Denzel used the spinner shown below to compare theoretical probability and experimental probability. He spun the spinner 180 times and recorded the letter that it landed on each time. The results are shown in the table..

Which statement correctly compares the theoretical probability and experimental probability for one of the letters on the spinner?

A. The theoretical probability of landing on a C is greater than the experimental probability of landing on an C.

B. The theoretical probability of landing on a D is greater than the experimental probability of landing on an D.

C. The theoretical probability of landing on a B is less than the experimental probability of landing on an B.

D. The theoretical probability of landing on an A is less than the experimental probability of landing on an A.

Triangles to total shapes because triangles= 5 total, and total shapes = 10. 5/10 simplifies to 1/2

The probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.

what is probability?

In general terms, probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty or randomness in various situations.

In formal terms, probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in an event. It is usually represented as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an adult being willing to change their diet can be calculated using the given information as follows:

Probability of an adult being willing to change diet = Number of adults willing to change / Total number of adults

Total number of adults = 400 (as given in the question)

Number of adults willing to change = 116 (as given in the question)

Therefore, the probability of an adult being willing to change their diet can be calculated as:

Probability = 116/400

Probability = 0.29 or 29%

So, the probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.

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Answer:

We can use the formula:

average speed = total distance / total time

To find the total distance, we add the distances for each event:

total distance = 1.5 km (swimming) + 40 km (cycling) + 1 km (running) = 42.5 km

To find the total time, we add the times for each event:

time for swimming = distance / speed = 1.5 km / 2.5 km/h = 0.6 hours

time for cycling = 40 km / 12 km/h = 3.33 hours

time for running = 1 km / 9 km/h = 0.11 hours

total time = 0.6 hours + 3.33 hours + 0.11 hours = 4.04 hours

Now we can calculate the average speed:

average speed = total distance / total time = 42.5 km / 4.04 hours ≈ 10.52 km/h

Therefore, Farhan's average speed for the entire competition is approximately 10.52 km/h.

The linear equations from the options given are expressed as: y = 5 and y = -2/5x + 4.

An equation is linear can be expressed in the following forms:

y = mx + b

x = b

y = b

In the above, y is the dependent variable and x is the independent variable, m = slope, and b = y-intercept.

Note that in a linear equation the exponent of the variable is always 1. On the other hand, a nonlinear equation has an exponent that is not equal to 1 and can be expressed as:

y = x²

Therefore, the equations that are linear are:

y = 5 and y = -2/5x + 4.

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Answer:

True, False, True, False, False (answered top to bottom)

Step-by-step explanation:

Answer:

Step-by-step explanation:

If cos a = 0.5, then sin a could equal √(1 - cos^2 a) = √(1 - 0.5^2) = √0.75 ≈ 0.866.

Answer: 4/5

Step-by-step explanation: In decimal form: 0.8

The licenses have space for 6 characters.

We need to note that there are 26 alphabets and 10 numbers to pick from.

So, for the first character, any of the 26 alphabets can take this spot.

For the second character, 25 alphabets are now available for that space. (Since repetition is not allowed)

For the third character, 24 alphabets are available for that.

For the fourth character, any of the 10 numbers can take up that spot.

For the fifth character, only 9 numbers can take this spot now. (No repetition rule too)

For the sixth character, 8 numbers can take that spot.

So, mathematically, the number of license tags possible will be

[tex]\bold{26 \times 25 \times 24 \times 10 \times 9 \times 8 = \underline{11,232,000} \ possible \ license \ tags}[/tex]

Answer:

11,232,000

Step-by-step explanation:

26 choices for the first letter.

25 choices left for the second letter (can't repeat letters)

24 choices left for the third letter

26 x 25 x 24 = 15,600 = possible first 3 characters.

10 choices for the first number

9 choices left for the second number (can't repeat numbers)

8 choices left for the third number

10 x 9 x 8 = 720 = possible last 3 characters.

chatgpt

Answer:

The lower quartile corresponds to the 25th percentile of the data set. To find the maximum value for the lower quartile, we need to find the largest number that is at or below the 25th percentile.

