kaleb and gage are waiting to get a rebound during a basketball game. if the height of the basketball hoop is 10 feet, the angle of elevation between kaleb and the goal is 40o , and the angle of elevation between gage and the goal is 30o. how far apart are kaleb and gage standing? (round to the nearest hundredth.)

Therefore, when y = 10 and z = 5, the value of the expression 0.3y + y/z is 5.

In mathematics, an expression is a combination of numbers, variables, and operators that are grouped together to represent a mathematical quantity or relationship. Expressions can be simple, such as a single number or variable, or they can be more complex, involving multiple operations and variables. Expressions are often used in mathematics to represent relationships between variables, to evaluate quantities, and to solve equations.

Here,

Substituting y = 10 and z = 5 in the given expression, we get:

0.3y + y/z = 0.3(10) + 10/5

= 3 + 2

= 5

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The solutions to the equation [tex]csc2(x) + 6 csc(x) − 7 = 0 are x = π/2, (2n+1)π/2, (2n+1)π + arcsec(-6)[/tex] and [tex](2n+1)π - arcsec(-6).[/tex]

The equation [tex]csc2(x) + 6 csc(x) − 7 = 0[/tex] can be rewritten as [tex]csc(x)(csc(x) + 6) − 7 = 0[/tex]. Factorizing the equation we have

Now, solving for csc(x) = 0, we have csc(x) = 0. This implies that x = π/2 or (2n+1)π/2, where n is an arbitrary integer.

Similarly, solving for[tex]csc(x) + 6 = 0[/tex], we have csc(x) = -6. This implies that [tex]x = (2n+1)π + arcsec(-6) or (2n+1)π - arcsec(-6)[/tex], where n is an arbitrary integer.

Therefore, the solutions to the equation[tex]csc2(x) + 6 csc(x) − 7 = 0 are x = π/2, (2n+1)π/2, (2n+1)π + arcsec(-6) and (2n+1)π - arcsec(-6).[/tex]

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The number of students who do not like both games is 3

John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The illustrations are used in probability, logic, statistics, linguistics, and computer science to demonstrate basic set relationships and to teach rudimentary set theory.

Students who like only volleyball=17-10=7

Students who like only basketball=15-10=5

Students who like both sports =10

Students who like one or more sports =7+5+10=22

Students who do not like any sport =25-22=3

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In a class of 25 students, 17 like volleyball, 15 like basketball and 10 like both games. Find the number of students who don't like any of the games.

In the given proof the blanks are ΔAED ≅ ΔABC using the AA criteria.

Every component of the set is connected to itself, according to the reflexive feature of sets. The reflexive property of congruence is known when the relation specified on a set is congruence, and the reflexive property of equality is known when the relation defined on a set of numbers is equality. When this occurs, the relation can be referred to as a reflexive relation or as a reflexive property being satisfied on that set. In the parts that follow, let's learn more about equality and congruence's reflexive attribute.

Given that angle A is congruent to angle A using the reflexive property.

Thus, ΔAED ≅ ΔABC using the AA criteria.

Hence, in the given proof the blanks are ΔAED ≅ ΔABC using the AA criteria.

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Answer:

C=2πr

Step-by-step explanation:

It will take them to meet this goal 10.01 years (or approximately 10 years and 1 month)

To solve this problem, we'll need to use a formula:

Simple interest = Principal × rate × time (in years)

We can rearrange the formula as follows:

Time (in years) = Simple interest / (Principal × rate)

As per the formula, to calculate the time it will take the family to earn the interest, we'll need to know the principal and the rate. These values are not given in the question, so we'll assume that the principal is $10,000 and the interest rate is 7.5 percent (or 0.075 as a decimal).

Simple interest = Principal × rate × time (in years)

$7,507.50 = $10,000 × 0.075 × time (in years)

Divide both sides by $10,000 × 0.075 to isolate the time (in years):

time (in years) = $7,507.50 / ($10,000 × 0.075)

time (in years) = 10.01 years

So, it will take the family 10.01 years (or approximately 10 years and 1 month) to earn $7,507.50 in interest in account 2.

