Why is it appropriate to use the trigonometric functions on triangle FGJ but not on triangle FHJ?

Answer:

7) B, C

8) D

Step-by-Step-Explanation:

The first thing you need to solve for is the the parenthesis

the second one simplifies to x ≤ -7

Answer:

\(\sf \dfrac{-1}{2}\)

Step-by-step explanation:

   Use KCF method.

\(\sf \dfrac{-10}{25} \div \dfrac{8}{10}=\dfrac{-10}{25}*\dfrac{10}{8}\)

                \(\sf =\dfrac{-1}{2}\)

hi

A = -10/25  / 8/10

As to divise by a number, you can  multiply by it's inverse, as the inverse of 8/10 is   10/8

so  

A = -10/25 *  10/8  

A  =  -10* 10   / 25*8

A  =  -100 / 200

 A  =  - 10 *10 / 2 *10 *10

  A  =   -1/2

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

To prove that n! < n^n for all integers n ≥ 2 using generalized induction, we'll follow these steps: 1. Base case: Verify the inequality for the smallest value of n, which is n = 2.

2. Inductive step: Assume the inequality is true for some integer k ≥ 2, and then prove it for k + 1.
Base case (n = 2): 2! = 2 < 2^2 = 4, which is true.
Inductive step:
Assume that k! < k^k for some integer k ≥ 2.
Now, we need to prove that (k + 1)! < (k + 1)^(k + 1).

We can write (k + 1)! as (k + 1) * k! and use our assumption: (k + 1)! = (k + 1) * k! < (k + 1) * k^k, To show that (k + 1) * k^k < (k + 1)^(k + 1), we need to show that k^k < (k + 1)^, We know that k ≥ 2, so (k + 1) > k, and therefore (k + 1)^k > k^k.
Now, we have (k + 1)! < (k + 1) * k^k < (k + 1)^(k + 1).Thus, by generalized induction, n! < n^n for all integers n ≥ 2.

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If the bond angle between two adjacent hybrid orbitals is 180 degree then the hybridization  is sp hybridization , it forms linear molecules with an angle of 180°.

Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.

In sp hybridization, the s orbital of the excited state carbon is mixed with only one out of the three 2p orbitals. It is called sp hybridization because two orbitals (one s and one p) are mixed.

The resulting two sp hybrid orbitals are then positioned at 90 degree and 180 degree, respectively, with the two 2p unhybridized orbitals:

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The number of 2x2 squares that can fit into a 9x9 square is 4x4 = 16. This can be answered by the concept from real number.

To find the greatest number of 2x2 squares that can fit into a 9x9 square without overlap and without breaking up any of the 2x2 squares, we need to divide the 9x9 square into 2x2 squares.

A 9x9 square can be divided into 16 2x2 squares. This is because 9/2 = 4 remainder 1. This means we can fit 4 full 2x2 squares along each side of the 9x9 square, leaving a 1x1 square in each corner. These 1x1 squares cannot be used to fit any more 2x2 squares.  

Therefore, the number of 2x2 squares that can fit into a 9x9 square is 4x4 = 16.

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Answer:

1115.49 feet

Step-by-step explanation:

To convert meters to feet, multiply 340 meters by 3.281 because there are approximately 3.281 feet in 1 meter.

340*3.281= 1115.49

Answer:

20.4

Step-by-step explanation:

136   ×   0.85% =

136   -   115.6 =

20.4

Answer:

Q11:  31 and 44

Q12: -5, 15, -9, 19

Q13: 16

Step-by-step explanation:

Question 10

Let x = smaller part

Let y = larger part

Given sum of parts is 75:

x + y = 75

Given the larger part is 13 more than the smaller part:

y = 13 + x

Substitute y = 13 + x into x + y = 75 and solve for x:

⇒ x + 13 + x = 75

⇒ 2x + 13 = 75

⇒ 2x = 62

⇒ x = 31

Substitute found value of x into y = 13 + x and solve for y:

⇒ y = 13 + 31

⇒ y = 44

Therefore, the smaller part is 31 and the larger part is 44

Question 11

Let x = first number

Let y = second number

Let z = third number

Let w = fourth number

Given the first is 20 less than the second:

x = y - 20

⇒ y = x + 20

Given the third is 1 more than twice the first:

z = 2x + 1

Given the fourth is 4 more than the second:

w = y + 4

Given the sum of the first and second equals the sum of the third and fourth numbers:

x + y = z + w

Substitute the first 3 equations into x + y = z + w  and rearrange to make y the subject:

⇒ (y - 20) + y = (2x + 1) + (y + 4)

⇒ 2y - 20 = 2x + y + 5

⇒ y = 2x + 25

Rearrange x = y - 20 to make y the subject:

x = y - 20

⇒ y = x + 20

Now equate the equations and solve for x:

