(L7) a=3 cm, b=√12.96 cm, c=4 cmThe triangle is a(n) _____ triangle.

The side lengths for this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For segment d, we have that it is opposite to the angle of 60º, while 7 is the adjacent segment, hence:

tan(60º) = d/7

[tex]\sqrt{3} = \frac{d}{7}[/tex]

[tex]d = 7\sqrt{3}[/tex]

For segment b, it is opposite/adjacent (does not matter as sin(45º) = cos(45º)) to an angle of 45º, while the hypotenuse is of 5 units, hence:

sin(45º) = b/5

[tex]b = 5 \times \frac{\sqrt{2}}{2}[/tex]

[tex]b = \frac{5\sqrt{2}}{2}[/tex]

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The length of AB is 10m.

Let's assume that the length of AC = x,

According to the problem statement, AB= 2x ...........(1)

Also, BC is 10 cm shorter than AB, so,

BC=AB-10 .......(2)

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

therefore,

1.95=AB+AC+BC

We can put the value from eq(1) & eq(2)

1.95=2x+x+(AB-10)

AB= 3x+8.05............... (3)

Now, we need to find the value of x

1.95= 2x+x+(AB-10)

or, 1.95 = 3x+ AB-10

Adding 10 to both sides

11.95 = 3x+AB.......(4)

Substituting the expression, we found for AB:

11.95=3x+3x=8.05

11.95= 6x

x= 0.65

So, the value of AB is

AB = 3x+8.05

AB = 3(0.65)+8.05

AB = 10 m

Therefore, The length of AB is 10m.

Read more about the triangle:

https://brainly.com/question/2773823

The area under the standard normal curve to the right of z = 0.69 is approximately 0.2451.

Using a standard normal table:

Locate the row for 0.6 in the left-hand column of the table and the column for 0.09 along the top row of the table.

The intersection of the row and column gives the area to the left of z = 0.69, which is 0.7549.

Subtract this area from 1 to find the area to the right of z = 0.69:

area to the right of z = 0.69 = 1 - 0.7549 = 0.2451

Learn more about normal distribution on

https://brainly.com/question/4079902

#SPJ4

30% of the scores in the dataset fall within one standard deviation of the mean.

To determine the percent of scores in a data table that fall within one standard deviation of the mean, you need to follow these steps:

Calculate the mean and standard deviation of the dataset.

Determine the lower and upper bounds of one standard deviation by subtracting the standard deviation from the mean to get the lower bound, and adding the standard deviation to the mean to get the upper bound.

Count the number of data points in the dataset that fall within the lower and upper bounds of one standard deviation.

Divide the number of data points within one standard deviation by the total number of data points in the dataset, and multiply the result by 100 to get the percentage of scores that fall within one standard deviation of the mean.

Let's say you have a dataset with a mean of 50 and a standard deviation of 10.

To determine the percent of scores that fall within one standard deviation of the mean, you would calculate the lower and upper bounds of one standard deviation as follows:

Lower Bound = 50 - 10 = 40

Upper Bound = 50 + 10 = 60

The number of data points in the dataset that fall within the lower and upper bounds of one standard deviation.

Let's say there are 30 data points that fall within this range.

The number of data points within one standard deviation by the total number of data points in the dataset, and multiply the result by 100 to get the percentage of scores that fall within one standard deviation of the mean:

Percent Within One Standard Deviation

= (30/100) × 100 = 30%

For similar questions on standard deviation

https://brainly.com/question/24298037

#SPJ11

The congruence postulate that applies is C. Congruent - SSS

When the properties (i.e length of sides and/or internal angles) of two or more triangles are equal, then it can be said that they are congruent. This congruent relations can be expressed using either of the following postulates: Angle-Side-Side, Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Side-Side-Side (SSS) etc.

Considering the given triangles ABC and DEF, it is was given that:

AB ≅ DE

BC ≅ EF

CA ≅ FD

Therefore, it can be concluded that the two triangles are congruent by Side-Side-Side (SSS) relations. So that the required congruence postulate that applies is C. Congruent - SSS

Learn more about congruent triangles at https://brainly.com/question/28794337

#SPJ1

The area of the base of Barbara's woodshed is 72 square feet.

To find the area of the base of Barbara's woodshed, we need to know the shape of the base. In this case, the base is in the shape of a rectangle. A rectangle is a four-sided figure with opposite sides parallel and equal in length.

To calculate the area of a rectangle, we need to multiply its length by its width. In this case, the length of the rectangle is 12 feet, and its width is 6 feet. So, the area of the base of the woodshed is:

Area = Length x Width

Area = 12 ft x 6 ft

Area = 72 square feet

To know more about area here

https://brainly.com/question/14994710

#SPJ4

Complete Question:

Barbara built a woodshed. She made the base of the woodshed in the shape of the drawing. What is the area of the base of Barbara's woodshed? Include the unit. When the dimensions are given as 12 ft,6 ft, 11 ft and 7 ft.

The names of the radius , chord and diameter of a circle are as follow,

Radius of the circle are PQ, PM , And PR.

Diameter of the circle is QM

Chord of the circle is ON.

Length of QM in the circle = 4units.

In the attached figure of the circle,

Center of the circle is P.

radius of the circle is a distance from the center of the circle to its circumference.

Radius = PQ, PM , And PR.

Diameter of the circle passing through center P is QM.

Chord of the circle representing a line segment having endpoints on the circumference of the circle.

Chords are ON and MQ.

Diameter is the longest chord.

length of PR is 2 units,

PR is radius

QM is diameter

QM = 2(PR)

length of QM = 2(2)

                      = 4 units.

Therefore, for the given circle we have,

Radius are PQ, PM , And PR.

Diameter is QM

Chord is ON.

Length of QM = 4units.

learn more about circle here

brainly.com/question/28998766

#SPJ1

The above question is incomplete, the complete question is:

A circle with center P is shown in the figure below.

(a) Name a diameter:

(b) Name a radius:

(c) Name a chord:

(d) If the length of PR is 2 units, what is the length of QM

Attached figure.

The solutions of the equation f(x) = g(x) include the following: B. -3, 0, 2, -4.

In Mathematics and Geometry, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in both Quadrant II and IV and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-3, 0) and (2, -4).

Read more on a graph here: brainly.com/question/4546414

#SPJ1

If another school is considering changing their pizza vendor, they may also select separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors to gather feedback from the students. By doing so, they can obtain a representative sample of the entire student population and ensure that each grade level is equally represented.

This will provide valuable insight into the preferences and opinions of the students, allowing the school to make an informed decision on which pizza vendor to choose. It is important to consider the feedback of all students in the decision-making process to ensure that the majority of the student body is satisfied with the food options provided by the school.

Step 1: Select random samples of students from each grade level.
Step 2: Provide the new pizza to each student in the samples.
Step 3: Ask the students to evaluate the pizza based on taste and quality.
Step 4: Collect the feedback from all 200 students.
Step 5: Analyze the data to determine if the majority of students prefer the new pizza vendor.

Based on the analysis, the school can make an informed decision about whether to change their pizza vendor or not.

another school is also cosidering changing thier pizza vendor. the school selects seperate random samples of 50 freshman, 50 sophiomres, 50 jjuniors, and 50 seniors. each student tries

Learn more about pizza vendor here : brainly.com/question/13932830

#SPJ11

The unit rate of the juice is 0.5 carrot juice per green apple juice

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

This means that

Carrot juice = 2

Green apple juice = 4

Using the above as a guide, we have the following:

Unit rate = Carrot juice/Green apple juice

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

Unit rate = 2/4

Evaluate

Unit rate = 0.5

Hence, the unit rate is 0.5 carrot juice per green apple juice

Read more abot unit rate at

https://brainly.com/question/4895463

#SPJ1

There will be 1, 2, 6, 21 non-isomorphic simple graphs for 2, 3, 4 and 5 vertices.

What are non-isomorphic simple graphs?

A non-isomorphic simple graph is a graph that is distinct from another graph, even if the two graphs have the same number of vertices and edges, and the same connectivity pattern. In other words, two graphs are non-isomorphic if they cannot be transformed into each other by a relabeling of their vertices.

For a small number of vertices, we can enumerate all non-isomorphic simple graphs by hand.

For n = 2, there is only one possible graph, which is the edge connecting the two vertices.

For n = 3, there are only two possible graphs: a triangle (complete graph on 3 vertices) and a single edge with an isolated vertex.

For n = 4, there are six possible graphs:

Complete graph on 4 vertices

Cycle graph on 4 vertices

Complete bipartite graph K2,2

Graph with a central vertex adjacent to all other vertices

Graph with two vertices of degree 3 and two vertices of degree 1

Graph with one vertex of degree 3 and three vertices of degree 1

For n = 5, there are 21 possible graphs, which can be generated by adding edges to the graphs for n = 4.

To learn more about non-isomorphic simple graphs visit the link:

https://brainly.com/question/30230000

#SPJ4

Answer: x=-7 y=7

Step-by-step explanation:

Once you have the required numerical values, plug them into the formula and calculate the minimum sample size needed for Big Corporation to be confident in their estimate of the mean amount of coffee dispensed per cup

We need to determine the minimum sample size required for Big Corporation to estimate the mean amount of coffee dispensed per cup with a certain level of confidence and margin of error.

Unfortunately, some of the numerical values are missing in question.

Step 1: Determine the desired confidence level (e.g., 90%, 95%, 99%).
Step 2: Identify the desired margin of error (e.g., within 0.1 ounces).
Step 3: Given the standard deviation of cup amounts (missing in the question, let's assume it as "σ").

Now, use the formula for determining the minimum sample size needed:

n = (Z² * σ²) / E²

where:
n = minimum sample size
Z = Z-score corresponding to the desired confidence level (e.g., 1.96 for 95% confidence)
σ = standard deviation of cup amounts
E = margin of error

Step 4: Calculate the minimum sample size (n) using the formula and round up to the nearest whole number.

By numerical values, plug them into the formula and calculate the minimum sample size needed for Big Corporation to be confident in their estimate of the mean amount of coffee dispensed per cup.

To know more about margin of error visit:

brainly.com/question/29100795

#SPJ11

A) the error term is 0.16039
B) number of households required to get a 95% confidence interval, with an error of ± 0.09 is 21.
C) The probability of 12 random households recycling more than 45% of their waste is approximately 0.045 or 4.5%.

Error term = z√(p(1-p)/n)

Error term = 1.75 √(0.30(1-0.30)/25)
= 0.16039

Thus, the error term is 0.16039

2 ) to find the ample size required to estimate the proportion of recycling in poor neighborhoods with an error of +/-0.09 and a 95% confidence level,

n = (z² * p * (1-p)) / E²

n = (1.96² * 0.5 * (1-0.5)) / 0.09²

= 21

So the number of households required to get a 95% confidence interval, with an error of ± 0.09 is 21.

3)  To calculate the probability of 12 random households recycling more than 45% of their waste,

P(X > 12) = 1 - P(X <= 12)

P(X > 12) = 1 - P(X <= 12)

= 1 - 0.955

= 0.045

So the the probability of 12 random households recycling more than 45% of their waste is 0.045.

Learn more about probability:
https://brainly.com/question/30034780
#SPJ4


Full Question:

In a small town, households recycle on average 30% of their waste. The new recycling committee wants to increase this proportion and study the relationship between recycling and income. They select 25 households from the two wealthier neighborhoods and estimate a 92% confidence interval for the true proportion of recycling. What is the error term of this interval?

The same recycling committee also focuses on poor neighborhoods. How many households do they need to sample to get a 95% confidence interval, with an error of +/-0. 09?

Finally, the same recycling committee wants to know the probability of 12 random households recycling more than 45% of their waste. This probability is: ?

Yes, it is true that if A is a 3×3 matrix and K is a scalar, then det(KA) = [tex]K^3[/tex] det(A).

To see why this is true, let's use the definition of the determinant of a matrix. For a 3×3 matrix A with entries[tex]ka_{11}, ka_{12}, ka_{13}, ka_{21}, ka_{22}, ka_{23}, ka_{31}, ka_{32}, ka_{33}[/tex], the determinant det(A) is given by:

[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]

Now consider the matrix KA, where K is a scalar. The entries of KA are simply the entries of A multiplied by K. In other words, the entries of KA are:

[tex]ka_{11}, ka_{12}, ka_{13}, ka_{21}, ka_{22}, ka_{23}, ka_{31}, ka_{32}, ka_{33}[/tex]