The range of the numbers that the random number generator can pick is 69 - 7 + 1 = 63. The 25th percentile corresponds to the value that is 25% of the way through this range, which is:

0.25 * 63 = 15.75

Since we can't pick a fractional number, we need to round down to 15. Therefore, the maximum value for the lower quartile is 15.

The numbers are characterized as rational and irrational numbers as below

1. 3.2 x 10³ - R (Rational)

2. 4/3 - R (Rational)

3. 1.423... - I (Irrational)

4. TT/6 - I (Irrational)

Rational numbers harmonized with a fraction of two integers where the denominator must not be zero. In simpler terms, it can be conveyed as p/q whereby both "p" and "q" are integers while "q" is unequal to zero.

As opposed to rational numbers, irrational ones cannot be expressed in a fraction or quotient of two integers. It's not possible to write them down in terms of the figure p/q whereby "p" and "q" are integers, differing from one another, and "q" is also inequivalent to zero.

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Answer:To evaluate the function for f(2), we simply substitute x = 2 into the function

:f(2) = 8(2) + 7

Simplifying the expression:

f(2) = 16 + 7f(2) = 23

Therefore, f(2) = 23.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, - 6) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m = [tex]\frac{0-(-6)}{6-(-6)}[/tex]= [tex]\frac{0+6}{6+6}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]

The transformations that are applied to the graph of the function [tex]f(x) = 10^x[/tex] to produce the graph of the function [tex]g(x) = 3(10)^x - 2[/tex] is: C. a vertical dilation by a factor of 3 and a vertical shift down 2 units.

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a function or object is transformed, all of its points would also be transformed.

In Mathematics and Geometry, a dilation refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Based on the parent function (exponential), we can logically deduce that the exponential function g(x) can be produced by vertically stretching the parent function by a scale factor of 3, followed by a vertical shift down 2 units;

[tex]f(x) = 10^x[/tex]

[tex]g(x) = 3(10)^x - 2[/tex]

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The prominent similar feature between f(x) and g(x) is the present y-intercept.

Since the discriminant is negative, there are no possible solutions to the given equation, which implies that f(x) has no x-intercepts.

It should be noted that to identify the y-intercept, we set x = 0 and evaluate f(x):

f(0) = 2(0)² - 3(0) + 4

f(0) = 4,

The y-intercept of f(x) can be determined as (0, 4).

Moreover, the function g(x) = 2x-4 is a power function having a negative exponent, which makes it a reciprocal function. It's domain comprises all real numbers but 0, while its range includes all real numbers excluding 0.

In order to obtain the x-intercept of g(x), we set g(x) equal to zero and solve for x:

0 = 2x-4

2x = 4

x = 2

Consequently, the x-intercept of g(x) is (2, 0), together with the y-intercept (0, -4).

The prominent similar feature between f(x) and g(x) is the present y-intercept. On the other hand, f(x) does not contain any x-intercepts, whereas g(x) has a single x-intercept. Also, f(x) is categorized as a second-degree polynomial function, whereas g(x) is classified as a reciprocal function.

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The number of triangles formed by triangle ABC is 1

In order to calculate the possible number of triangles ABC that can be made with the specified parts, it is essential to employ conditions for triangle congruence, which includes the Triangle Inequality Theorem.

If sides a, b, and angle A can create a valid triangle, then they must follow these requirements:

a + b > c

a + c > b

b + c > a

By replacing given values with assigned variables, we get:

38 + 77 > c,

38 + c > 77,

77 + c > 38.

After solving these inequalities, we determine that c should be

However, if the Triangle Inequality Theorem is not observed, an unfeasible configuration results. Therefore, it would be impossible to generate a triangle using the following: AB = 38, AC = 77, and angle BAC = 74 degrees.

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Answer:

!

Step-by-step explanation:

Therefore, the closest option to the calculated percentage is option (d) 44%.

