For the athletic banquet one adult ticket cost $15.00 and one student ticket cost $10.00. One hundred forty tickets were sold for a total of $1600. How many students tickets were sold

The given box plot represented by the data sets in option A and B.

From the given box plot, we have

Minimum value = 3

Maximum value = 18

First quartile (Q1) = 7

Third quartile (Q3) = 13

Median = 10

Option A:

3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18

Median = 12

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option B:

3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Option C:

3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option D:

2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Therefore, the correct options are B and D.

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ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.

The angle-angle-side theorem, or AAS, tells us that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.

If we consider triangle FSH and triangle FSI, we will observe the following;

So based on the  angle-angle-side theorem, or AAS, we can see that triangle FSH is congruent to triangle FSI.

Thus, our answer will be; ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.

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Answer:

increasing exponential function.

Step-by-step explanation:

We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.

It  must be exponential.

It is increasing at it increases in x, so it is an increasing exponential function.

The amount of debt per person in the small country is approximately $2,439. This means that, on average, each person in the country would be responsible for around $2,439 of the national debt.

To calculate the amount of debt per person in the small country, we divide the total national debt by the population and round the result to the nearest whole number. Let's perform the calculation.

The population of the small country is 2.457 million, which is equivalent to 2,457,000 people. The national debt is $5.99 billion.

To find the debt per person, we divide the national debt by the population:

$5.99 billion / 2,457,000 = $2,439.05 (rounded to two decimal places)

Since we want the answer in whole numbers, we round the result to the nearest whole number:

Debt per person = $2,439 (rounded to the nearest whole number)

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The factorization of[tex]8(p-q)^3-(p+q)^3 is 8(p-q)^3 - (p+q)^3 is [p - 3q][7p^2 - 8pq + 3q^2].[/tex]

The given expression is[tex]8(p-q)^{3}-(p-q)^{3}[/tex]

To factorize this expression, we can use the identity for the difference of cubes, which states that [tex]a^3 - b^3 = (a - b)(a^2 + ab + b^2).[/tex]

Let's apply this identity to the given expression:

[tex]8(p-q)^3 - (p+q)^3 = [2(p-q)]^3 - (p+q)^3.[/tex]

Now we can see that we have a difference of cubes:[tex](2(p-q))^3 - (p+q)^3.[/tex]

Using the identity, we can factorize this expression as follows:

[tex][(2(p-q)) - (p+q)][(2(p-q))^2 + (2(p-q))(p+q) + (p+q)^2].[/tex]

Simplifying further:

[tex][2p - 2q - p - q][(2(p-q))^2 + (2(p-q))(p+q) + (p+q)^2].[/tex]

Combining like terms:

[tex][p - 3q][(2(p-q))^2 + 2(p-q)(p+q) + (p+q)^2].[/tex]

Expanding the squared term:

[tex][p - 3q][4(p^2 - 2pq + q^2) + 2(p^2 - q^2) + (p^2 + 2pq + q^2)].[/tex]

Simplifying:

[tex][p - 3q][4p^2 - 8pq + 4q^2 + 2p^2 - 2q^2 + p^2 + 2pq + q^2].[/tex]

Combining like terms again:

[tex][p - 3q][7p^2 - 8pq + 3q^2].[/tex]

Therefore, the factorization of [tex]8(p-q)^3 - (p+q)^3 is [p - 3q][7p^2 - 8pq + 3q^2].[/tex]

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In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

[tex]4\frac{2}{4}[/tex] that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

[tex]4\frac{2}{4} = \frac{16+4}{2}[/tex]

=[tex]\frac{18}{4}[/tex]

Then [tex]4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}[/tex]

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that [tex]\frac{18}{4}[/tex] is less than [tex]\frac{37}{4}[/tex] Hence, Darren is wrong.

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in the dot plot given, A rating of 6 is not a good description of the center of this data set because it does not accurately represent the most common or typical response.

To determine the center of data set, we typically look for the measure of central tendency, such as the mean, median, or mode.

From the dot plot, we can observe that the mode is at the rating of 10, with six students giving this highest rating. In contrast, the rating of 6 has only two students, making it less representative of the center.

Therefore, a rating of 6 does not accurately capture the overall sentiment or the central tendency of the data set.

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Full Question:

Please see the attached.

Answer: 14 ounces

Step-by-step explanation:

         To find the mean, we add up all the values and divide by the number of values.

[tex]\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces[/tex]

The description of the image is one that has a four-horned star. The description is as follows:

It comprises of four equilateral triangles and One Square.

