It says find the measure of each angle indicated

Answer: the height of the pole is 16.782 meters

Step-by-step explanation: Let us take the height of the pole as "h".

i) Finding the height of the pole:

distance from the pole is 20m.

The angle of elevation is 40°

\(tan(40°) = h/20\)

Multiply both sides by 20:

\(20 * tan(40°) = h\)

\(h ≈ 20 * 0.8391 ≈ 16.782 meters\)

Therefore, the height of the pole is 16.782 meters.

ii) Finding the angle of depression

The angle of depression is the angle formed between the horizontal ground and the line of sight from the point of observation to the foot of the pole.

angle of depression = angle of elevation = 40°

Therefore, the angle of depression of the foot of the pole from the point of observation is 40°.

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Using trigonometric methods, it is determined that the height of the pole is found by using the formula for tangent, and adding the height of the observer. The angle of depression equals the angle of elevation, so both are 40 degrees.

To solve the problem, we use the properties of a right triangle and trigonometric functions. Since we know the angle of elevation and the length of one side, we can find the length of the other side using the tangent function.

For the height of the pole: we know that tan(θ) = opposite/adjacent, so,
tan(40) = height/20
height = tan(40) * 20

Let's denote the observer's height as h=1.54m, so the total height of the pole is height + h.

For the angle of depression: In a right triangle, the angle of depression and the angle of elevation are equal. Therefore, the angle of depression is also 40 degrees.

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Answer:

15 + 7= 22

Step-by-step explanation:

The statement "a = {1,2} and b = {3,4}" is true.

In this scenario, the sample space S represents all possible outcomes when rolling a fair die, and it consists of the numbers {1, 2, 3, 4, 5, 6}.

The event a represents the outcomes {1, 2}, which are the possible results when rolling the die and getting a 1 or a 2.

The event b represents the outcomes {3, 4}, which are the possible results when rolling the die and getting a 3 or a 4.

Therefore, the statement "a = {1,2} and b = {3,4}" accurately describes the events a and b.

The statement that is true in this scenario is that the sets A and B are disjoint. A set is considered disjoint when it has no elements in common with another set.

In this case, A = {1, 2} and B = {3, 4} have no elements in common, meaning they are disjoint sets. This is because the numbers 1 and 2 are not present in set B, and the numbers 3 and 4 are not present in set A.

Therefore, A and B do not share any common elements, making them disjoint sets.

(c) A and B are mutually exclusive events.

In this case, the sets A and B are mutually exclusive because they have no elements in common.

A represents the outcomes of rolling a fair die and getting either 1 or 2, while B represents the outcomes of rolling a fair die and getting either 3 or 4.

Since there are no common elements between A and B, they are mutually exclusive events. If an outcome belongs to A, it cannot belong to B, and vice versa.

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The probability that sample is greater than 418 will be is 6.533.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

Here we have

\(\mu=397.64,n=40,\sigma=20\)

According to central limit theorem, the sampling distribution of mean will be normal with mean

\(\mu_{\bar{x}}=\mu=397.64\)

and standard deviation

\(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{40}}=3.1623\)

The z-score for\(\bar{x}=418\) is

\(z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{418-397.34}{3.1623}=6.533\)

Therefore, the probability that sample is greater than 418 will be

\(P(\bar{x} > 418)=P(z > 6.533)\)

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Incomplete Question

Carbon dioxide (CO2) is one of the primary gases contributing to the greenhouse effect and global warming. The mean amount of CO2 in the atmosphere for March 2013 was 397.34 parts per million (ppm). Suppose 40 atmospheric samples are selected at random in May 2013 and the standard deviation for CO2 in the atmosphere is σ = 20 ppm. (1 pt.)

c) Suppose the sample mean CO2 level is 400. Is there any evidence to suggest that the population mean CO2 level has increased?

Using a moving average of order p = 3, a forecast for time period 6 is 46.

