In a class of students, the following data table summarizes how many students play
an instrument or a sport. What is the probability that a student chosen randomly
from the class plays a sport and an instrument?
Plays a sport
Does not play a sport
Plays an instrument Does not play an instrument
10
3
8
2

The length of the segment shown in the graph is 10 units

The endpoints on the line segment are : (2, - 1) and (-4,7)

The Length of a line segment can obtained using the relation :

Length = √(x2 - x1)² + (y2 - y1)²

Here,

x2 = - 4, x1 = 2, y2 = 7, y1 = - 1

Length of segment = √((-4) - 2)² + (7 - (-1))²

Length of segment = √(-6)² + (8)²

Length of segment = √36 + 64

Length of segment = √100 = 10 units

Therefore, the length of the segment on the graph shown is 10 units.

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The domain for n in the given Geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio (r).

In the given geometric sequence, the first term (a1) is -9 and the common ratio (r) is 5. Therefore, the sequence can be written as:

-9, -9 * 5, -9 * 5^2, -9 * 5^3, ...

To determine the domain for n, we need to determine the values of n for which the sequence is defined. In a geometric sequence, the term number n represents the position of a term in the sequence.

In this case, the first term corresponds to n = 1, the second term corresponds to n = 2, and so on. The domain for n consists of all the positive integers starting from 1, as the sequence extends indefinitely.

Therefore, the domain for n in the given geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.

the domain does not include zero or negative values, as these positions in the sequence do not exist. The sequence only starts from the first term (n = 1) and continues indefinitely in the positive integer domain.

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The y-intercept of the function is (0, c)

The coefficients b determine the horizontal shift of the parabola compared to the parent function

If a is negative, the parabola opens downward

The y-intercept of the function is (0, c).

This means that when x = 0, the y-value is equal to c.

The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.

The coefficient b determines the horizontal shift of the parabola compared to the parent function.

The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.

A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.

If a is negative, the parabola opens downward.

The coefficient a determines the shape of the parabola.

If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.

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Answer:

The sum of 33, 78, 23, 21, 98, and 32 is 325.

The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:

32/12 and 27/12.

The mixed numbers in the context of this problem are given as follows:

The fractions that represent each number are given as follows:

The least common factor of 3 and 4 is given as follows:

3 x 4 = 12.

Hence the equivalent fractions are given as follows:

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The area of the whole figure which is made up of 24 tiles would be = 54ft²

To determine the total area of tiles used by Jaylee, the area for a single tile with a square shape should first be calculated with the formula given below as follows;

Area of a square = a²

a= side length = 1.5ft

area = 1.5×1.5

= 2.25ft²

The total number of tiles he used = 24 tiles.

Therefore, the total area of the rules he used = 2.25×24 = 54ft²

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The total area of the quadrilateral DEFG is determined as 154 cm² .

option A.

The total area of the quadrilateral DEFG is calculated by applying the following method.

Consider triangle GDE in the quadrilateral;

base of the triangle = 16 cm

height of the triangle = 8 cm

Area of the triangle GDE = ¹/₂ x base x height

Area of the triangle GDE = ¹/₂ x 16 cm x 8 cm

Area of the triangle GDE = 64 cm²

Consider triangle GEF in the quadrilateral;

base of the triangle = 18 cm

height of the triangle = 10 cm

Area of the triangle GEF = ¹/₂ x base x height

Area of the triangle GEF = ¹/₂ x 18 cm x 10 cm

Area of the triangle GEF = 90 cm²

The total area of the quadrilateral DEFG is calculated as;

Area =  64 cm² +  90 cm²

Area = 154 cm²

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The probability that a given student said math was their favorite subject was 3.44

The mathematical notion of probability measures the possibility of an event happening. A number between 0 and 1 is used to indicate it, with 0 denoting impossibility (the event won't happen) and 1 denoting certainty (the event will unquestionably happen). In probability theory, the probability of an event is determined based on a set of assumptions or information available. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Here, the total outcome is 299 and favorable outcome is 87.

