30 POINTS!! PLEASE

A surveyor wants to determine the width of a river. She surveys the area and finds the following measures below.

She uses a pair of similar triangles, to help her find the answer.

The  total number of each type of ball:

Football: Given as 8

Basketball: 18

Baseball: 40

Softball: 15

For basketball:

2 + 2(8) = 18

First, we evaluate the expression inside the parentheses: 2(8) = 16

Then, we add 2 to the result: 16 + 2 = 18

So, the total number of basketballs is 18.

For baseball:

5(8) = 40

We simply multiply 5 by 8 to get the total number of baseballs, which is 40.

For softball:

6 + 1/2(18) = 24

First, we evaluate the expression inside the parentheses: 1/2(18) = 9

Then, we add 6 to the result: 9 + 6 = 15

So, the total number of softballs is 15.

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400Answer:

Step-by-step explanation:

The calculated measure of the angle 1 is 43 degrees

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

The circle

Also, we have

The line AB tangent to the circle

This means that

Angle 1 = 1/2 * the arc subtended by the line

So, we have

Angle 1 = 1/2 * 86

Evaluate

Angle 1 = 43

Hence, the measure of the angle 1 is 43 degrees

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Answer:

Volume = 105 cm³

Step-by-step explanation:

Volume of a cuboid = l × b × h (l = length. b = breadth. h = height)

Volume = 7 × 5 × 3

Volume = 35 × 3

Volume = 105 cm³

The area of the Rhombus-shaped keychain is 3 square centimeters.

The area of the rhombus-shaped keychain,

we can use the formula:

Area = (diagonal1 * diagonal2) / 2

Given that the horizontal diagonal has a length of 2 centimeters and

the vertical diagonal has a length of 3 centimeters,

we can substitute these values into the formula:

Area = (2 * 3) / 2

    = 6 / 2

    = 3 cm^2

Therefore, the area of the rhombus-shaped keychain is 3 square centimeters.

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Answer: Area = = 38.5 - Perimeter - 29.6819.

Step-by-step explanation:

To find the perimeter and area of a triangle with vertices L(5,5), M(-2,-4), and N(5,-6), we can use the distance formula and the formula for the area of a triangle.

Perimeter:

The perimeter of a triangle is the sum of the lengths of its sides. We can find the lengths of each side using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can calculate the lengths of LM, MN, and NL:

LM = √((-2 - 5)^2 + (-4 - 5)^2)

= √((-7)^2 + (-9)^2)

= √(49 + 81)

= √130

MN = √((5 - (-2))^2 + (-6 - (-4))^2)

= √((7)^2 + (-2)^2)

= √(49 + 4)

= √53

NL = √((5 - 5)^2 + (-6 - 5)^2)

= √((0)^2 + (-11)^2)

= √(0 + 121)

= √121

= 11

The perimeter of the triangle is the sum of these three sides:

Perimeter = LM + MN + NL

= √130 + √53 + 11 = 29.6819

Area:

To calculate the area of the triangle, we can use the formula for the area of a triangle using the coordinates of its vertices. The formula is given by:

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Using the coordinates of L(5,5), M(-2,-4), and N(5,-6), we can calculate the area:

Area = 0.5 * |5(-4 - (-6)) + (-2)(-6 - 5) + 5(5 - (-4))|

= 0.5 * |5(2) + (-2)(-11) + 5(9)|

= 0.5 * |10 + 22 + 45|

= 0.5 * |77|

= 38.5

Therefore, the perimeter of the triangle is given by √130 + √53 + 11 = 29.6819 units, and the area of the triangle is 38.5 square units.

The quadratic equation shown in the graph is:

y = x² + 2x - 8

Here we want to find the graph of the given quadratic equation, where we only know the zeros of it.

Remember that if a quadratic equation has the zeros:

x = a

x = b

Then we can write it as:

y = (x - a)*(x - b)

Here the zeros are:

x = -4

x = 2

Then we can write:

y = (x + 4)*(x - 2)

Expanding that we will get the standard form:

y = x² + 4x - 2x - 8

y = x² + 2x - 8

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The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.

Here we have the summatory:

[tex]\sum^{5}_{n = 1} 2^{n - 2}[/tex]

So we just need to add the 5 terms (between n = 1 and n = 5)

So we will get the sum:

S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]

S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]

S = [0.5 + 1 + 2 + 4 +8]

S = 15.5

So the correct option is the second one.

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The exponential regression equation that best fits the data is y = 2^x.

