The box plots summarize the attendance for the spring musical and the fall musical. Each musical was performed for six evenings. Which statement best describes the data represented in the box plots?

Answer:

Set your calculator to degree mode.

[tex] \tan( \alpha ) = \frac{23}{35} [/tex]

[tex] \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31[/tex]

The angle of elevation of the sun is about 33°.

The surface area of the trapezoid is calculated to be equal to 731 square feet

area of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel base. Also the trapezoid have four rectangle sides and two same trapezoid sides.

A = 10ft

B = 13ft

height = 7ft

area of two trapezoid side = 2[1/2 × (10 + 13) ft × 7 ft = 161 ft²

area of rectangle with length 15ft and width 8ft = 8 ft × 15 ft = 120 ft²

area of rectangle with length 15ft and width ft = 15 ft × 105 ft = 105 ft²

area of rectangle with length 15ft and width 13ft = 15 ft × 13 ft = 195 ft²

area of rectangle with length 15ft and width 10ft = 15 ft × 10 ft = 150 ft²

surface area of the trapezoid = 161 ft² + 120 ft² + 105 ft² + 195 ft² + 150 ft² = 731 ft².

Therefore, the surface area of the trapezoid is calculated to be equal to 731 square feet

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To find an expression for P(t), we can use the two given data points to create a system of equations. We can assume that the population is growing exponentially, which means that the population at time t is given by:

P(t) = a(b)^t

where a and b are constants that we need to determine.

Using the first data point, we have:

840,000 = a(b)^1

which simplifies to:

840,000 = ab

Using the second data point, we have:

882,000 = a(b)^2

We can solve for a in terms of b by dividing the second equation by the first equation:

882,000/840,000 = (a(b)^2)/(ab)

Simplifying, we get:

1.05 = b

Substituting this value of b into the first equation, we get:

840,000 = a(1.05)

Solving for a, we get:

a = 800,000

Therefore, the expression for P(t) is:

P(t) = 800,000(1.05)^t

This means that the city's population t years from now can be calculated by multiplying the initial population of 800,000 by 1.05 raised to the power of t.

Answer:

Step-by-step explanation:

city. The city's population has beengrowing, and based on recent trends,Jim expects it to continue growingexponentially. This table shows theexpected population in the next twoyears.Time (years)Population840,000882,000Time (years)12Find an expression for P(t), the city'spopulation t years from now. Write youranswer in the form P(t) = a(b)t, where aand b are integers or decimals. Do notround.P(t) =

Answer:

9.9 inches

Step-by-step explanation:

Visualize the scenario for a second. If the ladder is leaning against the wall, we can assume that it is the hypothenuse of the triangle that is forming here. The angle of elevation in this scenario is the angle formed by the ladder and ground.

Next, recall each trig function and determine which best belongs. We have the hypothenuse and we need the side opposite the angle. Therefore, we use sine. (probably using a calculator for trig questions)

Therefore, we can now set up our equation and solve. (x is the height of the wall)

sin 56 = [tex]\frac{x}{12}[/tex]         Initial equation

12 sin 56 = x     Multiply each side by 12 so that we get x by itself.

x ≈ 9.9               Punch 12 sin 56 into a calculator and your done!

Therefore, the answer is about 9.9 inches. (If you got something different, make sure that your calculator is in degrees and not radians! Some calculators abbreviate it as DEG and RAD respectively.)

95% confidence that the population mean is less than 6 minutes since the upper limit of the confidence interval is below 6 minutes.

95% confidence that the population mean is within the range of 4.897 to 5.763 minutes.

The t-based 95 percent confidence interval for the population mean:

CI =[tex]\bar x\pm t\alpha/2 \times (s/\sqrt n)[/tex]

[tex]\bar x[/tex]  is the sample mean, s is the sample standard deviation, n is the sample size, tα=/2 is the t-value corresponding to the desired level of confidence and (s/√n) is the standard error of the mean.

The sample size is 100, the sample mean is 5.33, and the sample standard deviation is 2.207, the standard error of the mean is:

s/√n

= 2.207/√100

= 0.221

The t-value corresponding to a 95% confidence level with 99 degrees of freedom (100 - 1), look it up in a t-distribution table or use a calculator.

The t-value is approximately 1.984.

The 95% confidence interval for the population mean is:

CI = 5.33 ± 1.984 × 0.221

= [4.897, 5.763]

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The opposite numbers that have a distance of 8 units between them on a number line are: -4 and 4.

We have,

The distance on a number line between two numbers is the number of units that separates both numbers.

Opposite numbers have the same distance to point zero on a that lies between them. For example, 4 on a number line is 4 units from point 0. -4 is also 4 units. 4 is the opposite number of -4.

Distance between -4 and 4

= |-4 - 4|

= |-8|

= 8 units.

Therefore, the opposite numbers that have a distance of 8 units between them on a number line are: -4 and 4.

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The length of the longer leg of this 30-60-90 triangle is 6.93 units.

In a 30-60-90 triangle, the length of the shorter leg is opposite to the 30-degree angle. The longer leg is opposite to the 60-degree angle, and the hypotenuse is opposite to the 90-degree angle.

The ratio of the sides in a 30-60-90 triangle is always the same. The length of the shorter leg is half of the length of the hypotenuse. The longer leg is the square root of three times the length of the shorter leg.

Let's use this information to solve a problem. Suppose you have a 30-60-90 triangle with a shorter leg of length 4 units. We can use the ratio to find the length of the longer leg.

The length of the hypotenuse is twice the length of the shorter leg, which is 2 times 4 units = 8 units.

The longer leg is the square root of three times the length of the shorter leg, which is the square root of three times 4 units = 6.93 units.

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By factoring and finishing the square , C is the right response. x = -5 or x =5

There are two ways to resolve quadratic equations: factoring and solving the square. A quadratic equation is factored when it is divided into two linear equations with the same solution. A method for rewriting quadratic equations in the form (x+a)²+b (x +a)² +b is known as "completing the square." This method enables us to change a quadratic expression or equation in the form an x² + b x + c to a (x - h) ² + k²from a provided quadratic expression or equation. This method can be applied to ease the process of solving complex quadratic equations .

The following techniques can be used to graphically solve the quadratic equation using at least two separate approaches:

Technique 1: Factoring

- Step 2: Finish the square

- Technique 3: Quadratic equation

- Step Four: Graphing

16x² - 400 = 0 is the quadratic equation that is provided.

First approach: factoring

The quadratic equation presented can be factored as follows:

16x²- 400 = 0

16(x² - 25) = 0

16(x + 5)(x - 5) = 0

Because of this, x = -5 or x = 5.

completing the square using method two

The square of the given quadratic equation can be completed as follows:

16x² - 400 = 0

16x² = 400

x² = (400/16)

x² = 25

x = ±√25

Because of this, x = -5 or x = 5.

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The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Out of the options given, A - Square meters and E - Square centimetres are both square units and could be used to measure the surface area of a tissue box.

Explain surface area

The surface area is the total area that covers the outer surface of a three-dimensional object. It is calculated by adding the areas of all the faces or surfaces of the object.

Explain area

The area is the measure of the size of a two-dimensional surface or region. It is expressed in units of square units (e.g., square meters, square inches).

According to the given information

The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Since area is measured in square units, the correct unit of measurement for the surface area of a tissue box would be a square unit. Out of the options given, A - Square meters and E - Square centimeters are both square units and could be used to measure the surface area of a tissue box.

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The values of x and y in the simplest form in the triangles are computed and listed below

Figure (1)

Using the proportion of similar triangles, we have

x/6 = 6/9

So, we have

x = 36/9

This gives

x = 4

Next, we have

y^2 = 6^2 + 4^2

y^2 = 52

y = 2√13

Figure (2)

Using the proportion of similar triangles, we have

x/6 = 6/2

So, we have

x = 36/2

This gives

x = 18

Next, we have

y^2 = 6^2 + 18^2

y^2 = 360

y = 6√10

Figure (3)

Using the pythagoras theorem of right triangles, we have

y^2 = 40^2 - 32^2

y^2 = 576

y = 24

Next, we have

x^2 = 30^2 - 24^2

x^2 = 324

x = 18

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Answer:

d

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

c

The point that is not on the same line as the others is E(9, 14).

The point that is not on the same line as the others would not have the same slope as the others.

Slope between A ( 3, 4) and B (2, 2):

= (4 - 2) / (3 - 2) = 2 / 1

= 2

Slope between B (2 , 2) and C (5, 8):

= ( 8 - 2 ) / (5 - 2)

= 6 / 3

= 2

Slope between C ( 5, 8) and D(7, 12):

= (12 - 8) / (7 - 5)

= 4 / 2

= 2

Slope between D ( 7, 12) and E ( 9, 14):

= ( 14 - 12) / (9 - 7)

= 2 / 2

= 1

We can therefore see that E ( 9, 14) is the odd one out and is not on the same line.