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If a ray QT bisects <RQS, then the measure of one  m ∠TQS = 23.5°

Bisector:

In geometry, bisector is the division of something into two equal or equal parts (of the same shape and size). This usually involves a bisector, also called the midline. The most commonly considered bisectors are the bisector (the line passing through the midpoint of a given line segment) and the angle bisector (the line passing through the vertex of the angle, the bisector equal to the angle ).

According to the Question:

Given :

a ray QT bisects <RQS

∠PQR and ∠RQS is a linear pair . It makes and angle 180 degree

m ∠PQR + m ∠RQS = 180

From the diagram,

m ∠PQR = 3x-5, and m ∠RQS= x+1

Substitute the expression and solve for x

     m ∠PQR + m ∠RQS = 180

⇒ 3x-5 + x+1 = 180

⇒ 4x -4 = 180

⇒ 4x = 184

⇒ x = 46

Now ,  

m ∠RQS = x +1

               = 46 +1

               = 47

Given  QT bisects <RQS. it means QT divides RQS equally

   m ∠TQS = m ∠RQS/2

⇒ m ∠TQS = 47/2

⇒ m ∠TQS = 23.5

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Answer:

-12i - 64j

Step-by-step explanation:

mean price for a theatre ticket in New York is $ 50.299

Mean can be expressed as the total sum of observations for the total number of observations.

In other words its the sum by the count

It gives the average measure of each entity.

The mean Price is sometimes called Average Price.

Total number of Tickets = 11.7 million

Total Cost = $588.5 million

Mean Price = Total Cost / Total Number of Tickets

= 588.5 million / 11.7 million

= $ 50.299

mean price for a theatre ticket in New York is $ 50.299

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The required area and the circumference of the given circle are 19.63 ft² and 15.70 ft respectively.

Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.

The points of the circle are at a fixed distance from the center.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”.

So, the area would be:

= πr²

= 3.14*2.5*2.5

= 19.63495

= 19.63 ft²

The circumference would be:

= 2πr

= 2*3.14*2.5

= 15.70796

= 15.70 ft

Therefore, the required area and the circumference of the given circle are 19.63 ft² and 15.70 ft respectively.

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Answer:

The equation X = √(-X + 6) can be solved using algebraic manipulation. Here are the steps:

Square both sides of the equation to eliminate the square root:

X^2 = -X + 6

Add X to both sides of the equation:

X^2 + X = 6

Rearrange the equation in standard quadratic form:

X^2 + X - 6 = 0

Factor the quadratic equation:

(X + 3)(X - 2) = 0

Use the zero product property to solve for X:

X + 3 = 0 or X - 2 = 0

X = -3 or X = 2

Step-by-step explanation:

The function f(-3) when evaluated graphically has its value to be 4 on the graph

To evaluate a function graphically, you need to follow these steps:

In this case, the function f(-3) has its value to be 4 on the graph

This means that

f(-3) = 4

Hence, the function has a value of 4

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The polynomial function of least degree possible using the given information is: f(x) = -7/3 (x+1)(x-1)(x-3)

What is polynomial function?

A polynomial function is a type of mathematical function that consists of one or more terms, each of which is a constant multiplied by a variable raised to a non-negative integer power.

To construct a polynomial function of least degree possible using the given information, we need to use the fact that the function has real roots at -1, 1, and 3. This means that the function can be factored as follows:

f(x) = a(x+1)(x-1)(x-3)

where a is a constant coefficient that we need to determine.

Next, we need to use the fact that the function passes through the point (2, 7) to determine the value of a. We substitute x=2 and f(x)=7 into the above equation and solve for a:

7 = a(2+1)(2-1)(2-3)

7 = -3a

a = -7/3

Therefore, the polynomial function of least degree possible using the given information is:

f(x) = -7/3 (x+1)(x-1)(x-3)

Note that this function has real roots at -1, 1, and 3, and passes through the point (2, 7).

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The function of given situation is 30x + 40y = 240. The x and y- intercept of function is  (8, 0), (0, 6).

To represent this situation, we can use the following function:

f(x, y) = 30x + 40y

where x is the number of picks and y is the number of shovels.

Since the function represents the total amount spent by Jack, we can set it equal to the given amount:

30x + 40y = 240

To find the x-intercept, we can set y = 0 and solve for x:

30x + 40(0) = 240

30x = 240

x = 8

Therefore, the x-intercept is (8, 0), which means that if Jack buys 8 picks and no shovels, he will spend $240.

To find the y-intercept, we can set x = 0 and solve for y:

30(0) + 40y = 240

40y = 240

y = 6

Therefore, the y-intercept is (0, 6), which means that if Jack buys 6 shovels and no picks, he will spend $240.

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_____The given question is incomplete, the complete question is given below:

Jack brought x picks costing $30 each and y shovels costing $40 each. In all he spent 240 write the function to represent this situation. what are the x and y intercepts of function

Answer:

x = 7

Step-by-step explanation:

In a trapezoid

each lower base angle is supplementary to the upper base angle on the same side , then

∠ S + ∠ V = 180

8x - 21 + 145 = 180

8x + 124 = 180 ( subtract 124 from both sides )

8x = 56 ( divide both sides by 8 )

x = 7

To calculate b, we can plug one of the points into the equation to solve for b. If we plug in (1,2) we get 2 = 1(1) + b, so b = 1. Therefore, the equation of the linear function is y = x + 1.

To find the equation of the linear function represented by the table, we can use the slope-intercept form of a linear equation, which is y = mx + b. To calculate m, we can take two points on the line and calculate the rise (y2 - y1) over the run (x2 - x1). In this case, we can take the points (1,2) and (3,4). The rise is 2 and the run is 2, so m = 1. To calculate b, we can plug one of the points into the equation to solve for b. If we plug in (1,2) we get 2 = 1(1) + b, so b = 1. Therefore, the equation of the linear function is y = x + 1.

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Answer:

that question is incomplete

The values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1

What are inequalities?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Here, we have

Inequality 1: f(4x - 3) ≥ f(2 - x²), Df = (-8 , 4)

The function increases at (-8,4).

So, we have:

4x - 3 ≥ 2 - x²

Rewrite as:

x² + 4x - 2 - 3 ≥ 0

Evaluate the like terms

x² + 4x - 5 ≥ 0

Expand

x² + 5x - x - 5 ≥ 0

Factorize the expression

x(x + 5) - 1(x + 5) ≥ 0

Factor out x + 5

(x - 1)(x + 5) ≥ 0

Solve for x

x ≥ 1 or x ≥ -5

Rewrite as:

-5 ≤ x ≤ 1

Inequality 2: g(3x² - 2x) ≥ g(3x - 2), Dg = all real numbers

g(3x² - 2x) ≥ g(3x - 2)

(3x² - 2x) ≥ (3x - 2)

Evaluate the like terms

3x² - 2x -3x + 2 ≤ 0

3x² - 5x + 2 ≤ 0

3x² - 3x -2x + 2 ≤ 0

3x(x-1) -2(x-1) ≤ 0

Solve for x

x≤1 or x≤2/3

Hence, the values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1

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The area of the semicircle that has a radius of 3 kilometers is calculated as: 14.13 square kilometers.

To find the area of a semicircle, you can follow these steps:

The semicircle's area = 1/2(πr²) = 1/2 * (3.14 * 3²)

= 14.13 square kilometers.

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Answer:

-18x + 54y + 60

Step-by-step explanation:

you get this answer by distributing the -6 to all 3 properties.

-6 x 3x = -18x

-6 x -9y = 54y

-6 x -10 = 60

The statement that is true about equations and expressions is that an example of an equation is because it shows that two expressions are equal.

While an example of an expression is because it is a mathematical phrase represented by numbers, a variable, and an operation.