To determine which exponential regression equation best fits the given data points (2, 4), (3, 8), (4, 16), and (5, 32), let's analyze the options for regression equations:

Option 1: y = 2^x

Option 2: y = 3^x

Option 3: y = 4^x

Option 4: y = 5^x

To find the best fit, we need to compare the predicted y-values from each equation with the actual y-values of the given data points.

The equation that produces the least amount of error or the closest predicted y-values to the actual ones will be the best fit.

Let's calculate the predicted y-values for each option using the given x-values:

Option 1: [tex]y = 2^2, 2^3, 2^4, 2^5 = 4, 8, 16, 32[/tex]

Option 2:[tex]y = 3^2, 3^3, 3^4, 3^5 = 9, 27, 81, 243[/tex]

Option 3:[tex]y = 4^2, 4^3, 4^4, 4^5 = 16, 64, 256, 1024[/tex]

Option 4:[tex]y = 5^2, 5^3, 5^4, 5^5 = 25, 125, 625, 3125[/tex]

By comparing the predicted y-values with the actual y-values of the data points, we can determine which option provides the closest fit.

Based on the given data points, we can observe that the predicted y-values from Option [tex]1 (y = 2^x)[/tex] match the actual y-values most closely.

The predicted values for Option 1 are 4, 8, 16, and 32, which exactly match the given data points.

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The complete question may be like: Consider the following data points: (2, 4), (3, 8), (4, 16), (5, 32). We need to determine which exponential regression equation best fits this data. Please provide the options for the regression equations so that I can assist you in finding the best fit.

The probability that a given student said math was their favorite subject was 3.44

The mathematical notion of probability measures the possibility of an event happening. A number between 0 and 1 is used to indicate it, with 0 denoting impossibility (the event won't happen) and 1 denoting certainty (the event will unquestionably happen). In probability theory, the probability of an event is determined based on a set of assumptions or information available. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Here, the total outcome is 299 and favorable outcome is 87.

Hence, the probability is 299/87 = 3.44

Therefore, probability that a given student said math was their favorite subject was 3.44.

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Answer: The answer is...

y = -2/3 x + 1

Step-by-step explanation:

The others would have crossed paths with y = -2/3 x + 10

The value of angle BCD is determined as 108⁰.

option B is the correct answer.

The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc AB =  m∠ACB

m∠ACB =  72⁰

The value of angle BCD is calculated as follows;

angle BCD = 180 - 72⁰ (sum of angles in a circle)

angle BCD = 108⁰

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The height of the average fourth grader is 137cm 1mm. This height can be determined by multiplying 3 by the average height of a newborn baby.

Given information,

The average height of babies = 45 cm 7mm

45 cm 7 mm is equivalent to 45.7 cm (since there are 10 millimeters in a centimeter).

Let the height of a fourth grader be x.

According to the question,

The height of a fourth grader (x) = 3 × the average height of a newborn baby

The height of a fourth grader (x) = 3 × 45.7

The height of a fourth grader (x)= 137.1 = 137cm 1mm

Therefore, the height of a fourth grader is 137cm 1mm.

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The function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

The given table is

Days After                        Number of

Release Date                   Games sold

       0                                   1024

       1                                     512

       2                                     256

       3                                     128

Here, the common ratio = 512/1024

= 1/2

The formula to find nth term of the geometric sequence is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.

Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]

Therefore, the function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

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1) The value of A ∪ B is,

A ∪ B = {<, +, =, /, >, x }

2) The value of A ∩ M is,

A ∩ B = {2}

3) The value of B ∩ C is,

B ∩ C = { }

4) The value of M - J is,

M - J = {soap}

5) The complement of set A is,

A' = (to, combat, coronavirus}​

Now, WE can simplify as;

1) We have;

A = {<, +, =, x) and B = {=, +, /, >}

Hence, We get;

The value of A ∪ B is,

A ∪ B = {<, +, =, /, >, x }

2) Given that,

A = {1, 2, 4) and M = {2, 3, 5}

Hence, The value of A ∩ M is,

A ∩ B = {2}

3) Given that;

B = {C, O, U, G, H) and C = {F, E, V, E, R)

Hence, The value of B ∩ C is,

B ∩ C = { }

4) Given that;

M = {soap, alcohol, sanitizer, mask) and J = {alcohol, sanitizer, mask, gloves}

Hence, The value of M - J is,

M - J = {soap}

5) Given that;

U = {Frontliners, sacrifice, their, lives, to, combat, coronavirus) and A = {Frontliners, sacrifice, their, lives)

Hence The complement of set A is,

A' = U - A

A' = (to, combat, coronavirus}​

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The lateral surface area of the triangular base prism is 288 m².

The lateral area of the triangular base prism can be found as follows:

Lateral area of the triangular base prism = (a + b + c)h

where

Therefore,

a = 7 m

b = 8 m

c = 9 m

h = 12 m

Therefore,

Lateral area of the triangular base prism = (7 + 8 + 9)12

Lateral area of the triangular base prism = 24 × 12

Lateral area of the triangular base prism = 288 m²

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Angle C of the triangle measures 40°.

Side AC = 18.84

Side AB= 25.79

Given triangle,

∠A = 112°

∠B = 28°

BC = 37

Now,

Sum of all the interior angles of triangle is 180.

So,

∠A + ∠B +∠C = 180°

112° + 28° + ∠C = 180°

∠C = 40°

Now,

According to sine rule,

Ratio of side length to the sine of the opposite angle is equal.

Thus,

a/SinA = b/SinB = c/SinC

Let,

BC = a

AC = b

AB = c

So,

a/Sin112 = b/Sin28 = c/Sin40

37/0.921 = b/0.469 = C/0.642

Solving,

AB = c = 25.79

AC = b = 18.84

Thus with the properties of triangle side length and angles can be calculated.

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The area of the parallelogram of triangle would be listed below as follows:

19A.) = 336mm²

19B.) = 416in²

To calculate the area of the parallelogram of triangle, the formula for the area of the parallelogram should be used and it is given as follows:

Area of parallelogram = base×height

For A.)

Base = 18+10 = 28mm

height = 12mm

Area = 28×12 = 336mm²

For B.)

Base = 26in

Height = 16(using the sine rule)

Area = 26×16 = 416in²

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The sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.

Using the formula:

D = 10 * log(I/I0),

where D represents the sound intensity in decibels, I is the given sound intensity, and I0 is the reference intensity of 10^-12 watts per square meter.

Substituting the given values:

D = 10 * log(8.2*10^2 / 10^-12).

To simplify the calculation, we can rewrite the division as multiplication by the reciprocal:

D = 10 * log(8.2*10^2 * 10^12).

Using the logarithm property log(a * b) = log(a) + log(b):

D = 10 * (log(8.2) + log(10^2) + log(10^12)).

Using the logarithm property log(a^b) = b * log(a):

D = 10 * (log(8.2) + 2 * log(10) + 12 * log(10)).

Since log(10) = 1:

D = 10 * (log(8.2) + 2 + 12).

D = 10 * (log(8.2) + 14).

Using a calculator or logarithm table, we can find log(8.2) ≈ 0.913.

D = 10 * (0.913 + 14).

D = 10 * 14.913.

D ≈ 149.13.

Therefore, the sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.

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Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

The value of x indicated in the right angle of EFG is determined as 36.

option D.

The value of x is calculated by applying the principle of sum of angles in a right angle triangle as follows;

A right triangle has a right angle and two angles that are complementary.

If angle EFG is a right angle, then the sum of angles at point F is 90 degrees.

The value of x is calculated by setting up the following equations;

2x + 6 + 12 = 90

2x + 18 = 90

2x = 90 - 18

2x = 72

x = 72/2

x = 36

Thus, the value of x is calculated by applying the principle of sum of angles in a right angle triangle.

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Answer:

Step-by-step explanation:

the of of 50 percent of people is married

The probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.

To find the probability that a customer ordered vanilla ice cream given they ordered a sundae, we can use the concept of conditional probability.

The conditional probability of an event A given event B is denoted as P(A|B) and is calculated as the probability of both events A and B occurring divided by the probability of event B.

In this case, we want to find P(vanilla|sundae), which represents the probability of a customer ordering vanilla ice cream given that they ordered a sundae.

Using the given probabilities:

P(vanilla) = 0.3

P(sundae) = 0.2

P(vanilla and sundae) = 0.15

The probability of a customer ordering a sundae is the denominator for the conditional probability. Therefore, P(sundae) will be the denominator.

P(vanilla|sundae) = P(vanilla and sundae) / P(sundae)

Substituting the given values:

P(vanilla|sundae) = 0.15 / 0.2

Now we can simplify:

P(vanilla|sundae) = 0.15 / 0.2

= 0.75

Therefore, the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.

In conclusion, based on the given probabilities, there is a 75% chance that a customer who ordered a sundae also ordered vanilla ice cream.

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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 correct statement regarding the association in the scatter plot is given as follows:

Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.

There can either be a positive association between variables or a negative association between variables, as follows:

In this problem, we have a decreasing scatter plot, hence there is a negative association between the variables.

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Answer:

65/100 that is the answer to this question

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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