A standard deck of 52 cards has 4 suits (spades, clubs, hearts, and diamonds) with 13 different cards (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) in each suit. If you are dealt exactly two cards from the deck without replacement, what is the probability that you are dealt a pair (matching cards in different suits)

Computing the limit directly:

[tex]\displaystyle\lim_{h\to0}\frac{f(2+h)-f(2)}h=\lim_{h\to0}\frac{((2+h)^2+(2+h)+1)-7}h\\\displaystyle=\lim_{h\to0}\frac{5h+h^2}h\\=\displaystyle\lim_{h\to0}(5+h)=\boxed{5}[/tex]

Alternatively, you can recognize the limit as being equivalent the derivative of f(x) at x = 2, in which case differentiating and plugging in 2 gives

f'(x) = 2x + 1   =>   f' (2) = 5

Problem 25

These triangles are congruent.

The reasoning is the AAS congruence theorem. We have two pairs of congruent angles, as shown by the arc markings, and a pair of congruent sides. The sides are not between the angles. That means AAS is slightly different from ASA. The order matters.

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Problem 26

The triangles are not congruent

Why not? Well it all comes down to the angle placement. For the triangle on the right side, the arc is between the shared segment and the segment with the double tickmarks. The other arc is not in the proper corresponding location to be able to use SAS. It would need to be adjacent to the arc on the right for us to use SAS.

If it's hard to visualize what I mean, refer to the diagram below.

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Problem 27

The triangles are congruent by SAS

The angles aren't marked, but recall that vertical angles are always congruent. So you could add in angle markers if you wanted, to help complete the diagram. The tickmarks of course tell us which segments are the same length. The angles are between the segments.

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Problem 28

The triangles are congruent by SSS

Like before, the tickmarks tell us which sides are the same length. So the tickmarks say that we have two pairs of congruent sides. The overlapping sides or shared sides are the third pair of congruent segments. So in reality, we have three pairs of congruent sides. It might help to break up the figure into two separate triangles.

Answer:

x=16.53cm

Step-by-step explanation:

1 liter = 1000 cm^3

The volume of water in the rectangular prism will be 11*11*x = 2000

121x=2000

x=2000/121

x=16.53cm

Answer:

[tex]99\% CI=4.1602 \pm 0.0009[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=8[/tex]

Mean [tex]\=x=4.1602[/tex]

Standard deviation [tex]\sigma=0.001gram[/tex]

Generally 99\% confidence from table  is mathematically given by

 [tex]99\% CI=4.1602 \pm *2.576*\frac{0.001}{\sqrt{{8}}}[/tex]

 [tex]P(-z<x<z)=0.99[/tex]

 [tex]Z_{\alpha/2}=2.576[/tex]

Generally the equation for 99\% confidence level (CI)  is mathematically given by

 [tex]99\% CI=\=x \pm Z_{\alpha/2*\frac{\sigma}{\sqrt{{n}}}[/tex]

 [tex]99\% CI=4.1602 \pm 0.0009[/tex]

Answer:

I only remember the funny thing my dad told me

9514 1404 393

Answer:

  (x, y) = (2, 1)

Step-by-step explanation:

The graph of these equations is attached. The solution is ...

  (x, y) = (2, 1)

Answer:

45

Step-by-step explanation:

9 ÷ 1/5

9 × 5/1

9 × 5

45

Answer:

The value of x in the triangle is 17.51

Option C is the correct answer.

We have,

From the figure,

We can use the tangent function.

This means,

Tan = perpendicular / Base

i.e

tan 35 = x / 25

0.700 = x / 25

x = 0.700 x 25

x = 17.5

Thus,

The value of x in the triangle is 17.51.

Learn more about trigonometric identities here:

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The value of x is 84 degrees.

The tangent line to a circle  at a given point is the straight line that just touches the circle at the point.

A tangent to a circle is perpendicular to the radius at the point of tangency.

According to the question

we have to find the value of x.

Let us assume that a circle have a center at O. And Mark the end of the given chord P and Q.

Connect OP and OQ.

here,

OP = OQ

⇒∠OQP = ∠QPO

Now in triangle POQ, we have

⇒∠QOP + 2∠ OPQ = 180

⇒168 +2∠OPQ =180

⇒2∠OPQ = 12

⇒∠OPQ =6 degrees.

As we know that, tangent to a circle is perpendicular to the radius at the point of tangency.

⇒ x + ∠QOP = 90

⇒ x + 6 = 90

⇒ x = 90-6 = 84 degrees.

Hence, value of x is 84 degrees.

Learn more about the tangent to the angle here:

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Answer:

C   y = 2sin(1/3) x

Step-by-step explanation:

It's a sin function since y = 0 at x = 0

The amplitude is 2

There are 2 cycles in 12π

so the period is 6π

The x coefficent is then 2π/6π  = 1/3

Answer

C   y = 2sin(1/3) x

Answer:

23x - 8 is the answer in simplify that expression

Answer:

[tex]3(7x)-2(4-x)[/tex]

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hope it helps...

have a great day!!

