30 people gathered to watch a baseball game. While talking, they realized that 11 of them were Toronto Blue Jays fans. What is the probability that a randomly selected person from the group is a Toronto Blue Jays fan?

​Type the answer in simple fraction form.

The total number of copies that the band sold is given as follows:

1.89 x 10^6 copies.

The total number of copies sold is obtained adding the number of copies of each album sold.

The amounts for each album are given as follows:

When we add two numbers in scientific notation, they must have the same exponent, hence we add the bases keeping the exponents, as follows:

(1.3 + 0.59) x 10^6 = 1.89 x 10^6 copies.

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Answer:

Step-by-step explanation:

37

Answer:

Find the value of b using the formula for the equation of a line.

y = mx+b

Replace the known value of m in the slope y-intercept form of the equation.

y=(1)x+b

Replace the known value of b in the slope y-intercept form of the equation.

y=(1)x+4

Simplify the slope y-intercept form of the equation.

Remove parentheses.

y=(1)x+4

Multiply 1 by x

y=1x+4

Remove parentheses.

y=(1)x+4

Multiply x by 1

this is the answer : y=x+4

i hope this helps.

The p value is calculated as 0.116

Null u = 70

alternate u ≠ 70

The alternate is a two tailed test

the test statistic calculation

t = x - u / s/√n

x = 85 + 77 + 82 + 68 + 72 + 69 / 6

= 75.5

standard deviation s = [tex]\sqrt{\frac{(85- 75.5)^2+(77- 75.5)^2+...(69- 75.5)^2}{6-1} }[/tex]

= 7.01

Test stat = (75.5 - 70) / 7.01/√6

= 1.92

degree of freedom = 6 - 1 = 5

this is 2 tailed

p value using excel = tdist( 1.8, 5 , 2)

= 0.116

We fail to reject the null hypothesis because it is greater than the level of significance

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The cash discount is $353.20 and the net amount due is $17,306.80.

Conditions of sale are the rules that govern a business transaction, including the cost, the method of payment, the delivery, and any other pertinent information. Normally, they are specified in a sales contract or invoice and acknowledged in advance of the transaction. The conditions of sale might alter based on the type of products or services being exchanged, the volume and complexity of the deal, and other elements.

We know that,

Cash discount = amount x discount rate

Net amount due = amount - cash discount

For 2/10:

Cash discount = $17,660 x 2% = $353.20

Net amount due = $17,660 - $353.20 = $17,306.80

Hence, the cash discount is $353.20 and the net amount due is $17,306.80.

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Since the center of the circle lies on the y-axis, the x-coordinate of the center must be 0.

Also, since the diameter of the circle is 12 units, the radius is half of that, or 6 units.

Using the standard form of the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, we can substitute the values we know and simplify the equations to see which ones match.

The equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:

   x^2 + (y - 6)^2 = 36 (center is at (0, 6))

   x^2 + (y + 6)^2 = 36 (center is at (0, -6))

Therefore, the two options that represent the circles with the given properties are:

x^2 + (y - 6)^2 = 36 and x^2 + (y + 6)^2 = 36.

Answer: 24 percent of 25 is 6.

Step-by-step explanation: The output of 24 percent of 25 is 6. To obtain this answer, we multiply 0.24 by 25.

Therefore , the solution of the given problem of interest comes out to be $630 ,   $659.15 ,  $638.89 and  $345.57 .

To determine simple interest, divide the sum by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a fraction of the principal amount.

Method 1: A basic interest rate of $2.50 per month for a year equals

=> $2.50 x 12 = $30 in interest.

The balance after a year equals $600 plus $30, or $630.

Response: $630

Step 2: Divide the monthly interest rate by 12 to get 0.4167%

Amount after a year:

=> $600 multiplied by (1 + 0.004167)/12 to arrive at $659.15

Response: $659.15

Option 3: $50 per month in deposits

Interest rate per month: 5% divided by 12 Equals 0.4167%

Surplus at the end of the year is equal to

=> $50 x (((1 + 0.004167)12 - 1) / 0.004167) x (1 + 0.004167) = $638.89

Response: $638.89

Method 4: Initial investment of $300, subsequent deposits of $25, and an interest rate of 5% divided by 12 equals 0.4167%.

Amount at the end of the year equals

=> $300 x (1 + 0.004167)12 + $25 x (((1 + 0.004167)12 - 1) / 0.004167) x (1 + 0.004167) = $345.57

Response: $345.57

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The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x with a horizontal shift of 2 units to the right, a vertical stretch by a factor of 3, and a vertical shift of 5 units up.

The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x.

Here are the transformations that were applied to f(x) to obtain g(x):

1. Horizontal shift: The denominator of f(x) is x, which means that the vertical asymptote is at x = 0. By subtracting 2 from x in the denominator of g(x), we are shifting the vertical asymptote to x = 2. This is a horizontal shift of 2 units to the right.

2. Vertical stretch: The coefficient 3 in front of the fraction means that the function is stretched vertically by a factor of 3 compared to f(x). This means that the distance between the horizontal asymptotes (which are at y = 0 for f(x) and y = 5 for g(x)) is three times larger for g(x) than for f(x).

3. Vertical shift: The constant 5 added to the fraction means that the entire function is shifted vertically by 5 units compared to f(x). This means that the horizontal asymptote of g(x) is at y = 5 instead of y = 0.

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Answer:

2(x+3)

Step by Step:

2(x)=2x

2(3)=6

2x+6=2(x+3)

2(x)+2(3) =2 (x+3)

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

Answer:10

Step-by-step explanation:3x2=6 and 4x1=4 4+6=10

Answer:

See below

Step-by-step explanation:

Perimeter = (7x2) + (2x2) = 18

Area (L x W) = Square + rectangle

= (3x2) + (4x1) = 6 + 4 = 10

Since the electorate have decided that Senator Wiggins is the best candidate for the position. The  logical form of this argument is option b. Disjunctive Syllogism

The argument is presented in the form of a disjunctive syllogism, which involves a logical form that states that either one of two alternatives must be true, and one of them has been found to be true; therefore, the other must be false.

In this case, the two alternatives are:

Thus, the logical form of the argument is:

Either A or B.

Not A.

Therefore, B.

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Step-by-step explanation:

To calculate the future value of a loan with simple interest, we can use the formula:

A = P(1 + rt)

where A is the future value or total amount due, P is the principal, r is the interest rate, and t is the time period in years.

In this case, we have:

P = $1000

r = 5.0% = 0.05 (expressed as a decimal)

t = 6 months = 0.5 years (since there are 12 months in a year)

Plugging these values into the formula, we get:

A = $1000(1 + 0.05 x 0.5)

A = $1000(1.025)

A = $1025

Therefore, the future value or total amount due on the loan after 6 months is $1025.

The probability for this problem is an Empirical probability, as it is taken from an experiment.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Empirical probability is based on observations or experimental data, for example, observing the number of students in a cafeteria and obtaining the percentage of male students and female students, as is done for this problem.

Theoretical probability, on the other hand, is based on mathematical analysis and is calculated using the principles of probability theory. It is the probability that an event will occur based on all possible outcomes. For example, a fair coin is equally as likely to be heads or tails.

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The number of years for 21% to remain is 78years

The time required for half of the original population of radioactive atoms to decay is called the half-life.

half life = 0.693/decay constant

decay constant = 0.693/34

= 0.02

21% of N(o) = 21N(o)/100 = N(y)

from the formula

N(t) = Noe^-kt

21N(o)/100 = Noe^-kt

21N(o)=100 Noe^-kt

divide bother sides by N(o)

21 = 100e^-kt

e^-kt = 21/100

e^-kt = 0.21

-0.02 t= ln0.21

-0.02 t= -1.56t

t = 1.56/0.02

t = 78years

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The function is increasing on (4, 6).

The function is decreasing on (- 6, - 2).

The function is constant on (-2, 4).

The domain of the function is, (- 6, 6).

The range of the function is, (- 3, 1).

A function f(x) is said to be increasing if the increase in the independent variable results in an increase in the dependent variable.

A function f(x) is said to be increasing if the increase in the independent variable results in a decrease in the dependent variable.

The function is increasing on the intervals (4, 6).

The function is decreasing on the interval (- 6, - 2).

The function is constant on the interval (-2, 4).

The domain of the function is, (- 6, 6).

The range of the function is, (- 3, 1).

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What is Function?

Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.

How to determine

Where F(x) = 2x^4 + x^2 - 10x + 1

So, to calculate f(-10)

f(x) = y

Where x = -10

f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1

f(-10) = 2(10000) + 100 + 100 + 1

f(-10) = 20000 + 100 + 100 + 1

f(-10) = 20201

For f(2),

f(x) = y

Where x = 2

f(2) = 2(2)^4 +2^2 -10(2) + 1

f(2) = 2(16) + 4 -20 + 1

f(2) = 32 + 4 -20 + 1

f(2) = 17

For f(3)

f(x) = y

Where x = 3

f(3) = 2(3)^4 + 3^2 -10(3) + 1

f(3) = 2(81) + 9 -30 + 1

f(3) = 162 + 9 - 30 + 1

f(3) = 142

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As a result, the equation in point-slope form for the line passing through the point (-3, -1) with a slope of -1/3 is: y - (-1) = (-1/3)(x - (-3)) or y + 1 = (-1/3)(x + 3)

Slope is a mathematical term that describes how steep a path is. The ratio of the vertical shift (rise) to the horizontal transition (run) between any two points on a line is more precisely known as the slope of a line. A line's inclination can be zero, positive, negative, or undefinable. A line that has a positive slope is rising as it travels from left to right, whereas a line that has a negative slope is falling as it moves in the opposite direction. A line has a slope of zero if it is straight, and a slope of infinity if it is vertical.

given

The linear equation's point-slope form is:

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is a spot on the line and m denotes the angle of the line's slope. The equation of the line can be expressed as follows using the provided point (-3, -1) and slope of -1/3:

y - (-1) = (-1/3)(x - (-3))

Streamlining the right side:

y + 1 = (-1/3)(x + 3)

Increasing the right side:

y + 1 = (-1/3)x - 1

Taking away 1 from both sides:

y = (-1/3)x - 2

As a result, the equation in point-slope form for the line passing through the point (-3, -1) with a slope of -1/3 is: y - (-1) = (-1/3)(x - (-3)) or y + 1 = (-1/3)(x + 3)

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Answer:

Step-by-step explanation:

[tex]A=\pi r^2\\[/tex]

  [tex]=\pi \times 9^2[/tex]   (radius = 9 feet)

  [tex]=81\pi[/tex]

  [tex]\approx 254.47[/tex] feet

Therefore , the solution of the given problem of equation comes out to be  y = 6x + 11.

Mathematical formulas frequently use the same letter to try to impose uniformity between two claims. Many variable academic numbers are shown to be equal using mathematical equations, also known as assertions. The normalise divides 12 and b + 6 into two parts using the result y + 6 = 12 as an illustration. It is possible to determine the connection between each sign component and the number of lines. The significance of a symbol usually contradicts itself.

Here,

In slope-intercept form, the provided equation y = -1/6x - 2 has a slope of -1/6. Consequently, this line's perpendicular inclination is as follows:

=> m2 = -(1/-1/6) = 6

Now that we know the desired line's slope and the spot through which it passes (-2, -1). To determine the solution of a linear equation, we can use its point-slope form:

=> y - y1 = m(x - x1) (x - x1)

where m is the slope 6 and (x1, y1) is the position (-2, -1). By replacing these numbers, we obtain:

=> y + 1 = 6(x + 2) y + 1

=> 6x + 12 y + 1

=> 6x + 11 y - (-1)

=> 6(x - (-2))

As a result, the equation for the line passing through the position (-2, -1) and perpendicular to y = -1/6x - 2 is y = 6x + 11.

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We can state this by responding to the provided question A direct function variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The coordinate plane with a line crossing between (0, -2) and (-2) is the graph that illustrates a function with direct variation (-4, 0).

If m is the line's slope and (x1, y1) is a point on the line, [tex]y - y1 = m(x - x1).[/tex]

The line's slope is as follows:

[tex]m = (y2 - y1)/(x2 - x1) = (-2 - 0)/(0 - (-4)) = 1/2[/tex]

The equation of the line going through (0, -2) and (-4, 0), expressed in point-slope form, is:

[tex]y - (-2) = 1/2(x - 0) (x - 0)[/tex]

When we simplify the equation, we obtain:

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

A direct variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).

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Answer:

Step-by-step explanation:

the range would be the answer as it shows the top and the bottom score.

Answer: To simplify the expression, we can apply the exponent rule for powers of powers which states that to raise a power to another power, we multiply the exponents.

So,

(4a^(-2))^(-1/2) = 4a^(-2 * (-1/2)) = 4a^(1) = 4a

Therefore, (4a^-2)^-1/2 simplifies to 4a.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Angle sum of a triangle = 180°. So we get:

[tex]62+69+(4x+5)=180[/tex]

[tex]136+4x=180[/tex]

[tex]4x=44[/tex]

[tex]x=11[/tex]°

Answer:

x = 11

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Accordingly,

62 + 69 + 4x + 5 = 180

Combine like terms.

136 + 4x = 180

Subtract 136 from both sides.

4x = 180 - 136

4x = 44

Divide both sides by 4.

x = 11

The simplification value of the expression is,

⇒ 5x³ - 12x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 2x³ - x² + 3 (x³ - 4x²)

Now, We can simplify the expression as;

⇒ 2x³ - x² + 3 (x³ - 4x²)

⇒ 2x³ - x² + 3x³ - 12x²

⇒ 5x³ - 12x²

Thus, The simplification value of the expression is,

⇒ 5x³ - 12x²

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The arc length of the arc is (11/5)π inches, or approximately 6.926 inches (rounded to three decimal places).

We may use the following formula to determine the arc length of an arc having a radius of 18 inches and a centre angle of 22°:

(Central angle / 360°) x (2r) Equals arc length

where r denotes the arc's radius.

Inputting the values provided yields:

arc length is equal to (22°/360°) x (2x18 inches).

arc length is equal to 11/180 times 36 inches.

11.5 inches is the length of an arc.

As a result, the arc's length is (11/5) inches, or roughly 6.926 inches (rounded to three decimal places).

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The slope of the given line is  [tex]m = \dfrac{1}{2}\\[/tex].

A line's slope is calculated as the tangent of the angle it makes with the x-axis. A straight line's slope remains constant throughout. Y = mx + b can be used to calculate a straight line's slope-intercept form.

Given that the line is passing through the points ( 0,1) and (-2, 0 ). The slope of the line is calculated by the application of the formula given below,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope of the line is  calculated by substituting the values of the coordinates in the formula,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \dfrac{1 - 0}{0 + 2 }[/tex]

[tex]m = \dfrac{1}{2}[/tex]

Therefore, the slope of the line will be  [tex]m = \dfrac{1}{2}\\[/tex].

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Answer: 3

Step-by-step explanation: