The angle measurements in the diagram are represented by the following expressions

In a given permutation of 52 cards, if the 3 of spades is to follow all of the hearts, that means the 3 of spades must be at least the 14th card in the deck.

Consider some possible orderings of the deck:

• If the 3 of spades is the 14th card, then the deck looks like

[all 13 ♥] … 3 ♠ … [all other 38 cards]

There are 13! ways to arrange the 13 hearts at the beginning and 38! ways to arrange the tail of 38 cards. Hence there are 13! × 38! possible rearrangements of the deck where 3 ♠ is the 14th card.

• If 3 ♠ is the 15th card, then the deck looks like

[13 ♥ and 1 other] … 3 ♠ … [all other 37 cards]

and there would be 14! × 37! ways of arranging the cards in this order.

There are 39 possible positions for 3 ♠. Extrapolating, it follows that the total number of permutations of the deck in which all hearts occur before 3 ♠ is

[tex]\displaystyle \sum_{k=0}^{38} (13+k)! \times (38-k)![/tex]

There are 52! total possible ways of rearranging the deck. Then the probability of rearranging the deck so that all hearts are drawn before 3 ♠ is

[tex]\displaystyle \frac1{52!} \sum_{k=0}^{38} (13+k)! \times (38-k)! = \frac{87,031,512,096,420,449}{221,360,321,731,856,907,600} \approx \boxed{0.000393}[/tex]

Answer:

Step-by-step explanation:

y is a function of x . TRUE

The graph of the relationship is a line.  TRUE

The graph of the relationship passes through the origin.  - it in standard form, when you plugin 0 for x or y, you get the other intersect( x-intercept: (12/-5,0) y-intercept: (0,4)) so it dosent go throught the origin. FALSE

When the input is 6, the output is 14. TRUE

-5(6)+3(14)=12

-30+42=12

12=12

Answer:

y is a function-TRUE

The graph of the relationship is a line-TRUE

The graph of the relationship passes through the origin-FALSE

When the input is 6, the output is 14-TRUE

Answer:

m - 46 = 54

Step-by-step explanation:

46 less than m is 54,

→ m - 46 = 54

Let's solve this equation,

→ m - 46 = 54

→ m = 54 + 46

→ [ m = 100 ]

So, the answer is 100.

Answer:

Step-by-step explanation:

[tex]\sqrt{\frac{7}{8} } = \sqrt{\frac{7}{8}*\frac{8}{8}[/tex]

= sqrt(56)/8

Answer:

  (√14)/4

Step-by-step explanation:

You can "rationalize the denominator" after you take the root, or you can make the denominator a perfect square before you take the root.

  [tex]\sqrt{\dfrac{7}{8}}=\dfrac{\sqrt{7}}{2\sqrt{2}}=\dfrac{\sqrt{7}}{2\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{14}}{4}\\\\\sqrt{\dfrac{7}{8}}=\sqrt{\dfrac{7}{8}\cdot\dfrac{2}{2}}=\sqrt{\dfrac{14}{16}}=\dfrac{\sqrt{14}}{4}[/tex]

Answer:

the answer is 3x as that is the slope

Answer:

3

Step-by-step explanation:

yeah < 3

Answer:

the answer is 10,700 :)

Step-by-step explanation:

Answer:

$5.16

Step-by-step explanation:

$25.80 x 20/100

Answer:

Step-by-step explanation:

Answer:

Tip Total: $ 5.16

Tip Each Person: $ 2.58

Total (Bill + Tip): $ 30.96

Total Each Person: $ 15.48

Answer:

see explanation

Step-by-step explanation:

Her error is in squaring (2y)²

She has (2y)² = 2y²

when it should be 2y × 2y = 4y²

Then

(2y)² = 6² + 8²

4y² = 36 + 64

4y² = 100 ( divide both sides by 4 )

y² = 25 ( take square root of both sides )

y = [tex]\sqrt{25}[/tex] = 5

Answer: 15 students in her second class.

Step-by-step explanation:

Let A, B, and C stand for the number of students in each class. See the attached table.

The column labelled "Students" is formed by assinging B to the second class and finding how the other two classes relate to B. Class A has twice as many students as class B, so A = 2B. Class C has 5 more students than B, so C = B+5.

The total students amount to 65, whcih is the sum of A, B, and C:

A + B + C = 65

Substitute the values of A and C into this equation:

A + B + C = 65

2B + B + (B+5) = 65

4B + 5 = 65

4B = 60

B = 16

Use B=16 and solve for the other two classes (dotted blue line).

Answer:

the required graph is in the attachment.

Step-by-step explanation:

[tex]y =\dfrac 12 \cdot x -4\\\\\implies y = \dfrac{x-8}2\\\\\implies 2y = x-8\\\\\implies x -2y=8[/tex]

Answer:

32 square millimeters

Step-by-step explanation:

Parallelogram area formula => B x h

Base = 6 mm

Height = 4 mm

Area = 24 mm^2

Triangle area formula B x h x 1/2

Base = 8 mm

Height = 2 mm

Area = 8 mm^2

Total area = 24 + 8 = 32 mm^2

The total surface area of the figure consists of a parallelogram and a triangle is 32 square millimeters so option (C) will be correct.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

If we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

As per the given parallelogram and a triangle,

The bigger side of parallelogram = 6 + 2 = 8mm

Smaller side = 6mm

The perpendicular distance between the sides of the parallelogram = 4mm

The base of the triangle = 2mm

Height of triangle = 4 mm

Therefore, the complete area ⇒

(1/2)[8 + 6)×4 + (1/2)×2×4 = 32 mm²

Hence "The total surface area of the figure consists of a parallelogram and a triangle is 32 square millimeters".

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Scott needs to work at least 30 hours to make at least $600 and buy a new computer.

Let's denote the number of hours Scott works as "x" for both babysitting and working at the grocery store.

For babysitting, he earns $12 per hour.

For working at the grocery store, he earns $8 per hour.

So, his earnings from babysitting are 12x dollars, and his earnings from working at the grocery store are 8x dollars.

He needs to make at least $600 to buy a new computer.

Therefore, we can write the equation:

12x + 8x ≥ 600

Combine the like terms:

20x ≥ 600

Now, solve for x by dividing both sides of the inequality by 20:

x ≥ 600 / 20

x ≥ 30

Hence, Scott needs to work at least 30 hours to make at least $600 and buy a new computer.

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Complete question:

"Scott earns $12 per hour babysitting and $8 per hour working at the grocery store. He wants to buy a new computer that costs at least $600. How many hours does Scott need to work, combining both jobs, to save up enough money for the new computer?"

Answer: 20 more minutes

Step-by-step explanation:

Grace has already read 40 minutes due to her reading 4 times a week and 10 minutes each time(4x10=40). She has 20 more minutes to read as there as 60 minutes in a hour  

Grace needs 20 minutes more to read.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Grace read 4 days a this week.

In one day she read= 10 minutes

So, in 4 days she read = 4 x 10

                                     = 40 minutes.

So, total time taken = 60 minutes.

Thus, she needs to read (60 - 40) = 20 minutes.

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Answer:

c=0.8

Step-by-step explanation:

Step 1: Subtract 5.96 from both sides.

c+5.96−5.96=6.76−5.96

c=0.8

Answer:

13

Step-by-step explanation:

Combine all like terms:

14x-2

Since there are 180 degrees in a triangle, all three angles are going to equal 180.

14x-2=180

Add 2

14x=182

Divide by 14

x=13

Answer:

97.6 in^3

Step-by-step explanation:

find the volume of the cylinder and then find the volume of the cone. the formula for the volume of the cylinder is pi*r^2*h. the formula for the volume of the cone is 1/3*pi*r^2*h. r=d/2=4/2=2, h(cylinder)=8, h(cone)=0.7. now just plug these values into the formulas.

cylinder: pi*2^2*8=100.531

cone: 1/3*pi*2^2*0.7=2.932

cylinder-cone= 100.531-2.932=97.599. round to the nearest tenth to get 97.6

Answer:

(7,-10)

Very educated guess

Answer:

The discount is list price minus the sale price then divided by the list price and multiplied by 100 to get a percentage. Where: L = List Price. S = Sale Price

Answer:

24.5

Step-by-step explanation:

8+6(1/2 +5) divided by 2

Answer:      Overview. An angle is the union of two rays with a common endpoint. The common endpoint of the rays is called the vertex of the angle, and the rays themselves are called the sides of the angle.

Step-by-step explanation:    just have done with before! i am really good at it

Answer:

Step-by-step explanation:

Answer:

27.8

Step-by-step explanation:

You need to do brackets first

3.6-1.8 = 1.8

Then substitute

4.5 x 8- (0.4 + 9.6- 1.8)

0.4+9.6-1.8=8.2

4.5 x 8 - 8.2 =27.8

Answer:

6x-6

Step-by-step explanation:

(2x+6)+(4x-12)=2x+6+4x-12

                      =6x-6

Rabbitton: 34 / 8 = 4 1/4

Rabbit Ville: 48 / 14 = 3 3/7

Rabbitton has more rabbits per garden

Answer:

A. 10A+10P+54

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x-2y=24

x+2y=12

add the two equations

(5x-2y)+(x+2y)=24+12

6x=36

x=6

Plug in x=6 into any of the two equations

5(6)-2y=24

30-2y=24

-6= -2y

y= 3

x=6

y=3

(6,3)