5. At a carnival cotton candy and hot dogs are two different prices. Adam buys one cotton candy and one hot dog for $5. Shannon buys 3 cotton candies and one hot dog for $11. How
much is one hot dog? How much is one cotton candy?

Step-by-step explanation:

Using the trig identity for  sin ( a- b) , this reduces to

sin ( pi/12 -7 pi/12)   = sin ( -6pi/12 )  = sin ( - pi/2)

The experimental probability closest to the theoretical probability is O.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.

Each letter should have the same probability of occurring since there are 15 of each.

There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability of 15/75 = 1/5 of being drawn.

This means one would expect a theoretical frequency of 1250/5 = 250, i.e. any given letter should get drawn 250 times.

Hence, the experimental probability closest to the theoretical probability is O.

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Point (D) (-7, 4) must be on the graph of the inverse function F¹(x)  if point (7,-4) is on the graph of the function F(x).

If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function.

The term "f inverse" is widely used to refer to this particular inverse function, which is singular.

A function's inverse will cause the input and output to be inverted.

If a function has an inverse, one can use algebra to find it by setting the function equal to y.

Then, swap x and y and solve for y in terms of x.

So, we have the coordinates:
(7, -4)

It lies in the 4th quadrant.

Then, its inverse would be in the 2nd quadrant.

Which would be:

(-7, 4)

Therefore, point (D) (-7, 4) must be on the graph of the inverse function F¹(x)  if point (7,-4) is on the graph of the function F(x).

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Answer:

Step-by-step explanation:

it's (-4,7)

Answer:

C

Step-by-step explanation:

given x = a is a solution of f(x) then (x - a) is a factor

here the solutions, where the graph crosses the x- axis, are

x = - 4 , x = - 2 , x = - 1 , then the corresponding factors are

(x - (- 4)) , (x - (- 2)) , (x - (- 1)) , that is

(x + 4) , (x + 2) , (x + 1)

f(x) is then the product of these factors, that is

f(x) = (x + 2)(x + 1)(x + 4) ← in factored form

Answer:

second option: 6

Step-by-step explanation:

The general term of a geometric sequence is given by: [tex]a_{n} = a_{1} r^{n-1}[/tex]

∴ [tex]a_{1}[/tex] is the first term

[tex]a_{8} = a_{1} (3)^{8-1}[/tex]

13122 = [tex]a_{1}[/tex] [tex](3)^{7}[/tex]

13122 = [tex]a_{1}[/tex] x 2187

13122/2187 = [tex]a_{1}[/tex]

6 = [tex]a_{1}[/tex]

Answer:

[tex]2 \frac{10}{23} [/tex]

Step-by-step explanation:

[tex] \frac{4u - 7}{ - 7} = \frac{u - 4}{4} [/tex]

Use the property of the proportion:

4 × (4u-7) = -7 × (u-4)

16u -28 = -7u + 28

16u + 7u = 28 + 28

23u = 56 / : 23

u =

[tex] 2\frac{10}{23} [/tex]

An angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

Vertex, the intersection of two lines, is used to measure angles. Internal angles are created by the sides of geometric shapes like triangles and rectangles.

With the triangles that are presented, prove the angle bisector theorem:

There will be equality in the side ratios.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, an angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

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Answer:

28

Step-by-step explanation:

2x+10+2(5y+3)

2×1+10+2(5×1+3)

2+10+10+6

28

Answer:

-8

Step-by-step explanation:

-0.5(3q+15) = 1.5(q+11)

3q + 15 = -3q - 33

6q = -48

q = -8

The measure of angle x and y in the cyclic quadrilateral are 93 and 59 degrees.

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.

The opposite angles in a cyclic quadrilateral add up to 180°. The opposite angles of a cyclic quadrilateral are supplementary.

Therefore, let's find the measure of x and y in the cyclic quadrilateral.

Hence,

x + 87 = 180

x = 180 - 87

x = 93 degrees

y + 121 = 180

y = 180 - 121

y = 59 degrees

Therefore,

x = 93°

y = 59°

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The two sides of the triangle are equal the triangle is an isosceles triangle.

Triangles with two equal sides are known as isosceles triangles. Triangles are three-sided polygons that can be categorised as equilateral, isosceles, or scalene depending on how long their sides are.

The uneven side of this triangle is referred to as the base since the other two sides are equal in it. The triangle's two equal sides are always opposing equal angles. An isosceles triangle's height is calculated from its base to its vertex (topmost point). The third angle of a right isosceles triangle is 90 degrees.

The coordinates of the triangle are J(-2, 4), K(8, 4) and L (6, -2).

Using the distance formula we have:

The distance between J and K: √((8 - (-2))² + (4 - 4)²) = 10

The distance between K and L: √((6 - 8)² + (-2 - 4)²) = 6.324

The distance between L and J: √((-2 - 6)² + (4 - (-2))²) = 10

Since two sides of the triangle are equal the triangle is an isosceles triangle.

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The number of possible ways you can distribute the balls among the three boxes so that each box contains at least one ball = 21

Here we have 3 empty boxes.

Let us assume that a, b and c be these empty boxes.

and the total number of balls = 8

We need to distribute the balls among the three boxes so that each box contains at least one ball.

This means that a + b + c = 8

By allotting 1 ball to each box so that no box remains empty.

We get an equation a + b + c = 5

So, the possible number of ways to by allotting 1 ball to each box so that no box remains empty would be:

⁷C₂

Using combination formula:

⁷C₂

= 7! / 2!(7 - 2)!

= 21

Therefore,  the required number of ways = 21

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The relationship between the angle of elevation and the angle of depression between two points is that they are alternate interior angles and are equal when measured from the same horizontal line.

The angle of elevation and the angle of depression are related to each other as follows. The angle of elevation is the angle between the horizontal line and the line of sight when an observer is looking upwards to an object. The angle of depression is the angle between the horizontal line and the line of sight when an observer is looking downwards to an object.

The two angles are complementary, which means that they add up to 90 degrees. This is because the horizontal line and the line of sight form a right angle.

So, if the angle of elevation is x degrees, then the angle of depression is (90 - x) degrees, and vice versa.

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To find the value of x in the triangle, we can use the law of sines, which states that in any triangle ABC, the following relationship holds:

a/sin A = b/sin B = c/sin C

where a, b, and c are the side lengths of the triangle opposite to the angles A, B, and C, respectively.

In this case, we can write:

x/sin 80° = 7/sin 50°

Using the properties of sines, we can simplify this expression to:

x = (7 x sin 80°) / sin 50°

Using a calculator, we can evaluate this expression to get:

x ≈ 9.05

Therefore, the value of x in the triangle is approximately 9.05.

Answer:

9.9

Step-by-step explanation:

Turn Fractions into decimals. 3 3/5 turns to 3.6 and 5 1/2 turns to 5.5

Multiply them and get 19.8 and divide by 2 to get 9.9

Answer:

Step-by-step explanation:

Area = s x s. So 3 3/5 x 5 1/2 = 99/5 = 19 4/5

bh, where b is the base and h is the height of the parallelogram.

In the case of the circle, the base of the parallelogram is the circumference of the circle, which is equal to 2πr, where r is the radius of the circle. The height of the parallelogram is the distance from the center of the circle to the edge of the circle, which is also the radius r. Therefore, we have:

b = 2πr

h = r

Substituting these values into the formula for the area of a parallelogram, we get:

Area = bh = (2πr)(r) = 2πr^2

So the formula for the area of a circle is derived from the formula for the area of a parallelogram by using the circumference of the circle as the base and the radius of the circle as the height.

The angle measures that satisfy cos theta = 1/2 are

To find all angle measures for which cos theta = 1/2, we can use the unit circle and look for the x-coordinate of the point where the angle intersects the unit circle.

The x-coordinate (cosine) is equal to 1/2 at two points on the unit circle:

However, the given angle measures are not all within one revolution (360 degrees or 2pi radians), so we need to find equivalent angles within one revolution.

To do this, we can add or subtract multiples of 360 degrees or 2pi radians from the given angles until they are within one revolution.

-120° = 360° - 120° = 240°

-60° = 360° - 60° = 300°

120° = 120°

600° = 600° - 1(360°) = 240°

660° = 660° - 2(360°) = 60°

So the angle measures that satisfy cos theta = 1/2 are -120° (or 240°), -60° (or 300°), and 660° (or 60°).

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The sum of the units 3 ft. 9 in, 4 ft. 7 in. and  10 ft. 3 in. is 18 ft. 7 in.

To add these lengths, we need to first convert all the measurements to the same units.

Let's convert everything to inches.

3 ft. 9 in. = (3 x 12) + 9 = 45 in.

4 ft. 7 in. = (4 x 12) + 7 = 55 in.

10 ft. 3 in. = (10 x 12) + 3 = 123 in.

Now we can add the lengths:

45 in. + 55 in. + 123 in. = 223 in.

We have 223 inches in total.

To convert this back to feet and inches, we can divide by 12 to get:

18 ft. 7 in.

So the final answer is 18 ft. 7 in.

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Answer:

So first you'll want to line your numbers in order. 0,3,4,6,6,7,7,7,

The median refers to number that is in the middle, so 6 is the median.

To find the range, you subtract the biggest number with the smallest. So 9 is the range.

And 7 is the mode because it's repeated the most.

hope this helps

median:6

range: 9

mode: 7

A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

The total of a triangle's angles is 180 degrees. As a result, we may begin by locating the missing angle in the triangle containing the angle denoted by y:

Angle missing = 180° - 40° - y = 140° - y

y + 160° + 30° = 180°

Mixing like terms and calculating y:

y = 180° - 160° - 30° = -10°

A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.

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The required cost of 34 inches of wire as per the cost of 23 inches of wire is 92 cents is equals to 136 cents.

