4
(1 pa
10. The table shows the results from home games for a specific team during the season leading up
to the World Series. The team's home field has a roof that can be closed for weather. If it is
closed, the fans could make more noise for the home team and possibly give them an
advantage. Find the test statistic needed to test independence for the contingency table.
Closed roof
Open roof
034.215
00.093
00.798
03.841
Win
36
15
Loss
17
11

Answer:

3. Substitution because it said angle HKI = angle GKH, so we substitutioned that angle for the other one. I'm not sure about 4. If you provide us with the answer choices for that one, then I could help

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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The graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Option C

The function C(x) = (1/4)√x + 2 represents the side length of the smaller granola bar, where x is the area of the larger granola bar in square inches. To determine which graph shows C(x), we need to analyze the characteristics of the function.

First, let's consider the behavior of the function C(x) = (1/4)√x + 2:

Square Root Function: The term √x indicates that the function involves the square root of x. This means that as x increases, C(x) will also increase, but at a decreasing rate.

Scaling Factor: The coefficient (1/4) scales the square root of x. It affects the steepness of the function and causes C(x) to increase more slowly compared to a simple square root function.

Vertical Shift: The constant term (+2) shifts the entire function vertically upward by 2 units. This means that the graph will be raised by 2 units compared to a standard square root function.

Based on these characteristics, we can conclude that the graph of C(x) will be an increasing curve with a flattened slope compared to a simple square root function, and it will be shifted upward by 2 units.

Among the answer choices, the graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Without the actual graphs provided, it is difficult to specify the exact choice, but it should exhibit these features described above.

It is essential to refer to the available graphs or visually analyze the functions to determine the correct graph that shows C(x). Option C is correct.

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Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

The length of the arc LM is 8.72 cm.

We have,

The length of an arc is the distance that runs through the curved line of the circle making up the arc.

The length of an arc is expressed as;

l = tetha/360 × 2πr

tetha = R

R = 100°

and, radius = 5 units

so, we get,

l = 100/360 × 2 × 3.14 × 5

l = 8.72 cm (1.dp)

therefore the length of the arc LM is 8.72 cm

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Answer:

[tex]a_{n}[/tex] = - 7n + 47

Step-by-step explanation:

there is a common difference between consecutive terms , that is

33 - 40 = 26 - 33 = - 7

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 40 and d = - 7 , then

[tex]a_{n}[/tex] = 40 - 7(n - 1) = 40 - 7n + 7 = - 7n + 47

Answer:

D = 90 FT

Step-by-step explanation:

40 / d = 20 / 45

cross multiply

45 × 40 = 20d

1800 = 20d

divide both sides by 20

1800 / 20 = 20d / 20

d = 90 ft

In the given triangle value of b is,

⇒ b = 16

We have to given that,

A triangle with three angles (b + 20), (b + 32) and 6b.

Now, WE know that;

Sum of all interior angles of triangle is 180 degree.

Hence., We can formulate;

⇒ (b + 20) + (b + 32) + 6b = 180

Solve for b,

⇒ 8b + 52 = 180

⇒ 8b = 180 - 52

⇒ 8b = 128

⇒ b = 128/8

⇒ b = 16

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The solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

Given the inequalities that include 3 in the following inequalities

x > 1.4, x < 2.6, x > 4.2, x < 5.1 and x < 8.2.

To find the solution set which include 3, write the solution set which consists of integer.

The solution set of x > 1.4 is { 2, 3, 4, 5, 6,     ........}

The solution set of x < 2.4 is { 2, 1. 0, -1, ...............}

The solution set of x > 4.2 is { 5, 6. 7, 8, ...............}

The solution set of x < 5.1 is { 5, 4, 3, 2, 1, ...............}

The solution set of x < 8.2 is { 8, 7, 6, 5, 4, 3, ...............}

Hence, the solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

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The calculated volume of the sphere is 44602.24 ft³

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

Radius = 22 ft

The volume of a sphere can be expressed as;

V = 4/3πr³

Where

r = 22

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

V = 4/3π * 22³

Evaluate

V = 44602.24

Therefore the volume of the sphere is 44602.24 ft³

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Question

Determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.

Radius = 22 ft

The formulas that represent the linear function in this problem are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The line has a slope of 2/3, hence:

y = 2x/3 + b.