⇒ x + 25 = 20

⇒ x = -5

Now we have found the value of x, substitute into z = 2x + 1 to find z:

⇒ z = 2(-5)+ 1

⇒ z = -9

and substitute the value of x into y = x + 20 to find y:

⇒ y = -5 + 20

⇒ y = 15

finally substitute the value of y into w = y + 4 to find w:

⇒ w = 15 + 4

⇒ w = 19

Therefore,

Question 12

Let x = unknown number

Given one quarter of a number is being increased by one half of the same number is 12:

\(\implies \dfrac14x+\dfrac12x=12\)

\(\implies \dfrac34x=12\)

\(\implies 3x=12 \times 4\)

\(\implies 3x=48\)

\(\implies x=16\)

The correct answer to the question is option d) 75 PCF.

To calculate the expected vertical load, we need to consider the weight of the concrete slab and the additional load due to the concrete's temperature and pouring rate. The weight of the slab can be calculated by multiplying the density of the concrete (150 PCF) by the depth (6 inches) and the area (1 square foot). This gives us a weight of 75 pounds per square foot (PSF).

The temperature and pouring rate do not directly affect the vertical load. The temperature and pouring rate are factors that may affect the structural integrity of the slab or the time it takes for the concrete to fully cure. However, they do not contribute to the actual load borne by the slab itself. Therefore, the correct answer is 75 PCF, as it represents the weight of the concrete slab alone.

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Suppose that 20% of people own dogs, if you pick two people at random,  the probability that they both own a dog is 0.04.

Suppose that 20% of people own dogs.

So the probability of selecting own dogs = 0.20

The probability that a population unit will be included in a sample obtained through probability sampling is known as probability of selection. Each subset of a population has a probability of being chosen in the sample, which is determined by the sampling design.

If you pick two people at random, then the probability that they both own a dog = 0.20 × 0.20

If you pick two people at random, then the probability that they both own a dog = 0.04

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a). Exact volume of cylinder is equal to 4224 cm³

b). Exact volume of the cone is equal to 1408 cm³

c). The approximate volume of the cone is equal to 1406.7 cm³

a). volume of the cylinder = 22/7 × (8cm)² × 21cm

volume of the cylinder = 22 × 64 cm² × 3 cm

exact volume of the cylinder = 4224 cm³

b). volume of the cone = 1/3 × 22/7 × (8cm)² × 21cm

exact volume of the cone = 22 × 64 cm² × 1 cm

exact volume of the cone = 1408 cm³

c). using the approximate vale of π = 3.14

approximate volume of the cone = 1/3 × 3.14 × (8cm)² × 21cm

approximate volume of the cone = 3.14 × 64 cm² × 7 cm

approximate volume of the cone = 1406.7 cm³

Therefore, the Exact volume of the cylinder and cone are 4224 cm³ and 1408 cm³ respectively. While the approximate volume of the cone is equal to 1406.7 cm³

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Answer:

40.8

Step-by-step explanation:

60% = 60/100

60/100 * 68

4080/100

40.8

Answer:

40.8

Step-by-step explanation:

d/68=60/100

60×68=4080

d×100=100d

4080=100d

4080÷100=40.8

100d÷100=d

d=40.8

hope this helps

Where r = radius of the base of the cone

h = height (perpendicular height) of the cone

for this figure, r = 4.5cm, h = 6cm

Its volume is calculated by :

From the options, the closest to the maximum volume of water the cup can hold is 127cm^3

Answer: $15

Step-by-step explanation:  1.25 X 12 = 15

Answer:

The price before the discount is $ 16

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

The height of the tree to the nearest foot is 75.

Step-by-step explanation:

The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.

tangent = opposite/adjacent

\(\frac{tan(59)}{1} = \frac{h}{45}\)

h = tan(59) * 45

h ≈ 74.89

To the nearest foot, 74.89 is 75 ft.

By using the vertex of the quadratic equation, we will get the equation:

y = -2*(x + 6)^2

For a quadratic equation with a leading coefficient "A" and a vertex (h, k), the equation can be written as:

y = A*(x - h)^2 + k

Here we can see that the vertex is (-6, 0), so we have:

y = A*(x + 6)^2

We also can see that the parabola passes through the point (-4, -8), replacing these values above we will get:

-8 = A*(-4 + 6)^2

-8 = A*(2)^2

-8 = 4A

-8/4 = A

-2 = A

Then the quadratic equation is:

y = -2*(x + 6)^2

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The coordinates of the missing vertex of the rectangle is (2,1).

To determine the missing vertex of a rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.

Given three vertices of a rectangle: (2,5), (7,5), and (7,1), we can observe that the missing vertex should form a right angle with the vertex (7,1) and lie on the same horizontal line as the vertex (2,5).

Since the y-coordinate of the missing vertex should be the same as the y-coordinate of the vertex (2,5), we can determine that the missing vertex has the coordinates (2,1).

Therefore, the missing vertex of the rectangle is located at (2,1).

Correct Question:

Three vertices of a rectangle are shown on the grid.

What are the coordinates of the missing vertex?

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The coordinates of the missing vertex are determined by finding the midpoint of the given vertices and adding the vector from the midpoint to the third vertex. By following this process, we can find the missing vertex of a rectangle on a grid.

To find the missing vertex of a rectangle on a grid, we need to use the properties of rectangles. Let's say the given vertices are A(x1, y1), B(x2, y2), and C(x3, y3). We can determine the coordinates of the missing vertex D by following these steps:

By following these steps, we can determine the coordinates of the missing vertex D.

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The statement which best describes the triangle or triangles, if any, that can be formed with the sides measuring 60 centimeters, 100 centimeters, and 40 centimeters include the following: A. No triangle.

In Mathematics, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of triangles that can be formed would be determined as follows:

60 + 40 > 100 (False and no triangle).

In conclusion, we can logically deduce that the two (2) short side lengths does not exceed the long side lengths and as such no triangle can be formed with the sides measuring 60 centimeters, 100 centimeters, and 40 centimeter.

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Complete Question:

Which best describes the triangle or triangles, if any, that can be formed with the sides measuring 60 centimeters, 100 centimeters and 40 centimeter?

A. No triangle

B. One unique scalene triangle

C. infinitely small similar scalene triangles

D. Two unique scalene triangles.

The time taken by the jet will be equal to 6.58 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

The time taken by the jet will be calculated as:-

Average speed = 525 - 150 = 375 miles per hour.

The time is taken to cover the distance of 2468 miles will be:-

Time = 2468 / 375 = 6.58 hours.

Therefore time taken by the jet will be equal to 6.58 hours.

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Answer:

If im not wrong, the correct answer is 752.4cm cube

Step-by-step explanation:

First, we find volume of hemisphere, then find the volume of the cone, once we get those, we add them together and find our final answer. I hope this helps :)

Answer:

C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.

Step-by-step explanation:

An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.

In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.

What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.

Answer:The answer is C

Step-by-step explanation:I did the test.

Answer:  The top graph.

Step-by-step explanation:  The inflection is at x = 0, since the absolute value of x starts becoming greater as x decreases.  E.g., at x = -2,

f(x) = |x| - 4

f(x) = |-2| - 4

f(x) = 2 - 4

f(x) = - 2

At x = -4

f(x) = |x| - 4

f(x) = |-4| - 4

f(x) = 4 - 4

f(x) = 0

Let length of the big piece be x.

It is told that the length of the small piece of the carpet is 5m greater (+5) than 1/4 the length of the larger piece (1/4 × x)

Putting it all together in an equation we can calculate the length of the big piece:

12 m (length of the smaller piece)  = \(\frac{1}{4}\) × x (length of larger piece) + 5m

Solving the equation for x we get,

12m - 5m = \(\frac{1}{4}\) x

7m × 4 = x

28m = x

Therefore, the length of the larger piece is:

x = 28m

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The coach can select the players in 1081575 ways .

A combination is a technique for finding the number of possible arrangements in a set of items where the order of the selection is irrelevant. .

The formula for determining the number of possible arrangements by selecting only a few objects from a set with no repetition is expressed mathematically as follows:

\(nC_r=\frac{n!}{r!(n-r)!}\)

Where:n denotes the total number of elements in a set,

k denotes the number of selected objects

! - the factorial

Factorial (noted as "!") is the sum of all positive integers that are less than or equal to the number preceding the factorial sign.

For instance, \(3! = 1 * 2 * 3 = 6\).

Given,

Total number of players,n = 25

Number of selected players,r = 8

Number of ways that players are selected is determined by,

\(25C_8=\frac{25!}{8!(25-8)!}\\\\=\frac{15511210043330985984000000}{(40320)*(355687428096000)}\\\\=1081575\)

Thus, by combination, the selection can be done in 1081575 ways.

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Your question is incomplete  , here is the complete question.

There are 25 players in a basketball team. The coach must select 8 players to travel to an away game. How many ways are there to select the players who will travel?

Answer:

20 feet by 12 feet

Step-by-step explanation:

15/3 = 5 · 4 = 20

9/3 = 3 · 4 = 12

Answer:

Step-by-step explanation:

m ≥ 2-3

m ≥ -1   (graph this on  a number line)