the valve could fail under and above the spec value ( 7,6 ) therefore we must develop a two-tail test

α/2  =  0,01

Hypothesis Test

Null hypothesis                                      H₀       μ   =  μ₀

Alternative Hypothesis                         Hₐ        μ   ≠  μ₀

for  α  =  0,01    z(c)  = - 2,3

To calculate  z(s)

z(s)  =  ( μ   -  μ₀ ) / s/√n

z(s)  =  ( 7,5 - 7,6 ) /0,8/√290

z(s) = - 0,1 * 17 /0,8

z(s) =  - 1,7 / 0,8

z(s) =  - 2,15

Comparing   z(s)  and  z(c)

- 2, 15  < - 2,3

|z(s)|  <  | z(c)|

Then z(s) is in the acceptance region. We don´t have evidence to reject H₀