Hence, the probability is 299/87 = 3.44

Therefore, probability that a given student said math was their favorite subject was 3.44.

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The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.

The null hypothesis in this case would be that there is independence between the type of sleeping pill and the presence of any adverse health condition.

The critical value needed to test for this is the chi-squared statistic with a significance level of 0.05.

To calculate the critical value, we first need to calculate the degrees of freedom,  which is calculated by (rows-1) * (columns-1).  In this case, the degrees of freedom is (2-1)*(2-1) = 1.

The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. This means that if the calculated chi-squared statistic is greater than 3.84, then we can reject the null hypothesis and claim that there is a significant relationship between the type of sleeping pill and the presence of any adverse health condition.

Therefore, the critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.

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Answer:

The correct answer is 2.

The measure for NS is 3.5 cm and the value of x is 2.

We have,

JK = 16, MP= 8, LP = 2x + 4, and PS= 3.5.

Since PS is perpendicular to ML then

MP = LP

So, 8 = 2x+ 4

2x = 8-4

2x= 4

x= 4/2

x= 2

Now, ML = MP + PL = 16

and, JK = ML= 16

Then, NS = PS

NS = PS = 3.5 cm

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The Domain of the function would be the interval [0, 6].The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.Average rate of change = (f(5) - 120) / (5 - 3)

Part A:

The x-intercepts of the graph, located at the ordered pairs (0, 0) and (6, 0), represent the points where the profit function intersects the x-axis. In the context of the problem, these x-intercepts indicate the price values at which the company sells pens, resulting in zero profit. When the price is $0, the company does not make any profit, and when the price is $6, the company also does not make any profit. The x-intercepts represent the break-even points where the company covers its costs but does not generate any profit.

The maximum value of the graph, located at the vertex (3, 120), represents the peak profit achieved by the company. The vertex is the highest point on the graph and indicates the optimal price at which the company can maximize its profit. In this case, when the price of pens is $3, the company achieves a maximum profit of $120.

Regarding the intervals of increasing and decreasing profit, the function is decreasing to the left of the vertex (3, 120) and increasing to the right of the vertex. This means that for prices less than $3, the profit decreases, and for prices greater than $3, the profit increases. The decreasing interval represents the point where the company is pricing the pens too low, resulting in decreasing profit. The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.

Part B:

To find the approximate average rate of change of the graph from x = 3 to x = 5, we need to calculate the slope of the line segment connecting the two points. The average rate of change represents the average amount by which the profit changes per unit increase in price over the given interval.

Using the coordinates (3, 120) and (5, f(5)) on the graph, we can determine the change in profit and price:

Change in profit = f(5) - 120

Change in price = 5 - 3

Substituting the values of the points into the equation, we can calculate the approximate average rate of change:

Average rate of change = (f(5) - 120) / (5 - 3)

Part C:

The constraints of the domain refer to the limitations or restrictions on the values that x (the price of pens) can take. Based on the given information, the x-intercepts of the graph are at (0, 0) and (6, 0), indicating that the price cannot be negative or exceed $6. Therefore, the domain of the function would be the interval [0, 6]. The constraint is that the price of the pens must be within this range for the profit function to be applicable.

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Note the full question may be :

A bakery sells cupcakes for $2 each. The bakery's total revenue from selling cupcakes is given by the function R(x) = 2x, where x represents the number of cupcakes sold.

Part A: What does the x-intercept of the graph of R(x) represent? Explain its significance in the context of the bakery's revenue.

Part B: What is the slope of the graph of R(x)? Interpret the meaning of this slope in terms of the bakery's revenue and the price of cupcakes.

Part C: If the bakery wants to maximize its revenue, what should be the ideal number of cupcakes to sell? Explain your answer based on the graph of R(x).