When x = 1, y = 2, hence the intercept b is obtained as follows:

2/3 + b = 2

b = 6/3 - 2/3

b = 4/3.

Hence the slope-intercept equation of the line is given as follows:

f(x) = 2x/3 + 4/3.

The line goes through points (1,2) and (4,4), hence the point-slope equations to the line are given as follows:

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The average utility price in Orlando for the 6 month period, and the way it compares to the national average is d. $ 308. 83 ; higher than the national average .

The information for Orlando is April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.

The average is:

= ( 288 + 310 + 325 + 294 + 293 + 343 ) / 6

= 1, 853 / 6

= $ 308. 83

This average is higher than the national average of $ 308. 83.

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Full question is:

The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How does this compare with the national average?

A graph titled Orlando, Florida, has month on the x-axis and utility price on the y-axis. In April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.

a. $370.60; higher than the national average

b. $292.17; higher than the national average

c. $38.35; lower than the national average

d. $308.83; higher than the national average

Consecutive Interior Angles.

They are on the same side of a line that cuts through two other lines.

Answer:

13.48 - 8.263 = 5.217

Answer:5.217

Step-by-step explanation: caculate it

The equation of the circle is (x - 2)² + (y - 3)² = 36

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

The circle

Where, we have

Center = (a, b) = (2, 3)

Radius, r = 6 units

The equation of the circle is represented as

(x - a)² + (y - b)² = r²

So, we have

(x - 2)² + (y - 3)² = 6²

Evaluate

(x - 2)² + (y - 3)² = 36

Hence, the equation is (x - 2)² + (y - 3)² = 36

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The figures are similar because the ratio of segment BC to segment EF is equal to the of segment AB to segment DE.

The scale factor is equal to 3/2.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following:

Scale factor = BC/EF = AB/DE

Scale factor = 9/6 = 6/4

Scale factor = 3/2 = 3/2 (similar)

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Answer:  log w²v⁵

Step-by-step explanation:

2log w + 5log v                        >Use exponent log rule

log w² + log v⁵                         >There is addition between, use

                                                   multiplication rule

log w²v⁵

Rounded to the nearest hundredth, the value of y at [tex]x = 7[/tex] is approximately [tex]12.78[/tex], according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form [tex]y = mx + b[/tex], where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

[tex]\[ y = 1.3642x + 3.2324 \][/tex]

To find the value of [tex]y[/tex] at [tex]x = 7[/tex], we substitute [tex]x = 7[/tex] into the equation:

[tex]\[ y = 1.3642(7) + 3.2324 \][/tex]

Simplifying the equation, we get:

[tex]\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \][/tex]

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is [tex]y = 1.3642x + 3.2324[/tex]. By substituting [tex]x = 7[/tex] into the equation, we find that the estimated value of y is approximately [tex]12.78[/tex]. This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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The base 10 equivalent of the base 7 number 463421 is 83174.

To convert a number from base 7 to base 10, we multiply each digit of the base 7 number by the corresponding power of 7 and sum up the results.

For the number 463421 in base 7:

= 4 x 7⁵ + 6 x 7⁴ + 3 x 7³ + 4 x 7² + 2 x 7¹ + 1 x 7⁰

= 4 x 16807 + 6 x 2401 + 3 x 343 + 4 x 49 + 2 x 7 + 1 x 1

= 67228 + 14406 + 1029 + 196 + 14 + 1

= 83174

Therefore, the base 10 equivalent of the base 7 number 463421 is 83174.

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The required sum of mixed fraction answer is 12 35/24.

Given that 6 5/8 + 6 5/6.

To find the sum of two or more mixed fractions, add the whole part of two fractions, add the fraction part of two fractions, then add these sums.

The sum (s1) of whole parts of two fractions is

s1= 6 + 6 = 12.

The sum(s2) of fraction parts of two fractions is

s2 = 5/8 +5/6.

L.C.M of 8 and 6 is 24.

Multiply each fraction by 12/12 gives,

s2 = 5/8 × 24/24 + 5/6 × 24/24.

s2 = 15/24 + 20/24.

s2 = 35/24.

The sum of mixed fractions is s1 + s2

Sum = 12 + 35/24

Thus, the required sum of mixed fraction is 12 35/24.

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The probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.

We know that, probability of an event

= Number of favourable outcomes/Total number of outcomes.

