Out of a population of 1,000 students, 80 were asked by a random sampling what color they would prefer for their first car. Their responses are shown in the table below.

Car Color
Favorite Color
Number of Students
Blue
5
Red
18
Gray
27
Silver
14
White
16

Using proportional reasoning, how many students out of the 1,000 would you expect to prefer a silver car?

Answer:

∠ AEC = 49°

Step-by-step explanation:

the sum of the angles in Δ ACE = 180° , that is

∠ AEC + 90° + 41° = 180°

∠ AEC + 131° = 180° ( subtract 131° from both sides )

∠ AEC = 49°

Answer:

49°

Step-by-step explanation:

<AEC = 180°_(41°+90°)

=180°_131°

<AEC= 49°

**90° (Complementary Angles)**

[And if u add: 41°+90°+49°= 180°]

{180° is the area of all triangles}

Hope I helped :)

Answer:

2

Step-by-step explanation:

lucky guess from my boi tony

The value of cosine theta (cosθ) for the given triangle is determined as 4.58/5.

For a given sine value of a triangle, the remaining side length of the triangle can be calculated as follows;

sinθ = opp/hypo = 2/5

b² = 5² - 2²

b² = 21

b = 4.58

Value of cosine θ

Cosθ = adj/hypo

Cosθ = 4.58/5

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The option that best describes the graphed function is: D. inverse variation; k = 4

Given two variables x and y has an inverse variation, the equation that models the relationship of the inverse variation is: y = k/x, where k = xy.

This means that as x increases, y decreases. This is the same for the graph given. So, it is an inverse variation.

When x = 2, y = 2. Therefore:

k = (2)(2)

k = 4

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I don't understand your question

Answer:

[tex]\frac{k+5}{k-2}[/tex]

Step-by-step explanation:

[tex]\frac{1-\frac{25}{k^2} }{1-\frac{7}{k}+\frac{10}{k^2} }[/tex]

multiply numerator and denominator by k² to eliminate fractions

= [tex]\frac{k^2-25}{k^2-7k+10}[/tex] ← factor numerator and denominator

------------------------------

k² - 25 ← is a difference of squares

= (k - 5)(k + 5)

k² - 7k + 10

= (k - 5)(k - 2)

------------------------------

= [tex]\frac{(k-5)(k+5)}{(k-5)(k-2)}[/tex] ← cancel (x - 5) on numerator / denominator

= [tex]\frac{k+5}{k-2}[/tex]

Answer:

A

Step-by-step explanation:

Set the equation equal to bx.

[tex](3x + 3)(ax - 2) - {x}^{2} + 6 = bx[/tex]

[tex]3a {x}^{2} - 6x + 3ax - 6 - {x}^{2} + 6 = bx[/tex]

Cancel out the constants

[tex]3 {ax}^{2} - 6x + 3ax - x {}^{2} = bx[/tex]

In order to cancel out the quadratics, we must solve for a.

[tex]3 {ax}^{2} - {x}^{2} = 0[/tex]

[tex]3 {ax}^{2} = {x}^{2} [/tex]

[tex]3a = 1[/tex]

[tex]a = \frac{1}{3} [/tex]

So plug in 1/3 for a.

[tex]3( \frac{1}{3} ) {x}^{2} - 6x + 3( \frac{1}{3} )x - {x}^{2} = bx[/tex]

[tex] - 6x + x = bx[/tex]

[tex] - 5x = bx[/tex]

[tex]b = - 5[/tex]

The sequence of transformations will be relection and dilation. Then the correct option is A.

A spatial transformation is each mapping of feature shapes to itself and it maintains some spatial correlation between figures.

The sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent.

Reflection does not change the size and shape of the geometry.

Rotation does not change the size and shape of the geometry.

Translation does not change the size and shape of the geometry.

Dilation does not change the shape but changes the size of the geometry.

Then the correct option is A.

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Answer: 44

What is [tex]S\frac{O}{H} C\frac{A}{H}T\frac{O}{A}[/tex] ?

[tex]S\frac{O}{H} C\frac{A}{H}T\frac{O}{A}[/tex] is an abbreviation for how to making finding the angle measurements of right triangles easier!

[tex]S\frac{O}{H}[/tex] is also known as sine. Using the opposite side length of the triangle [O] and the hypothenuse [H], can help you find the missing angle measurement of a triangle.

As stated before, this abbreviation is typically used to help find missing angles, but in this question, you already have your angle measurements. You are missing a side length.

Using the angle 54° as a reference point, the side length 32 is adjacent to it, so you have [A]. With A, you can use either Cosine or Tangent.

The missing side is opposite the 54° angle, so you have [O]. The only ratio with O and A belongs to Tangent, so we will use this ratio to solve for the missing side.

Write this equation down and use your calculator to solve for x:

      *make sure your calculator is in degrees*

tan (54°) = [tex]\frac{x}{32}[/tex]

32 × tan (54°) = x

44.04 ≈ 44 =x

Transformation involves changing the position and size of a shape.

