Find the standard form of the equation of the circle with endpoints of a diameter at the points

Answer:

12 π inches

Step-by-step explanation:

1) Since semicircles = 180 degrees, semicircle HJI = 180 degrees.

2) Make a ratio: 180/360. Simplify it: 1/2.

3) Then do: 1/2 x π d  -->  1/2 x π 24. You should get: 12 π.

4) So, the exact length of semicircle HJI = 12 π inches.

(The reason you are supposed to leave it 12 π centimeters is because only if the question asks you to find the approximate length of the arc, then you can use 3.14 instead of π. But if the question asks you to find the exact length of the arc, you have to leave it as said above because you would still have to round the answer (if you multiply 12 by pi), which makes it an approximate answer, not an exact answer.)

pi (π) = 3.14159265359......................

Pi is an endless number.

Hope this helps!  :)

Answer:

The length of HN is 19 unit.

Step-by-step explanation:

Consider the provided information:

It is given that the length of line segment AN is 38 units.

Now consider figure 1:

It is given that the point H is in between A and N. Also with the concurrency markings on segment AH and segment HN.

Therefore, the length of the segment AH = HN

AH + HN = AN

Consider the length of AH = HN = x

Therefore,

[tex]x+x=38[/tex]

[tex]2x=38[/tex]

[tex]x=\frac{38}{2}[/tex]

[tex]x=19[/tex]

Hence, the length of HN is 19 unit.

Answer:

the answer is the option C

[tex]KJ=3\sqrt{5}\ units[/tex]

Step-by-step explanation:

we know that

The triangle KMJ is a righ triangle

so

Applying the Pythagoras Theorem

[tex]KJ^{2}=KM^{2}+MJ^{2}[/tex]

in this problem we have

[tex]KM=6\ units[/tex]

[tex]MJ=3\ units[/tex]

substitute

[tex]KJ^{2}=6^{2}+3^{2}[/tex]

[tex]KJ^{2}=45[/tex]

[tex]KJ=\sqrt{45}=3\sqrt{5}\ units[/tex]

Final answer:

The composition h = f о g is only guaranteed to be an odd function if both g and f are odd functions. If f is an even function or neither odd nor even, h will not necessarily be an odd function. The property of the composition depends on the nature of both functions involved.

Explanation:

Whether the composition of functions h = f о g is always an odd function when g is an odd function depends on the nature of f. If g(x) is an odd function, it follows that g(-x) = -g(x). However, for h to also be odd, f must satisfy the condition h(-x) = -h(x). This can only be the case if f is also an odd function.

If f were an even function, then f(g(-x)) = f(-g(x)) would equal f(g(x)) due to the even property of f. In this scenario, h would not be an odd function since h(-x) = f(g(-x)) = f(g(x)) = h(x), which violates the definition of an odd function.

When an odd function and an even function are multiplied, the result is an odd function, as exemplified by g(x) = x³ - 3x and h(x) = x². But when composing functions, the outer function's properties dominate the result. Therefore, the composition h = f о g can only be assured to be odd if f itself is odd.

divide 32 miles by 2 1/3 hours

32/2.33333 = 13.7143

 to nearest tenth = 13.7 miles per hour

Answer: [tex]13.7\text{ miles per hour}[/tex].

Step-by-step explanation:

Given : A snowmobile traveled 32 miles in [tex]2\dfrac{1}{3}[/tex] hours i.e.[tex]\dfrac{7}{3}[/tex] hours.

The distance is the product of the rate and the time.

i.e. The formula we use to find the average speed is given by :-

[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}\\\\\Rightarrow\ \text{Average Speed}=\dfrac{32}{\dfrac{7}{3}}=\dfrac{32\times3}{7}=13.7142857143\approx13.7\text{ miles per hour}[/tex]

Hence, the average speed of the snowmobile was [tex]13.7\text{ miles per hour}[/tex].

The domain will consist of all non-negative real numbers (x ≥ 0).

And, the range will consist of all real numbers (-∞, +∞).

Given that;

The function is,

c (x) = 10x - 50

Now for the domain and range of the function c(x) = 10x - 50,

Since the domain refers to all the possible input values (x) for the function.

In this case, since c(x) represents the profit from selling candles, x would represent the number of candles sold.

The number of candles sold cannot be negative, as it wouldn't make sense to sell a negative number of candles.