Answer:

4.816

Step-by-step explanation:

5.66sin45 = 4.816
sin = opposite over hypotenuse

The transformed vertices are;

A''  => (-7, -1)

B''  => (-7, 4)

C''=> (-9,4)

D''=> (-9, -1)

Here, we have,

given that,

we have to translate by (x,y) => (x-5, y+4)

so, the rectangle will be transformed as;

the transformed vertices are;

A' => ( 4-5, 3+4) => (-1, 7)

B' => (9-5, 3+4) => (4,7)

C'=>(9 -5, 5 +4 ) => (4, 9)

D'=> (4 -5, 5+4 ) => (-1, 9)

now, For clockwise rotation of a triangle by 90 degree, then x coordinate is similar to the y coordinate of original point and y coordinate is negative times of x coordinate of original point.

So (x,y) changes to (-y,x).

the transformed vertices are;

A'' => ( 4-5, 3+4) => (-1, 7) => (-7, -1)

B'' => (9-5, 3+4) => (4,7) => (-7, 4)

C''=>(9 -5, 5 +4 ) => (4, 9) => (-9,4)

D''=> (4 -5, 5+4 ) => (-1, 9)=> (-9, -1)

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The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.

Here, we have,

given that,

the product of two number in scientific notation is: 0.0258 × 10⁻⁸

now, let the two numbers be:

0.43× 10⁻⁵ and, 0.06× 10⁻³

we get,

 0.43× 10⁻⁵ × 0.06× 10⁻³

= 0.43 × 0.06× 10⁻⁵ × 10⁻³

= 0.43 × 0.06 × 10⁻⁵⁻³

=0.43 × 0.06× 10⁻⁸

=0.0258 × 10⁻⁸

Hence, The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.

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The correct option is: 5x² - 8x + 10 - 25/(x + 2)

Given that we need to determine, what is the quotient of 5x³+2x2-6x-5 divided by x+2,

Long division can be used to determine the polynomial 5x³+2x2-6x-5 divided by x + 2.

Here is how to accomplish it:

         5x² - 8x + 10

   ____________________

x + 2 | 5x³ + 2x² - 6x - 5

       - (5x³ + 10x²)

       _________________

                  -8x² - 6x

             - (-8x² - 16x)

             _______________

                       10x - 5

                  - (10x + 20)

                  ___________

                          -25

The quotient is 5x² - 8x + 10, and the remainder is -25/(x + 2).

Therefore, the correct option is: 5x² - 8x + 10 - 25/(x + 2)

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The equation for the function shown is f(x) = (x + 1)² - 2. Option B

From the information given, we have the deductions;

The vertex of the parabola is given as (-1, -2)

Using the form;

f(x) = a(x - h)^2 + k

Such that (h, k) represents the vertex coordinates.

Substitute the vertex coordinates into formula, we get;

f(x) = a(x - (-1))² + (-2)

= a(x + 1)² - 2

Now, substitute the value for a, we get;

2 = a(-3 + 1)² - 2

find the square and collect like terms

4 = a(4)

a = 1

Put value back into the equation

f(x) = 1(x + 1)² - 2

Multiply the value, we get;

f(x) = (x + 1)² - 2

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The probability that a aimlessly  named person's triglyceride  position is  lower than 80 milligrams per deciliter is  roughly0.0618 or6.18.    

To calculate the probability that a aimlessly  named person's triglyceride  position is  lower than 80 milligrams per deciliter, we can use the conception of standard normal distribution.  

First, we need to  regularize the value of 80 using the z- score formula  z = ( x- μ)/ σ  Where  x =  80( the value we want to calculate the probability for)  μ =  134( mean triglyceride  position)  σ =  35( standard  divagation)  Plugging in the values, we get  z = ( 80- 134)/ 35  z = -54/ 35  z ≈-1.543

Next, we need to find the corresponding area under the standard normal distribution  wind for a z- score of-1.543. We can use a standard normal distribution table or a calculator to find this area.

Looking up the z- score in the table or using a calculator, we find that the area to the left wing of z = -1.543 is  roughly0.0618.  

thus, the probability that a aimlessly  named person's triglyceride  position is  lower than 80 milligrams per deciliter is  roughly0.0618 or6.18.

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Answer:

  150 m²

Step-by-step explanation:

You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.