The moving average is a mathematical method for calculating a series of averages using various subsets of the full dataset. It is also known as a rolling average or a running average. The moving average smoothes the underlying data and lowers the noise level, allowing us to visualize the underlying patterns and patterns more readily. In other words, a moving average is a mathematical calculation that employs the average of a subset of data at various time intervals to determine trends, eliminate noise, and better forecast future outcomes. Answer: 46.

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Answer:

Faye's probability of pulling out a white marble is 3/80.

Step-by-step explanation:

To find the probability, we must first add everything up.  10 + 13 + 16 + 10 + 11 = 60 marbles.  Now we divide 60 by the amount of white marbles there are.  60 ÷ 16 = 3.75% or 3/80.  Therefore, the probability of Faye pulling out a white marble is 3/80.

Answer:

the answer is x=12

Answer:

x = 6

y = -1

Step-by-step explanation:

We have to use substitution for the system of equations.

x = -6y

4x + 10y = 14

Because we know that [x = -6y], we can get rid of the x value by substituting y into the equation, [4x + 10y = 14].

4 x -6y + 10y = 14

Simplify.

-24y + 10y = 14

-14y = 14

Divide both sides by -14.

-14y = 14

÷-14   ÷-14

y = -1

From y, we can also find out the x value, as [x = -6y].

We now know that y = -1.

Therefore, we have to substitute again.

x = -6y

y = -1

x = -6 x -1

x = 6

Hence, x = 6 and y = -1.

Sorry it took so long to answer.

There is only one different square root of A.(a) To find the square roots of matrix A = [2 2; 2 2]: Let's consider two matrices B1 and B2: B1 = [1 1; 1 1]; B2 = [-1 -1; -1 -1].

Now, let's check if BB = A for each matrix: B1B1 = [1 1; 1 1] * [1 1; 1 1] = [2 2; 2 2] = A; B2B2 = [-1 -1; -1 -1] * [-1 -1; -1 -1] = [2 2; 2 2] = A. Both B1 and B2 satisfy BB = A, so they are two possible square roots of matrix A. (b) For matrix A = [5 0; 0 9], let's consider a matrix B: B = [√5 0; 0 √9] = [√5 0; 0 3] .We can see that BB = [√5 0; 0 3] * [√5 0; 0 3] = [5 0; 0 9] = A.

Thus, there is only one different square root of A. (c) Not every 2x2 matrix has a square root. For a square root of a matrix to exist, the matrix must be positive definite or positive semidefinite. If the eigenvalues of the matrix are negative or complex, there won't be any real square root. Additionally, if the matrix has zero eigenvalues with multiplicities greater than one, it may not have a unique square root. Therefore, the existence of a square root for a 2x2 matrix depends on its eigenvalues and their properties.

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Answer:

3p(p - 4) = 0

p = 0 or p = 4

Step-by-step explanation:

Given expression:

         3p² - 12p = 0

Now, let us factor;

  The common terms in the expression is 3p;

          3p(p - 4) = 0

Solution:

        3p = 0 or p - 4  = 0

           p = 0 or p = 4

Using the given the box plot:

the first quartile of the data set is: 12

the median value of the data set is: 16

How to Determine the Five-number Summary of a Box Plot?

The five-number summary that is displayed by a box plot include:

Minimum value: this is the value which is at the far end of the left whisker.

First Quartile: which is the value at the beginning of the edge of the box.

Median value: this is the value at the point where the vertical line divides the box.

Third Quartile: which is the value at the beginning of the edge of the box.

Using the box plot given, the five-number summary that is displayed include:

Minimum value: 9

First Quartile: 12

Median value: 16

Third Quartile: 19

Maximum value: 24

Thus, we can state that, given the box plot:

the first quartile of the data set is: 12

the median value of the data set is: 16

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The most appropriate statement that expresses a possible relationship between the variables, rate of pedaling and speed of a bicycle, is option A: "As the rate of pedaling increases, the speed of a bicycle increases."