Using the same formula as above, we can calculate the determinant of KA:

[tex]det(KA) = (K a_{11})(K a_{22})(K a_{33}) - (K a_{11})(K a_{23})(K a_{32}) - (K a_{12})(K a_{21})(K a_{33})+ (K a_{12})(K a_{23})(K a_{31}) + (K a_{13})(K a_{21})(K a_{32}) - (K a_{13})(K a_{22})(K a_{31)[/tex]

Substituting in the entries of KA, we get:

[tex]det(KA) = (K a_{11})(K a_{22})(K a_{33}) - (K a_{11})(K a_{23})(K a_{32}) - (K a_{12})(K a_{21})(K a_{33})+ (K a_{12})(K a_{23})(K a_{31}) + (K a_{13})(K a_{21})(K a_{32}) - (K a_{13})(K a_{22})(K a_{31)[/tex]

Simplifying this expression, we get:

[tex]det(KA) = K^3 (a_{11} a_{22}a_{33} - a_{11}a_{23}a_{32} - a_{12}a_{21}a_{33} + a_{12}a_{23}a_{31} + a_{13}a_{21}a_{32} - a_{13}a_{22}a_{31})[/tex]

But this is just the same as[tex]K^3[/tex] times the determinant of A! Therefore, we have shown that det(KA) =[tex]K^3[/tex]det(A) for any 3×3 matrix A and scalar K.

for such more question on matrix

https://brainly.com/question/31043586

#SPJ11

Question

Is it true that If A is a 3×3 matrix, then det (KA) = K^3 * det(A)

If the price of corn feed is $4 and corn feed is on the horizontal axis, and the price of soybean feed is $5 and soybean feed lies on the vertical axis, then the expansion path is C =5S/2 (option a).

To find the expansion path, we need to find the optimal combination of inputs that will maximize pig production while keeping the cost of production at a minimum. This can be achieved by calculating the ratio of the prices of the two inputs, which is given by:

Price ratio = Price of soybean-based feed/Price of corn-based feed

Price ratio = 5/2

Now, we can use this price ratio to find the optimal combination of inputs that will minimize the cost of production while maximizing pig production. This can be done by solving for the quantity of soybean-based feed used in terms of the quantity of corn-based feed used:

S = (5/2)C

This equation represents the expansion path, which shows the optimal combination of inputs that will minimize the cost of production while maximizing pig production. We can prove this by substituting the value of S into the production function:

P = 8C + 25((5/4)C)

P = 8C + 31.25C

P = 39.25C

Hence the correct option is (a)

To know more about function here

https://brainly.com/question/28193995

#SPJ4

For a = 1 and m = 1 does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1.

To find the values of a and m that give the function f(x) a horizontal asymptote at y = 2 and a vertical asymptote at x = 1, we need to analyze the behavior of the function as x approaches 1 and as x goes to infinity.

When x approaches 1 from the left and right sides, the denominator of f(x) approaches 0, so there is a vertical asymptote at x = 1. To have a vertical asymptote at x = 1, the numerator of f(x) cannot approach 0 as x approaches 1, so m must be greater than or equal to 1.

When x goes to infinity or negative infinity, the function f(x) approaches 2, which means there is a horizontal asymptote at y = 2. To have a horizontal asymptote at y = 2, the degree of the numerator must be equal to or less than the degree of the denominator. The degree of the numerator is m, and the degree of the denominator is 1.

So, the values of a and m that give f(x) a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 are:

a = 1, m = 1

Substituting a = 1 and m = 1 into f(x), we get:

f(x) = 2x/(x+1)

which has a vertical asymptote at x = 1 and a horizontal asymptote at y = 2.

Therefore, the answer is a = 1, m = 1. The other values of a and m do not give a vertical asymptote at x = 1 and/or a horizontal asymptote at y = 2.

To learn more about horizontal asymptote here:

https://brainly.com/question/4084552

#SPJ1

Answer:

CCCCCCCC

Step-by-step explanation:

Edg 2023

For a jar contains 5 red discs, 10 blue discs and m green discs,

a) The probability that the first disc selected is red is equals to

[tex]\frac{5}{15 + m}.[/tex]

b) The smallest value of m for which Var(X)< 0.6 is equals to 13.

