Last year, Mr. Manning collected data to determine the association between the
number of hours that students spent on a research project and their final grades on
the project. The equation y = 5x + 60 was a good linear for determining y, a student's
final grade on the project, after working on it for x hours.
Mr. Manning assigned the same project this year. If a student spends 6 hours
working on the project, which grade does the linear model predict the student will
receive?
a) 30
b) 90
c) 93
d) 70

Therefore, sin θ is equal to 15/17 using trigonometric ratios.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving distances, angles, and heights, and is commonly used in fields such as engineering, physics, and navigation. Trigonometry involves the study of the trigonometric functions, such as sine, cosine, and tangent, and their relationships to the angles of a right triangle. These functions are used to determine the lengths of the sides of a triangle and the measures of its angles, as well as to model periodic phenomena in various areas of science and engineering.

Here,

Since cos θ = adjacent/hypotenuse, we can draw a right triangle in Quadrant I with the adjacent side equal to 8 and the hypotenuse equal to 17. We can use the Pythagorean theorem to find the opposite side:

opposite² = hypotenuse² - adjacent²

opposite² = 17² - 8²

opposite² = 225

opposite = 15

So, the opposite side is equal to 15. Since sin θ = opposite/hypotenuse, we can substitute in the values we found:

sin θ = opposite/hypotenuse

= 15/17

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Answer:

A regular dodecagon has 12 sides and rotational symmetry. This means that if you rotate it by a certain angle about its center, it will look the same as before the rotation. The angle of rotation that would carry a regular dodecagon onto itself is equal to 360 degrees divided by the number of sides.

In this case, 360 degrees / 12 sides = 30 degrees.

So a regular dodecagon can be rotated onto itself by any multiple of 30 degrees. Out of the options you provided, only option 3 (330 degrees) is a multiple of 30 degrees. Therefore, an angle of rotation of 330 degrees would carry a regular dodecagon onto itself.

Answer:

72 Sayfa

Step-by-step explanation:

50% = (50/100) = 0.50

30% = (30/100) = 0.30

0.3 x 360 = 108

0.5 x 360 = 180

180 - 108 = 72

The simplified expression is  [tex]\frac{1-4i\sqrt3}{7}[/tex].

What is simplification?

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.

Here the given expression is

=> [tex]\frac{2-i\sqrt3}{2+i\sqrt3}[/tex]

Multiply and divide by [tex]2-i\sqrt3[/tex] then

=> [tex]\frac{2-i\sqrt3}{2+i\sqrt3}\times\frac{2-i\sqrt3}{2-i\sqrt3}[/tex]

=> [tex]\frac{(2-i\sqrt3)^2}{2^2-(i\sqrt3)^2}[/tex]

=> [tex]\frac{4+i^2\sqrt3^2-4i\sqrt3}{4-i^2\sqrt3^2}[/tex]

=> [tex]\frac{4-3-4i\sqrt3}{4+3}[/tex]

=> [tex]\frac{1-4i\sqrt3}{7}[/tex]

Hence the simplified expression is  [tex]\frac{1-4i\sqrt3}{7}[/tex].

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Answer:

8 miles i think

Step-by-step explanation:

i hope this helps

The values of the lengths of the sides and segments obtained using the equivalent ratios of the sides of similar triangles are;

1. AA

2. AA

3. 200 ft

4. 21 feet

5. 37.5 meters

6. 4.2 meters

7. 6 feet

Similar triangles are triangles that posses similar shape, but may have varied sizes.

1. Two angles in triangle ORS are congruent to two angles in triangle VUT, therefore, the triangles are similar by the Angle-Angle, AA similarity postulate

2. Whereby the angle ∠ABC is congruent to the angle ∠ADF, and the angle ∠ABC and ∠ADGF are corresponding angles, we get by the conversed of the corresponding angles theorem;

BC ║ DF

However, angle A is congruent to itself, by reflexive property, therefore;

Triangle ABC is similar to triangle ADF, according to the AA similarity postulate.

3. Using the proportional sides relationship between similar triangles or the definition of the tangent of an angle, we get;

50/12.5 = h/50

h = 50 × 50/12.5 = 200

The height of the building is 200 ft

4. Using similar triangles relationship, we get;

7/2 = h/6

h = (7/2) × 6 = 21

The height of the taller flagpole is 21 ft

5. Using the equivalent ratio of the sides of similar triangles, we get;

x/25 = 12/8

x = 25 × (12/8) = 37.5

The distance is 37.5 meters

6. The equivalent ratio of the sides of similar triangles indicates;

h/7 = 9/15

h = 7 × (9/15) = 4.2

The height of the brace is 4.2 meters

7. The ratios of the sides of similar triangles indicates that we get;

136/34 = h/(1 1/2)

h = 1 1/2 × (136/34) = 6

The height of the man is 6 feet

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Answer:

Let the cost of each bag of potatoes be x.