This statement suggests that there is a positive correlation between the rate of pedaling and the resulting speed of the bicycle. When a cyclist pedals faster, it generates more force and power, translating into increased speed. This relationship aligns with basic principles of physics, as a greater input of energy and effort through pedaling leads to a higher velocity or speed output.

Option B implies that decreasing bicycle speed necessitates an increase in the rate of pedaling, and option C indicates that increasing bicycle speed is associated with a decrease in the rate of pedaling.

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68 is the wrong number in the sequence 808, 408, 208,108, 68

A number system is defined as a system of writing to express numbers.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 808, 408, 208,108, 68

Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.

808, 408, 208,108, 68

Let us find the difference between the consecutive numbers

400, 200, 100, 40

As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.

Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68

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A company conducts a survey to measure customer satisfaction on a scale of 1 to 10. The range of customer satisfaction scores is a. 4

To find the range of customer satisfaction scores, we need to calculate the difference between the highest and lowest scores.

The highest score in the given data set is 10, and the lowest score is 6. Therefore, the range is 10 - 6 = 4.

The range is a measure of variability and represents the spread of the data. In this case, the customer satisfaction scores range from 6 to 10, indicating a spread of 4 points on the scale.

It's important to note that the range only considers the highest and lowest scores and does not take into account the distribution of the remaining scores.

Therefore, it provides a limited understanding of the overall variability in customer satisfaction.

Other measures such as standard deviation or interquartile range may provide a more comprehensive analysis of the data distribution.

The correct option is: a. 4

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Complete question below :

A company conducts a survey to measure customer satisfaction on a scale of 1 to 10. The survey results for a sample of 50 customers are as follows: 8, 9, 7, 6, 9, 8, 10, 7, 8, 6, 7, 9, 10, 9, 8, 7, 6, 9, 8, 10, 7, 6, 7, 8, 9, 10, 8, 7, 9, 8, 6, 7, 9, 8, 10, 7, 8, 6, 9, 8, 7, 10, 9, 8, 6, 7, 9, 8, 10, 7, 8.

What is the range of customer satisfaction scores?

a. 4

b. 3

c. 5

d. 2

e. 1

-6p³ + 14p² -6 is the final polynomial after all operations

In order to get final polynomial we nedd to complete all operations on different polynomials provided velow.

A polynomial is a mathematical expression involving a sum of powers in one or more variables with real or complex coefficients. It is a type of algebraic expression which can be of degree 0,1,2,3,..n. It is represented by a letter such as "P" or "f", with one or more variables such as x, y, z, etc. and coefficients, which are numbers or constants. The degree of a polynomial is the highest power of the variable in it.

-3p³ - 3p³ + 5p² + 2p² + 7p² - 3 - 3

=> -6p³ + 14p² -6

so the required polynomial is -6p³ + 14p² -6 which is obtained after all the operation on the numbers.

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Answer:

The answer is 12

Step-by-step explanation:

36/9=4

4x3=12

The matrix A must have the following form:
A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

In order for a matrix A to define a mapping from R4 into R5 by the rule T(x) = Ax, the matrix A must have 5 rows and 4 columns.

This is because the number of rows in the matrix determines the dimension of the output space, while the number of columns determines the dimension of the input space. In this case, the output space is R5 and the input space is R4, so the matrix must have 5 rows and 4 columns.

In general, if a matrix A is used to define a mapping from Rn into Rm by the rule T(x) = Ax, then the matrix A must have m rows and n columns.

So, the matrix A must have the following form:

A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

where each aij is a scalar.

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a. To calculate the solid angle subtended by the thunderstorm cloud, we can use the formula for the solid angle of a cone-like region given by: Solid Angle = ∫∫ sin(θ) dθ dφ.