We have a jar contains different colour discs. Number of red discs = 5

Number of green discs = m

Number of blue discs = 10

Total number of discs = 5 + 10 + m

= 15 + m

The process is performed four times, so, possible value n = 4. We have to determine the probability that the first disc selected is red.

a) Probability is defined as the ratio of favourable outcomes to the total possible outcomes. So, the probability that the first disc selected is red,[tex] P(red) = \frac{ 5}{(15 + m)}[/tex]

(b) The variance is calculated as

[tex]σ_{X²} = Var (X)[/tex]

[tex]= ∑_i (x_i − μ)² p(x_i) \\ [/tex]

= np(1 - p)

= [tex] 4(\frac{5}{15 + m})×(1- \frac{5}{15 + m}) < 0.6[/tex]

[tex] \frac{20( 10 - m)}{(15 + m)²} < 0.6[/tex]

=> 200 - 20m < 0.6( 15 + m)²

=> 200 - 20m < 9.0 + 0.6 m² + 18

=> 0.6m² + 20m - 200 + 27 > 0

=> 0.6m² + 20m - 173 > 0

=> m > 12.2075, so, m = 13

Hence, the smallest value of m for which Var(X)<0.6 is 13.

For more information about probability, refer: https://brainly.com/question/25870256

#SPJ4

Answer:

Approximately 20.33 (rounded to two decimal places)

Step-by-step explanation:

To find the standard deviation, we will first find the mean (average) of the scores, then find the variance, and finally take the square root of the variance to get the standard deviation.

Calculate the mean:

(80 + 30 + 34 + 32 + 55 + 27 + 38 + 41 + 84) / 9 = 421 / 9 = 46.78 (rounded to two decimal places)

Calculate the variance:

a. Find the difference between each score and the mean, and then square the differences (rounded to two decimal places).

(80 - 46.78)^2 = 1103.57

(30 - 46.78)^2 = 281.57

(34 - 46.78)^2 = 163.33

(32 - 46.78)^2 = 218.45

(55 - 46.78)^2 = 67.57

(27 - 46.78)^2 = 391.25

(38 - 46.78)^2 = 77.09

(41 - 46.78)^2 = 33.41

(84 - 46.78)^2 = 1385.33

b. Find the sum of the squared differences.

1103.57 + 281.57 + 163.33 + 218.45 + 67.57 + 391.25 + 77.09 + 33.41 + 1385.33 = 3721.57

c. Divide the sum of the squared differences by the number of scores (n = 9).

3721.57 / 9 = 413.51 (rounded to two decimal places)

Calculate the standard deviation:

Take the square root of the variance.

√413.51 = 20.33 (rounded to two decimal places)

The standard deviation of the scores is approximately 20.33 (rounded to two decimal places).

The submarine depth after the dive is determined as 17 feet.

The current depth of the submarine is calculated as follows;

If the submarine is currently at a depth of -15 feet and then dives an additional 32 feet down, the new depth can be calculated by adding the two depths.

-15 feet + 32 feet = 17 feet

Therefore, the submarine is at a depth of 17 feet after the dive.

Learn more about depth here: https://brainly.com/question/1441593

#SPJ4

The force on the square loop is F = i(a²)(B), where B is the strength of the magnetic field in the x direction.

A current-carrying loop refers to a closed circuit consisting of a conductor (usually a wire) bent into the shape of a closed loop, through which an electric current flows. The loop may be any shape or size, but its geometry and the amount of current flowing through it determine the magnetic field it produces.

When a current-carrying loop is placed in a magnetic field, a force is exerted on the loop due to the interaction between the magnetic field and the current. The force on the loop can be calculated using the following formula:

=> F = iABsinθ

where F is the force on the loop, i is the current flowing through the loop, A is the area of the loop, B is the magnetic field, and θ is the angle between the normal to the loop and the direction of the magnetic field.

In this case, the loop is in the yz plane and centered at the origin. The magnetic field is assumed to be in the x direction. Since the loop is perpendicular to the x direction, the angle between the normal to the loop and the magnetic field is 90 degrees.

The area of the loop is given by A = a².

The current flowing through the loop is i.

Thus, the force on the loop is given by:

F = iABsinθ = i(a^2)(B)(sin90) = i(a^2)(B)

Therefore, the force on the square loop is F = i(a^2)(B), where B is the strength of the magnetic field in the x direction.