So, the domain will consist of all non-negative real numbers (x ≥ 0).

And, The range refers to all the possible output values (c(x)) of the function.

In this case, c(x) represents the profit. The profit can be any real number because it can be positive, negative, or zero.

Therefore, the range will consist of all real numbers (-∞, +∞).

Thus, Domain: All non-negative real numbers (x ≥ 0).

Range: All real numbers (-∞, +∞).

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The required three consecutive even integers are 56, 58, and 60.

Given that,
The sum of three consecutive even integers is 174 what are integers is to be determined?

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
Let the three even integers be 2x, 2x+ 2 and 2x + 4
Now, accoding to the question,

2x + 2x + 2 + 2x + 4 = 174
6x + 6 = 174
x = 28

Now,
2x =28 * 2 = 56

2x + 2 = 56 + 2 = 58
2x + 4 = 56 + 4 = 60

Thus, the required three consecutive even integers are 56, 58, and 60.

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Approximately 99.73% of Jen's phone bills are between $49 to $103. This is calculated by transforming the prices into z-scores regarding the normal distribution and then checking these z-scores in a standard normal distribution table.

The problem is a question about the normal distribution. Using the properties of a normal distribution, we can solve it as follows:

In conclusion, about 99.73% of Jen's phone bills are between $49 and $103.

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99.74% of Jen's monthly phone bills are between $49 and $103.

To answer this question, we need to understand the properties of the normal distribution. For a normally distributed variable with a mean (μ) of $76 and a standard deviation (σ) of $9, we can use the Z-score formula:

[tex]Z = \frac{(X - \mu)}{\sigma}[/tex]

We now convert $49 and $103 to Z-scores:

For $49:

[tex]Z = \frac{(49 - 76)}{9} = -3[/tex]

2. For $103:

[tex]Z = \frac{(103 - 76)}{9} = 3[/tex]

Next, we use the Z-table to find the probabilities corresponding to these Z-scores:

For Z = -3, the probability is 0.0013 (or 0.13%)

For Z = 3, the probability is 0.9987 (or 99.87%)

To find the percentage of phone bills between $49 and $103, we subtract these values:

[tex]P(49 < X < 103) = 0.9987 - 0.0013 = 0.9974[/tex]

Finally, converting this to a percentage, we get:

[tex]0.9974 \times 100\% = 99.74\%[/tex]

Therefore, 99.74% of Jen's monthly phone bills are between $49 and $103.

Answer:

1,507,000,000

Step-by-step explanation:

We are asked to write 1507 million in standard form.

We know that 1 million equals 1,000,000.

To convert 1507 million in standard form, we will multiply 1507 by 1,000,000 as shown below:

[tex]\text{1507 million in standard form}=1507\times 1,000,000[/tex]

[tex]\text{1507 million in standard form}=1,507,000,000[/tex]

Therefore, 1507 million in standard form would be 1,507,000,000.

The required number, whose sum with its square is 210, is -15 and 14.

Given that,
The sum of a number and its square is 210. To determine the​ number(s).

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the number be x,
according to the question,
x + x² = 210
x² + x -210 = 0
x² + 15x - 14x  - 210 = 0
x(x + 15) -14 (x + 15) = 0
(x + 15)(x - 14) = 0
x = -15 and 14

Thus, the required number, whose sum with its square is 210, is -15 and 14.

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Answer:

2DE = DF.

Hence Proved.

Step-by-step explanation:

Given  :  E is the midpoint of DF.

To Prove  :  2DE = DF

Proof :

We have given a line DF .

D____________F.

Mid point = E

Mid point : It is that point that divide the line in to two equal parts .

D______E______F.

So, DE = EF.

We can say DE=  [tex]\frac{1}{2}DF[/tex].

On multiplying both sides by 2.

2DE = DF.

Hence Proved.

Therefore, 2DE = DF.

Hence Proved.

Answer:

A:All rational numbers are integers

Step-by-step explanation:

We are given that a set of numbers

We have to find not  true statement about the regarding set of numbers

We know that all integers are rational number but all rational  number .

are not integers.

All whole numbers are rational number but all rational number are not whole numbers.

All irrational numbers are real numbers but all real numbers are not irrational numbers.

Hence, option A is true.

Answer:All rational numbers are integers.