The surface areas of two similar solids are 340 yd2 and 1,158 yd2. The volume of the larger solid is 1,712 yd3. What is the volume of the smaller solid?

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

-261 / 3 =-87

-87 + -86 + -88 = -261

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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By setting the given height (6 feet) in the height equation and using the quadratic formula to solve for time 't', we get two solutions. Since the ball reaches 6 feet twice in its ascension and decension, the latter value of t = 3.79 seconds would be the time it is caught.

The question is regarding the time at which a baseball, hit with an initial upward velocity and caught at 6 feet above the ground, is caught. Firstly, input the given height of 6 feet into the height equation h= -16t^2 + 70t + 4 and solve for

t

. Based on the quadratic formula, we receive two solutions: t = 3.79 s and t = 0.54 s. Since the ball has two points at which it reaches the height of 6 feet during its trajectory - once while going up and once while coming down - the time when it is caught would be the larger value,

t = 3.79 s

. Therefore, approximately 3.79 seconds after being hit, the ball is caught.

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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]

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

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:

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.

The arrangement of the 864 cubes would be 18 6 by 8 layers.

All 48 would be touching the bottom of the box on the bottom layer and all 48 would be touching the top of the box on the top layer.

The cubes along both lengths would be touching the sides of the box for the remaining 16 layers. That would be16 cubes per layer or 256 cubes after counting both sides.

The cubes along the width would be touching the ends of the box for those 16 layers. Those need to be eliminated from the count since the corner cubes were already counted as part of the ones touching the sides. 4 cubes have not been previously counted for each width of 6 cubes. Both ends of the 16 layers has 8 cubes per layer or 128 cubes.

Therefore, that is 256 (sides) + 128 (ends) + 48 (top) + 48 (bottom) and that totals to 480 cubes touching the box.

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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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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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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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.

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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Crystal would read 37.5 pages in [tex]\( \frac{3}{4} \)[/tex] hour.

To represent the relationship between the number of pages Crystal reads and the time she spends reading, we can use the formula:

[tex]\[ \text{Pages Read} = \text{Reading Rate} \times \text{Time Spent Reading} \][/tex]

In this case, Crystal reads 25 pages in 1/2 hour, so her reading rate can be calculated as follows:

[tex]\[ \text{Reading Rate} = \frac{\text{Pages Read}}{\text{Time Spent Reading}} \][/tex]

[tex]\[ \text{Reading Rate} = \frac{25 \text{ pages}}{\frac{1}{2} \text{ hour}} \][/tex]

[tex]\[ \text{Reading Rate} = 25 \times 2 \][/tex]

[tex]\[ \text{Reading Rate} = 50 \text{ pages per hour} \][/tex]

Now, we can substitute this reading rate into the equation to represent the relationship:

[tex]\[ \text{Pages Read} = 50 \times \text{Time Spent Reading} \][/tex]

This equation describes the relationship between the number of pages Crystal reads and the time she spends reading.

To illustrate how to use this equation, let's say Crystal reads for [tex]\( \frac{3}{4} \)[/tex] hour. We can plug this value into the equation to find out how many pages she reads:

[tex]\[ \text{Pages Read} = 50 \times \frac{3}{4} \][/tex]

[tex]\[ \text{Pages Read} = 37.5 \][/tex]

So, Crystal would read 37.5 pages in [tex]\( \frac{3}{4} \)[/tex] hour.

The difference is a multiple of 9, so it is always divisible by 9.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The difference between the larger of the two numbers and the smaller of the two numbers.

A - B or B - A (whichever is greater)

If we transpose the digits of a two-digit number A to form B, then:

A = 10a + b, where a is the tens digit and b is the one's digit

B = 10b + a, where b is the tens digit and a is the one's digit

The difference between the two numbers.

= A - B

= (10a + b) - (10b + a)

= 9a - 9b

= 9(a - b)

or

B - A

= (10b + a) - (10a + b)

= 9b - 9a

= 9(b - a)

Either way, the difference is a multiple of 9, so it is always divisible by 9.

Therefore,

The difference is a multiple of 9, so it is always divisible by 9.

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