Percent, denoted by the symbol "%", is a way of representing a fraction or proportion out of 100. It is used to express a part of a whole in terms of hundredths. For example, 50% is the same as 50 out of 100, which simplifies to 1/2 or 0.5 as a decimal. Percentages are commonly used in many areas such as finance, statistics, and everyday life to express changes, rates, or comparisons.

Here,

To calculate the percentage of customers who prefer cookies, we need to add up the number of customers who prefer cookies from each survey and divide it by the total number of customers who took the survey.

Number of customers who prefer cookies: 25 + 9 + 28 + 11 = 73

Total number of customers who took the survey: 17 + 11 + 20 + 13 + 25 + 8 + 9 + 30 + 26 + 11 = 170

Percentage of customers who prefer cookies: (73/170) x 100% ≈ 44%

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Based on the Tangent Chord Theorem:

The Tangent Chord Theorem states that if a chord and a tangent intersect at the point of tangency, then the measure of each angle formed is equal to half the measure of its intercepted arc.

Considering the given angles;

m∠1 = ¹/₂ AB

m∠1 = ¹/₂ ACB

m∠DEG = ¹/₂ * 308°

m∠DEG = 154°

m∠DBC =  ¹/₂ * (360 - 192)

m∠DBC = 84°

m XY = 360 - (151 * 2)

m XY = 56°

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The coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

A triangle is a closed, two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and can be formed by connecting three non-collinear points. Triangles can be classified based on their side lengths and angles.

To solve this problem, we can use the fact that the area of a triangle is equal to half the product of its base and height. Let's first find the length of the sides of the square.

Since the area of the square is 1320 square centimeters, we can find its side length by taking the square root of 1320:

√(1320) ≈ 36.32

So the side length of the square is approximately 36.32 cm.

Next, let's find the coordinates of points E and F. Since E is the midpoint of AB, its coordinates are:

E = ((0+36)/2, (36+0)/2) = (18, 18)

Similarly, since F is a quarter point of BC close to point B, its coordinates are:

F = (36, (3/4)36) = (36, 27)

Now let's find the equation of line CE. Since we know two points on the line (C and E), we can use the point-slope form of a linear equation to find its equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line. We can find the slope of the line by taking the difference in y-coordinates and dividing by the difference in x-coordinates:

m = (0 - 36)/(36 - 18) = -2

Using the point-slope form with point C, we get:

y - 0 = -2(x - 36)

y = -2x + 72

Similarly, the equation of line DB can be found using points D and B:

m = (0 - 36)/(0 - 18) = 2

y - 0 = 2(x - 0)

y = 2x

Finally, we can find the coordinates of point P by solving the system of equations:

y = -2x + 72

y = 2x

Setting the two expressions for y equal to each other, we get:

-2x + 72 = 2x

4x = 72

x = 18

Substituting x = 18 into either equation, we get:

y = 2x = 36

So the coordinates of point P are (18, 36). To find the coordinates of point Q, we can use the fact that it lies on line DF. Since we know two points on the line (D and F), we can again use the point-slope form of a linear equation:

m = (27 - 0)/(36 - 0) = 3/4

y - 0 = (3/4)(x - 0)

y = (3/4)x

To find the intersection point of lines DF and CE, we need to solve the system of equations:

y = (3/4)x

y = -2x + 72

Setting the two expressions for y equal to each other, we get:

(3/4)x = -2x + 72

(11/4)x = 72

x = 64/11

Substituting x = 64/11 into either equation, we get:

y = (3/4)(64/11) ≈ 14.73

So the coordinates of point Q are (64/11, 14.73).

Hence, Now that we have the coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

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Answer: Angle aeb

Step-by-step explanation: To be supplementary, the angle(s) must add up to 180. Angle AEB and angle DEA add to 180. Another way to find this is to find the angle that the angle is adjacent to in a straight line.

