a. For which angle measures, 0, between 0 and
2π radians is cos(0) = 0? Label the
corresponding points on the unit circle.
b. What are the values of sin(x) for these angle
measures?

The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex],  so the value of a+b is given as 107.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

Let x be the probability that it rains on Sunday given that it doesn't rain on Saturday then we have,

3/5x + 2/5(2x) = 3/10

7/5x = 3/10

x = 3/14.

Therefore, the probability that it doesn't rain on either day is,

[tex]$\left(1-\dfrac{3}{14}\right)\left(\dfrac{3}{5}\right)=\dfrac{33}{70}$[/tex]

Therefore, the probability that rains on at least one of the days is

[tex]$1-\dfrac{33}{70}=\dfrac{37}{70}$[/tex],

so adding up the 2 numbers, we have,

37 + 70 = 107.

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Complete question;

There is a 40% chance of rain on Saturday and a 30% chance of rain on Sunday. However, it is twice as likely to rain on Sunday if it rains on Saturday than if it does not rain on Saturday. The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex], where a and b are relatively prime positive integers. Find a+b.

Answer: 37.5

Step-by-step explanation:

If a ball is drawn randomly from a jar that contains 8 red balls, 3 white balls, and 6 yellow balls, the probability of drawing a red ball from the jar is approximately 0.47 or 47%.

The probability of a red ball being drawn from the jar can be calculated as follows:

Total number of balls in the jar = 8 red + 3 white + 6 yellow = 17

Probability of drawing a red ball = (Number of red balls in the jar) / (Total number of balls in the jar) = 8/17 ≈ 0.47

This means that if we were to draw a ball from the jar randomly, there is a 47% chance that the ball we draw will be red.

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Complete question is:

A ball is drawn randomly from a jar that contains 8 red balls, 3 white balls, and 6 yellow balls. find the probability of the given event.

What is what is the probability of a Red ball being drawn?

Answer:

75°

Step-by-step explanation:

The angle in the given figure is 90°.

x + 15 = 90

x = 90 - 15

x = 75°

Answer:

(5^3)^(-2)

Step-by-step explanation:

5^2 × 5^-8 = 5^-6

(5^3)^(-2) = 5^-6

Answer:

Hope this is what you were looking for :)

Step-by-step explanation:

tan = opposite/adjacent

IF YOU DONT NEED TO FIND THE VALUES OF THE SIDES:

tan A =  [tex]\frac{x}{11}[/tex]

tan B = [tex]\frac{11}{x}[/tex]

Replace the x for whatever the value of BC is or if it doesn't have a value, you can just leave it as x.

IF YOU DO NEED TO FIND THE VALUES OF THE SIDES:

tan 45 = 1

tan 45 =  [tex]\frac{BC}{11}[/tex]

(11) tan 45 = BC

BC = 11

tan 45 = [tex]\frac{11}{AC}[/tex]

AC = [tex]\frac{11}{tan 45}[/tex]

AC = 11

This can also be done without using tangent from taking a look at special right triangles.

In 45-45-90 triangles, the two legs are the same size while the hypotenuse is equal to one of the legs multiplied by [tex]\sqrt{2}[/tex]. In doing this, we can find that both legs are 11 and the hypotenuse is [tex]11\sqrt{2}[/tex].

A dependent variable that maintains constant measurements throughout an experiment will be depicted by a straight, horizontal line in a graph.

In an experiment, the dependent variable is the variable being measured, and it is expected to change in response to changes in the independent variable. However, if the dependent variable remains constant throughout the experiment, it indicates that it is not affected by the independent variable.

When such a situation arises, the data points for the dependent variable will be located at the same level or value, resulting in a horizontal line in the graph.

This straight, horizontal line represents the constant measurements of the dependent variable, and it can provide valuable insights into the nature of the relationship between the independent variable and the dependent variable.

A dependent variable that maintains constant measurements throughout an experiment may indicate a flaw in the experimental design, such as an incorrect assumption about the nature of the relationship between the independent variable and the dependent variable, or an uncontrolled confounding variable.