Next,

The image or shape has twelve (12) symmetrical lines.

Next,

It must be rotated 90° (clockwise or anticlockwise) in order for the image to match itself.

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Answer: each base angle in an isosceles right triangle measures 45 degrees.

Step-by-step explanation:

In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).

Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.

To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:

x + x + 90 = 180

Simplifying the equation:

2x + 90 = 180

Subtracting 90 from both sides:

2x = 90

Dividing both sides by 2:

x = 45

Susan has 875 grams of grapes left.

1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).

2. Susan ate 125 grams of the grapes on her way home.

3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.

  1000 grams - 125 grams = 875 grams

4. Thus, Susan has 875 grams of grapes left.

measurement units:

In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.

This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.

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Answer:

Step-by-step explanation:

Remember PEMDAS

7+(2x4)-8÷(12-6)x(6÷2)​

7 + 8 - 8 : 6 × 3 =

7 + 8 - 8/6 × 3 =

7 + 8 - 4 =

11

The length of the arc RT is 11.72 units.

An arc is defined as a portion of the boundary of a circle or a curve.

To calculate the length of the arc RT, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.

To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.

The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:

Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).

Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.

Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.

If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.

In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.

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If the height (h) of the prism is less than or equal to 0.978 cm, then Andrea has enough modeling clay for both prisms. If the height exceeds 0.978 cm, she will be short of modeling clay.

Let's calculate the volumes of both prisms:

Volume of the first prism: V1 = (8.4 cm²) × h

Volume of the second prism: V2 = (16 × 8.4 cm²)×(4h)

= 537.6 cm³ h

We know that Andrea has 533.8 cm³ of modeling clay.

To determine if she has enough clay for both prisms, we need to compare the total volume of the prisms to the amount of clay she has:

Total Volume = V1 + V2 = (8.4 cm²) × h + (537.6 cm³ × h)

Total Volume = (546 cm²) × h

Now we can set up the equation:

Total Volume ≤ Amount of Clay

(546 cm²) × h ≤ 533.8 cm³

Solving for h:

h ≤ 533.8 cm³ / (546 cm²)

h ≤ 0.978 cm

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Answer:

Approx 8.47 [tex]m^2[/tex]

Step-by-step explanation:

First, find the area of the entire figure. Which can be found by multiplying the two sides of the square by each other=  [tex]6*6=36m^2[/tex]

Now, ignore the square and just focus on the pentagon and finding the area of that. The formula for the area of a pentagon is [tex]A=1/2Apothem*Perimeter[/tex]

In order to find the apothem, you can make a mini triangle and use trig (Tangent) to find the height (apothem) of the triangle. Then, you take the side length of the base of the pentagon which is 4 and then you multiply it by the number of sides (5) to get 20. Then, by plugging it into our formula, you use the apothem*10 (divided by 2) and you get the area, and then you just subtract that from 36.

Answer:

40

Step-by-step explanation:

plugging in a and b will get us:

[tex]2^{2} + 6^{2} = c^{2}[/tex]

4 + 36 = [tex]c^{2}[/tex]

40 = [tex]c^{2}[/tex]

c= [tex]\sqrt{40\\[/tex]

May Kawasaki's required minimum distribution (RMD) is $3,808. This is calculated by dividing her IRA balance of $98,000 by the distribution period of 26.2, which is found in the Uniform Life Table on page 45 for a 72-year-old.

b) If May Kawasaki fails to take her RMD, she will incur a 50% penalty on the amount she should have withdrawn. In this case, the penalty would be $1,904.

c) If May Kawasaki had made an early withdrawal of $10,000 to take a vacation, she would have paid a 10% penalty on the amount withdrawn. In this case, the penalty would have been $1,000.

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1. May Kawasaki is 72 and has an IRA with a fair market value of $98,000. a) Use the Uniform Life Table on p. 45 to determine her required minimum distribution. b) What penalty would she incur if she failed to take the distribution? c) What penalty would she have paid if she had made an early withdrawal of $10,000 to take a vacation?

The linear function that models the situation is given as follows:

d = 0.85t.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The constant ratio for this problem is given as follows:

k = 0.83, as each division of d by t has a result of 0.83.

Hence the equation is given as follows:

d = 0.83t.

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The number that belongs in the green box is 32.8

From the question, we have the following parameters that can be used in our computation:

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 37 - 64

Evaluate

Third angle = 79

If the number that belongs in the green box is x, then we have

x/sin(79) = 30/sin(64)

This gives

x = sin(79) * 30/sin(64)

Evaluate

x = 32.8

Hence, the number that belongs in the green box is 32.8

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The solution to the inequality 2x + 7 > 27 is x > 10

From the question, we have the following parameters that can be used in our computation:

2x + 7 > 27

Subtract 7 from both sides of the inequality

So, we have

2x > 20

Divide both sides by 2

x > 10

Hence, the solution to the inequality 2x + 7 > 27 is x > 10

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Among the mean, mode, and median, the unique one is the b. mode.

The mode is the data value that occurs many times more than other data values.

Unlike the mean that shows the average value of all the data values, the mode occurs more.  While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.

Similarly, the median can be computed when two values occur as the middle values.

Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.

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Answer:

? ≈ 20.1

Step-by-step explanation:

using the Sine rule in the triangle

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]

with a = ? , b = 30 , ∠ A = 37° , ∠ B = 64° , then

[tex]\frac{?}{sin37}[/tex] = [tex]\frac{30}{sin64}[/tex] ( cross- multiply )

? × sin64° = 30 × sin37° ( divide both sides by sin64° )

? = [tex]\frac{30sin37}{sin64}[/tex] ≈ 20.1 ( to the nearest tenth )

Answer: N= 12

Step-by-step explanation: if you follow PEMDAS, you take (4^3)^4 and multiply 3*4 which is 12.

Because the base of 4^12=4^n is the same you leave it alone and N is equal to 12

Answer:

Hi

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Thanks

The point B that partitions the segment AC into a 2:3 ratio is B (4.6, 9.6). To find the point B that partitions the segment AC into a 2:3 ratio, we can use the concept of section formulas or the concept of ratios of the coordinates.

Let's assume the coordinates of point B are (x, y). We can calculate the coordinates of point B using the following steps:

Step 1: Calculate the differences in the x and y coordinates between points A and C:

Δx = x-coordinate of C - x-coordinate of A = 5 - 3 = 2

Δy = y-coordinate of C - y-coordinate of A = 11 - 4 = 7

Step 2: Divide the differences by the sum of the ratios (2 + 3 = 5) to get the ratios of the segments AB and BC:

Ratio_AB = (2/5)[tex]\times[/tex] Δx = (2/5) [tex]\times[/tex]2 = 4/5

Ratio_BC = (3/5) [tex]\times[/tex] Δx = (3/5) [tex]\times[/tex] 2 = 6/5

Step 3: Apply the ratios to the coordinates of point A to find the coordinates of point B:

x-coordinate of B = x-coordinate of A + Ratio_AB [tex]\times[/tex] Δx = 3 + (4/5)[tex]\times[/tex]2 = 3 + 8/5 = 23/5

y-coordinate of B = y-coordinate of A + Ratio_AB [tex]\times[/tex]Δy = 4 + (4/5) [tex]\times[/tex] 7 = 4 + 28/5 = 48/5

Therefore, the coordinates of point B are (23/5, 48/5).

In decimal form, the coordinates of point B are approximately (4.6, 9.6).

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Rolling two sixes in a row on a number cube (a fair six-sided die) is an independent event. The outcome of one roll does not affect the outcome of the subsequent roll. Each roll of the number cube is an independent trial, and the probability of rolling a six on each trial is always 1/6, regardless of the previous outcome.

Each of the other two angles in the roof gable measures approximately 34.8°.

If the roof gable on Charlene's house has two equal sides, and one angle measures 110.4°, we can determine the measure of each of the other two angles by using the fact that the sum of the angles in a triangle is always 180°.

Let's denote the measure of the other two angles as x.

Since the two equal sides of the gable form an isosceles triangle, the two angles opposite those sides are equal.

Therefore, we have:

x + x + 110.4° = 180°

Combining like terms:

2x + 110.4° = 180°

Now, let's solve for x:

2x = 180° - 110.4°

2x = 69.6°

x = 69.6° / 2

x = 34.8°

Therefore, each of the other two angles in the roof gable measures approximately 34.8°.

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Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.

f(x) = 2x

g(x) = [tex]2x^2[/tex] + 3x

To find (fg)(x), we substitute g(x) into f(x):

(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)

Now we substitute f(x) = 2x into the expression above:

(fg)(x) = 2([tex]2x^2[/tex] + 3x)

Distribute the 2:

(fg)(x) = [tex]4x^2[/tex] + 6x

So, (fg)(x) = [tex]4x^2[/tex] + 6x.

Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

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An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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