What is the volume of the sphere? Use 3.14 for π and round to the nearest whole number. Enter your answer in the box.

Using the inscribed angle theorem:

7. m<A = 79°

8. m<B = 90°

9. m(BC) = 152°

The Inscribed Angle Theorem states that if two chords of a circle intersect, the measure of the inscribed angle formed by the two chords is equal to half the measure of the central angle that subtends the same arc as the inscribed angle.

Applying the inscribed angle theorem, we have:

7. m<A = 1/2(158)

m<A = 79°

8. m<B = 1/2(180)

m<B = 90°

9. m(BC) = 2(76)

m(BC) = 152°

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lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4, If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist,  If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2, If lim t→0 h(t) does not exist, then h(0) cannot exist all these Limits statement are False

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

lim x -> c f(x) = L

(a) False.

According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.

(b) False.

According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.

In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.

(c) False.

A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.

Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.

(d) False.

The absence of a limit does not imply the existence of the function's value at that time.

In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.

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All these given Limit statement are False.

(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4

(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist

(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2

(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

lim x -> c f(x) = L

(a) False.

According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.

(b) False.

According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.

In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.

(c) False.

A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.

Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.

(d) False.

The absence of a limit does not imply the existence of the function's value at that time.

In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.

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The required probabilities = 0.16

The required probabilities = 0.68

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a particular data collection.

As given that,

μ = 36.2

σ = 10

As per empirical Rule:

μ± σ = 36.2 ±10 = 26.2, 46.2 = 68%

μ± 2σ = 36.2 ±20 = 16.2, 56.2 = 95%

μ ± 3σ = 36.2 ±30 = 6.2, 66.2 = 99.7%

less than 26.2:

13.5% + 2.35% + 0.15% = 0.16

between 26.2 and 36.2:

68% = 0.68

The required probabilities = 0.16

The required probabilities = 0.68

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The value of x in the equation (x + 7)² - 11 = 0 are x = -7 + √11 and x = -7 - √11

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The variable to be solved is x . Variables are numbers represented by letters in an equation.]

Therefore,

(x + 7)² - 11 = 0

(x + 7)(x + 7) - 11 = 0

x² + 7x + 7x + 49 - 11 = 0

x² + 14x + 38 = 0

Therefore, let's factorise the quadratic equation as follows:

x² + 14x + 38 = 0

Using the quadratic formula,

[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

Hence,

a = 1

b = 14

c = 38

Therefore,

x = -7 + √11 and x = -7 - √11

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The system of equations has a unique solution. The solution is (0,-5.5).

What is the system of equations?

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables.

The system of equations is

4x - 4y = 22 ....(i)

y = -5.5  ...(ii)

Putting x = 0 in 4x - 4y = 22:

4 × 0 - 4y = 22

- 4y = 22

y = -5.5

Putting x = 1 in 4x - 4y = 22:

4 × 1 - 4y = 22

- 4y = 18

y = -4.5

The points on equation (i) are (0,-5.5) and (1, -4.5).

The points on the line y = -5.5 are (-3,-5.5), (2,-5.5).

Plot the points and join them.

The intersection point is the solution of the system of equations.

The solution is x = 0 and y = -5.5

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The area of the walkway around the garden as the sum of two terms is

19x + 24.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The area of the garden is 6​ (5.5x + 2.5​).

The combined area of the garden and the walkway is 6.5​ (8x + 6​).

Now,

The area of the walkway around the garden.

= Combined area - Area of the garden

= 6.5​(8x + 6​) - 6​(5.5x + 2.5​)

= 52x + 39 - 33x - 15

= 19x + 24

Thus,

The area of the walkway around the garden is 19x + 24.

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Answer: -10x - 15

Step-by-step explanation:

The distributive property is used when you multiply a number over an addition or subtraction problem.

5  x  (-2x - 3)

Step 1

Take 5 and multiply it by -2x

5  x  -2x = -10x

Step 2

Take 5 and multiply it by - 3

5  x  - 3 = -15

Step 3

Put the entire problem together.

5  x  (-2x - 3) = -10x - 15

Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.

Links are regarded to as appropriate when they typically have the same ratio. For instance, the trees in an estate and or the number of peaches in a harvest in apples depend on the average number of apples provided by each tree. A linear correlation between two numbers as well as variables is referred to as being proportional in mathematics. When the primary quantity doubles, the other amount also does so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two components are proportional, it suggests that if one rises, the other climbs as well, and their correlation is continuous at all values. The diameter and circumference of such a circle are used as an example.

given

The true statement is

starting salary = $60,000

average = $60,000 / 3

= $ 20,000

Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.

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Yes, we can find the area of the triangle by forming a parallelogram.

The area of a triangle is equal to half the area of a parallelogram.

The conditions are given below.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The area of the triangle can be calculated by forming a parallelogram under the conditions:

1)

If the triangle and the parallelogram are on the same base.

2)

If the triangle and the parallelogram are between the same parallels.

Then,

The area of the triangle is equal to half the area of a parallelogram.

Thus,

The area of the triangle is equal to half the area of a parallelogram.

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For the given the formula f (n) = 35 - 5n, the 5th term of the sequence is f(5) = 10.

A sequences is an ordered sets of integers (usually called ad "terms"), such as 1, 5, 9. Some sequences follow a specific pattern that can be exploited to indefinitely expand them. For example, 4, 9, 14 follows the pattern "add 5," and we can now proceed with the sequence. Formulas that tell us how to discover any term in a series can be found in sequences.

The formula of the sequence in this case is:

f(n) = 35 - 5n.

Then

n = 1  -->  f(1) = 35 - 5(1) = 30

The 5th term means we substitute n = 5 into the formula.

n = 5   -->  f(5) = 35 - 5(5) = 35 - 25 = 10

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Answer:

Step-by-step explanation:

3/6

When 65 inches are converted to feet, the result is 5.41667 feet.

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The function g(x) is defined as follows:

g(x) = 2x - 12.

The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:

The fact that the variables are exchanged means that the functions are symmetric over the line y = x.

As the lines are symmetric over the line y = x, these following statements regarding the composition of a function with it's inverse is given as follows:

We have that f(2x - 12) = x, hence the function g(x) is defined as follows:

g(x) = 2x - 12.

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Answer:

4x/5

Step-by-step explanation:

the price of the jacket before goes down = x

20/100*x = x/5

the original price of the jacket= x-(x/5) = 4x/5

Answer:

11.55m², 181.12mm²,11ft,

Step-by-step explanation:

Simplify the expression.

and multiply A=1/2bh

Answer:

25,000g

Step-by-step explanation:

multiply the mass value by 1000

25 x 1000 = 25,000g

The weight of Jenna's dog is 32.375 pounds

From the question, we have the following parameters that can be used in our computation:

Tara = 9.25 pounds

Also, we have

Jenna = 3.5 * Tara's dog

Substitute the known values in the above equation, so, we have the following representation

So, we have

Jenna = 3.5 * 9.25 pounds

Evaluate

Jenna = 32.375 pounds

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The value for the following order of the given iterative formula of xₙ + 1 = 3/4 xₙ₋₁ are:

Iterative formula is used to process a repeating procedure to produce a series of results

We have an iterative formula of:

xₙ + 1 = 3/4 xₙ₋₁

We know that:

x₁ = 2

Hence:

x₂ + 1 = 3/4 x₁

x₂ + 1 = 3/4 (2)

x₂ + 1 = 3/2

x₂ = 1/2 = 0.5

x₃ + 1 = 3/4 x₂

x₃ + 1 = 3/4 (1/2)

x₃ + 1 = 3/8

x₃ = -5/8 = - 0.63

x₄ + 1 = 3/4 x₃

x₄ + 1 = 3/4 (-5/8)

x₄ + 1 = -15/32

x₄  = - 47/32 = -1.47

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Yes, the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation.

To verify this we can use Implicit Function Theorem. According to the theorem, if a relation f(x,y) = c is given, then if the partial derivative of f(x,y) concerning y is nonzero at the point (x0,y0), there is a unique function y = g(x) such that f(x,g(x)) = c.

In this case, the partial derivative of f(x,y) concerning y is -2 sin(x-y). At the point (x0,y0), this derivative is nonzero, so there exists a unique function y = g(x) such that f(x,g(x)) = c. This implies that the given relation does indeed define an implicit solution of the differential equation.

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By using permutations and combinations, We can arrange 12 people into 3 teams of 4 in 5775 different ways.

Here, we will use the concept of permutations and combinations to solve the question.

We have to arrange 12 people into 3 teams of 4.

We know that ⁿCr = n! / [(n - r)! × r!]

No. of ways to select the first 4 people in the first group = ¹²C₄

                                                                                        = 12! / [(12 - 4)! × 4!]

                                                                                            = 12! / [(8! × 4!)]

                                                                                            = 495

No. of ways to select 4 people from the remaining 8 for the second group = ⁸C₄   = 8! / [(8 - 4)! × 4!] = 8! / [(4! × 4!)] = 70

No. of ways to select 4 people from 4 for the third group = ⁴C₄  = 4! / [(4 - 4)!] × 4!] = 4! / [(0! ×4!)] = 1

Total no. of ways to select people for group = (495 x 70 x 1) / 3! = 34650 /6 = 5775

Hence, we can split 12 people into 3 teams of 4 in 5775 different ways.

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To reach the goal of $1,200, the organization needs to sell at least 28 standard tickets (1,200 / 42 = 28.57) or 28 VIP tickets (1,200 / 43 = 27.91). They can also combine the sales of standard and VIP tickets to reach the goal.

The charitable organization is hosting a black-tie benefit event and aims to raise at least $1,200 through ticket sales.

The standard tickets are priced at $21 each, while the VIP tickets are priced at $43 each.

To reach the goal of $1,200, the organization needs to sell a minimum of 28 standard tickets ($1,200 / $21 = 57.14).

However, if they only sell VIP tickets, they will need to sell at least 28 VIP tickets ($1,200 / $43 = 27.91).

Finally, they can also achieve their goal by selling a combination of standard and VIP tickets.

For example, they can sell 20 standard tickets and 8 VIP tickets, which would result in a total of 20 * $21 + 8 * $43 = $840 + $344 = $1,184, reaching their goal of $1,200.

In conclusion, the charitable organization has multiple options to reach their goal of $1,200 through ticket sales for their black-tie benefit event.

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Value 02 = 16 represents the population variance.

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The total amount earned by Tanisha will be $180.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Tanisha is a waitress at a restaurant. Each day she works, Tanisha will make a guaranteed wage of $40, however, the additional amount that Tanisha earns from tips depends on the number of tables she waits on that day. From past experience, Tanisha noticed that she will get about $14 in tips for each table she waits on.

The amount of money earned by Tanisha in 10 days will be:-

Amount = Fixed Wage + Tip

Amount = 40 + ( 10 x 14 )

Amount = 40 + 140

Amount = $180

Hence, Tanisha will have earned $180 in total.

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Answer is 2.7 million liters/hour

What is speed?

Speed tells us how fast something or someone is travelling.

The flow rate of water can be calculated as the cross-sectional area of the channel multiplied by the speed of the water.

The cross-sectional area of the channel can be calculated as width x depth = 15 cm x 2.5 cm = 37.5 cm^2

The flow rate of water can be calculated as 37.5 cm^2 x 20 cm/s = 750 cm^3/s

To convert this to liters, we need to multiply by 1000 to convert cubic centimeters to cubic centimeters:

750 cm^3/s x (1000 cm^3/L) = 750 L/s

Finally, to find the amount of water that flows into the lake in 1 hour, we need to multiply the flow rate by the number of seconds in an hour:

750 L/s x (3600 s/hr) = 2700000 L/hr = 2.7 million liters/hour.

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Answer:

y = $24,500 * (1 + 0.03x)

Step-by-step explanation:

Please find the attachment for detail

The cube root of a cube of the number is the same number for any number. Thus, option A is the answer.

In the given question,

[tex]\sqrt[3]{7} = 7^{1/3} \\[/tex]

We have to prove L.H.S = R.H.S

Let's take R.H.S

= [tex]7^{1/3}\\[/tex]

Taking a cube for this,

[tex]= (7^{1/3} )^{3}[/tex]

We can separate this into three terms.

[tex]= 7^{1/3} . 7^{1/3} . 7^{1/3}[/tex]

We know that [tex]x^{n}. x^{m} = x^{n+m}[/tex]

Then,

[tex]= 7^{1/3 + 1/3 +1/3} \\= 7^{3/3}\\ = 7[/tex]

From L.H.S

We have to take cube root,

[tex](\sqrt[3]{7})^{3} \\= 7[/tex]

Hence, L.H.S = R.H.S, and it is verified.

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The effects of poor scale interpretation in maths​ are discussed below.

Poor scale interpretation in mathematics can have significant effects on various areas of life and work that require the use of mathematical concepts and skills. Some of the consequences of poor scale interpretation are:

1. Inaccurate Results: Poor interpretation of scales on graphs, charts, and other mathematical representations can lead to incorrect conclusions and decisions based on the resulting data.

2. Miscommunication: Poor scale interpretation can result in misinterpretation of information and lead to miscommunication between individuals and groups.

3. Ineffective Problem Solving: Poor scale interpretation can hinder the ability to solve mathematical problems effectively, resulting in incorrect solutions and wasted time and resources.

4. Limited Career Opportunities: Poor scale interpretation skills can limit career opportunities in fields that require mathematical proficiency, such as engineering, finance, and technology.

5. Low Confidence and Motivation: Poor scale interpretation skills can lead to frustration and low confidence in mathematics, causing students and individuals to lose interest in the subject.

To avoid the negative effects of poor scale interpretation, it is important to receive proper mathematical education and training, and to continually practice and improve one's mathematical skills. Additionally, seeking help and guidance from teachers and mentors can be beneficial in improving one's scale interpretation skills.

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Answer:

y = 3x + c

Step-by-step explanation:

c - any number which is not 3

Answer:

10

Step-by-step explanation:

The GCF of 80 and 90 is 10.