Therefore, it is important to carefully analyze the data and the experimental design to identify and address any potential issues.


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Answer:

14/24, 21/36, 28/48, 35/60, 42/72, 49/84, 56/96 are equivalent fractions of 7/12.

10/12, 15/18, 20/24, 25/30. are equivalent fractions of 5/6

Step-by-step explanation:

The equation of the circle is with the diameter given is x² + y² = 9.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

We can quickly determine the circle's centre and radius thanks to this form. We must first square the x and y terms before rearranging the components in order to transform a circular equation into standard form.

The endpoints of the diameter is (-3,0) and (3,0).

Now, using the section formula the coordinates of radius are:

((-3+3)/2, (0+0)/2) = (0,0

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

Substituting the values:

(x - 0)² + (y - 0)² = 3²

Hence, the equation of the circle is x² + y² = 9.

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The total number of different dinner special combinations offered by Lewis' Restaurant is 28 different dinner special combinations.

Lewis' Restaurant offers a dinner special that consists of a main dish, a vegetable, a salad, and a roll.

There are 4 main dishes, 7 vegetables, 1 salad, and 1 type of roll to choose from.

To determine the total number of different dinner special combinations that Lewis' offers, you have to multiply the number of options available for each course.

To find the total number of different dinner special combinations offered by Lewis' Restaurant, you have to use the multiplication rule.

The multiplication rule states that if an event can occur in 'a' different ways and another independent event can occur in 'b' different ways,

then the two events can occur in 'a x b' different ways.

Therefore, the total number of different dinner special combinations offered by Lewis' Restaurant can be calculated as follows:

4 main dishes × 7 vegetables × 1 salad × 1 type of roll= 28 different dinner special combinations

Note that we multiply the number of options for each course because the courses are independent.

This means that the choice of the main dish does not affect the choice of the vegetable, salad, or roll, and vice versa. Therefore, we can multiply the number of options for each course to determine the total number of different dinner special combinations that Lewis' Restaurant offers.

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Method 1: Graphing

Graphing is best when the both equations are shown in slope-intercept form. For example:

[tex]y=\frac{1}{2} x+2\\y=-\frac{1}{2} x+4[/tex]

[tex](2,3)[/tex]

You can easily graph this system of equations and find the intersecting point. The graph is displayed below. This may not always be the case, however and you may get complicated fractions in your answer. In this case, substitution or elimination may be better.

Method 2: Substitution

Substitution is a good method to solve a system of equations when one of the equations can be rearranged to isolate one variable, or the equation already solves for a variable. This isolated expression can then be substituted into the other equation(s) to create a new equation(s) with only one variable.

For example, consider the system of equations:

[tex]y=x-2\\2x-5y=1[/tex]

Since y is much easier to substitute, we can choose y to substitute into the other equation:

[tex]2x-5(x-2)=1[/tex]

We can then simplify the equation:

[tex]2x-5x+10=1\\-3x=-9\\x=3[/tex]

Then you can substitute x into the original equation:

[tex]y=3-2\\y=1[/tex]

Solution: [tex](3,1)[/tex]

Substitution can be a useful method when the system involves two or three variables and one equation can be easily rearranged to isolate a variable. However, it can become more difficult or time-consuming when the system involves more variables or when the equations are not solving for a variable or can be easily solved. In these cases, other methods such as elimination is more efficient.

Method 3: Elimination

Elimination is a good method to solve a system of equations when the equations can be added or subtracted in a way that eliminates one of the variables.

For example, consider the system of equations:

[tex]x+y=90\\x-y=18[/tex]

We can cancel out the variable y and add the other numerals and variables:

[tex]2x=108[/tex]

This simplifies to:

[tex]x=54[/tex]

We can then solve for y:

[tex]54+y=90\\y=36[/tex]

Solution: [tex](54, 36)[/tex]

Once we have the value of x, we can substitute it back into one of the original equations to solve for y.