Answer:

A.the annual premium can be found by multiplying the monthly premium by 12:

Annual premium = Monthly premium x 12

Annual premium = $65 x 12 = $780

b. The semiannual premium can be found by dividing the annual premium by 2:

Semiannual premium = Annual premium / 2

Semiannual premium = $780 / 2 = $390

c. To calculate how much less Ronald's semiannual payments would be if he dropped the optional collision insurance, we need to subtract the cost of the optional insurance from the semiannual premium:

Semiannual payment with optional insurance = Semiannual premium - $120

Semiannual payment with optional insurance = $390 - $120 = $270

Semiannual payment without optional insurance = Semiannual premium - $120

Semiannual payment without optional insurance = $390 - $120 = $270

Therefore, Ronald's semiannual payments would be $270 if he dropped the optional collision insurance.

The length of the arc of the circle that has a radius of 16 inches and a central angle of 75 degrees is calculated as 6.66π inches (to two decimal places).

The length of an arc is calculated using the formula below:

arc length = θ/360 * 2 * π * r

Given the variables:

Central angle (θ) = 75 degrees

radius (r) = 16 inches

Plug in the values:

arc length = 75/360 * 2 * π * 16

length of arc ≈ 6.66π inches (to two decimal places).

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R2, since the model only has one independent variable.

Find R2:

R^{2} = [tex]\frac{SSR}{SST}[/tex]

R^{2} = [tex]\frac{18.26347892}{26.24578040}[/tex]

R^{2} = 0.6958634

[tex]R^{2} = 0.6959}}[/tex]

Part 2 of 3:

Find Ra2:

[tex]R^{2}_{a}= 1-\frac{(1-R^{2}) \\times (n-1)}{n-k-1}[/tex]

where

n = 9

since dftotal = n -1 = 8

thus n = 8+1=9

and k = number of independent variables = 1

Thus

[tex]R^{2}_{a}= 1-\frac{(1-0.6958634 ) \\times (9-1)}{9-1-1}[/tex]

[tex]R^{2}_{a}= 1-\frac{0.3041366 \\times 8}{7}[/tex]

[tex]R^{2}_{a}= 1-0.3475846[/tex]

[tex]R^{2}_{a}= 0.6524154[/tex]

[tex]R^{2}_{a}= 0.6524}}[/tex]

Part 3 of 3:

R2, since the model only has one independent variable.

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[tex]x^2-5x+22=7x+2\implies x^2-12x+20=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-12}x\stackrel{\stackrel{c}{\downarrow }}{+20}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-12)^2-4(1)(20)\implies 144-80\implies 64[/tex]

After using synthetic division, the answer are given as follows;

first row          = -4, 4, 12

Second Row = -2 2 -6 -5

Answer = 6 + [-5/x-2]

-2x^3+6x^2-10x+7 / x-2

Coefficient of the numerator polynomial are:

- 2, 6, -10 , 7

the zeros of the denominator are:

x -2 = 0
x = 2

              X³       X³    X¹     X⁰
               -2        6     -10    7

2                                                  

      X³       X³    X¹     X⁰
               -2        6     -10    7

2               ↓        -4        4   -12                

                 -2        2     -6     -5

So the quotient is -2x² +2x - 6 remainder -5

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Answer: In that picture the slope is increasing

Step-by-step explanation: positive rise and positive run (uphill from left to right)

BGC or AGF

Adjacent means next to or adjoining something else and both of the mentioned angles are next to angle AGB.

Answer: 1204 cm²

Step-by-step explanation:

The upper bound of the area of a page would be the area of a rectangle with the upper bound of the length and width measurements.

Given that each page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest centimetre, the upper bound of the length would be 43.5 cm (since we round up to the nearest centimetre) and the upper bound of the width would be 28.5 cm.

Therefore, the upper bound of the area of a page would be:

43.5 cm x 28.5 cm = 1240.25 cm²

Rounding this value to the nearest whole number, we get:

1204 cm²

So, the upper bound of the area of a page is 1204 cm².

Answer:

1204 cm 2

Step-by-step explanation: