In a random population, out of 500 people, 160 had blue eyes. In a group of 2500 people, how many would have blue eyes?

The equation of the line of the best fit on the scatter plot is y = 150x  + 598

From the line in the scatter plot, we have the following points

(x,y) = (3,1048) and (6,1498)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} *(x - x_1) + y_2[/tex]

The equation becomes

[tex]y = \frac{1498 -1048}{6 - 3} *(x - 3) + 1048[/tex]

Evaluate

y = 150 *(x - 3) + 1048

Expand the bracket

y = 150x - 450 + 1048

Evaluate the sum

y = 150x  + 598

Hence, the equation of the line of the best fit is y = 150x  + 598

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Answer:

y = (2x/9) + 1

Step-by-step explanation:

Solving for y we get 3(-2y+x) = 5(-3y+x)+9

Expand the above we get -6y+3x=5(-3y+x)+9

which is -6y+3x = -15y+5x+9

then 9y = 2x+9

which y = (2x/9) + 1

Answer:

x - 2

Step-by-step explanation:

x^3 + 3x^2 - 4x - 12 simplifies to (x + 2)(x - 2)(x + 3)

x^2 + 5x + 6 simplifies to (x + 2)(x + 3)

(x + 2)(x - 2)(x + 3)

 (x + 2)(x + 3)

The (x + 2) and (x + 3) cancel

x - 2

Kayden Kohl

9th Grade Student

(Algebra 2)

The distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees.

From the above information, we can draw a right-angle triangle.

Let's suppose the distance between point A and point B is x

In right-angle triangle, BCD

tan31 = DC/BC = 107/BC

BC = 107/tan31

BC = 178.07 ft

In right-angle triangle, ACD

tan20 = DC/AC

tan20 = 107/(x + BC)

Plug the value of BC

tan20 = 107/(x+178.07)

x + 178.07 = 293.980

x = 115.91 ft

Thus, the distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

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Answer:

square rooted numbers like the square root of 2 are irrational because when calculated they don't equal a whole number.

Step-by-step explanation:

3+5√3 = 11.66   // not whole - irrational

√2 =  1.4 // not whole - irrational

√25 = 5 // whole - rational

The expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.

It is defined as the combination of constants and variables with mathematical operators.

We have:

Sheryl makes $7 per a pair of earrings, e, and $13 per necklace, n, she sells.

Let's suppose the total income of Sherly is T:

Then,

T = 7e + 13n

Here e is the number of earrings she sells and n is the number of necklace she sells.

T is the total income and the expression T = 7e + 13n represents the total income of Sherly.

Thus, the expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.

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The conditions for which it is possible to construct a triangle include:

This is defined as a three-sided polygon which has three edges and three vertices and a total internal angles of 180 degrees.

The triangle with side lengths 4 cm, 5 cm, and 15 cm can't be constructed due to the length of sides not being equal according to pythagoras theorem.

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Answer: See the screenshot below.

Explanation:

We'll be using these trig functions

The inverse of those help us find the angle. Notation like arcsine is the same as inverse sine denoted as [tex]\sin^{-1}[/tex] on many calculators.

The decimal results are approximate.

Another way to write the absolute value inequality lp|≤12 is -12≤p≤12

Inequality are expression not separated by an equal sign. Given the inequality expression

lp|≤12

The modulus can be positive or negative

If positive, p ≤12 and if negative -p≤12 or p ≥- 12

Combine both solutions

-12≤p≤12

Hence another way to write the absolute value inequality lp|≤12 is -12≤p≤12

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Answer:

-17, -10, -6, -5, 3, 8 only change is between 3 and 8

The correct situation for the given condition are as follows:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e.,  A = 1/2 × b × h.

The area of a triangle =  (base x height) / 2

and,

both lights illuminate the same base and height = (60 x 38) / 2

                                                                                 =  1,140 sq ft

Both Dylan's and Nikki's proposed placement will lit exactly half of the yard.

The yard's total area = 60 x 38 = 2,280 sq ft,

which is twice the area lit by the lights.

Thus, The correct situation for the given condition are as follows:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

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Answer:

<

Step-by-step explanation:

5.62x10^4=56200, 4.7x10^5=470000, so it is <.