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The x-coordinate when Q has a y-coordinate of -4 is given as follows:

x = 3 or x = -3.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The circle in this problem has the parameters given as follows:

Hence the equation is given as follows:

x² + y² = 25.

When the y-coordinate is of -4, the x-coordinate is given as follows:

x² + (-4)² = 25

x² + 16 = 25

x² = 9

x = -3 or x = 3.

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Answer:

0.535 is the correct choice.

Answer:

Usemos la variable s para representar la cantidad de CD que tiene Sonya.

Luego, dado que Dana tiene 1/5 de la cantidad que tiene Sonya, podemos escribir la siguiente ecuación y resolverla para s:

1 s = 9

5

Multiplica ambos lados de la ecuación por 5 para resolver:

5 * 1 s = 9 * 5

    5

s = 45

Sonya tiene 45 CD.

Yes, Ms. Ouzts will have enough to purchase the purse as $125 is greater than the total cost of the purse including tax, which is $108.50.

The sales tax in South Carolina is 8.5%, which means that the total cost of the purse including tax will be

= Cost of purse + Sales tax

Substitute the values in the equation

= $100 + (8.5% of $100) = $100 + $8.50 = $108.50

If Ms. Ouzts has $125 to spend on the purse, then she will have enough to purchase it because $125 is greater than $108.50.

In fact, she will have $125 - $108.50 = $16.50 left over after buying the purse.

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High clouds are those that form at altitudes of at least 20,000 ft (6000 m).

At high altitudes, ice crystals form due to which cloud formation occurs.   Cirrus, cirrostratus, and cirrocumulus clouds are a few types of clouds. Cirrostratus clouds frequently form a thin, white layer that resembles a veil and covers the entire sky. Small, spherical, white clouds called cirrocumulus develop in long rows. Because they can provide information about changes in atmospheric pressure, temperature, and moisture levels in the upper atmosphere, these high clouds are crucial for meteorologists to investigate.

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Required polynomial is (x+3) where x is amount of average snowfall.

Here given in January, the amount of snowfall was 3 inches above average.

1. The average snowfall for January was a certain amount (let's call this 'A' inches).

2. The actual snowfall for January was 3 inches more than the average.

3. To calculate the actual snowfall for January, we can use the equation: Actual Snowfall = Average Snowfall (A) + 3 inches.

So, if we knew the average snowfall (A), we could easily find the actual snowfall by adding 3 inches to it.

Let amount of average snowfall be x inches.

So, snowfall in January month = (x+3) inches .

Therefore, required polynomial is (x+3) where x is amount of average snowfall.

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Correct answer is " Find a polynomial of the statement For the month of January, the amount of snowfall was 3 inches above average"

Regularly depositing the same amount into a savings account can lead to a large rise in the account balance over time with the appropriate plan and dedication.

An undefined number or quantity of something is referred to as an amount and can be used in a variety of different settings. Any number, quantity, length of time, or amount of data can be referred to as an amount. Amount in terms of money refers to the total amount being paid or received. The quantity of physical items is the total number of those items. The length or duration of a work or event can be referred to as the amount in terms of time. The entire quantity of data points or pieces of information is referred to as the amount in terms of data.

Here in the question:

Month | Amount Deposited | Account Balance

1           | 150                           | 150

2          | 150                           | 300

3          | 150                           | 450

4          | 150                           | 600

5          | 150                           | 750

As seen in the table above, after five months, a 150 initial deposit into a savings account can grow to a balance of 750 with monthly deposits of the same amount for the next four months. This demonstrates that consistent saving can have a considerable impact on a savings account's overall balance.

Since interest is calculated using the compounding principle, regular deposits can enhance the amount that can be earned over time. This indicates that interest may be accumulated on both the initial deposit and any prior interest in the account. So, by consistently contributing the same amount of money to a savings account, it is feasible to dramatically raise the account's overall balance.

In conclusion, it is clear that consistent contributions to a savings account can be an excellent strategy to build wealth. Regularly depositing the same amount into a savings account can lead to a large rise in the account balance over time with the appropriate plan and dedication.

