The box plot represents the number of tickets sold for a school dance.

A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.

Which of the following is the appropriate measure of center for the data, and what is its value?

The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.

A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

Given that;

Function is,

⇒ f (x) = x³ - 3x² - 7x + 6

Now, We can check (x + 2) is a factor of function or not as;

If x + 2 is a factor of function, then x = - 2 is satisfy the function.

So, Put x = - 2;

⇒ f (x) = x³ - 3x² - 7x + 6

⇒ f (- 2) = (- 2)³ - 3 (- 2)² - 7 (- 2) + 6

⇒ f (- 2) = - 8 - 12 + 14 + 6

⇒ f (- 2) = 0

Thus, (x + 2) is a factor of the function,

Hence, We can find all the zeroes as;

(x + 2) ) x³ - 3x² - 7x + 6 (x² - 5x + 3

          x³ + 2x²

         ------------

              - 5x² - 7x

              - 5x² - 10x

              ----------------

                       3x + 6

                       3x + 6

                      ------------

                              0

Thus, We get;

⇒ x³ - 3x² - 7x + 6

⇒ (x + 2) (x² - 5x + 3)

Since, x² - 5x + 3 = 0

x = - (- 5) ± √(- 5)² - 4×1×3 / (2×1)

x = (5 ± √25 - 12) / 2

x = (5 ± √13)/2

Thus,

A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

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The surface area of the cylinder is 603.19 square meters

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

Radius, r = 8 meters

Height, h = 4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 8 * (8 + 4)

Evaluate

Surface area = 603.19

Hence, the surface area is 603.19 square meters

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The value of sin(θ - φ) = sin(A - B) in simplest form is sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800

Use the trigonometric identity sin(α - β) = sin α cos β - cos α sin β to find sin(θ - φ), where θ = A and φ = B.

First, find cos A and sin B using the given information:

Since sin A = 53/45, use the Pythagorean identity cos² A + sin² A = 1 to find cos A:

cos² A + (53/45)² = 1

cos² A = 1 - (53/45)²

cos A = ± √(1 - (53/45)²)

Since A is a positive acute angle, take the positive square root:

cos A = √(1 - (53/45)²)

Similarly, since cos B = 29/20, use the Pythagorean identity cos² B + sin² B = 1 to find sin B:

sin² B = 1 - cos² B

sin B = ± √(1 - cos² B)

Since B is a positive acute angle, take the positive square root:

sin B = √(1 - (29/20)²)

Use the identity sin(α - β) = sin α cos β - cos α sin β to find sin(A - B):

sin(A - B) = sin A cos B - cos A sin B

= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)

Simplifying this expression:

sin(A - B) = (53/60) - √(2561)/900

Finally, use the identity sin(θ - φ) = sin θ cos φ - cos θ sin φ to find sin(θ - φ) = sin(A - B):

sin(A - B) = sin θ cos φ - cos θ sin φ

= sin A cos B - cos A sin B

= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)

= (53/60) - √(2561)/900

Therefore, the value of sin(θ - φ) = sin(A - B) in simplest form is:

sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800

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By using the given graph of the function​ f, the key features include the following:

​(a) the​ y-intercept is (0, 10).

​(b) its domain is [-∞, ∞] and the range is [0, ∞].

​(c) it is​ increasing over the interval [-∞, ∞].

​(d) The function is​ even.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the graph, we would calculate the value of a and b as follows;

f(x) = a(b)^x

10 = a(b)⁰

a = 10

Next, we would determine value of b as follows;

12 = 10(b)¹

12 = 10b

b = 12/10

b = 1.2

Therefore, the required exponential function is given by;

[tex]y = 10(1.2)^x[/tex]

Part a.

When x = 0, the y-intercept can be determined as follows;

[tex]y = 10(1.2)^0[/tex]

y = 10(1)

y = 10.

Part b.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞].

Range = [0, ∞] or {y | y ≥ 0}

Part c.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce that the exponential function is always increasing over the interval [-∞, ∞].

Part d.

In conclusion, this exponential function is an even function because it is symmetric with respect to the y-coordinate (y-axis).

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Answer:

6in

Step-by-step explanation:

angle C = 55 <-- 180-70-55=55
meaning the triangle is an isosceles so two sides would be the same.

Answer:

1.91

Step-by-step explanation:

12+4.67+1.42=18.09

20-18.09=1.91

The angle between the vectors is given as follows:

θ = 60º.

The formula for the angle between the vectors in this problem is given as follows:

cos(θ) = uv/(|u||v|)

The vectors are given as follows:

The dot product between the vectors is given as follows:

uv = <-2,3><1,2> = -2 + 6 = 4.

The norms for each vector are given as follows:

Applying the arccosine function, the angle is given as follows:

[tex]\theta = \arccos{\left(\frac{4}{\sqrt{13} \times \sqrt{5}}\right)}[/tex]

θ = arccos(0.49613893835)

θ = 60º. (approximately).

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The area of a right triangle is 70 yds².

We have,

Base= 17 yards

Height = 8 yards

The area of a triangle is given by the formula:

Area = (1/2) x base x height

Substituting the given values, we get:

Area = (1/2) x 17 x 8

Area = 68 square yards

Therefore, the area of a right triangle is 70 yds².

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The sine of an angle 0 in the third quadrant is -0.5. So the value of cos∅ is -√(3)/2.

In the third quadrant, both sine and cosine are negative. We know that the sine of ∅ is -0.5, so we can use the Pythagorean identity to find the cosine of ∅:

sin²(∅) + cos²(∅) = 1

Substituting -0.5 for sin(∅), we get:

(-0.5)² + cos²(∅) = 1

Simplifying:

0.25 + cos²(∅) = 1

cos²(∅) = 1 - 0.25

cos²(∅) = 0.75

Taking the square root of both sides:

cos(∅) = ±√(0.75)

Since we're in the third quadrant where cosine is negative, we take the negative square root:

cos(∅) = -√(0.75)

Simplifying the square root:

cos(∅) = -√(3/4)

cos(∅) = -√(3)/2

Therefore, the value of cos(∅) is -√(3)/2.

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The two numbers are 15 and 15. The product of the two numbers is 225.

Let x and y be the two numbers we are searching for. We know that x + y = 30, so we can settle for y to get y = 30-x. The result of x and y is then, at that point:

[tex]P(x, y) = x(30 - x) = 30x - x^2[/tex]

To find the greatest item, we can take the subsidiary of P(x, y) concerning x and set it equivalent to 0:

dP(x, y)/dx = 30 - 2x = 0

Settling for x, we get x = 15. Subbing x = 15 into y = 30-x, we get y = 15. Hence, the two numbers that have an amount of 30 and produce the biggest conceivable item are 15 and 15.

The result of the two numbers is:

P(15, 15) = 15 * 15 = 225

So the result of the two numbers is 225.

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Answer:

10

Step-by-step explanation:

If you multiply the width with the length and height , you will get nine, then add that lonely brick on top to get ten

The measure of angle m∠XKZ is 218°.

An angle is formed when two straight lines or rays meet at a common endpoint.

The six types of angles are,

To find the measure of angle m∠XKZ, we use the formula below

Formula:

From the question,

Given:

Substitute these values into equation 1 and solve for x

Hence, m∠XKZ = [(15×15)-7] = 218°

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The total length of the chord PR is 30.

Given a circle Q.

Given a chord named as PR.

We have to find the length of the chord.

Here Q is the center of the circle.

Given that ∠QSP is a right angle.

Then clearly, ∠QSR is also a right angle.

Consider the triangle QSR and QSP.

QP = QR, since they are radius of the circle.

So, QP = QR = 17

QS ia a common side.

So QS = 8

Then it is clear that,

PS = SR

Using Pythagoras theorem,

(PS)² = 17² - 8²

        = 225

PS = √225 = 15

So the length of the chord, PR = 15 + 15 = 30.

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a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.

b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:

[tex]A_t = A_0 e^{(-10.498t)}[/tex]

where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.

Substituting t = 0.5, we get:

[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]

Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.

(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:

[tex]A_t = A_0 e^{(-10.498t)[/tex]

Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:

ln(At/A₀) = -10.498t

Substituting At = 115 grams and A₀ = 1000 grams, we get:

ln(115/1000) = -10.498t

Solving for t, we get:

t = (ln(115/1000)) / (-10.498) ≈ 2.1 years

Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

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Transactions are larger than others Bank B may be the cheaper option even if you make more than 35 transactions.

To compare the cost of using Bank A and Bank B need to consider the total cost based on the number of transactions.

Let's say you make x transactions in a month.

For Bank A the monthly cost is a fixed fee of $45 regardless of the number of transactions.

For Bank B the monthly cost is a fee of $20 plus $0.70 for each transaction.

So the total cost for Bank B is:

Total cost = $20 + $0.70x

The break-even point where the total cost of Bank A and Bank B are equal need to solve the following equation:

45 = 20 + 0.70x

Subtracting 20 from both sides, we get:

25 = 0.70x

Dividing both sides by 0.70, we get:

x = 35.71

If you make more than 35 transactions in a month Bank A is the cheaper option.

If you make fewer than 35 transactions Bank B is the cheaper option.

Analysis assumes that all transactions are of the same amount.

To compare the total cost of both banks based on the actual amounts of the transactions.

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The number of jerseys they can purchase for $430 is 53 jerseys.

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Based on the information provided about the cost of the jerseys, we have the following quadratic function;

C = 0.1x² + 2.4x + 25

430 = 0.1x² + 2.4x + 25

0.1x² + 2.4x + 25 - 430 = 0

0.1x² + 2.4x - 405 = 0

By solving the quadratic function using the quadratic formula, we have:

[tex]x = \frac{-(-2.4)\; \pm \;\sqrt{(2.4)^2 - 4(0.1)(-405)}}{2(0.1)}\\\\[/tex]

x = 52.76 ≈ 53 jerseys.

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The height if the squared-based pyramid is given as 34 cm

We have BD / 2

= 10 / 2

= 5 cm

AC = [tex]\sqrt{AB^2-BC^2}[/tex]

= √12² - 5 ²

= 12 cm

The height is given as 10 + 12 + 12

= 34 cm

Hence the height if the squared-based pyramid is given as 34 cm

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The calculated dimensions of the sticker are 11 mm by 5 mm

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

shape = rectangle

perimeter = 32 mm

Area = 55 square mm

Represent the dimensions of teh sticker with x and y

So, we have

Area = xy

Perimeter = 2(x + y)

substitute the known values in the above equation, so, we have the following representation

xy = 55

2(x + y) = 32

So, we have

xy = 55

x + y = 16

When x = 11 and y = 5, we have

11 * 5 = 55

11 + 5 = 16

Hence, the dimensions of the sticker are 11 mm by 5 mm

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Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

Holden drinks 1/8 gallon of water every 2 miles, so after hiking 14 miles, he would have drank (14/2) * (1/8) = 7/16 gallons of water.

Melissa drinks 3/8 gallon of water every 2 miles, so after hiking 14 miles, she would have drank (14/2) * (3/8) = 21/32 gallons of water.

The difference in the amount of water they drink is:

21/32 - 7/16 = 21/32 - 14/32 = 7/32 gallons

Therefore, Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

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The solution to the system of equations is given as follows:

Considering the augmented matrix, the system of equations is defined as follows:

Adding the first and third equations, we have that:

-4x - 6y = -36.

From the second equation, we have that:

2x + 3y = 18.

The addition equation is a multiple of this equation, hence the system has an infinite number of solutions.

From the second equation, we have that:

2x + 3y = 18.

x + 1.5y = 9

x = 9 - 1.5y.

The definition for z is given as follows:

z = x + y - 7.

Hence the variable y is:

y = z - x + 7.