Then, the total cost of 4 bags of potatoes would be 4x.

According to the problem, Serenity pays a total of $31.69.

This can be written as:

4x + 4.09 = 31.69

Subtracting 4.09 from both sides, we get:

4x = 27.60

Dividing both sides by 4, we get:

x = 6.90

Therefore, each bag of potatoes costs $6.90.

Step-by-step explanation:

[tex]\text{Yesterday} = \$9.80[/tex]

[tex]\text{Today} = \$9.71[/tex]

[tex]\% \ \text{Increase} = ((9.71 - 9.80) \div 9.80) \times 100\%[/tex]

                    [tex]= (-0.09\div9.80) \times 100%[/tex]

                    [tex]\thickapprox -0.0092 \times 100%[/tex]

                   [tex]\thickapprox -0.92\%[/tex]

                  [tex]\thickapprox \bold{-0.9 \%}[/tex]   [tex]\bold{to \ the \ nearest \ tenth.}[/tex]

Two positive consecutive even integers such that the square of the smaller integer decreased by five times the larger integer is 536 are 22 and 24.

Let's start by using algebra to solve the problem.

Let x be the smaller of the two consecutive even integers. Then the larger integer is x+2.

According to the problem statement, we have:

x² - 5(x+2) = 536

Expanding the left side, we get:

x² - 5x - 10 = 536

Moving all the terms to one side, we have:

x² - 5x - 546 = 0

We can solve for x using the quadratic formula:

x = (5 ± √(5² - 4(1)(-546)))/ (2(1))

x = (5 ± √(2201)) / 2

x ≈ 23.52 or x ≈ -18.52

Since we are looking for positive even integers, we can discard the negative solution and round the positive solution down to the nearest even integer, which is 22. Therefore, the two consecutive even integers are 22 and 24.

We can check that these numbers satisfy the original equation:

22² - 5(24) = 484 - 120 = 364

And indeed, 364 is 536 less than 900 (which is 30²).

Therefore, the two positive consecutive even integers that satisfy the given condition are 22 and 24.

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Answer: x = 8

Step-by-step explanation:

As you can see 15 is divided by 3 and so is 9 so you divide 24 by 3 and you get 8 because 24 divided by 3 = 8

Answer is correct. Maximum vertical distance between the line y = x + 6 and the parabola y = x² for -2 ≤ x ≤ 3 is 6.25.

Follow these steps:

1. Subtract the equation of the line from the equation of the parabola to find the difference between their y-values: (x²) - (x + 6).

2. Simplify the expression: x² - x - 6.

3. Now we need to find the maximum value of this expression in the given interval. To do this, find the vertex of the parabola formed by the expression.

4. The vertex of a parabola with the form y = ax² + bx + c is given by the formula x = -b/(2a). In this case, a = 1 and b = -1, so the x-coordinate of the vertex is x = 1/2.

5. Since 1/2 is within the interval -2 ≤ x ≤ 3, the maximum vertical distance occurs at this x-coordinate.

6. Substitute x = 1/2 into the expression x² - x - 6 to find the maximum vertical distance: (1/2)² - (1/2) - 6 = 1/4 - 1/2 - 6 = -6.25.

7. Since we're looking for the maximum vertical distance, we need to consider the absolute value of the difference: |-6.25| = 6.25.

So, the maximum vertical distance between the line y = x + 6 and the parabola y = x² for -2 ≤ x ≤ 3 is 6.25.

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The option D:  {(3,7), (6,-2), (7,-5), (8,-8)} is a set of ordered pairs that represent the linear function.

The straight line is a representation of a linear function.

It is possible to determine whether the slope between any two points in a set of ordered pairs reflects a linear function. If any two points have the same slope, the set of ordered pairs is said to describe a linear function.

Let's calculate the slopes between the pairs of points in each set:

Let's determine the slopes between the spots in each set's pairs:

To calculate the slope between points (-2, -2) and (0, 2):

m = (2 - (-2))/(0 - (-2)) = 4/2 = 2

The slope between (0, 2) and (2, 5):

m = (5 - 2)/(2 - 0) = 3/2

The slope between (2, 5) and (4, 8):

m = (8 - 5)/(4 - 2) = 3/2

The slopes are not the same, so set A does not represent a linear function.

B: To calculate the slope between (-2, 5) and (1, 2):

m = (2 - 5)/(1 - (-2)) = -3/3 = -1

Slope between (1, 2) and (4, -1):

m = (-1 - 2)/(4 - 1) = -3/3 = -1

Slope between (4, -1) and (7, -5):

m = (-5 - (-1))/(7 - 4) = -4/3

The slopes are not the same, so set B does not represent a linear function.

C: to calculate slope between (-7, -6) and (-5, -4):

m = (-4 - (-6))/(-5 - (-7)) = 2/2 = 1

The slope between (-5, -4) and (1, 0):

m = (0 - (-4))/(1 - (-5)) = 4/6 = 2/3

Slope between (1, 0) and (4, 2):

m = (2 - 0)/(4 - 1) = 2/3

The slopes are the same, so set C represents a linear function.

D: The slope between (3, 7) and (6, -2):

m = (-2 - 7)/(6 - 3) = -3

The slope between (6, -2) and (7, -5):

m = (-5 - (-2))/(7 - 6) = -3

Slope between (7, -5) and (8, -8):

m = (-8 - (-5))/(8 - 7) = -3

The slopes are the same, so set D represents a linear function.

Therefore, the sets of ordered pairs that represent linear function is and D.

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If Fred and Rhoda together had 97 more apples than Tom, then the number of apples that Fred has is 105 apples.

Let the number of apples Fred had be denoted by variable "F".

We know that, Rhoda had 17 apples and Tom had 25 apples. We also know that Fred and Rhoda had 97 more apples than Tom.

We can write this information in equation as :

⇒ F + 17 = 97 + 25,

Simplifying this equation:

We get,

⇒ F + 17 = 122

Subtracting 17 from both sides:

⇒ F = 105

Therefore, Fred had a total of 105 apples.

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The given question is incomplete, the complete question is

Tom, Fred, and Rhoda combined their apples for a fruit stand. Fred and Rhoda together had 97 more apples than Tom. Rhoda had 17 apples. Tom had 25 apples. How many apples did Fred have?

Answer:

43.9

Step-by-step explanation:

Complementary angles add to 90 degrees.

x  + 46.1 = 90

x = 90-46.1

x =43.9

The complementary angle is 43.9.

Answer: No

Step-by-step explanation:

If you added 11 + 24 + 25 you would get 60.

A right angle is 90 degrees and you can tell if it's a right angle or not if it forms an "L".

Hint:

Try drawing a square where the 2 lines in the word "L" meet if you can draw a square then that means it's a right angle and that it equals 90 degrees.

For the given equation of function, the production is equal when x = 1/3 and x = 3.

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function. y = f is how functions are typically represented (x).

The equation of the functions are:

A(x) = 3x²

B(x) = 8x + 3

The production when the functions are equal is given by:

3x² = 8x + 3

3x² - 8x - 3 = 0

3x² - 9x + x - 3 = 0

3x (x - 3) + 1 (x - 3) = 0

(3x + 1) (x - 3) = 0

x = 1/3 and x = 3

Thus, the production is equal when x = 1/3 and x = 3.

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We can only conclude that the minute hand rotated six times as many minutes passed during class because we don't know the exact starting and ending times.

An object's length, or the separation between its two points or the range of it along a specific direction, is described by the physical property of length.

It can be measured in a variety of units, including metres, centimetres, inches, and feet. It is one of the fundamental measurements in geometry. Often, the letters "l" or "L" are used to denote an object's length.

given

A clock's minute hand revolves six degrees per minute, or 360 degrees, in the course of an hour, or 60 minutes.

If the lesson was less than an hour in length, we can calculate the number of minutes by deducting the start time from the end time.

Say Monique began class at time A and finished at time B.

The number of minutes spent in class is equal to B - A.

The minute hand would have thus rotated:

6 degrees per minute equals 6(B - A) minutes.

We can only conclude that the minute hand rotated six times as many minutes passed during class because we don't know the exact starting and ending times.

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The value of x using Pythagoras Theorem on the triangle is: 27.741

Pythagoras Theorem is defined as the manner in which we find the missing lengths of a right angled triangle.

The triangle has three sides, namely the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras theorem is in the form of;

a² + b² = c²

Using Pythagoras Theorem, we can find the smaller side of the triangle as:

y² = 12² - 10.5²

y = √(12² - 10.5²)

y = √33.75

y = 5.809

From the other triangle, we have:

x' = √(25² - 12²)

x' = √481

x' = 21.932

Thus:

x = 21.932 + 5.809

x = 27.741

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A product is something that has undergone one maybe more multiplications. For instance, the mathematical formula "times equals" would be written with the terms "times," "multiplicand," and "product," respectively.

Let's look at an illustration.

To purchase oranges, Sarah headed to the supermarket. She understood that there were four oranges in each bag of produce. She purchased five orange bags. How many oranges in total did she purchase?

Since we are aware that "of" frequently denotes multiplication, the operator "" is necessary.

The operator "=" can be used because the word "total" denotes equality.

We can turn the following into a mathematical statement since Sarah purchased 5 bags of oranges, and each bag includes 4 oranges.

Oranges total: 5 bags x 4 oranges, or 20 oranges.

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Lily drives 342 miles in [tex]4\frac{1}{2}[/tex] hours. Her speed is 76 miles per hour.

To find Lily's speed in miles per hour, we need to divide the distance she traveled by the time it took her to travel that distance.

First, we need to convert the time of [tex]4\frac{1}{2}[/tex] hours to a fraction of an hour. We can do this by converting the 1/2 hour to 0.5 hours and adding it to the whole number of hours:

[tex]4\frac{1}{2}[/tex] hours = 4 + 0.5 hours = 4.5 hours

Now we can use the formula:

Speed = Distance ÷ Time

where:

Distance = 342 miles

Time = 4.5 hours

So, Lily's speed in miles per hour is:

Speed = 342 miles ÷ 4.5 hours

Speed = 76 miles per hour (rounded to the nearest whole number)

Therefore, Lily's speed was 76 miles per hour.

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the ratio of the height of the model to the height of the actual Arch is 0.0024.

To find the ratio of the height of the model to the height of the actual Arch, we need to divide the height of the model by the height of the actual Arch. We can convert the height of the actual Arch from feet to inches to make the units consistent.

First, we convert 630 feet to inches by multiplying by 12 (since there are 12 inches in a foot):

630 feet * 12 inches/foot = 7,560 inches

Next, we can simply divide the height of the model by the height of the actual Arch:

Ratio = Height of Model / Height of Actual Arch

Ratio = 18 inches / 7,560 inches

Ratio = 0.0024

So the ratio of the height of the model to the height of the actual Arch is 0.0024.

This means that for every 1 inch of height in the model, there are 416.67 inches of height in the actual Arch (1 / 0.0024 = 416.67). In other words, the model is 416.67 times smaller than the actual Arch in terms of height.

This ratio can be useful in determining the scale of other objects or models that relate to the Gateway Arch. For example, if we wanted to create a model of the Gateway Arch's surrounding park, we could use the same ratio to ensure that the scale is consistent with the model of the Arch itself.

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If a randomly selected person is considered, and the probability of them having a blue pen is 1/4.

Probability is a fundamental concept in mathematics and statistics that allows us to quantify uncertainty and make predictions based on available information Probability can range from 0 to 1, where 0 means the event is impossible and 1 indicates a certain event

We need to know the total number of people with pens as well as the number of people with blue pens to calculate the probability of a randomly selected person having a blue pen.

According to the assumption that each person has a single pen, and that the only colors available are blue, red, and black, a randomly selected person is likely to have a blue pen:

The number of people with blue pens divided by the total number of people gives P(blue)

P(blue) = 9 / 36

P(blue) = 1/4

Out of all the pens that this person has, the probability of selecting a blue pen is 1/4.

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Answer:

12×(5+25)-2

this is the answer to the question

The equation representing the least amount of money needed is 23x + 15.

What is an equation?

An equation is a statement stating the equality of two expressions containing variables and/or numbers. The attempts to logically resolve equations, which are essentially questions, have been the basic driving forces behind the development of mathematics.

Let the number of people be x.

Cost of tickets = $12x

Cost of food = $11x

Cost of large kettle corn = $15

Now, on adding all the values, we get the equation as

M = 12x + 11x + 15

M = 23x + 15

Hence, the equation representing the least amount of money needed is 23x + 15.

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so we have two triangles touching each other at a point on that vertical line, and the angles on either side of the vertical line are vertical angles and thus congruent, which means both triangles are similar by AA.

[tex]\cfrac{4}{2}=\cfrac{x}{3.5}\implies 2=\cfrac{x}{3.5}\implies 7=x[/tex]

The graph of y= 3- (1/2)x, is attached below.

The x-axis represents the independent variable and the y-axis represents the dependent variable. Each point on the graph represents a unique combination of values for the variables being plotted. The shape of the graph is determined by the nature of the data or function being plotted.

To draw the graph of y = 3 - (1/2)x, we can use the slope-intercept form of the equation, which is y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope is -1/2 and the y-intercept is 3. To plot the graph, we can start by plotting the y-intercept at the point (0, 3), which is on the y-axis.

Then, using the slope of -1/2, we can find another point on the line. To do this, we can move 1 unit to the right and 1/2 unit down from the y-intercept, since the slope tells us that for every 2 units to the right, the line goes down 1 unit. This gives us the point (1, 2.5).

We can continue this process to find more points on the line. For example, we can move 2 units to the right and 1 unit down from the y-intercept to get the point (2, 2), and we can move 4 units to the right and 2 units down to get the point (4, 1).

Once we have a few points on the line, we can connect them with a straight line to get the graph of y = 3 - (1/2)x.

Graph is attached below.

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Once the line has a few nodes, we can join them with a straight line to create the graph is y = 3 - (1/2)x.

The x-axis is used to represent the independent variable, and the y-axis is used to represent the dependent variable. A distinct combination of numbers for the variables being plotted is represented by each point on the graph. The type of data or function being displayed determines the graph's shape.

We can use the slope-intercept form of the equation, which is y = mx + b, where m is the slope and b is the y-intercept, to create the graph of y = 3 - (1/2)x.

In this instance, the y-intercept is three, and the slope is -1/2. Plotting the y-intercept at the y-axis's (0, 3) position will serve as the initial step in creating the graph.

Then, we can locate another spot on the line by using the slope of -1/2. Since the slope informs us that the line descends one unit for every two units to the right, we can shift 1 unit to the right and 1/2 unit down from the y-intercept to achieve this. This demonstrates our argument.(1, 2.5).

We can carry on in this manner to locate additional locations along the line. For instance, from the y-intercept, we can shift 2 units to the right and 1 unit down to get the point (2, 2), and 4 units to the right and 2 units down to get the point (4, 2). (4, 1).

The graph of y = 3 - (1/2)x can be obtained by joining a few spots on the line with a straight line.

Graph is attached below.

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The volume of the rectangular prism is 8 cubic meters when it takes 8 blocks with a side lengths of one fourths meter to fill a rectangular prism.

If it takes 8 blocks with a side length of one fourths meter to fill a rectangular prism, we can assume that the volume of each block is:

[tex](1/4)^3 = 1/64m^3[/tex]

To find the volume of the rectangular prism, we need to know its dimensions. We can express its volume as one of the given options:

One eights cubic meters: This means the volume is 1/8 cubic meters. We can find the number of blocks needed to fill this volume by dividing the total volume by the volume of each block:

(1/8) ÷ (1/64) = 8 blocks

This doesn't match the given information, since we were told that it takes 8 blocks to fill the prism, not that the volume of the prism is 8 times the volume of a block.

One fourths cubic meters: This means the volume is 1/4 cubic meters. We can find the number of blocks needed to fill this volume in the same way:

(1/4) ÷ (1/64) = 16 blocks

This also doesn't match the given information.

Half cubic meters: This means the volume is 1/2 cubic meters. We can find the number of blocks needed to fill this volume:

(1/2) ÷ (1/64) = 32 blocks

Since it takes 8 blocks to fill the prism, this option doesn't match either.

One cubic meter: This means the volume is 1 cubic meter. We can find the number of blocks needed to fill this volume:

1 ÷ (1/64) = 64 blocks

This matches the given information, since it takes 8 blocks to fill the prism, which means there are 8 layers of 8 blocks each. Therefore, the dimensions of the prism are:

length = 8 × (1/4) = 2 meters

width = 8 × (1/4) = 2 meters

height = 8 × (1/4) = 2 meters

So the volume of the rectangular prism is:

volume = length × width × height = 2 × 2 × 2 = 8 cubic meters.

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(1) The probability of getting tails and a 3 is the probability of following the path T-3, which is 1/2 x 1/4 = 1/8.

(ii) The probability of getting heads and an even number is the probability of following the path H-2 or H-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.

(iii) The probability of not getting heads and an even number is the probability of following the paths T-2 or T-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.