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The appropriate statistical test for comparing the difference in maintenance quality ratings at two tirezone locations, where there are two independent groups of customers, would be the Mann-Whitney test or Wilcoxon rank-sum test.

The Mann-Whitney test would be appropriate for this scenario because it is used to compare the difference between two independent groups. In this case, we have two independent groups of customers from different locations, and we want to determine if there is a significant difference in their ratings of maintenance quality.

The test compares the ranks of the observations in the two groups and uses that information to determine if there is a significant difference between them. The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is another name for the same test.

Therefore, the Mann-Whitney test or Wilcoxon rank-sum test is the appropriate statistical test to use in this scenario.

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The solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line is {1/3, 1}.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

We can solve this equation by considering two cases:

Case 1: 3z-2 = 1

Solving for z, we get:

3z-2 = 1

3z = 3

z = 1

Case 2: 3z-2 = -1

Solving for z, we get:

3z-2 = -1

3z = 1

z = 1/3

Therefore, the solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line as follows:

The solution set is {1/3, 1}.

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The interval over which both functions are positive is (4, ∞).

In Mathematics and Geometry, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = alog(±x + h) + k

Where:

Based on the given logarithm function g(z) = log₂(z + 3) - 2, we can reasonably infer and logically deduce that it is a vertical translation of this logarithmic function f(z) = log₂(z + 3).

Additionally, the logarithm function g(z) has a vertical asymptote at z = -3 and would be positive on the interval (-3, ∞). This ultimately implies that, an intersection of the intervals over which each function is positive is given by;

Intersection of intervals = (4, ∞) ∪ (-3, ∞).

Positive interval = (4, ∞).

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The total surface area of the wire-screen chicken coop is 10512 square inches.

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area

the total surface area of the right rectangular prism, we use the formula:

2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively.

We are given the height, width, and length of the wire-screen chicken coop, which are 42 inches, 36 inches, and 48 inches, respectively.

Substituting these values in the formula, we get:

2(36)(48) + 2(36)(42) + 2(48)(42)

Multiplying out, we get:

= 3456 + 3024 + 4032

Adding these terms, we get the total surface area:

= 10512

Therefore, the total surface area of the wire-screen chicken coop is 10512 square inches.

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Answer:

yes it will be the same

Step-by-step explanation:

Let’s call the amount of stock traded “x”. Then we can set up an equation like this:

$19 = 0.02x

To solve for x, we can divide both sides by 0.02:

$950 = x

Therefore, if you trade $950 worth of stock, both Fierro Brothers and Sondo Investment House would charge you the same commission.

The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .

To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.

The scale factor is:

= 31 / 8

= 3. 875

Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :

= 13. 7 x 3. 875

= 53. 09 units

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The best measure of variability for the data is A. The range is the best measure of variability, and it equals 8.

The range is the difference between the highest value and the lowest value in the dataset. In this case, the highest number of rose bouquets is 9, and the lowest is 1. This is the data shown on the line plot.

Range = Highest Value - Lowest Value

Range = 9 - 1

Range = 8

The range is the best measure of variability, and it equals 9. The IQR is used when there are outliers that can affect the data.

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The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].

Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.

The slope of the secant line is

m = (0 - 0)/(2π - (-2π)) = 0

Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form

y - (x + sin(x)) = 0

y = x + sin(x)

To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is

f'(x) = 1 + cos(x)

Setting this equal to 0 and solving for x, we get

cos(x) = -1

x = π

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The given question is incomplete, the complete question is:

At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?

It would take about 8.59 months for the football player to double his current following, assuming that his follower count continues to increase at a rate of 9% per month.

To find out how long it would take for the football player to double his current online following of 105,326, we need to find the distance from his starting point to the doubling point. In other words, we need to find out how many followers he needs to gain in order to have 2 times his current following.

To do this, we can use the formula for exponential growth:

A = P(1 + r)ⁿ

where A is the final amount, P is the initial amount, r is the rate of growth (in decimal form), and t is the time (in months).

In this case, we want to find t, the time it would take for the football player to double his current following. So we can rewrite the formula as:

2P = P(1 + 0.09)ⁿ

Simplifying this equation, we can divide both sides by P:

2 = (1 + 0.09)ⁿ

Taking the natural logarithm of both sides, we get:

ln(2) = t ln(1 + 0.09)

Solving for t, we divide both sides by ln(1 + 0.09):

t = ln(2) / ln(1 + 0.09)

Using a calculator, we get t ≈ 8.59 months.

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