Pls help i need to pass

Pls Help I Need To Pass

Answers

Answer 1

The total surface area of the square pyramid is 39 ft².

What is the total surface area?

The total surface area of a square pyramid can be determined by adding the area of the lateral surfaces and the base together.  A square pyramid has four lateral sides and one base.  

Total surface area= area of the base + area of the lateral sides

Area of the base = area of a square = length² = 3² = 9 ft²

Area of the lateral sides = 2 x base x height

2 x 3 x 5 = 30 ft²

Total surface area = 30 + 9 = 39 ft²

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Related Questions

A database system assigns 32 character id to each record where each character is either a number from 0 to 9 or a letter from a to f assume that each number or letter being selected equally likely find the probability that at least 20 characters in the ID are numbers round your answer to three decimal places

Answers

0.578

hope this helps

This is a binomial distribution problem with the following parameters:

Number of trials: n = 32Probability of success: p = probability that a character is a number = 10/16 = 5/8Probability of failure: q = 1 - p = probability that a character is a letter = 6/16 = 3/8

We want to find the probability that at least 20 characters are numbers. We can use the complement rule and find the probability that fewer than 20 characters are numbers, and subtract that from 1:

P(at least 20 numbers) = 1 - P(fewer than 20 numbers)

Using the binomial probability formula, we have:

P(fewer than 20 numbers) = Σ[k=0 to 19] C(n,k) * p^k * q^(n-k)

where C(n,k) is the binomial coefficient "n choose k". This can be calculated using a calculator or software that has a binomial probability function. For example, in Python, we can use the scipy.stats.binom.cdf() function:

from scipy.stats import binom

n = 32

p = 5/8

q = 3/8

prob_fewer_than_20 = binom.cdf(19, n, p)

This gives prob_fewer_than_20 = 0.04903110366420758.

Therefore,

P(at least 20 numbers) = 1 - 0.04903110366420758 = 0.9509688963357924

Rounding to three decimal places, the answer is 0.951.

Use a formula to find the surface area of the square pyramid.
3 ft
6 ft
3 ft

Answers

The surface area of the square pyramid is 89.4 ft² as the lateral area is  80.4 ft².

How to calculate the surface area of a square pyramid?

The surface area of a square pyramid is calculated by the formula

SA = B + 4ℓ, where B is the area of the base and ℓ is the lateral area.

In this case, the base area is 9 square feet (3 ft x 3 ft). The lateral area is 4ℓ, which is calculated by multiplying the slant height by the perimeter of the base.

The slant height of a square pyramid is calculated by the formula

s = √(h² + (a/2)²), where h is the height of the pyramid and a is the length of one side of the base.

In this case, the height is 3 ft and the length of one side of the base is 3 ft. Therefore, the slant height is

s = √(3² + (3/2)²)

= √(9 + 2.25)

= √11.25

= 3.35 ft.

The perimeter of the base is 6 ft (3 ft x 2). Therefore, the lateral area is

4ℓ = 4 x 3.35 ft x 6 ft

= 80.4 ft².

The surface area of the square pyramid is then

SA = B + 4ℓ

= 9 ft² + 80.4 ft²

= 89.4 ft².

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83
ces
Required information
[The following information applies to the questions displayed below.]
Ramirez Company installs a computerized manufacturing machine in its factory at the beginning of the year at a cost of
$84,600. The machine's useful life is estimated at 20 years, or 393,000 units of product, with a $6,000 salvage value.
During its second year, the machine produces 33,300 units of product.
Determine the machine's second-year depreciation and year end book value under the straight-line method.
Choose Numerator: /
Year 2 Depreciation
Year end book value (Year 2)
Straight-Line Depreciation
Choose Denominator:
=
=
Annual Depreciation
Expense
Depreciation expense

Answers

The machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

What is depreciation?

The cost of a tangible asset is spread out throughout the course of depreciation. It symbolises the asset's value dropping over time as a result of damage, obsolescence, or other circumstances. Depreciation is crucial because it enables firms to account for an asset's cost over the course of its useful life rather than just in the year it was purchased.

Depreciation can be calculated using a number of different approaches, such as the straight-line method, the decreasing balance method, and the sum-of-years' digits method.