An equation is a mathematical statement where two expressions are equal. It's important to note that an equation has an equals sign, so the left side of the equation is equal to the right side of the equation.

Expressions are combinations of numbers, symbols, and operators that represent a value. A symbol or letter that represents a value is a variable. It's important to note that an expression does not have an equals sign, so the value of the expression is not defined.Why is an example of an equation true?An equation can be written in the form x = y. The equals sign indicates that x and y are equal. This means that two expressions, x and y, are equal. Therefore, an equation shows that two expressions are equal.

An example of an equation is 3x + 4 = 10. This equation is an example of an equation because it shows that two expressions, 3x + 4 and 10, are equal. The left side of the equation (3x + 4) equals the right side of the equation (10). Therefore, this statement is true: "An example of an equation is because it shows that two expressions are equal."

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Changing  from rectangular to spherical coordinates is: (2, π/2,0)

Spherical Coordinates:

In mathematics, a spherical coordinate system is a coordinate system in three-dimensional space in which the position of a point is specified by three numbers: the radial distance of the point from a fixed origin, the polar angle measured at from a fixed zenith direction, and its Azimuth orthogonal projection on a reference plane passing through the origin and normal to the vertex, measured from a fixed reference direction on this plane.

According to the Question:

To change the coordinates from rectangular to spherical we have to use these formulae:

     [tex]A = \sqrt{x^{2} + y^{2} + z^{2} }[/tex]

And, ∅ = arctan (y/x)

θ = [tex]arccos = \frac{z}{\sqrt{x^{2} +y^{2} +z^{2} } }[/tex]

So, the given points is (0,-2,0)

     [tex]A = \sqrt{0^{2} + (-2)^{2} + 0^{2} }[/tex]

Or, A = √4

Or, A = 2

And, ∅ = arctan (2/0)

           =  arctan (∞) = π/2

    θ = [tex]arccos = \frac{0}{\sqrt{0^{2} +(-2)^{2} +0^{2} } }[/tex]

⇒ θ = [tex]arccos = \frac{0}{\sqrt{(-2)^{2} } }[/tex]

⇒ θ = arcos (0)

Therefore,

The point becomes: (2, π/2,0)

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Thus, the cost would be $60 + $56 = $116 for a group of two persons and $60 + $52 + $52 = $164 for a party of three for number n.

The pricing structure for the tour company is based on a base price of $60 per person, which is then discounted by $4 for each additional person up to a maximum of 8 people. This means that for a group of 2 people, the price would be $60 + $56 = $116, while for a group of 3 people, the price would be $60 + $52 + $52 = $164.

The pricing structure incentivizes larger groups to go on the tour, as they can benefit from the discounted price per person. However, the discount stops at 8 people, which means that larger groups do not receive any further discounts. This is likely because the tour company may have a limit on the number of people they can accommodate on a single tour.

It is important for customers to be aware of the pricing structure when considering booking a tour with the company. They should also consider the benefits and drawbacks of going with a larger group versus a smaller one, such as the potential for a more personalized experience with a smaller group versus a more social experience with a larger group. Overall, the pricing structure is designed to be fair and encourage group bookings, while also accommodating the needs of the tour company.

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The mean, median, mode, and range of times for the second week are

Mean: 13.857 hours

Median: 14 hours

Mode: 16 and 10 hours

Range: 8 hours

To find the mean, median, mode, and range for the second week, we first need to calculate the new set of values by adding 6 to each entry in the first week.

New set of values for the second week:

16 14 18 12 11 10 16

Mean

To find the mean, we add up all the values in the set and divide by the total number of values

Mean = (16 + 14 + 18 + 12 + 11 + 10 + 16) / 7

Mean = 97 / 7

Mean = 13.857

Therefore, the mean for the second week is 13.857 hours.

Median

To find the median, we need to arrange the values in ascending order:

10 11 12 14 16 16 18

The median is the middle value in the set. Since there are an odd number of values in the set, the median is the fourth value, which is 14.

Therefore, the median for the second week is 14 hours.