Answer:

see below

Step-by-step explanation:

I would use the sine function for the info given

 in a right triangle    sine = opp leg / hypotenuse

        so  sin 57 =  10.8/x  

           then x =  10.8 / sin 57 = 12.87

The polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

The given parameters are:

A polynomial equation is represented as:

P(x) = (x- Root)

So, we have:

P(x) = (x - (-1))(x - (-1))(x - (-1))(x - 4)

Open the inner brackets

P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

Hence, the polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

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Answer:

15

Step-by-step explanation:

Just substitute the x for 5
In this case:

Original function: f(x) = [tex]x^{2}[/tex] - 2x

Substitute function: f(5) = [tex](5)^{2}[/tex] - 2(5)

Now solve for the substitute function

[tex](5)^{2}[/tex] - 2(5)

25 - 10

15

Therefore, f(5) is equal to 15

Using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]

The volume of a cone is calculated using:

[tex]V = \frac 13\pi r^2h[/tex]

The parameters are not given.

So, we use the following assumed values

Radius, r = 5

Height, h =10

Using the assumed values, we have:

[tex]V = \frac 13\pi * 5^2 * 10[/tex]

Evaluate the product

[tex]V = \frac {250}3\pi[/tex]

Hence, using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]

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Answer: C (490/3

Step-by-step explanation:

Answer:

C. 8/17

Step-by-step explanation:

Given:

Hypotenuse = 17

BC = 8

Cos (B) = leg adjacent to ∠B / hypotenuse

= BC/BA

Substitute

Cos (B) = 8/17

Hence option C is correct

Answer:

11

Step-by-step explanation:

10/15=6/x-2

then solve for x

x=11

Answer:The data set that is represented in the histogram is {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} Definition of a histogram An histogram is a graph that organises numerical data. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.Explaining the graphLooking at the histogram, the age group of 5 - 10 have 3 children in the carpool. the age group of 11 - 13 have 7 children in the carpool. the age group of 14 - 18 have 4 children in the carpool. This means that there are 14 children in the carpool. The correct option should have 14 ages that range between 5 and 18. Here are the options of this question: A. {3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4} B. {5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18} C. {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} D. {3, 5, 10, 11, 13, 7, 18, 14, 4}

Step-by-step explanation:

In the proof given, BC║AD and CD║BA because: B. slopes of opposite sides are equal.

If two lines are parallel, they will have the same slope value,.

Slope = rise/run.

Slope of BC = rise/run = -2/5

Slope of AD = -2/5

Slope of BA = rise/run = -6/1 = -6

Slope of BA = rise/run = -6/1 = -6

Therefore, we can conclude that BC║AD and CD║BA because: B. slopes of opposite sides are equal.

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[tex]~~~~~~\cos 45^{\circ} = \dfrac{\text{Base}}{\text{Hypotenuse}}\\ \\\implies \dfrac 1{\sqrt 2} = \dfrac{x}{22}\\\\\implies x = \dfrac{22}{\sqrt 2}\\\\\implies x = \dfrac{22\sqrt 2}{2}\\\\\implies x = 11\sqrt 2\\[/tex]

Answer: number 4 (43º, 62º, 75º)

Step-by-step explanation:

26 + 42 + 106 ≠ 180 so number 1 is not a triangle.

34 + 63 + 79 ≠ 180 so number 2 is not a triangle.

62 + 34 +80 ≠ 180 so number 3 is not a triangle.

43 + 62 + 75 = 180 so number 4 is a triangle.

Because only the angles are given and not the sides, there is an infinite number of triangles. The answer is number 4 (43º, 62º, 75º).

The correct option is option B :    -4 ≤ x ≤ 1

Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis. Increasing and decreasing functions are also called non-decreasing and non-increasing functions.

Here, from graph

as we can observe from x = -4 graph starts increases upto x = 1 and after that graph becomes constant.

Thus, between x belongs -4 to 1 the graph is increasing.

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The function's behavior at vertical asymptote x = 2 is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]

The attached graph represents the missing information in the question.

From the attached graph, we have the following highlights:

This means that the limit of f(x) approaches negative infinity and positive infinity at this value of x

Hence, the function's behavior is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]

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For both problems, we can use the section formula.

1) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]

2) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]