In this case, the limits of integration are π/6 < θ < π/2 and 0 < φ < π/8. ∫∫ sin(θ) dθ dφ = ∫(π/8 to π/2) ∫(0 to π/8) sin(θ) dθ dφ. Evaluating this integral will give us the solid angle subtended by the thunderstorm cloud. b. To determine the percentage of the sky occupied by the thunderstorm cloud, we need to calculate the ratio of the solid angle subtended by the cloud to the total solid angle of a full sphere (4π steradians), and then multiply by 100. Percentage of Sky Occupied = (Solid Angle / 4π) * 100.

By substituting the value of the solid angle obtained in part (a) into this formula, we can determine the percentage of the sky occupied by the thunderstorm cloud. Please note that without specific numerical values for the limits of integration, it is not possible to provide a numerical answer in this case.

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Answer:

A

Step-by-step explanation:

If the area of the rectangle (as shown below in the reference.jpeg attached hereby for reference) is 32 sq. units, then the area of the triangle shown besides the rectangle will be 16 sq. units.

As per the question statement, area of a rectangle (as shown below in the reference.jpeg attached hereby for reference) having a length of 8 units and width of 4 units is 32.

We are required to calculate the area of the triangle (shown beside the above-mentioned rectangle in the reference.jpeg attached hereby).

From the diagram, it is clear that that base of the triangle is 4 units and since it is a right-angled triangle, it's altitude or height is 8 units.

Now the formula to calculate the area of a triangle (A) having base "b" and height "h", goes as \(A=(\frac{1}{2}*b*h)\)

Inserting the values of our concerned triangle in the above mentioned formula, we get, Area = \((\frac{1}{2}*4*8)=(\frac{4*8}{2})=\frac{32}{2}=16\).

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Answer:

-1/2  

or -2/4

Step-by-step explanation:

they are the same

Answer:

1

Step-by-step explanation:

X power y would be written as 2^0, and any number to the power of 0 is equal to 1.

1

I didn't know this was possible so I looked it up :)

Have an amazing day/afternoon/night! <3

Answer:

5(d) = miles student A ran

8(d-3) = miles student B ran

Step-by-step explanation:

when d = days passed

5(d) = miles student A ran

8(d-3) = miles student B ran

Answer:  \(\bold{y=-\dfrac{1}{3}x+6}\)

                \(\bold{y=-\dfrac{1}{4}x+\dfrac{25}{4}}\)

Step-by-step explanation:

  x + 3y = 18

- x           -x

        3y = -x + 18

      ÷3     ÷3 ÷3

         y = (-1/3)x + 6

-3x - 12y = -75

+3x           +3x

        -12y = 3x - 75

       ÷-12    ÷-12 ÷-12

           y = (-1/4)x + (25/4)

Answer:

1.75

Step-by-step explanation:

y=14÷8

y= 1.75

Answer:1.75

Step-by-step explanation

Answer:

i think it should be around 30.975 :))

Step-by-step explanation:

lmk if this helps <3

The expression is equivalent to \(5^2\).

Given

Expression; \(\rm \dfrac{(5^2)^{-3}\times 5^4}{5^{-4}}\)

The definition of exponential form is a way of writing a number that is multiplied by itself more than once.

To solve the exponential equation follow all the steps given below.

Therefore,

The expression is equivalent to;

\(\rm =\dfrac{(5^2)^{-3}\times 5^4}{5^{-4}}\\\\=\rm \dfrac{(5)^{-6}\times 5^4}{5^{-4}}\\\\=\rm \dfrac{(5)^{-6+4}}{5^{-4}}\\\\=\rm \dfrac{5^{-2}}{5^{-4}}\\\\=5^{-2+4}\\\\=5^2\)

Hence, the expression is equivalent to \(5^2\).

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Answer:

i would say 18/24

Step-by-step explanation:

E = mc² is the  famous math formula.

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes

E = mc² is the famous formula of maths and physics.

Energy equals mass times the speed of light squared.

Whether one is versed in mathematics or physics, or knows nothing of the vocabulary of maths, everyone knows Albert Einstein's famous formula: E = mc².

Hence, E = mc² is the  famous math formula.

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