Let x be the cost (in cents) of 34 inches of wire.

We know that 23 inches of wire costs 92 cents,

Use a proportion to solve this problem,

23 inches / 92 cents = 34 inches / x cents

To solve for x, apply cross-multiply and simplify,

⇒ 23 inches × x cents = 92 cents × 34 inches

⇒ 23x = 3128

⇒ x = 3128/23

⇒ x ≈ 136.00 cents

Therefore, the cost of 34 inches of wire will be approximately 136 cents.

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In Linear equation, 5/8 golf balls per ounce are the number of golf balls per Ounce.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Number of golf balls (n) = 20

Total weight (w) = 32 ounces

total weight = number of balls (n) * weight of 1 golf ball

∴ weight of 1 golf ball = w/n =32/20 ounces

⇒ the weight distribution is 1.6 ounce per golf ball

Now, apply unitary method :

32 ounces is total weight of 20 golf balls

∴ 1 ounce amounts to 20/32 golf balls

⇒ there are 5/8 golf balls per ounce

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Answer: y intercept = (0.6)

Step-by-step explanation:

plug in 0 for x since the y-intercept is when x=0. then solve the equation. 2y=12. divide both sides by 2. y=6

i’m sorry i’m not sure about the slope

The correct order is: 2%, 0.09, 19/100, 7/10, 0.1. We can calculate it in the following manner.

First, we need to convert all the fractions and percentages to decimals, and then we can compare them in ascending order:

0.09, 0.1, 0.02, 0.7, 0.19

Therefore, the ascending order of the given numbers is:

0.02, 0.09, 0.19, 0.7, 0.1

So the correct order is: 2%, 0.09, 19/100, 7/10, 0.1

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

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Based on proportions, the numbers of students in the senior form and junior form are 615 and 885, respectively.

Proportion refers to the equation of two ratios.

Proportion is a fractional value depicted using ratios, percentages, fractions, and decimals.

The percentage of senior form students in the school = 41%

The percentage of junior form students = 59% (100% - 41%)

The additional percentage of junior over senior students = 18% (59% - 41%)

The additional number of junior form students over the seniors = 270

Proportionately, if 18% = 270, the total number of students (both junior and senior) = 1,500.

Therefore, the number of senior and junior students is as follows:

Check:

The difference in the numbers = 270 (885 - 615)

Thus, using proportions, we can state that there are 1,500 students in the school, consisting of 615 seniors and 885 juniors.

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The solution of the inequality is 7 < x < 13 and graph is attached.

The inequality 5 < x - 2 < 11 represents a range of values for x that satisfy the inequality. To graph its solution, we can start by adding 2 to each part of the inequality:

5 + 2 < x - 2 + 2 < 11 + 2

This will be simplified to:

7 < x < 13

This solution represents all values of x that make the inequality true. To graph this on a number line, we can draw a line with a point at 7 and a point at 13, and shade in the region between them. The shaded region represents all values of x that satisfy the inequality.

In words, the solution can be described as follows: x is greater than 7 and less than 13. Alternatively, we can use interval notation to represent the solution as (7, 13).

It is important to note that the solution to the inequality is not a single value, but rather a range of values. The graph helps to visualize this range and make it easier to understand.

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Answer:

1. It's a quadratic expression bcs the highest power in a quadratic expression is 2. Hence its in standard form. basically anything that follows ax^2 + bx + c
2. x^2-6x+8 (separate the coefficient into 2, where they add to get the coefficient number (-6), and multiply to get the number (8)
x^2-4x-2x+8 (separate it into 2 parts, and factorize each part)
x(x-4)-2(x-4)
(x-2)(x-4)
Hence, x^2-4x-2x+8 is equivalent to (x-2)(x-4)

For this situation, the example size is 45 and the standard deviation is 3.1 inches, which is known. Hence, a one-example t-test is fitting for testing the scientist's hypothesis about the normal length of salmon getting back to generate from the Alaskan waterway.

The proper test for the scientist's hypothesis that the typical length of salmon getting back to generate from an Alaskan river is not exactly the verifiable normal length of 24 inches is a one-example t-test for a populace mean.

This is on the grounds that the specialist is looking at the example mean length (22 inches) to a realized verifiable populace mean (24 inches), and needs to decide whether the contrast between the two means is measurably huge. A one-example t-test is utilized to contrast an example mean with a realized populace mean and is suitable when the example size is little and the populace standard deviation is obscure.

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The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

A numerical expression is characterized as the assortment of numbers factors and works by utilizing operations like expansion, deduction, multiplication, and division.

Considering that;

The expression is,

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

Presently, We can place x and y in the above expression as;

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

⇒ [- 5/(- 2 - 1) ] (- 4) - [-5×-2 + (- 3)]/(- 1)

⇒ [ - 5/ - 3 ] (- 4) - [10 - 3]/(- 1)

⇒ - 20/3 + 7

⇒ 1/3

In this way, The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

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