The area of the rectangle is the product of its length and width:

  A = LW

  A = (12 m)(5 m) = 60 m²

The area of the triangle is half the product of its base and height.

  A = 1/2bh

  A = 12/(12 m)(20 -5 m) = 90 m²

The area of the whole figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 60 m² +90 m² = 150 m²

The area of the figure is 150 m².

__

Additional comment

Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².

<95141404393>

Answer:

  47.5%    (rounds to 48%)

Step-by-step explanation:

You want the probability that a tree has between 240 and 300 apples, given the distribution of numbers of apples is normal with mean 300 and standard deviation 30.

The given diagram shows the center 95% of numbers of apples lies between 240 and 360. The number between 240 and 300 is half that symmetical distribution, so is ...

  95%/2 = 47.5%

The probability a tree will have between 240 and 300 apples is about 47.5%.

__

Additional comment

The figure "95%" is an approximation. A closer value is 95.45%. Hence, a closer value to the probability is 47.7%.

No rounding requirement is shown. To the nearest whole percentage point, the probability would be 48%.

<95141404393>

The area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.

From the given figure, the dimensions of trapezium are parallel sides a=7 ft, b= 13 ft and height = 5 ft.

Here, area of trapezium = 1/2 (Sum of parallel sides)×Height

= 1/2 ×(7+13)×5

= 1/2 ×20×5

= 50 square feet

Dimensions of triangle are base = 8 ft and height = 6 ft

Area of a triangle = 1/2 ×8×6

= 24 square feet

Therefore, the area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.

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To find the other two numbers in the set, we need to determine the missing numbers that satisfy the given conditions.

The mode of a set of numbers is the value(s) that appear(s) most frequently. In this case, the mode is given as 19, which means that 19 appears more times than any other number in the set.

The mean of a set of numbers is calculated by summing all the numbers and dividing by the total count. In this case, the mean is given as 20.

Given that the seven numbers provided are 16, 17, 19, 19, 21, 21, and 25, we can calculate the sum of these numbers:

16 + 17 + 19 + 19 + 21 + 21 + 25 = 138

To find the sum of all nine numbers in the set, we can use the mean formula:

Mean = (Sum of all numbers) / (Total count)

20 = (138 + x + y) / 9

Simplifying the equation, we have:

180 = 138 + x + y

x + y = 42

Now, since the mode is 19, we know that either x or y (or both) must be 19. Since the mode appears twice, we can assign 19 to both x and y:

x = 19

y = 19

Therefore, the other two numbers in the set are both 19.

The equation of the parabola with the given focus (2, 7) and directrix y = -1 is [tex](x - 2)^2 = 12(y - 3)^2[/tex].Option C.

To find the equation of the parabola with a focus and directrix, we can use the standard form of the equation of a parabola:

For a vertical parabola:

[tex](x - h)^2 = 4p(y - k),[/tex]

where (h, k) is the vertex, and p is the distance from the vertex to the focus and directrix.

In this case, the focus is given as (2, 7), which means the vertex is also (2, 7) since the focus and vertex lie on the axis of symmetry. Additionally, the directrix is given as y = -1, which means the directrix is a horizontal line.

First, let's determine the distance from the vertex to the focus and directrix, which is the value of p. The distance is the absolute difference between the y-coordinate of the focus (7) and the y-coordinate of the directrix (-1):

p = |7 - (-1)| = 8.

Now we can substitute the values of the vertex (h, k) = (2, 7) and p = 8 into the standard form equation:

[tex](x - 2)^2 = 4(8)(y - 7).[/tex]

Simplifying further:

[tex](x - 2)^2 = 32(y - 7).[/tex]

Expanding the equation:

[tex]x^2 - 4x + 4 = 32y - 224.[/tex]

Rearranging the terms:

[tex]x^2 - 4x - 32y + 228 = 0.[/tex]

Therefore, the equation of the parabola with the given focus (2, 7) and directrix y = -1 is  [tex](x - 2)^2 = 12(y - 3)^2.[/tex] SO Option C is correct.