Here, area of a rectangle = Length × Breadth

= 15×8

= 120 square units

Area of a triangle = 1/2 × Base × Height

= 1/2 ×(√10²-6²)×6

= 0.5×8×6

= 24 square units

Area of a trapezium = 1/2 (Sum of parallel sides)×Height

= 1/2 ×(5+7)×2

= 12 square units

Area of a square = side² = 2²

= 4 square units

(a) Probability of landing in trapezium or Square = 12/120 + 4/120

= 16/120

= 2/15

(b) Probability of landing inside the rectangle but outside the triangle = 16/120

= 2/15

Therefore, the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.

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Answer:3x-4y=8

Step-by-step explanation:

Answer:

3(5)^6

Step-by-step explanation:

There is 6, 5's in the expression meaning our answer has to be 3(5)^6.

:)

Answer:

the answer for the question given above is equal to 46875

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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The Surface Area of Cone is 706.5 cm².

We have dimension of Cone

height = 12 cm

Radius = 9 cm

Now, l = √9² + 12² = √81 + 144 = 25 cm

So, the Surface Area of Cone

= πrl

= 3.14 x 9 x 25

=  706.5 cm²

Thus, the Surface Area of Cone is 706.5 cm².

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Answer:

Height = 64 feet

Step-by-step explanation:

(***It's very important to model these kinds of problems.  I attached a picture modeling the problem so show how modeling makes it easier to solve the problem)

We know that the building is vertical, and the ground is horizontal.  Thus, the ground and the building make a right angle.  

Therefore, the top of the building, the base of the building, and the surveyor form a right triangle, where

Because we're working with a right triangle, we can now find h, the heigh of the building using one of the trigonometric ratios.

We know that the angle of elevation is made by the ground and the distance between the surveyor and top of the building.

When the 65° (angle of elevation) is our reference angle, the height of the building is the opposite side and the distance between the base of the building and the surveyor is the adjacent side.

Thus, we can use the tangent ratio, which is:  tan (θ) = opposite / adjacent:

We can now plug in 65 for θ and 30 for the adjacent side.  This will allow us to find the opposite side, which is the heigh of the building:

tan (65) = h / 30

30 * tan(65) = h

64.33520762

64 = h

Thus, the height of the building to the nearest foot is 64 feet.

Answer:

x = 8 units

Step-by-step explanation:

Because this is a right triangle, we can find x using the Pythagorean theorem, which is given by:

a^2 + b^2 = c^2, where

In the triangle, the 6 unit side and the x unit sides are the legs while the 10 unit side is the hypotenuse.

Thus, we can solve for x by plugging in 6 for a and 10 for c in the theorem and solving for a (aka x, simply a in the theorem):

a^2 + 6^2 = 10^2

a^2 + 36 = 100

a^2 = 64

a = 8

x = 8

Thus, x is 8 units.

There are 1365 different ways for Andre to select the blue fabrics for his quilt.

To determine the number of different ways Andre can select the blue fabrics for his quilt, we can use the concept of combinations.

Andre wants to select 4 different fabrics from a pool of 15 options for the blue portion of the quilt. This can be calculated using the formula for combinations:

C(n, r) = n! / (r! × (n-r)!)

where n is the total number of options and r is the number of selections.

In this case, we have:

n = 15 (number of options for blue fabrics)

r = 4 (number of fabrics to be selected)

Plugging in these values into the combination formula, we get:

C(15, 4) = 15! / (4! × (15-4)!)

Simplifying the equation, we have:

C(15, 4) = 15! / (4! × 11!)

Now, let's calculate the factorial terms:

15! = 15 × 14 × 13 × 12 × 11!

4! = 4 × 3 × 2 × 1

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Substituting these factorial terms into the equation:

C(15, 4) = (15 × 14 × 13× 12 × 11!) / (4 × 3 × 2 × 1 × 11!)

Simplifying further:

C(15, 4) = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1)

C(15, 4) = 1365

Therefore, there are 1365 different ways for Andre to select the blue fabrics for his quilt.

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The measure of angle BDC is 42° and the measure of angle BAC is 21°.

Given that, the measure of arc BC of circle = 42°.

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

From the given circle,

The measure of arc BC = Angle BDC = 42°

Here, Angle BDC = 2×Angle BAC

42° = 2×Angle BAC

Angle BAC = 21°

Therefore, the measure of angle BDC is 42° and the measure of angle BAC is 21°.

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