Which of the following shows 2.1851 rounded to the nearest tenth?

A. 2.1
B.2.185
C.2.19
D.2.2

The probability of rolling a sum greater than 7 with a pair of dice is [tex]\( \frac{5}{12} \).[/tex]

To find the probability of getting a sum greater than 7 when rolling a pair of dice, let's first list all the possible outcomes when rolling two dice:

1. (1,1)

2. (1,2)

3. (1,3)

4. (1,4)

5. (1,5)

6. (1,6)

7. (2,1)

8. (2,2)

9. (2,3)

10. (2,4)

11. (2,5)

12. (2,6)

13. (3,1)

14. (3,2)

15. (3,3)

16. (3,4)

17. (3,5)

18. (3,6)

19. (4,1)

20. (4,2)

21. (4,3)

22. (4,4)

23. (4,5)

24. (4,6)

25. (5,1)

26. (5,2)

27. (5,3)

28. (5,4)

29. (5,5)

30. (5,6)

31. (6,1)

32. (6,2)

33. (6,3)

34. (6,4)

35. (6,5)

36. (6,6)

Out of these 36 possible outcomes, the sums greater than 7 are:

12, 17, 18, 22, 23, 24, 27, 28, 29, 30, 32, 33, 34, 35 and 36.

There are 15 favorable outcomes. So, the probability of getting a sum greater than 7 is:

[tex]\[ \frac{15}{36} = \frac{5}{12} \][/tex]

Answer:

6 miles.

Step-by-step explanation:

We have been given that on a city map 2.5 inches represents 5 miles the library and the bank are 3 inches apart on the map. We are asked to find the actual distance between the library and the bank.

[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{\text{5 miles}}{\text{2.5 inches}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{3 inches}}=\frac{\text{5 miles}}{\text{2.5 inches}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{3 inches}}*\text{3 inches}=\frac{\text{5 miles}}{\text{2.5 inches}}*\text{3 inches}[/tex]

[tex]\text{Actual distance}=\frac{\text{5 miles}}{2.5}*3[/tex]

[tex]\text{Actual distance}=\text{2 miles}*3[/tex]

[tex]\text{Actual distance}=\text{6 miles}[/tex]

Therefore, the actual distance between the library and the bank is 6 miles.

Answer:

90, 74, 16 degrees

Step-by-step explanation:

Given that a right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

We find that

AC square + BC square = AC square

[tex]7^2 +24^2 =625 = 25^2[/tex]

So angle C = 90 degrees.

sin A = 24/25

So A = 74 degrees and B = 16 degrees

Answer: [tex]\dfrac{1}{2}[/tex]

Step-by-step explanation:

The dilation is a transformation which makes similar shapes.

We know that In two similar geometric figures, the ratio of their corresponding corresponding x-coordinate is known as the scale factor.

For the given situation, the x-coordinate of A in pre-image = 12

The x-coordinate of A' in image = 6

Then , the scale factor for the dilation is given by :-

[tex]k=\dfrac{6}{12}=\dfrac{1}{2}[/tex]

Hence, the scale factor = [tex]\dfrac{1}{2}[/tex]

The following expressions 4x - 2(3x - 9) is equal the expression of

-2x + 18.

An expression is a set of terms combined using the operations +, -, x or ÷.

Given that:

4x - 2 (3x-9)

= 4x - 6x +18

= -2x +18

Hence, the expression  4x - 2 (3x-9) is equal to -2x+18.

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It will takes 3  mexican pesos to buy one brazilian real .

According to the given condition

It takes 0.20 dollars to buy a mexican peso and 0.60 dollars to buy a brazilian real,

We have to determine that  it takes how many mexican pesos to buy one brazilian real.

This question can be solved by  applying the principles of unitary method

One peso will be bought in  $ 0.20

One real will be bought in $ 0.60

1 dollar is equivalent to

[tex]\rm 1 \; dollar = \dfrac{1}{0.2} peso \\\\\rm 1 \; dollar = \dfrac{1}{0.6 } \; real[/tex]

[tex]\rm 1/0.2\; peso = 1/0.6 \; real \\1 \; real = 0.6/0.2 = 3 \; peso[/tex]

So it will take 3 pesos to buy one real

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Answer: [tex]x=49.6^{\circ}[/tex]

Step-by-step explanation:

In the given figure , we have right triangle with hypotenuse 21 units and the side opposite to angle x is 16 units.

According to the trigonometry,

[tex]\sin \theta = \dfrac{\text{side opposite of }\theta}{\text{Hypotenuse}}[/tex]

So for , the given figure , we have

[tex]\sin x = \dfrac{16}{21}\\\\\Rightarrow\ \sin x\approx0.7619\\\\\Rightarrow\ x=\sin^{-1}(0.7619)=0.8662\text{ radian}[/tex] (using sine calculation)

Convert radian into degrees , we have

[tex]x=0.8662\times\dfrac{180^{\circ}}{\pi}\\\\=0.8662\times\dfrac{180^{\circ}}{3.14159}=49.6319852107\approx49.6^{\circ}[/tex]  [Round to the nearest tenth.]

Hence, [tex]x=49.6^{\circ}[/tex]

In the given right triangle, x = 49.6°

The triangle shown is a right triangle

The angle, θ = x

The opposite = 16

The hypotenuse = 21

Using the formula:

[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]

Substitute opposite = 16, hypotenuse = 21, and θ = x into the formula above to solve for x

[tex]sin x = \frac{16}{21} \\\\sin x = 0.7619\\\\x = sin^{-1}0.7619\\\\x=49.6^0[/tex]

Therefore, in the given right triangle, x = 49.6°

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Answer:

Option B is correct.

Step-by-step explanation:

We will work with the formula : [tex](a+b)^{2}[/tex]

= [tex]a^{2}+2ab+b^{2}[/tex]

Given polynomial is :

[tex]64x^{2} +49x+8[/tex]

here a = [tex]\sqrt{64x^{2} } =8x[/tex]

b = [tex]\sqrt{8}= 2\sqrt{2}[/tex]

2ab = [tex]2*8x*2\sqrt{2} =32\sqrt{2}x[/tex]

Now, we can see that the middle term should be [tex]32\sqrt{2} x[/tex] but in the question, it is given 49x

So, option B is true that - The x^2 coefficient does permit the factoring, but the x coefficient does not permit the factoring.

Answer:

option (2) and (5) are correct.

ΔABC ≅ ΔJLK

ΔDEF ≅ ΔGHI

Step-by-step explanation:

Given  four right angled triangle with measure of sides.

We have to check for the pairs of triangle to be similar.

Two triangles are said to be similar if their corresponding angles are equal or their corresponding sides are same ratio.

Consider, ΔABC and ΔJLK.

∠C = ∠L = 90° (given)

Also ratio of corresponding sides are same ratio, that is

[tex]\frac{AC}{LJ}=\frac{14}{7}=\frac{2}{1}[/tex]

Also, [tex]\frac{CB}{KL}=\frac{20}{10}=\frac{2}{1}[/tex]

Thus, ΔABC ≅ ΔJLK.

Option (5) is correct.

Consider, ΔDEF and ΔGHI.

∠I = ∠F = 90° (given)

Also ratio of corresponding sides are same, that is

[tex]\frac{DF}{GI}=\frac{8}{12}=\frac{2}{3}[/tex]

Also, [tex]\frac{EF}{HI}=\frac{10}{15}=\frac{2}{3}[/tex]

Thus, ΔDEF ≅ ΔGHI.

Option (2) is correct.    

Thus, option (2) and (5) are correct.

Answer:

Plug in 3 for x on the right side

3^2+2,

3 squared equals 9 plus 2 equals 11

Final answer: 11

Step-by-step explanation:

.

-261 / 3 =-87

-87 + -86 + -88 = -261

The given model of the equation y = 10000/x represents inversely proportional variation.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

The model of the equation is given in the question, as follows:

y = 10000/x

A corporation's CEO has $10,000 available for bonuses. The amount each employee earns is determined by the number of employees that receive a bonus.

We can see that the given equation characterizes inversely proportional variation.

Hence, this variation is an example of inversely proportional.

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1 yard = 3 feet:

21 feet / 3 ft = 7 yards

12 feet  / 3 feet = 4 yards

7 x 4 = 28 square yards

he will need 28 tiles

The area of the rectangular floor will be 28 square yards.

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L × W square units

A rectangular floor is 21 ft long and 12 ft wide.

We know that 1 foot = 1/3 yards.

Then the dimension of the rectangle in yards will be

L = 21 x 1/3 = 7 yards

W = 12 x 1/3 = 4 yards

Then the area of the rectangle will be

A = 7 x 4

A = 28 square yards

The area of the rectangular floor will be 28 square yards.

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rugby 7 has 3 out of 5 sold out = 3/5 = 0.6

Junior Athletics has 3 out of 5 sold out = 3/5 = 0.6

Volley ball has 2 out of 5 sold out = 2/5 = 0.4

Volleyball is the answer for the first part

 Part 2 =  3/5 x 3/5  =9/25

The volume [tex]\( V \)[/tex] of the solid [tex]\( S \)[/tex] is 32 cubic units.

To find the volume [tex]\( V \)[/tex] of the solid [tex]\( S \),[/tex] where the base is an elliptical region defined by the equation [tex]\( 4x^2 + 9y^2 = 36 \),[/tex] and the cross-sections perpendicular to the [tex]\( x \)[/tex]-axis are isosceles right triangles with their hypotenuse lying on the base, we proceed as follows:

  The equation [tex]\( 4x^2 + 9y^2 = 36 \)[/tex] represents an ellipse centered at the origin with semi-major axis [tex]\( \sqrt{9} = 3 \)[/tex] along the [tex]\( y \)[/tex]-axis and semi-minor axis [tex]\( \sqrt{4} = 2 \)[/tex] along the [tex]\( x \)[/tex]-axis.

Each cross-section perpendicular to the [tex]\( x \)[/tex]-axis is an isosceles right triangle with its hypotenuse on the elliptical base. The height [tex]\( h(x) \)[/tex] of each triangle at a given [tex]\( x \)[/tex] is determined by the elliptical equation.

  For a fixed [tex]\( x \),[/tex] the corresponding [tex]\( y \)[/tex] values on the ellipse satisfy [tex]\( 4x^2 + 9y^2 = 36 \).[/tex] Solving for [tex]\( y \)[/tex], we get:

[tex]\[ y = \frac{2}{3} \sqrt{36 - 4x^2} \][/tex]

The height  of the triangle is [tex]\( \frac{2}{3} \sqrt{36 - 4x^2} \).[/tex]

  To find the volume [tex]\( V \)[/tex] of the solid [tex]\( S \),[/tex] integrate the area of each triangular cross-section along the [tex]\( x \)[/tex]-axis from [tex]\( x = -3 \) to \( x = 3 \):[/tex]

[tex]\[ V = \int_{-3}^{3} \text{Area of triangle at } x \, dx \][/tex]

The area of each triangle is [tex]\( \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 2h(x) \cdot h(x) = h(x)^2 \).[/tex]

Thus,

[tex]\[ V = \int_{-3}^{3} h(x)^2 \, dx = \int_{-3}^{3} \left( \frac{2}{3} \sqrt{36 - 4x^2} \right)^2 \, dx \][/tex]

[tex]\[ V = \int_{-3}^{3} \frac{4}{9} (36 - 4x^2) \, dx \][/tex]

[tex]\[ V = \frac{4}{9} \int_{-3}^{3} (36 - 4x^2) \, dx \][/tex]

[tex]\[ V = \frac{4}{9} \left[ 36x - \frac{4x^3}{3} \right]_{-3}^{3} \][/tex]

Solving further,

[tex]\[ V = \frac{4}{9} \left[ \left( 36 \cdot 3 - \frac{4 \cdot 27}{3} \right) - \left( 36 \cdot (-3) - \frac{4 \cdot (-27)}{3} \right) \right] \][/tex]

[tex]\[ V = \frac{4}{9} \left[ (108 - 36) - (-108 + 36) \right] \][/tex]

[tex]\[ V = \frac{4}{9} \left[ 72 \right] \][/tex]

[tex]\[ V = \frac{4 \cdot 72}{9} \][/tex]

[tex]\[ V = 32 \][/tex]

Therefore, the volume [tex]\( V \)[/tex] of the solid [tex]\( S \)[/tex] is 32 cubic units.

The area f the helicoid ramp  is:

∫∫A) | r(u) *r( v) | dudv

The solution is:

A = 10.35×π  square units

r ( u , v ) = u×cosv i +  u×sinv j +v k

To get

r (u ) = δ(r ( u , v ) ) / δu   = [ cosv , sinv , 0 ]

r ( v ) = δ(r ( u , v ) ) / δv  = [ -u×sinv , u×cosv , 1 ]

The vectorial product is:

                                 i                    j              k

r (u ) * r ( v )            cosv             sinv           0

                            -u×sinv           u×cosv       1

r (u ) * r ( v )  =  i × ( sinv - 0 )  - j × ( cosv - 0 ) + k ( u×cos²v + u× sin²v )

r (u ) * r ( v )  = sinv i - cosv j + u k

Now

| r (u ) * r ( v ) |  = √sin²v + cos²v + u²  = √ 1 + u²

Then  

A = ∫₀ (9π) dv    ∫₀¹  √ 1 + u²  du    

 ∫₀¹  √ 1 + u²  du    = 1.15  

A = 1.15 × v |( 0  , 9π )

A = 10.35×π  square units

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Final answer:

Expected value of proposition will be 20.134.

Explanation:

Given that the player made 184 out of 329 throws, the probability of making the next throw will be:

P(x)=[Number of shots made]/[Total number of throws]

=184/329

=0.559

Thus the expected value of proposition will be:

0.599 x 24+0.559 x 12

=20.134