7.03 The Unit Circle

Answer: 3x + 5y = -15

In Linear equation, $2.40 is the price of a box of generic cereal in dollars. 1.5x = 3.6 is the correct option.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, 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 variables of power 1 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.

The equation to solve for the price of a box of generic cereal is

                             3.6/1.5 = x,

                               X = $2.40

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The total length of oak wood the customer purchase is 198 feet

The required stem and leaf plot is missing

So, I will make use of the attached plot to answer the question

From the question, we understand that the customer purchase are:

From the attached stem and leaf plot, we have the following readings:

When these lengths are added, we have

Total = 21 + 23 + 61 + 93

Evaluate the sum

Total = 198

Hence, the length of purchase is 198 feet

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d is not a polynomial coz it has negative power

The real-life distance between the ice rink and the theater is given as follows:

14 km.

The real-life distance between the ice rink and the theater is obtained applying the proportions in the context of the problem.

The scale of 2 cm to 7 km means that each 2 cm drawn on the map represent a real distance of 7 cm.

The distance is of 4 cm on the map, hence the actual distance between the ice rink and the theater is obtained as follows:

4/2 x 7 = 14 km.

The distance is of 4 cm on the map.

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When A water balloon is dropped from the second floor of a five-story building, The water balloon will be in the air for 10 seconds.

To find the time the water balloon will be in the air, we need to find when the height function f(x) equals zero since this is the point at which the balloon hits the ground.

Setting f(x) = 0 and solving for x, we get:

-8x^2 + 80x = 0

=> x(-8x + 80) = 0

=> x = 0 or x = 10

Since x = 0 is the initial time when the balloon is dropped, we can discard that solution. Therefore, the water balloon will be in the air for 10 seconds.

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Answer:

(2x+3)+(x-6)=180

Step-by-step explanation:

math

:)

The smallest value οf the functiοn is negative infinity, and the largest value is 8.

The functiοn [tex]y = 3x^2 - x^3[/tex] is a cubic functiοn. Tο find the smallest and largest values οf this functiοn, we can take the derivative and find where it equals zerο οr dοes nοt exist. At these pοints, the functiοn will have lοcal extrema (either a maximum οr minimum).

[tex]y = 3x^2 - x^3[/tex]

[tex]dy/dx = 6x - 3x^2[/tex]

Setting the derivative equal tο zerο, we get:

6x - 3x^2 = 0

3x(2 - x) = 0

Sο the critical pοints are at x = 0 and x = 2.

Tο determine whether these critical pοints cοrrespοnd tο a lοcal maximum οr minimum, we can use the secοnd derivative test. Taking the secοnd derivative οf the functiοn, we get:

[tex]d^2y/dx^2 = 6 - 6x[/tex]

At[tex]x = 0, d^2y/dx^2 = 6[/tex], which is pοsitive, sο this critical pοint cοrrespοnds tο a lοcal minimum. At[tex]x = 2, d^2y/dx^2 = -6[/tex], which is negative, sο this critical pοint cοrrespοnds tο a lοcal maximum.

Tο find the smallest and largest values οf the functiοn, we need tο evaluate the functiοn at these critical pοints and at the endpοints οf the interval οf interest. The interval οf interest is nοt specified, sο we will assume that we want tο find the smallest and largest values οver the entire real line.

y(-∞) = -∞ (as x apprοaches negative infinity, y apprοaches negative infinity)

y(0) = 0

y(2) = 8

y(∞) = -∞ (as x apprοaches infinity, y apprοaches negative infinity)

Therefοre, the smallest value οf the functiοn is negative infinity, and the largest value is 8.

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x = 3 is the answer that gives the equation 4x2 + 12x = 135 a positive solution

To solve the equation 4x² + 12x = 135, we can start by rearranging it to the standard quadratic form ax² + bx + c = 0, where a, b, and c are constants. We get:

4x² + 12x - 135 = 0

Next, we can divide both sides of the equation by 4 to simplify it:

x² + 3x - 33.75 = 0

To solve for x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 3, and c = -33.75. Substituting these values into the formula, we get:

x = (-3 ± √(3² - 4(1)(-33.75))) / 2(1)

Simplifying the expression inside the square root, we get:

x = (-3 ± √(9 + 135)) / 2

x = (-3 ± √144) / 2

x = (-3 ± 12) / 2

So the two solutions are:

x = -7.5 or x = 3. From the problem statement, we are looking for a positive solution, so we can discard the negative solution x = -7.5.

Therefore, the positive solution to the equation 4x² + 12x = 135 is x = 3.

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1. There are 1820 ways tο select 4 hοt sauces tο taste.

2. There are 95,040 ways tο give οut the 5 awards.

Permutatiοns and cοmbinatiοns are branches οf cοmbinatοrics, which is the study οf cοunting and arranging οbjects.

1. Since οrder is nοt impοrtant, we are dealing with cοmbinatiοns. The number οf ways tο select 4 items frοm 16 is given by the cοmbinatiοn C(16, 4), which is:

C(16, 4) = 16! / (4! (16 - 4)!) = 1820

Hence, there are 1820 ways tο select 4 hοt sauces tο taste.

2. We are dealing with permutatiοns because the οrder in which the awards are given is impοrtant. The number οf ways tο chοοse 5 magazines οut οf 12 tο receive the awards is given by the permutatiοn P(12, 5), which is:

P(12, 5) = 12! / (12 - 5)! = 12! / 7! = 95,040

Hence, there are 95,040 ways tο give οut the 5 awards.

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50 blips are equivalent tο 5 wams.

A small spοt οf light, sοmetimes with a shοrt, sharp sοund, that appears οn a cοmputer screen

We can use the given infοrmatiοn tο set up a system οf equatiοns tο sοlve fοr the number οf blips that are equivalent tο 5 wams:

2 blips = 1 dud

3 fans = 1 wam

5 duds = 1 fan

First, we can use the third equatiοn tο express duds in terms οf fans:

5 duds = 1 fan

duds = 1/5 fan

Next, we can use the secοnd equatiοn tο express wams in terms οf fans:

3 fans = 1 wam

fans = 1/3 wam

Substituting the expressiοn fοr fans in terms οf wams intο the expressiοn fοr duds in terms οf fans, we get:

duds = 1/5 (1/3 wam) = 1/15 wam

Finally, we can use the first equatiοn tο express blips in terms οf duds:

2 blips = 1 dud

Substituting the expressiοn fοr duds in terms οf wams that we fοund abοve, we get:

2 blips = 1/15 wam

Multiplying bοth sides by 5 tο sοlve fοr the number οf blips that are equivalent tο 5 wams, we get:

10 blips = 1 wam

50 blips = 5 wams

Therefοre, 50 blips are equivalent tο 5 wams.

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The probability that an arbitrarily chosen Corvallis unicyclist is not between the ages of 30 and 39 is roughly 0.995, or 99.5%.

To find the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39, we need to first determine the total number of unicyclists in Corvallis. We can find this by summing up the frequencies for all age groups:

Total number of unicyclists = 16 + 86 + 1 + 1 + 68 + 15 + 14 = 201

Next, we need to determine the frequency of unicyclists who are not between 30 and 39. We can do this by adding up the frequencies for all age groups that are not between 30 and 39:

Frequency of unicyclists not between 30 and 39 = 16 + 86 + 1 + 68 + 15 + 14 = 200

Finally, we can calculate the probability of selecting a unicyclist who is not between 30 and 39 by dividing the frequency of unicyclists not between 30 and 39 by the total number of unicyclists:

P(not between 30 and 39) = Frequency of unicyclists not between 30 and 39 / Total number of unicyclists

P(not between 30 and 39) = 200 / 201

P(not between 30 and 39) ≈ 0.995

Therefore, the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39 is approximately 0.995 or 99.5%.

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Around 76.5% of the 200 students polled said they would eat two or three servings, with 48.2% saying they would eat two and 28.3% saying they would eat three.

To get the percentage of students who select two or three servings, we must first add the 48 and 73 students who select two and three servings, respectively, for a total of 121 students.

The percentage is then calculated by dividing this sum by the total number of students polled (200), and multiplying the result by 100: (121/200) x 100 = 60.5%

As a result, 2. or 3. servings were selected by 60.5% of the students questioned. It's important to note that this estimate makes the assumption that each student will only select one option (2 servings or 3 servings), not both.

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Answer: 28

Step-by-step explanation:        4+4+4+4+4+4+4=28 :)

Step-by-step explanation:

Not sure about this question ...it seems to be worded improperly.

 IF you are looking for 5/8 as a decimal:

    5/8  is the same as   5 ÷ 8  

        using a calculator , this equals  0.625

pilot error = 25.9%

The most serious threat to aviation safety is pilot error. Pilot error accounts for 25.9% of all fatal plane crashes during the past 70 years, making it the most prevalent threat. Fortunately, there are measures that can be taken to reduce pilot error, such as providing pilots with additional training and stricter qualifications.

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Answer:

15

Step-by-step explanation: BECAUSE THAT IS THE ANSWER

The value of the length of side v is

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

w/sinW = v/sinV

using the sum of angle in a triangle

V + W + U = 180°

V + 79 + 82 = 180°

V = 180-(79+82)11

V = 180 - 161

V = 19°

1690/sin 79 = v/ sin19

sin79 v = 690 sin 19

0.982 v = 690 × 0.33

0.982v = 227.7

v = 227.7/0.982

v = 231.87 inches

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Answer: uh don't know

Step-by-step explanation: look it up

The nth term of an AP with the first term a_1 and the common difference d is given by a_n = a_1 + (n-1)d. The nth term of the given AP is a_n = -54 + (n-1)7.

Arithmetic Progression (AP) is a sequence of numbers in which the difference between the two consecutive numbers is always the same. Each number in the sequence is called a term of the progression. It is a type of sequence where the difference between consecutive terms is constant.

The given expression is an arithmetic progression (AP), in which the common difference between consecutive terms is 7. An AP is a sequence of numbers where each term after the first is formed by adding a fixed value to the preceding one.

The first term of the AP is given as a_1=-54 and the common difference (d) is 7. Thus, the nth term of the given AP can be found using the formula a_n = a_1 + (n-1)d. Substituting the values in this formula, we get a_n = -54 + (n-1)7.

Therefore, the nth term of the given AP is a_n = -54 + (n-1)7.

For example, if n = 10, then the 10th term of the given AP is a_10 = -54 + (10-1)7 = -54 + 63 = 9.

In general, the nth term of an AP with the first term a_1 and the common difference d is given by a_n = a_1 + (n-1)d.

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The nth term of the given AP is [tex]a_n[/tex] = -54 + (n-1)7. The nth term of an Arithmetic Progression with the first term [tex]a_1[/tex] and the common difference d is given by [tex]a_n[/tex] =    [tex]a_1[/tex]  + (n-1)d.

It is a sequence of numbers in which the difference between the two consecutive numbers is always the same. Each number in the sequence is called a term of the progression.

The given expression is an arithmetic progression (AP), in which the common difference between consecutive terms is 7.

The first term of the AP is given as [tex]a_1[/tex] =-54 and the common difference (d) is 7.

Thus, the nth term of the given AP can be found using the formula

[tex]a_n[/tex] =  [tex]a_1[/tex] + (n-1)d.

Substituting the values in this formula, we get

[tex]a_n[/tex] = -54 + (n-1)7.

Therefore, the nth term of the given AP is

[tex]a_n[/tex] = -54 + (n-1)7.

In general, the nth term of an AP with the first term [tex]a_1[/tex] and the common difference d is given by [tex]a_n[/tex] =  [tex]a_1[/tex]  + (n-1)d.

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Question:

Find the nth term by using the given data.

[tex]a_1[/tex] =-54 ; [tex]a_n[/tex] = [tex]a_(n-1)[/tex] +7

Answer:

1018 miles

Step-by-step explanation:

To find the area of a circle, the area is  πr². This means you can simply put in the value of 18 as the radius:

 π x (18)²

= 1017.88

Then round to the nearest whole number:

= 1018 miles

The markup is 73.17 percentage , calculated by subtracting the wholesale price ($41) from the retail price ($71) and then dividing the difference by the wholesale price ($41).

The markup is the difference between the wholesale price and the retail price, divided by the wholesale price. To calculate the markup on each club, subtract the wholesale price from the retail price and then divide the difference by the wholesale price. In this example, the wholesale price is $41 and the retail price is $71, so the difference is $30. Dividing $30 by $41 gives a result of 0.7317, which is the markup expressed as a decimal. To express the markup as a percentage, multiply the result by 100, giving a final answer of 73.17%. This means that the retailer is marking up their clubs by 73.17% of the wholesale price.

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There are 44 Democratic senators and no Independent senators based on ratio.

Since the ratio of Republicans to Democrats is 5:4, we can represent the number of Republican senators as 5x and the number of Democratic senators as 4x, where x is a positive integer. The total number of senators is given as 100, so we have:

5x + 4x + Independent = 100

Simplifying:

9x + Independent = 100

To find the values of x and Independent, we need to solve for these variables. We can start by subtracting Independent from both sides of the equation:

9x = 100 - Independent

Now, we need to find a value of x that makes the right-hand side of the equation divisible by 9. Since the sum of the digits of 100 is 1 + 0 + 0 = 1, which is not divisible by 9, we need to find a value of Independent that makes the sum of the digits of 100 - Independent divisible by 9. The only value that works is Independent = 1, which gives us:

9x = 99

x = 11

Now we can substitute this value of x back into the equation to find the number of Republican and Democratic senators:

Republican = 5x = 5(11) = 55

Democrat = 4x = 4(11) = 44

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The measure of angle PQR is 50 degrees thus correct option is C) 50 degrees.

What is proportion?

A proportion is a statement that two ratios or fractions are equal. In proportion, the numerator of one fraction is proportional to the numerator of another fraction, and the denominator of one fraction is proportional to the denominator of another fraction. For example, if we have two ratios, a/b, and c/d, we can write them as a proportion as follows:

a/b = c/d

This means that the ratio of a to b is equal to the ratio of c to d. We can also write this as a fraction:

a/b = c/d = (a/b)/(c/d)

If the measure of angle PQR to the measure of angle PQS is in the ratio of 5:9, and the measure of angle PQS is 90 degrees, we can use this information to find the measure of angle PQR.

Let x be the measure of angle PQR in degrees. Then we can set up the following proportion:

5/9 = x/90

To solve for x, we can cross-multiply:

9x = 5 * 90

9x = 450

x = 50

Therefore, the measure of angle PQR is 50 degrees. Answer choice C) 50 degrees is the correct answer.

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Answer:

Let's work backwards to figure out how many cookies were left after Mrs. Johnson ate 3 cookies:

Before Mrs. Johnson ate the cookies, the class had eaten 5/6 of the cookies, which means that 1/6 of the cookies were left.

Let's call the number of cookies in 1/6 of the batch "x". So the total number of cookies is 6x.

After the class ate 5/6 of the cookies, there were 1/6 of the cookies left, which is x.

Then Mrs. Johnson ate 3/4 of the cookies that were left, which means she ate 3/4*x cookies.

We know that Mrs. Johnson ate 3 cookies, so we can set up the equation: 3 = 3/4*x

Solving for x:

3 = 3/4x

34/3 = x

4 = x

So there were 4 cookies in 1/6 of the batch, which means there were 6 times as many, or 6*4 = 24 cookies in the whole batch.

Therefore, Mrs. Johnson brought 24 cookies to class that day.

Answer: 24 cookies.

Step-by-step explanation:

the answer to the questions is as below

Let's start by using variables to represent the number of cookies that Mrs. Johnson brought to class. Let's say she brought "x" cookies.

We know that the class ate five-sixths of the cookies, which means that there were only one-sixth of the cookies left. This can be represented as:(1/6)x cookies left

We also know that Mrs. Johnson ate three-fourths of the cookies that were left, which is equal to 3 cookies. We can set up an equation to represent this:

(3/4)(1/6)x = 3

Simplifying this equation, we get:

(1/24)x = 1

x = 24

Therefore, Mrs. Johnson brought 24 cookies to class that day.

For rectangle type books,  the difference in the heights of their stacks of books is 15 3/4 inches.