Although elimination is slightly more complicated, it is the most efficient method out of all of the three methods I have shown here.

Hope this helped you :)

(This took like 30 minutes ;-;)

Answer:

The density of the wood is 0.6 g/cm^3

Step-by-step explanation:

The density of an object can be calculated by dividing the mass of the object by its volume. In this case, the mass of the block of wood is 120g and its volume is 200cm^3.

Density = mass / volume

Density = 120g / 200cm^3

Density = 0.6 g/cm^3

Therefore, the density of the wood is 0.6 g/cm^3.

Equation:

89.50=2.35c+5.50d

If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).

So we try pats numbers 8 cats and 14 dogs so

89.50=2.35(8)+5.50(14)

89.50=18.8+77

89.50=95.8

So pats numbers were wrong so we try different numbers

So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation

89.50=2.35(10)+5.50(12)

89.50=23.5+66

89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats

The given functions in GeoGebra and determine by analytically checking:

a. function type is [tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

b. Domain and range Range (-2, +2).

c. Asymptotes is HA = 2 and VA = ±2

The function y = f( x) is classified into different types of functions, grounded on factors similar as the sphere and range of a function, and the function expression. The functions have a sphere x value that's appertained as input. The sphere value can be a number, angle, numeric, bit.

[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

Functions in mathematics can be compared to the operations of a dealing (soda pop) machine. When you put in a certain quantum of plutocrat, you can elect different types of tonics. also, for functions, we input different figures and we get new figures as the result. sphere and range are the main aspects of functions.

[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

x² = 4

x = ± 2

Range (-2, +2).

An asymptote is a line being approached by a wind but noway touching the wind. i.e., an asymptote is a line to which the graph of a function converges. We generally don't need to draw asymptotes while graphing functions. But graphing them using dotted lines( imaginary lines) makes us take care of the wind not touching the asymptote. Hence, the asymptotes are just imaginary lines.

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Complete question:

Represent the given functions in GeoGebra and determine by analytically checking: a. function type b. Domain and range c. Asymptotes, both vertical and horizontal, if it has them:

Between 4 and 4.5

sqrt(20)

Between 4.5 and 5

sqrt(22)

sqrt(23.1)

Between 5 and 5.5

sqrt(30)

sqrt(25.9)

sqrt(27.3)

Between 5.5 and 6

sqrt(31)

sqrt(34.9)

The system of linear inequalities to model the number of hours that you could work at each location in a week is:

x ≥ 4

x + y ≤ 15

What is system of linear inequality?

A system of linear inequalities is a set of two or more linear inequalities with the same variables. It describes a region in the coordinate plane that satisfies all of the inequalities in the system.

In this case, we are trying to model the number of hours that someone could work at two different jobs.

The first inequality given is that the person must work at least 4 hours per week at the trampoline park. Let x be the number of hours worked at the trampoline park. This can be represented as:

x ≥ 4

The second inequality given is that the total number of hours worked at both jobs cannot be greater than 15. Let y be the number of hours worked at the landscaping company. Then, the total number of hours worked can be represented as:

x + y ≤ 15

Together, these two inequalities form a system of linear inequalities that model the possible number of hours that the person can work at each job in a given week.

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Answer:

The answer to your problem is, [tex]16cm^{2}[/tex]

Step-by-step explanation:

Sophie has a small cube shaped box.

Volume of the box is [tex]64cm^{3}[/tex]

We have to find the area of one face of the box.

Let one side of the box is x

Then volume = [tex]x^{3}[/tex] = 64

x³ = 4³

= 4

Now area of one face of the cube = x²

then area = 4² = 16 cm²

Thus the answer to your problem is, [tex]16cm^{2}[/tex]

Step-by-step explanation:

2 pictures are attached

sin waves are used in many medical devices like to measure heart beats

The probability of getting 0 toppings when ordering a hamburger with a choice of up to 6 toppings is 0.0154, rounded to four decimal places.

The total number of ways to choose 6 toppings out of a possible 6 is given by the combination formula:

[tex]$${ \choose 6} = \frac{6!}{6!(6-6)!} = 1$$[/tex]

This is the total number of possible outcomes.

To get 0 toppings, we need to choose 0 toppings out of 6. The number of ways to do this is:

[tex]{6_{0} =[/tex] [tex]\frac{6!}{0!(6-0)!} = 1$$[/tex]

So the probability of getting 0 toppings is:

[tex]$$P(\text{0 toppings}) =[/tex]  [tex]\frac{number of ways to get 0 toppings}{total number of possible outcomes} $$[/tex] [tex]\frac{1}{1} = 1$$[/tex]

However, this is assuming that the cashier chooses the toppings randomly and without replacement. If the cashier has some bias or preference towards certain toppings, this probability may be different.

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The inequality representing the number of players on the court is given by 0 ≤ x ≤ 5.

Let us consider variable 'x' represents the number of players in the basketball team.

As we know,

Number of players is always greater than or equal to zero.

As number of players in the basketball team cannot be negative players.

As per condition,

Number of players in the basketball team = At most 5 players.

This implies,

Number of players in the basketball team is less than or equal to 5

The inequality that best describes the number of players on the basketball court is written as,

⇒ 0 ≤ number of players ≤ 5

⇒ 0 ≤ x ≤ 5

Therefore, the inequality used to represents the number of players in the basketball court is equal to 0 ≤ x ≤ 5.

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Since mXOY = mWOV, we can form the following equations so, m--XZ = m--ZV.

An equation is a mathematical statement that states the equality of two expressions. It usually consists of two terms, with an equals sign between them, representing the relationship between the terms. Equations are often used to describe relationships between variables, such as in physics and chemistry, and can be used to calculate unknown values.

Proof:

Since mXOY = mWOV, we can form the following equations:

m--YZ = m--ZW (Given)

Subtract both sides of the equation by m to get:

YZ = ZW

Then, multiply both sides of the equation by X to get:

XZ = XW

Now, substitute Y for V and W for V in the equation to get:

XZ = ZV

Finally, subtract both sides of the equation by m to get:

m--XZ = m--ZV

Therefore, m--XZ = m--ZV.

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We can see here that the figures that have the same area are: A. Figures I and II.

Area is a measure of the size of a two-dimensional surface or shape. It refers to the amount of space inside the boundaries of a flat object, such as a rectangle, triangle, or circle. Area is typically measured in square units, such as square meters, square feet, or square centimeters.

The area of Figure I which is a rectangle is = l × b = 2cm × 5.8cm = 11.6cm².

The area of Figure II which is a parallelogram is = b × h = 4cm × 2.9cm = 11.6cm².

Thus, Figures I and II have the same area.

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The sequence follows a pattern of adding 7 to the previous term, and its formula is 7n - 3. The sum of the first 100 terms of the sequence is 35,350, which was found using the formula for the sum of an arithmetic series.

The next term in the sequence can be found by adding 7 to the previous term, so the next term is 25.

To find a formula for the nth term of the sequence, we can observe that each term is 7 more than a multiple of 7. In other words, the nth term is given by the formula 7n - 3.

To find the sum of the first 100 terms of the sequence, we can use the formula for the sum of an arithmetic series:

S = (n/2)(a1 + an)

where S is the sum of the first n terms, a1 is the first term, and an is the nth term. Substituting n = 100, a1 = 4, and an = 703, we get:

S = (100/2)(4 + 703) = 35,350

Therefore, the sum of the first 100 terms of the sequence is 35,350.

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Therefore , the solution of the given problem of inequality comes out to be Gary and Jamal are the students who created an inequality that holds true for all values in the collection "0, 1, 3, 4, 6, 12".

Algebra does not have an equal symbol, but a partner or group of integers can be used to represent the difference. Equilibrium is typically followed by equity. Inequality comes from the continued divergence of ideals. Disparity and expression fairness are not identical. Despite the fact that the parts are typically not connected or close to one another, that was our most popular symbol. (). Any difference, no matter how small, can be used to determine worth.