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Answer:

13.48 - 8.263 = 5.217

Answer:5.217

Step-by-step explanation: caculate it

Final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

Let's break down the steps to determine the final speed:

Step 1: Convert the speed from miles per minute to miles per hour.

Since you're driving one and a half miles per minute, we need to convert it to miles per hour. There are 60 minutes in an hour, so we multiply 1.5 by 60 to get 90 miles per hour.

Step 2: Slow down by 15 miles per hour.

Subtract 15 from the initial speed of 90 miles per hour, resulting in 75 miles per hour.

Step 3: Reduce the speed by one third.

To find one third of 75 miles per hour, we divide it by 3, which gives us 25 miles per hour.

Therefore, the final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

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Answer:

n this question, you are asked how much the maximum revenue. Since candy Y sold for a higher price than candy X, that means you have to sell candy Y as much as possible.The number of candy Y must be >= 3 times candy X. Since this won't limit candy Y selling, then you can convert all 36 candy into candy Y and 0 candy X36 candy (Y) >= 0 candy(X) ----> the requirement is met.The revenue would be 36 candy Y * $3/candy Y= $108

Step-by-step explanation:

Tom's estimated travel time is approximately 13.6 hours.

Based on the given scenario, Tom is traveling a distance of approximately 340 nautical miles from Houston to New Orleans by boat. He will be using a medium-sized recreational boat with an average speed of 25 miles per hour.

To estimate the time it will take for his journey, we can use the formula:

Time = Distance / Speed

Substituting the values, we have:

Time = 340 miles / 25 miles per hour

Calculating the division, we find that Tom's estimated travel time is approximately 13.6 hours.

However, it is important to note that this estimate assumes a continuous journey without considering other factors that may affect the travel time. Various elements can impact the actual duration, such as weather conditions, water currents, navigational challenges, refueling stops, and any necessary rest breaks.

Additionally, it is essential for Tom to adhere to all boating regulations and safety guidelines to ensure a smooth and secure voyage.

To obtain a more accurate estimate, Tom should consult local boating authorities, marinas, or experienced sailors familiar with the route.

They can provide valuable insights into the specific conditions and offer guidance on potential challenges that may affect the travel time. Planning for additional buffer time is also recommended to account for unforeseen circumstances and to prioritize safety during the journey.

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The complete question may be like:

Tom plans to travel by boat from Houston, Texas, to New Orleans, Louisiana. He wants to estimate the time it will take for his journey. The distance between the two cities by water is approximately 340 nautical miles. Tom will be traveling on a medium-sized recreational boat that has an average speed of 25 miles per hour. Considering normal weather conditions and assuming a continuous journey, how long will it take Tom to reach New Orleans?

Please provide an answer based on this scenario, taking into account the distance, average speed, and any other relevant factors.

The total amplitude of the tip of King Arthur's sword is s +  [tex]\sqrt{3}[/tex]t/2.

Given that the length of the line segment connecting the centre of the regular hexagon to one of its vertices as  the length of the line segment connecting centre of the regular pentagon to one of its vertices.

To find the amplitude by adding these two lengths.

For the regular hexagon, the distance from the centre to a vertex is equal to the radius of the circumscribed circle. The radius  of the circumscribed circle is equal to length of a side.

Therefore, the amplitude of the hexagon is s.

For a regular pentagon, divide it into three triangles. One of these triangles is an isosceles triangle where the base is the side of the pentagon and the other two sides are radii of the circumscribed circle.

The amplitude of pentagon is the height of the isosceles triangle.

In an isosceles triangle, the height(h) is calculated from formula

h =  [tex]\sqrt{3}[/tex]t/2.

Therefore, the amplitude of the pentagon is   [tex]\sqrt{3}[/tex]t/2.

Hence, the total amplitude of the tip of King Arthur's sword is s +  [tex]\sqrt{3}[/tex]t/2.

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The function g(x) in the context of this problem is given as follows:

A. [tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

[tex]f(x) = \sqrt[3]{x}[/tex]

The translated function was moved 4 units left and 3 units up, hence the function is defined as follows:

[tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]

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