What exactly is a rectangle?

A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.

In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.

The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The formula for the area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Now,

To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:

Rick's stack = 3 x Trevor's stack

Rick's stack = 3 x 7 7/8 inches

Rick's stack = 23 5/8 inches

Now that we know the height of both stacks, we can find the difference between them:

Difference = Rick's stack - Trevor's stack

Difference = 23 5/8 inches - 7 7/8 inches

Difference = 15 6/8 inches

Difference = 15 3/4 inches

Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.

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The area of the shape that includes squares will be 9 m² and perimeter will be 16m.

What are squares?

A square has four equal sides and four right angles. It is a special type of rectangle, and like rectangles, it is also a two-dimensional shape with all its sides lying in a plane.

A square has several important properties. Its sides are equal in length, and its diagonals are congruent (equal in length) and bisect each other at right angles. All angles in a square are also right angles, which means that it is a special type of rectangle where all angles measure 90 degrees.

The area of a square is calculated by squaring the side. For example, if a square has a side length of s, its area would be A = s². The perimeter of a square is found by adding up the lengths of all four sides, which is P = 4s.

Now,

The sides of the squares will be 2m, 2m and 1 m.

then area of the figure will be =2²+2²+1²

=4+4+1

=9 m²

and

Perimeter = sum of all sides

then Perimeter=5+2+2+2+2+1+1+1

=16 m

Hence,

          The area of the shape that includes squares will be 9 m² and perimeter will be 16m.

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The volume of Joey's toy box is 24 cubic inches.

If the base of the toy box is filled with 8 1-inch cubes, then the volume of the base is:

Volume of base = 8 cubes x [tex](1 inch/cube)^3[/tex] = 8 cubic inches

If the toy box has two more layers on top of the base, then it has a total of three layers. Let's call the height of each layer "h". Then the total height of the toy box is:

Total height = 3h

The volume of each layer is the same as the volume of the base, which is 8 cubic inches. Therefore, the volume of the entire toy box is:

Volume of toy box = volume of base + volume of 2 layers

Volume of toy box = 8 cubic inches + 2(8 cubic inches)

Volume of toy box = 8 cubic inches + 16 cubic inches

Volume of toy box = 24 cubic inches

Therefore, the volume of Joey's toy box is 24 cubic inches.

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The probability of either A or B occurring is 0.55625.

The probability of either A or B occurring when given that events A and B are independent, and P(A) = 0.25 and P(B) = 0.45, can be calculated as follows: 0.25 + 0.45 - 0.25*0.45= 0.55625.:

When the events A and B are independent, then the probability of the two events occurring together is given as:P(A ∩ B) = P(A) × P(B)This is a formula for independent events, and when events A and B are independent, it implies that P(A ∩ B) = 0.

Therefore:P(A ∪ B) = P(A) + P(B) - P(A ∩ B)When the probability of A and B is given as P(A) = 0.25 and P(B) = 0.45, we can substitute these values in the above equation as:P(A ∪ B) = P(A) + P(B) - P(A) × P(B)Thus:P(A ∪ B) = 0.25 + 0.45 - 0.25*0.45= 0.55625Therefore, the probability of either A or B occurring is 0.55625.

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The today is 19th February 2023, it will print '19FEB2023'.

Answer:In order to create a categorical variable based on the variable GRE using SAS, we will use conditional logic as mentioned in the question. Here's how the code will look like:proc import datafile='/.../m3_admission_data.csv' /* update .../ with path containing m3_admission_data.csv*/ dbms=csv replace out=score; run;data score; set score;if GRE < 305 then GRE_Category = 'LOW'; else if 305 <= GRE <= 325 then GRE_Category = 'MEDIUM'; else if GRE > 325 then GRE_Category = 'HIGH'; run;In order to generate today's date, we will make use of the date function which will return today's date. We will then use the PUT function to format the date in the desired format 'ddmonyyyy'. Here's how the code will look like: data _null_; today = date(); /* get today's date */ today_formatted = put(today, date9.); /* format the date */ put today_formatted; run; This will print today's date in the format 'ddmonyyyy'. For example, if today is 19th February 2023, it will print '19FEB2023'.

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