The true statements are:

The complete question is as follows:-

The composition do,0.75(x,y) ∘ do,2(x,y) is applied to △lmn to create △l''m''n''. which statements must be true regarding the two triangles? check all that apply. ∠m ≅ ∠m'' △lmn ~ △l''m''n'' △lmn ≅ △l''m''n'' the coordinates of vertex l'' are (-3, 1.5). the coordinates of vertex n'' are (3, -1.5). the coordinates of vertex m'' are (1.5, -1.5).

The process of changing the location of the image on the coordinate system will be known as the translation.

The coordinates of the triangle are:

L =(-1,2)

M = (-1,-1)

N = ( 2,-1)

The transformation rule is given as:

do 0.75 (x,y) 2 (x,y)

The transformation rule is a dilation by a factor of 0.75, and then a factor of 2.

Uniform dilation changes the size of a shape, but the angles remain unchanged. This means that:

∠l≅∠l''

∠m≅∠m''

∠n≅∠n''

Δlmn⇒Δl'm'n'

The above highlights mean that:

The angles of both triangles are congruent

The triangles are similar

Next, we apply the rule on the coordinates of the triangle

L'' = 0.75 x 2 x (-1,2)

L'' = ( -1.5,3)

M'' = 0.75 x 2 x (-1,-1)

M'' = ( -1.5 , -1.5)

N'' = 0.75 x 2 x (2,-1)

N'' = (3 , -1.5)

Hence, the true statements are: The coordinates of n" are.

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Answer:

a^2+b^2=c^2

Step-by-step explanation:

You can apply this formula to any quadratic equation.

The Pythagorean Theorem is basically a way to find the side of a right triangle from the other two sides.

Take a look at this triangle labeled, a, b, c. (attachment)

Side a and b are called the legs. The largest side,  c  is called the hypotenuse.

In order to find a side, we have to use the formula…

Let’s do an example.

Consider the following triangle.

(attachment)

We want to find side c, which is actually the hypotenuse as it is unknown.

In order to find the missing side, we have to use the formula or the Pythagorean theorem. We substitute our values into a and b, while leaving the c-side as it is because that is what we are trying to find.

[Math Processing Error]

What does 13=c mean? It means that the missing side, c, from the triangle above is 13.

Fatoumata's salary after 3 years will be $58,000.

Fatoumata's salary after tt years will be $43,000 + (5,000tt).

The linear equation that can be used to determine Fatoumata's salary after the passage of time is:

Initial salary + (yearly increase x number of years)

$43,000 + 5000t

$43,000 + 5000(3) =  $58,000.

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Answer:

B and D

Step-by-step explanation:

A is not a intersecting angles they are like doodles, B makes intersecting lines, C doesnt intersect properly its only like a Y with and extra angle and D is absolutely perfect. So, thats why its B and D

Step-by-step explanation:

Line L → 2x - 3y = 6

Where a = 2 and b = -3

• So, we can use this formula to find the gradient of Line L.

m = -a/b

m = -2/-3

m = 2/3 IS THE ANSWER

Answer:

gradient = 2/3

Step-by-step explanation:

Here is another way....manipulate the equation to y = mx+ b form

  where m = slope ( gradient)

2x - 3y = 6          add 3 y to both sides

6 + 3y = 2x         subtract 6 from both sides

3y = 2x - 6          divide by 3

y = 2/3 x - 2        gradient = 2/3

Based on the values of x and y for the company and its school desks, the equation that best models the situation is D. y = 34x² - 334x + 1,075.

The best equation would be the one that gives the closest value of y to the value of the actual value of y on the table.

The first two equations can be ruled out because the table shows that this is not a linear model as there is no constant rate of change.

Test the other two equations:

x=1:

y = -34(1)² + 334(1) + 1,075

= 1,075

This is too high.

Other equation:

y = 34(1)² - 334(1) + 1,075

= 775

This is close to 800 so this is the best equation.

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Answer:

Inequality Form:

b ≥ 1

Interval Notation:

[1,∞)

Step-by-step explanation:

Answer: B

Step-by-step explanation:

A quadratic equation has degree 2.

Step-by-step explanation:

if it is cloudy, then it is snowing. False.  This is obviously not true since sometimes it's just cloudy and it's also cloudy when it rains.

all quadrilaterals are rectangles. False. A quadrilateral has four straight sides which don't have to be parallel to each other unlike a rectangle which has four straight sides with all four sides being parallel to one other side.

All chocolates like students? False? Not sure if I'm writing the converse correctly for this one but if I am this isn't true because chocolate doesn't have feelings...

All triangles with two or more congruent angles are a right triangle. False. This is only true when those two congruent angles add up to 90 which is when they're both 45. But they could also both be 30, 29, 28, etc... which won't result in a right triangle.

Answer:

If it is cloudy, then it is snowing.

   Counter-argument: It can be cloudy in the summer.

If a figure is a quadrilateral, then it is a rectangle.

   Counter-argument: Trapezoids are not rectangles.

If someone likes chocolate, then they are a student.

    Counter-argument: many people like chocolate who are not students.

If a triangle has 2 or more congruent angles, then it is a right triangle.

    Counter-argument: Equilateral tr6iangles have 3 congruent angles.

    None are right angles.

Step-by-step explanation:

Converse statements reverse the If Then in the original.

Answer:

60

Step-by-step explanation:

4(5+4+6)

4(15)

60

It is called the y-coordinate

The point itself is called a coordinate, vertically, the vertical component of the coordinate is called the y-coordinate, while horizontally, the horizontal component of the coordinate is called the x-coordinate.

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The equation can be used to find the time it took student  to hike the trail will be 3t= 5(3-t)

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The formula for the distance for the to and fro motion is;

x= v × t

The total time required for to and fro motion is;

[tex]\rm t_1 + t_ 2 = 3 \\\\ \frac{x}{v_)1} +\frac{x}{v_2}=3 \\\\ \frac{x}{3} +\frac{x}{5}= 3 \\\\ x = \frac{45}{8} \\\\ x = 3 \times \frac{15}{8} \\\\\ x =v \times \frac{15}{8} \\\\ x = v \times t[/tex]

From the equation B;

3t= 5(3-t)

3t=15-5t

8t=15

t=15/8

The equation can be used to find the time it took Stu to hike the trail will be  3t= 5(3-t)

Hence option B is correct.

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Answer:

Look down below and you will know the answer↓:

Step-by-step explanation:

He will have to work as between the range (of 20,0) and (0,20) points to earn more than $125.

So, What is inequality?

Inequality means is the relationship between two expressions that are not equal, so employing a sign such as ≠ “is not equal to,” > “greater than,” or < “less than.”.

Since then: Liam can work at most 20 hours a week, but he also needs to earn at least $125. His dog-walking job pays $7 per hour and his job as a car-wash attendant pays $11 dollars an hour. How can he earn $125.

He Let the Dog walking hours are represented by x and Car wash hours will be represented by y. The inequality will be formed as:

7x + 11y ≥ 125

x+y = 20

When we plot these two equations on the graph, we will get the range for the time from (20,0) and (0,20).

We Suppose that we will take a random point-like (5,15) when we put this value in the inequality, we get the total earning greater than $125.

7x + 11y ≥ 125

7 (5) + 11 ( 15 ) ≥ 125

35  + 165  ≥ 125

200 ≥ 125

Therefore, He has to work between the range (of 20,0) and (0,20) points to earn more than $125.

Answer:

1/

Step-by-step explanation:

There are 360 degrees in a circle. There are 40 people in this survey. Each person is 9 degrees, so 1 degree is 1/9 of a person.

Answer:

false

Step-by-step explanation:

falswe

The expression p+2 will denote the statement given

A variable is a unknown quantity in an equation , which is used to denote the parameter that needs to be determined.

It is given that

the total number of parrots in the jungle and the 2 parrots your neighbor owns

Let p be the total parrots in the jungle

p+2 will denote the statement given

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Answer:

Given that A cereal manufacturer decides to offer a new family-sized box based on the regular-sized box. They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box.

If original dimensions are l,w and h then volume = lwh

Volume of new box is= 3lwh

But here w becomes 2w and l remains the same.  Let h' be the new height

Then we have

So by 1.5 factor height should be dilated.

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

factor and you get

(x + 1)(x + 1) or (x + 1)^2

now set it equal to zero

x + 1 = 0

subtract one from both sides

x = -1

Answer:

The first option

Step-by-step explanation:

The domain of a rational function should be all real numbers except for when the denominator is equal to 0. To find when the denominator is equal to 0 you simply need to find the zeroes of the denominator... but in this case you can do that through factoring and using the quadratic equation.

So first step is going to be to factor out the GCF, which in this case is x. This gives you the equation. [tex]x(2x^2-x-15)[/tex]. So one of the zeroes is when x=0. Now to find the other two zeroes you can use the quadratic equation which is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\[/tex]. So to find the other zeroes you simply plug the values in. a=2, b=-1, c=-15

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-15)}}{2(2)}\\\\x=\frac{1\pm\sqrt{1-4(2)(-15)}}{4}\\\\x=\frac{1\pm\sqrt{121)}}{4}\\\\x=\frac{1\pm11}{4}\\\\x=\frac{12}{4}\\x=3\\\\x=\frac{-10}{4}\\x=-\frac{5}{2}[/tex]

Answer:

∠ ABD = 20°

Step-by-step explanation:

since BD bisects ∠ ABC , then

∠ ABD = ∠ CBD ( substitute values )

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Then

∠ ABD = 3x - 1 = 3(7) - 1 = 21 - 1 = 20°