The variable x is of:

x = 9 - 1.5(z - x + 7)

x = 9 - 1.5z + 1.5x - 10.5

0.5x = 1.5 + 1.5z

x = 3z + 3.

The variable y is:

y = z - 3z - 3 + 7

y = -2z + 4.

Hence the solution is:

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The sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

To find the percentage of hospitals that provide at least some charity care, we need to use the given sample data.

(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean percentage x and the sample standard deviation S.

[tex]x = \frac{56.9 + 55.9 + 52.5 + 65.7 + 59.0 + 64.7 + 70.1 + 64.7 + 53.5 + 78.2}{10}\\\\ = 62.3% \\\\\\\\S = \sqrt{\frac{((56.9 - 62.3)^2 + (55.9 - 62.3)^2 + ... + (78.2 - 62.3)^2) }{ 9}}\\\\ = 8.08\%[/tex]

Therefore, the sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

(b) To find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care, we can use the formula:

[tex]CI = x \pm z*(S/sqrtn)[/tex]

where CI is the confidence interval, x is the sample mean percentage, z is the z-score for the desired confidence level (90% in this case), S is the sample standard deviation, and n is the sample size (10 in this case).

From the z-table, the z-score for a 90% confidence level is 1.645.

Plugging in the values, we get:

CI = 62.3 ± 1.645*(8.08/sqrt(10)) = (55.5%, 69.1%)

Therefore, we can be 90% confident that the true population average percentage of hospitals providing at least some charity care is between 55.5% and 69.1%.

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Answer:

Part A: The point z1 is at (4, 6) and the point z2 is at (-5, 2). The distance between them is √((4-(-5))^2 + (6-2)^2) = √(9^2 + 4^2) = √(81 + 16) = √97.

Part B: The complex conjugate of z2 is (-5, -2). Geometrically, it can be found by reflecting the point z2 across the x-axis.

Part C: To find z2 − z1 geometrically, you can draw a vector from z1 to z2. The coordinates of this vector are (-5-4, 2-6) = (-9, -4). So z2 − z1 = -9 - 4i.

The likelihood of rain occurring on precisely two out of the four days they are there is 0.323.

The binomial probability formula is given by:

P(X = k) = C(n, k) . [tex]p^k[/tex] . (1 - [tex]p)^(n - k)[/tex]

Where:

P(X = k) is the probability of exactly k successes,

C(n, k) is the number of combinations of n items taken k at a time,

p is the probability of success on a single trial, and

n is the total number of trials.

Using the formula, we can calculate the probability as follows:

P(X = 2) = C(4, 2) x (0.71)² x  (1 - 0.71)²

P(X = 2) = 6 x (0.71)² x (0.29)²

P(X = 2) ≈ 0.323

Therefore, the probability that it will rain on exactly two of the four days they are there is 0.323.

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The molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

To solve this problem, we can use the equation:

M₁V₁= M₂V₂

where M₁ is the initial molarity, V₁ is the initial volume, M₂ is the final molarity, and V₂ is the final volume.

We are given that the initial volume is 50.0 mL and the initial molarity is 1.25 M. We are also told that 100.0 mL of water is added to the solution, so the final volume is 50.0 mL + 100.0 mL = 150.0 mL.

Plugging these values into the equation, we get:

(1.25 M)(50.0 mL) = M2(150.0 mL)

Solving for M₂, we get:

M₂ = (1.25 M)(50.0 mL) / (150.0 mL) = 0.4167 M

Therefore, the molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

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The cost of one gallon of gas is given as follows:

$2.75.

The cost of one gallon of gas is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per gallon is obtained dividing the total cost by the number of gallons.

The parameters for this problem are given as follows:

Hence the cost of one gallon of gas is given as follows:

22/8 = $2.75.

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Answer:

0.3947368421 = approx 39%

Step-by-step explanation:

Add up all the number of times rolled on the right column.

=6+3+5+6+9+9

= 38 total rolls

Add up the number of times a 4 or a 5 were rolled:

= 6+ 9 = 15

Divide 15/38

=15/38=0.3947368421 = approx 39%.

The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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