Mode

The mode is the value that appears most frequently in the set. In this case, there are two values that appear twice: 16 and 10. Therefore, the set has two modes.

Therefore, the mode for the second week is 16 and 10 hours.

Range

The range is the difference between the highest and lowest values in the set. In this case, the highest value is 18 and the lowest value is 10.

Therefore, the range for the second week is 18 - 10 = 8 hours.

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The given question is incomplete, the complete question is:

We are given set of entries in that the number of hours taken by a group of teammates spent in their first week of training is:

10            8            12             6             5            4              10

Now in the second week the each of the entry is increased by 6 so the data for the second week is given as:

16             14            18            12              11             10             16  . The table shows the number of hours that a group of teammates spent in their first week of training for the track finals. In the second week, they each add 6 hours to their training times. What are the mean ,median ,mode , and range of times for the second week?

Option A includes values within the range (6 and 53), so it is suitable. However, it includes decimal values which might not be necessary for this dataset.

What is scatter graph?

A scatter graph, also known as a scatter plot or scatter chart, is a type of graph used to display the relationship between two variables. The graph consists of a set of points that are placed on a coordinate plane, with one variable represented on the horizontal (x) axis and the other variable represented on the vertical (y) axis. Each point on the graph represents a pair of corresponding values for the two variables.

According to the question:

To choose the suitable options for the Length axis, we need to consider the range of values in the dataset. The minimum value for the Length variable is 6, and the maximum value is 53. Therefore, any options that do not include values within this range would not be suitable for the Length axis.

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To maximize the revenue, the bookstore should charge $13 for the book.

Given:

p = book's price in dollars,   where

p is less than or equal to 26.

number of books sold per month = 130-5p

Price that maximizes revenue = ?

Revenue = Price × QuantityofUnitsSold

Revenue = p(130-5p)

Revenue = [tex]130p - 5p^2[/tex] , This is quadratic equation so, The vertex of the parabola, which gives the price that maximizes revenue, can be determined by calculating the value of x-coordinate of the vertex.

Let x = p

The formula for the x-coordinate of the vertex is [tex]-b/2a[/tex]

where,

a = -5

b = 130

c = 0

x = [tex]-b/2a=-130/-10 = 13[/tex]

So, to maximize the revenue, the bookstore should charge $13 for the book.

Maximum revenue will be:-

Revenue = Price × QuantityofUnitsSold

Revenue = p(130-5p)

where p = 13

Revenue = (13)(130-5(13))

Revenue = $845

The maximum revenue at (price = 13) will be $845.

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The equation of the line made by the rice flour joining the remaining two opposite banana plants is y = 2x - 7.

We are given the coordinates of two opposite banana plants, (3, 4) and (7, 2). Since the consecutive plants are fixed at equal distances, the other two plants will lie on the perpendicular bisector of the line segment joining (3, 4) and (7, 2).

First, let's find the midpoint of the line segment joining (3, 4) and (7, 2):

Midpoint = ((x1 + x2)/2, (y1 + y2)/2) = ((3 + 7)/2, (4 + 2)/2) = (5, 3)

Find the slope of the line segment joining (3, 4) and (7, 2):

Slope = (y2 - y1)/(x2 - x1) = (2 - 4)/(7 - 3) = -2/4 = -1/2

Now, we can use the point-slope form of a linear equation to find the equation of the line made by the rice flour joining the remaining two opposite banana plants:

y - y1 = m(x - x1)

Here, m is the slope, and (x1, y1) is the midpoint (5, 3):

y - 3 = 2(x - 5)

y - 3 = 2x - 10

y = 2x - 7

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Answer:

170.16 ft

Step-by-step explanation:

tan10° = 30/x

x = 30x/ tan 10° = 30/0.1763

=170.16 ft

Answer:

(5, 13)

Step-by-step explanation:

Points (4, 8)

Translation right 1 unit. Meaning x + 1

(4, 8) → (5, 8)

Up 5 units. Meaning y + 5

(5, 8) → (5, 13)

So, the final point at (5, 13)