There are 6 speakers at a conference: Ms. Sally, Ms. Elaine, Ms. Boo-Koo, Mr. Adam, Mr. Jones, and Mr. Tall. In how many ways can we order the speakers so that Mr. Adam doesn’t speak first?

Answer:

C. 124.3 ft

Step-by-step explanation:

Let h represent Nick's distance from ground.

We have been given that Nick is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. The angle of elevation from nick's mom to nick is 73 degrees.

Nick, his mother and angle of elevation forms a right triangle with respect to ground, where, h is opposite side and 38 feet is adjacent side.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{tan}(73^{\circ})=\frac{h}{38}[/tex]

[tex]\text{tan}(73^{\circ})*38=\frac{h}{38}*38[/tex]

[tex]3.270852618484*38=h[/tex]

[tex]h=3.270852618484*38[/tex]

[tex]h=124.292399502392[/tex]

[tex]h\approx 124.3[/tex]

Therefore, Nick is 124.3 feet above the ground.

The result of the sum of the three numbers is: [tex]\frac{-767}{60}[/tex]

The numbers are given as:

Start by calculating the sum of numbers 2 and 3 as follows:

[tex]Sum = -8\frac 34 -2\frac 56[/tex]

Express the numbers as improper fraction

[tex]Sum = -\frac{35}4 -\frac{17}6[/tex]

Take LCM

[tex]Sum = \frac{-3 \times 35 - 2 \times 17}{12}[/tex]

[tex]Sum = \frac{-139}{12}[/tex]

The opposite of number 1 is: -1 1/5

So, the overall sum is:

[tex]Sum = -1\frac 15 - \frac{139}{12}[/tex]

Express as improper fraction

[tex]Sum = -\frac 65 - \frac{139}{12}[/tex]

Take LCM

[tex]Sum = \frac{-72 - 695}{60}[/tex]

[tex]Sum = \frac{-767}{60}[/tex]

Hence, the result of the sum is: [tex]\frac{-767}{60}[/tex]

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The term that describes the relationship the three points must have is known as: collinear.

Collinear points are points positioned on a shared straight line, forming a linear arrangement.

In the figure referred to above, we see that point U is on the same straight line as point R and point N. This makes than have a linear arrangement, hence, we can use the term known as collinear to describe the relationship between the three points.

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We have a golden rule about similarity of figures. It is "All circle are always similar to each other".

In other words, Every circle is dilated version of another circle. To find the value of dilation, we can find the ratio of its redii.

The ratio of radii of two circles is called the scale factor of dilation between them.

Given are two circles with following information :-

Circle 1: center (0, 9) and radius 14

Circle 2: center (0, 9) and radius 7

Finding the ratio of their radii :-

[tex] \frac{Circle\; 1\; radius}{Circle\; 2\; radius} =\frac{14}{7} = 2 [/tex]

So, scale factor is 2. It means circle 1 is a dilation of circle 2 with a scale factor of 2.

Hence, option A is correct i.e. Circle 1 is a dilation of circle 2 with a scale factor of 2.

y - x > -3

(6, 2) → x = 6, y = 2

substitute

2 - 6 = - 4 < -3 NOT

(2, 6) → x = 2, y = 6

substitute

6 - 2 = 4 > -3 CORRECT

(2, -1) → x = 2, y = -1

substitute

-1 - 2 = -3 NOT

Answer: (2, 6)

Answer:  Option (2) is correct.

Step-by-step explanation:

Since we have given that

KLM is a right triangle, in which KM = 15, and ln is an altitude.

As we know that for right angled triangle, there are 3 conditions :

[tex]KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)[/tex]

So, According to the options ,

Put LM = 12, NM = 9,

[tex]\text{Using eq. (3), we have}\\\\LN^2=KM.MN\\\\12^2=9\TIMES 16\\\\144=144[/tex]

Since, it satisfies that KLM is a right triangle.

Hence, Option (2) is correct.

Using Pythagorean theorem, Option D: [tex]\( LM = 8 \)[/tex] and [tex]\( NM = 10 \)[/tex], satisfies [tex]\( KM^2 = LM^2 + NM^2 \)[/tex].

[tex]\( LM = 12 \) and \( NM = 9 \).[/tex]To determine which lengths would make triangle [tex]\(KLM\)[/tex] a right triangle when [tex]\(\overline{LN}\)[/tex] is an altitude and [tex]\(KM = 16\)[/tex], we can use the Pythagorean theorem to check each given set of values. We know that [tex]\(\overline{LN}\)[/tex] divides [tex]\(KLM\)[/tex] into two right triangles, [tex]\( \triangle KNL \)[/tex] and [tex]\(\triangle LNM\)[/tex].

We will check each given option to see if the Pythagorean theorem holds.

Option A: [tex]\( LM = 13 \)[/tex] and [tex]\( KN = 6 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then [tex]\( KM = KN + NM \)[/tex], so:

[tex]\[ x = 16 - 6 = 10 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ 13^2 = LN^2 + 10^2 \][/tex]

[tex]\[ 169 = LN^2 + 100 \][/tex]

[tex]\[ LN^2 = 69 \][/tex]

[tex]\[ LN = \sqrt{69} \approx 8.3 \][/tex]

For [tex]\( \triangle KNL \)[/tex]:

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ KL^2 = 6^2 + 69 \][/tex]

[tex]\[ KL^2 = 36 + 69 \][/tex]

[tex]\[ KL^2 = 105 \][/tex]

[tex]\[ KL \approx 10.2 \][/tex]

These calculations do not match the given [tex]\(KL\)[/tex] value.

Option B: [tex]\( LM = 12 \) and \( NM = 9 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:

[tex]\[ x = 16 - 9 = 7 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ 12^2 = LN^2 + 9^2 \][/tex]

[tex]\[ 144 = LN^2 + 81 \][/tex]

[tex]\[ LN^2 = 63 \][/tex]

[tex]\[ LN = \sqrt{63} \approx 7.9 \][/tex]

For [tex]\( \triangle KNL \):[/tex]

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ KL^2 = 7^2 + 63 \][/tex]

[tex]\[ KL^2 = 49 + 63 \][/tex]

[tex]\[ KL^2 = 112 \][/tex]

[tex]\[ KL \approx 10.6 \][/tex]

These calculations do not match the given [tex]\(KL\)[/tex] value.

Option C: [tex]\( KL = 11 \)[/tex] and [tex]\( KN = 7 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then:

[tex]\[ x = 16 - 7 = 9 \][/tex]

For [tex]\( \triangle KNL \)[/tex]:

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ 11^2 = 7^2 + LN^2 \][/tex]

[tex]\[ 121 = 49 + LN^2 \][/tex]

[tex]\[ LN^2 = 72 \][/tex]

[tex]\[ LN = \sqrt{72} \approx 8.5 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ LM^2 = 72 + 9^2 \][/tex]

[tex]\[ LM^2 = 72 + 81 \][/tex]

[tex]\[ LM^2 = 153 \][/tex]

[tex]\[ LM \approx 12.4 \][/tex]

These calculations do not match the given [tex]\(LM\)[/tex] value.

Option D: [tex]\( LN = 8 \) and \( NM = 10 \)[/tex]

Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:

[tex]\[ x = 16 - 10 = 6 \][/tex]

For [tex]\( \triangle LNM \)[/tex]:

[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]

[tex]\[ LM^2 = 8^2 + 10^2 \][/tex]

[tex]\[ LM^2 = 64 + 100 \][/tex]

[tex]\[ LM^2 = 164 \][/tex]

[tex]\[ LM \approx 12.8 \][/tex]

For [tex]\( \triangle KNL \)[/tex]:

[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]

[tex]\[ KL^2 = 6^2 + 8^2 \][/tex]

[tex]\[ KL^2 = 36 + 64 \][/tex]

[tex]\[ KL^2 = 100 \][/tex]

[tex]\[ KL = 10 \][/tex]

These calculations match the given lengths.

Thus, the correct answer is:

D. [tex]\( L N = 8 \) and \( N M = 10 \)[/tex]

The correct question is given below:

The range of this data set will be 8. The range of the data set is simply the difference between the maximum and the minimum value.

A data set is a set of information that corresponds to one or more database tables in the case of tabular data,

The maximum value is 12

The minimum value is 4

The range of  the data set will be;

R = M-m

R=12-4

R=8

Hence the range of this data set will be 8.

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The value of expression with the given x and y value is 8/15.

The given expression is -x+4y, -x=-4/5 and y=1/3.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Now, put x=4/5 and y=1/3 in the given expression and simplify

That is, -4/5 + 4(1/3)

=-4/5 + 4/3

Take LCM of denominators 5 and 3 is 15

Now, -12/15 + 20/15

=(-12+20)/15

=8/15

Therefore, the value of expression with the given x and y value is 8/15.

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Answer:

$11,840.85

Step-by-step explanation:

The numbers between 61 and 100 are given as 80 and 100.

The LCM or least common multiple of two numbers is such a small number that is divisible by both. It can be obtained by taking the prime factors of both the numbers and then taking the product of them having highest power.

The required numbers between 61 and 107 are given as follows,

The LCM of 2,4 and 5 is 20.

Thus, the numbers divisible by 2, 4 and 5 are multiples of 20.

Now, the multiples of 20 are 20, 40, 60, 80 and 100.

80 and 100 lies between 61 and 107.

Hence, the numbers that Ali can choose are given as 80 and 100.

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Answer:  [tex]x-100[/tex]

Step-by-step explanation:

Given : Phil received a prize of x dollars from a poker tournament.

The tournament cost him 100 dollars to enter.

To find Phil's net winnings from the tournament, we need to subtract the tournament cost from the prize amount he had won.

Thus, the expression to show Phil's net winnings from the tournament :-

[tex]x-100[/tex]

Answer:

106.8 in2

Step-by-step explanation:

The congruence statements that are correct for the given scenario are △GHI ≅ △LMN, △IHG ≅ △NML, and △GIH ≅ △NML.

The correct congruence statements for the given scenario are:

These congruence statements indicate that the corresponding sides and angles of the triangles are equal, leading to overall congruence.

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Answer:

(A)[tex]G(F(x))=(x-5)^2[/tex]

Step-by-step explanation:

Given: It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex].

To find: [tex]G(F(x))[/tex]

Solution:

It is given that  [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex], then [tex]G(F(x))[/tex] is written as:

[tex]G(F(x))=G(x-5)[/tex]

⇒[tex]G(F(x))=(x-5)^2[/tex]

Thus, it matches with the option A of the given options.

The domain of a function is the set of all possible input values, while the range is the set of possible output values. In the given example, the function's domain is {-3, 0, 2}, which means the input data will be either -3, 0, or 2. Similarly, the function's range is {3, 0, -2}, which means the output data will be either 3, 0, or -2.

In mathematics, the domain of a function refers to the set of all possible input values (often represented as 'x' values) that the function can accept without producing an undefined result. Similarly, the range of a function refers to the set of all possible output values (often represented as 'y' values) that the function can produce.

To address your examples: for a function with domain {-3, 0, 2} and range {3, 0, -2}, it means all input data ('x' values) will be either -3, 0, or 2; and all output data ('y' values) will be either 3, 0, or -2.

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