Here,

We can test each inequality with each value in the set, 0 through 1, 3, 4, 6, and 12, to identify which inequality holds true for all values.

6 > 0.5t, where t is a member of the collection, is Gary's inequality. When we compare each value in the collection to this inequality, we discover:

When t = 6: 6 > 0.5(6) is true

When t = 12: 6 > 0.5(12) is true

Therefore, for each value in the collection, Gary's inequality holds true.

30 - t  18 is Nancy's inequality, where t is a number from the collection. When we compare each value in the collection to this inequality, we discover:

When t = 6: 30 - 6 ≤ 18 is true

When t = 12: 30 - 12 ≤ 18 is true

Therefore, not all values in the collection satisfy Nancy's inequality.

Gary and Jamal are the students who created an inequality that holds true for all values in the collection "0, 1, 3, 4, 6, 12".

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Answer:

For problem a: 0,4 0,5 0,6

For Problem B: 1,0 2,0 3,0

Step-by-step explanation:

Graph each equation on a graph Figure out either solid or dotted line. Then depending on <=,<,>,>= is whre you shade on your graph. The spot where both lines meet when shaded is your solution area and you pick any spot on that. You can check your answer by plugging in ordered pairs for your X,Y values in the system.

"The speed of a randomly selected car on a highway" and "the percent change in the price of a share of IBM stock in a month" are examples of continuous random variables. Options A and C are the correct answers.

Continuous random variables are those that can take on any value within a given range, as opposed to discrete random variables, which can only take on certain values.The speed of a randomly selected car on a highway and the percent change in the price of a share of IBM stock in a month are examples of continuous random variables.

These variables have a range of values and can take on any value within that range.The number of claims on a medical insurance policy on a given year, the number of customers that enter a particular store on a randomly selected day, and the time that elapses between two customer service calls are examples of discrete random variables. These variables can only take on certain values, such as whole numbers or specific times.

Thus option A and option C are the correct answers.

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Answer:

area=36.5

Step-by-step explanation:

8×4=32

8-5=3 for the base of the triangle

7-4=3 for the height of the triangle

3×3=9

9÷2=4.5

4.5+32=36.5

area=36.5

The percentage change in the visit of total number of customers in the second week as compare to first week is equal to 16.67%.

Total number of customers visited the store in the first week = 360

Total number of customers visited the store in the second week = 300

Percentage Change = (|First week - second week / First week) x 100%

Substitute the value of the number of customers in different weeks in the formula we get,

Percentage Change

= (|300 - 360| / 360) x 100

= (60 / 360) x 100

=( 100 / 6 )

= 16.66666%

= 16.67%

Therefore, the percentage change in the number of customers that visited the store from the first week to the second week is a decrease of 16.67%.

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The above question is incomplete, the complete question is:

Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.

What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?

Factor  72 + 32 in the form of a ( b + c)  with A having gcf is 72 + 32 is 8(9 + 4).

To factor 72 + 32, we first need to find the greatest common factor (GCF) of 72 and 32.

The prime factorization of 72 is 2³ x 3², and the prime factorization of 32 is 2⁵.

The common factors of 72 and 32 are 1, 2, 4, 8, and 16. The greatest common factor is 8, since it is the largest factor that they both share.

So, we can write 72 + 32 as:

72 + 32 = 8 x (9 + 4)

Therefore, the factored form of 72 + 32 is 8(9 + 4).

To factor 72 + 32, we need to find the greatest common factor (GCF) of 72 and 32, which is 8. We can then use this GCF to write 72 + 32 in factored form as 8(9 + 4). This expression can also be simplified as 8(13), which equals 104. This means that 72 + 32 can be written as the product of 8 and 13, where 8 is the GCF of 72 and 32, and 13 is the sum of the quotients of 72 and 32 when divided by 8. Factoring expressions is an important skill in algebra and is used in many areas of mathematics and science.

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