Answer:

3. pollution

4. the land becomes fertile

9514 1404 393

Answer:

  (b) 3x^2 +6x+4

Step-by-step explanation:

  (6x+7+x^2)+(2x^2-3)

  = (1 +2)x^2 +(6)x +(7 -3) . . . . combine like terms

  = 3x^2 +6x +4

Answer:

3x ² + 6x + 4

Step-by-step explanation:

( 6x + 7 + x² ) + ( 2x² -3 )

6x + 7 + x² + ( 2 x² - 3 )

6 x + 7 + x² + 2x ² - 3

6 x + 7 - 4 + x² + 2x²

6x + 4 + 3x²

3x ² + 6x + 4

Answer:

3.7821 (SDF)

Step-by-step explanation:

Take the number by 378 21 and place it in the right forms/place marks. Such as ones and tens place ect. Then there is your answer.

Answer:

x= 2, y= 5

Step-by-step explanation:

5x -4y= -10 -----(1)

3x +2y= 16 -----(2)

(2) ×2:

6x +4y= 32 -----(3)

(1) +(3):

5x -4y +6x +4y= -10 +32

11x= 22

x= 22 ÷11 (÷11 on both sides)

x= 2

Substitute x= 2 into (2):

3(2) +2y= 16

6 +2y= 16

2y= 16 -6

2y= 10

y= 10 ÷2

y= 5

Step-by-step explanation:

9/11=0.81818181....

the digits that repeat is 81

Answer:

.81 repeating

Step-by-step explanation:

9/11 = 0.81 repeating.

Answer:

Option C: 20 cm^2

Step-by-step explanation:

Essentially, surface area is just area added up. In this question, there are 4 same rectangles and 2 squares with the areas given. So you have to figure out the total.

Since there are 4 rectangles and each of them has an area of 4cm just multiply 4 by 4 to get 16.

Then, since there are 2 squares with an area of 2 cm each just multiply 2 by 2 to get 4.

Add both numbers, 16 + 4 = 20 and you get your answer.

The total surface area would be 20cm^2.

Answer:

A)$60

B)$9

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW

Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio

Cleopatra : Dalila : Ebony =

5 : 7 : 8

Cleopatra has $15.

A) How many dollars do they have in total?

B) Dalila spends 12$ on a hat, how many dollars does she have left?

A)

Total ratio=(5 +7 +8)= 20

Cleopatra has $15.

Let X = total money

Ratio of Cleopatra= 5/20 ×X=15

5X /20 = 15

5X= (15×20)

X= $60

They have $60 in total

B) ratio of Dalila= 7/20 × 60 = $21

But 12$ was spent by Dalila on a hat

Then Dalila will have ($21 - 12$) Left

= $9

Answer and Step-by-step explanation:

The answer is that A'C' will be 1.5 times longer than AC.

This is because you are dilating the figure by a scale of 1.5.

#teamtrese #PAW (Plant and Water)

Answer:

A = [12 + 9(pi)] yd^2 = 40.3 yd^2

Step-by-step explanation:

A = area of triangle + area of semicircle

A = bh/2 + (pi)r^2

A = (6 yd)(4 yd)/2 + (pi)(3 yd)^2

A = 12 yd^2 + 9(pi) yd^2

A = [12 + 9(pi)] yd^2 = 40.3 yd^2

Answer:

The scatter plot is attached in the image

There exists a positive linear relationship between the two variables i.e sales and advertisements.

Step-by-step explanation:

The scatter plot is attached in the image

There exists a positive linear relationship between the two variables i.e sales and advertisements.

Answer:

ans : option 2nd

Step-by-step explanation:

total angle substand perimeter of circle so,

so solve by using unitary methods

Answer:

Step-by-step explanation:

2, 6, 10, 14

Entonces, como puede ver, el patrón en la secuencia se suma por 4 como (+4)

(So, as you see that the pattern in the sequence is added by 4 )

2

2+4=6

6+4=10

10+4=14

Entonces, los próximos tres términos serán (Then, the next three terms will be)

14+4=18

18+4=22

22+4=26

Answer:

6/20 or in simplification, 3/10 would be the correct answer.

30% would also be correct :)

And 0.3

Answer:

I don't know for sure, but I'm pretty sure its 1,640.

Step-by-step explanation:

80% of 8,200 is 6560, and then do 8,200- 6,560, you get 1,640.

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According to question, The price at which it was sold is equal to :

The car was sold at $ 6560

Now, loss is equal to :

Answer:

111.35

Step-by-step explanation:

effective rate: .085/12= .00708333333333

[tex]3000=x\frac{1-(1+.00708333333333)^{-30}}{.00708333333333}\\x=111.35[/tex]

Answer:

33.5 kg

Step-by-step explanation:

Each 59 cans are about 1 kg.

He collected 1978 cans.

How many times 59 cans did he collect?

1978/59 = 33.5

He collected 1978 cans which is 33.52 times 59 cans, so he collected 33.5 kg

Answer:

143 degrees

Step-by-step explanation:

First find angle ACB which is 180-83=97

Then angle ABC which is 180-134=46

Then angle CAB (97+46)-180=37

Finally angle HAB 180-37=143

Answer:

The average rate of change between x = 2 and x = 4 is of 4.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function f(x) in an interval [a,b] is given by:

[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]

In this question:

[tex]f(x) = 4x - 2, b = 4, a = 2[/tex]

Thus:

[tex]f(b) = f(4) = 4(4) - 2 = 16 - 2 = 14[/tex]

[tex]f(a) = f(2) = 4(2) - 2 = 8 - 2 = 6[/tex]

Average rate of change:

[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]

[tex]A = \frac{14-6}{4-2}[/tex]

[tex]A = \frac{8}{2}[/tex]

[tex]A = 4[/tex]

The average rate of change between x = 2 and x = 4 is of 4.