To know more about Current-carrying loop visit:

https://brainly.com/question/15710600

#SPJ4

The area of the figure below is 58 in².

Area is the region bounded by a plane shape.

To calculate the area of the figure, we use the formula below

Formula:

Where:

Substitute these values into equation 1

Learn more about area here: https://brainly.com/question/25092270

#SPJ1

The number of respondents needed in a poll to adequately represent a larger population depends on several factors, such as the size of the population, the level of confidence desired, and the margin of error tolerated.

The general rule of thumb is that a sample size of at least 400 respondents is needed to provide a representative sample for a population of 100,000 or less. However, for larger populations, a sample size of at least 1,000 respondents may be required.

It is also important to note that a larger sample size does not always guarantee more accurate results. Other factors such as the sampling method, the wording of the questions, and the response rate can also impact the accuracy of poll results. Therefore, it is essential to carefully design and conduct polls to ensure their results are adequately representative of the larger population.

Learn more about Population here: brainly.com/question/29885712

#SPJ11

The length from least to greatest is √3, √5, π, 2√3.

We have the lengths as π, √3, 2√3, √5.

Now, writing the decimals for each

π= 3.14

√3 = 1.732

2√3 = 3.464

√5= 2.23

So, arranging the length from least to greatest is √3, √5, π, 2√3.

Learn more about Ascending Order here:

https://brainly.com/question/31324289

#SPJ1

The segment bisector of QR is Ml.

The length of QR is equal to 32 units.

In Mathematics, the midpoint of a line segment with two end points can be determined or calculated by adding each end point on a line segment together and then divide by two (2).

Since Ml is the midpoint and segment bisector of line segment QR, we have the following:

Line segment QM = Line segment MR

2x + 6 = 5x - 9

5x - 2x = 9 + 6

3x = 15

x = 15/3

x = 5.

Now, we can determine line segment QR as follows:

QM = 2x + 6 = 2(5) + 6 = 16 units.

MR = 5x - 9 = 5(5) - 9 = 16 units.

QR = QM + MR

QR = 16 + 16

QR = 32 units.

Read more on segment bisector here: https://brainly.com/question/29957844

#SPJ4

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The circumference of a circle is given by $C = \pi d$, where $d$ is the diameter of the circle. In this case, the diameter of Annie's bicycle wheels is $20$ inches, so the circumference of each wheel is:

$C = \pi d = \pi (20\text{ in}) \approx 62.83 \text{ in}$

Since each wheel makes 3 full revolutions every second, the distance that Annie travels in one second is:

$distance = 2C \cdot \text{revolutions per second} = 2 \cdot 62.83 \text{ in} \cdot 3 \approx 377 \text{ in}$

Converting inches to feet, we get:

$distance = 377 \text{ in} \cdot \frac{1 \text{ ft}}{12 \text{ in}} \approx 31 \text{ ft}$

Rounding to the nearest foot, Annie travels approximately $\boxed{31}$ feet in one second.

Learn more about Circumference here:- brainly.com/question/27447563

#SPJ11

The lowest angle of elevation at which the astronomer can observe the star is 20.8°

We know that the angle of elevation is nothing but the angle between the horizontal line of sight and the straight line to a given object.

In this scenario, let us ssume that θ be an angle of elevation.

Since an astronomer is in the middle of the field,the 100 value is split in half.

The field is surrounded by the trees 20 m tall and the tripod holding the telescpoe 1 m above the ground.

This means that the vertical distance is 19 m and the horizontal distance is 50 m.

Consider the tangent of angle θ

tan(θ) = opposite side of angle θ / adjacent side of angle θ

tan(θ) = 19/50

tan(θ) = 0.38

θ = arctan(0.38)

θ = 20.8°

This is the angle of elevation.

Learn more about the angle of elevation here:

https://brainly.com/question/21137209

#SPJ1

This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

Visit here to learn more about  interviewer bias : https://brainly.com/question/4961173
#SPJ11

Answer:  Hence, the length of swimming pool is 52 m and its breadth if 25 m.  

Step-by-step explanation:

The perimeter of rectangular swimming pool is 154 m and its length is 2 meter more than twice its breadth.

Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b