The annual depreciation expense is:

Annual Depreciation Expense = (Cost of Asset - Salvage Value) / Useful Life in Units

Annual Depreciation Expense = ($84,600 - $6,000) / 393,000

Annual Depreciation Expense = $0.20 per unit

For second year we have:

Second-Year Depreciation = Annual Depreciation Expense x Units Produced in Second Year

Second-Year Depreciation = $0.20 x 33,300

Second-Year Depreciation = $6,660

Now, the year-end book value is:

Accumulated Depreciation = Annual Depreciation Expense x Number of Years

Accumulated Depreciation = $0.20 x 2

Accumulated Depreciation = $0.40 per unit

For:

Accumulated Depreciation = $0.40 x 33,300

Accumulated Depreciation = $13,320

Also,

Book Value = Cost of Asset - Accumulated Depreciation - Salvage Value

Book Value = $84,600 - $13,320 - $6,000

Book Value = $65,280

Hence, the machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

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The population of Medina, Ohio is currently 26,190 people. The population is predicted to grow at a rate of 3.7% per year. What will the population of Mediana be in 7.3 years? (round your answer to the neareat hundreth)

a.) 43210.82
b.) 87896.05
c.) 34144.47
d.) 50369.13

Answers

The population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

What do you mean by Percentage?

A number can be expressed as a fraction of 100 using a percentage. It is represented by the number %.

A decimal or fraction can be multiplied by 100 to become a percentage. For instance, multiplying 0.75 (a decimal) by 100 yields 75% when converted to a percentage. The same can be done to convert 3/4 (a fraction) to a percentage by dividing 3 by 4 to get 0.75, then multiplying that number by 100 to get 75%.

To calculate the population of Medina, Ohio in 7.3 years, we can use the formula:

Population after n years = Population before ×(1 + r/100)²

where r is the annual growth rate and n is the number of years.

Substituting the given values, we get:

Population after 7.3 years = 26,190 × (1 + 3.7/100)^7.3

Population after 7.3 years = 26,190 * 1.037^7.3

Population after 7.3 years = 26,190 * 1.301

Population after 7.3 years = 34,052.9

Rounding to the nearest hundredth, we get:

Population after 7.3 years = 34,052.90 ≈ 34,052.89

Therefore, the population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

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Need help with question #7

Answers

The coordinates of the matrix A with the given base S are:

<1, 2, 0, 2>

How to find the coordinates?

The coordinates will be a vector of the form:

<x, y, z, k>

Such that these four values are each of the coefficients that affect each one of the matrices in the base respectively.

Then we can write a system of equations like:

x + y + z + k = 5

x - y - z  = 3

x + y = 3

x = 1

We can replace the last equation in the third one to get:

1 + y = 3

y = 3 - 1

y = 2

Now we can replace x and y in the second equation:

1 + 2 - z = 3

z = 1 + 2 - 3

z = 0

And the with the first equation:

1 + 2 + 0 + k = 5

3 + k = 5

k = 5 - 3 = 2

Then the coordinates of the matrix A are:

<1, 2, 0, 2>

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Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a multiple-choice test consisting of 18 questions, with each question having four possible answers (a, b, c, or d).

Answers

D I think that’s just an obvious answer

find the ratio of 4 inches to 3 yards

Answers

every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.

How to solve ratio?

To find the ratio of 4 inches to 3 yards, we need to convert both measurements to a common unit of measurement.

Firstly, let's convert the 3 yards to inches, since inches are already given. There are 36 inches in a yard (3 feet in a yard, and 12 inches in a foot), so:

3 yards = 3 x 36 inches = 108 inches

Now we can compare the two measurements:

Ratio of 4 inches to 108 inches = 4/108

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4 in this case:

4/108 = 1/27

So, the ratio of 4 inches to 3 yards is 1:27.

This means that for every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.

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When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.

ℎ=ℎ0−162



is the height of the object in feet.
ℎ0
is the initial height of the object in feet.

is the time in seconds after the drop.

Which equation and solution tells how long it takes the object to reach a height of 84
feet if its initial height is 180
feet?

Answers

The equation is 84= h₀ -16t² and

Solving the equation we get the time taken by the object will be √6 seconds.

What is equation?

An equation is a mathematical statement which is built by two expressions connected by an equal sign ('='). There must be  at least one unknown variable which is to be determined. For example, 3x – 8 = 16 is an equation. Solving this equation, we get  x = 8.

When an object is dropped vertically from a platform, its height after

seconds can be estimated with the formula shown.

ℎ=ℎ₀−16t²

where ℎ is the height of the object in feet.

and ℎ₀ is the initial height of the object in feet.

t is the time in seconds after the drop.

If the object reach the height 84 feet then the equation will be,

                     84= h₀ -16t²

If the initial height is 180 feet then the equation will be

                        84 = 180- 16t²

Solving the equation we get,

                       ⇒ 16t² = 180- 84

                        ⇒ 16t² = 96

                       ⇒ t² = 6

                      ⇒ t= ±√6

As time can't be negative so t= √6

Hence solving the equation we get the time taken by the object will be √6 seconds.

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A person is planting one garden bed that is 15 feet in length and another that is 9 feet in length. What is the total length, in inches, of the two garden beds combined
HELP PLEASE

Answers

Answer:

awnser is 288 seriously  15 x 12 = 180

and 9 x12 =108 add together is 288

PLEASE DONT GNORE!!M BEGGNG!!
Riley conducted a survey to see which is the most favorite subject among the students in her grade. She randomly chose to survey the first 53 students who entered the gym. She has a total of 424 students in her grade. What is true about the number of students who chose art??


____________students chose art as their favorite subject.

Answers

According to the table, the complete sentence would be: 96 students chose art as their favorite subject.

How to complete the sentence correctly?

To complete the sentences correctly we must read the information and analyze the table. Once we have done these procedures we can establish how many students chose each of the subjects as their favorite. According to the above, the sentence would be as follows:

96 students chose art as their favorite subject.

How do we know the number of students who chose arts?

According to Riley's survey, 12 out of 53 students chose art as their favorite. We then divide the total number of students (424) by the sample size (53) and multiply the number of students who chose art in the sample by the result of the division.

424 / 53 = 88 * 12 = 96

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Which is the largest angle?
A4
OC
B
5
Cannot tell
OA
с
7
6
B

Answers

Answer is angle C

Explanation

The Angle of a Triangle Opposite The Longest Side is the Largest Angle

7 is the longest side and angle C is it’s opposite angle

Please help with this equation I’ll give brainliest

Answers

Answer:

a. A linear equation would best represent the total cost a shopper will pay for an order.

b. y = .7x + 5 would model this situation.

answer this for me please and thank you​

Answers

Answer: w = -13

Step-by-step explanation:

    To solve, we will isolate the variable with inverse operations.

Given:

   4 + w = -9

Subtract 4 from both sides of the equation:

   w = -13

please help Find the common ratio for this geometric sequence. 1 1 1 2'8'32 8, 2, O A. 1/10 O B. -12 OC. 4 OD. 2​

Answers

The common ratio is the factor by which each term is multiplied to get the next term, which in this case is 4.

Equations

To find the common ratio of a geometric sequence, you can divide any term in the sequence by the previous term.

Looking at the sequence: 1, 1, 1, 2, 8, 32, 128, ...

To get from the 1st term to the 2nd term, we multiply by 1.

To get from the 2nd term to the 3rd term, we multiply by 1.

To get from the 3rd term to the 4th term, we multiply by 2.

To get from the 4th term to the 5th term, we multiply by 4.

To get from the 5th term to the 6th term, we multiply by 4.

What is common ratio?

The constant ratio between succeeding words is known as the common ratio in a geometric progression (GP). Any phrase in the progression must be divided by the term before it in order to compute it.

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which is equivalent to (3/125)*?
​125 1/3×
125 1/3X
125 3x
125 [1/3]×

Answers

The answer is (B) 125 1/3×, which is equivalent to (3/125) times approximately 18.048.

What do you mean by Equivalent fraction?

Equivalent fractions are fractions that have the same value but are written in different forms. They represent the same portion of a whole or a set, but their numerators and denominators may have different values.To find equivalent fractions, you can multiply or divide both the numerator and denominator of a fraction by the same number. This does not change the value of the fraction, but it changes its form.

The expression is (3/125) times something, but the value of that something is missing.

To solve the problem, we can simplify the expression (3/125) as a fraction in its lowest terms:

(3/125) = (3/5³)

Now, let's look at each of the answer choices:

125

If we multiply (3/5³) by 125, we get:

(3/5^3) * 125 = 3/5

Therefore, 125 is not equivalent to (3/125) times something.

1/3 × 125

If we multiply (3/5³) by (1/3 × 125), we get:

(3/5^3) * (1/3 × 125) = 1/5

Therefore, 1/3 × 125 is not equivalent to (3/125) times something.

125 1/3 ×

If we interpret "125 1/3 ×" as 125 and one-third multiplied by something, then we can write it as a mixed number fraction:

125 1/3 = 376/3

If we multiply (3/5³) by 376/3, we get:

(3/5³) ×(376/3) = 2256/125 = 18.048

Therefore, 125 1/3 × is equivalent to (3/125) times approximately 18.048.

125× 3x

If we interpret "125 3x" as 125 multiplied by 3 times something, then we can write it as:

125 ×3x = 375x

Therefore, 125 3x is not equivalent to (3/125) times something.

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Given the equation d over 11 equals 14, solve for d.

Answers

Step-by-step explanation:

To solve for d in the equation d/11 = 14, we can multiply both sides by 11 to isolate d on one side of the equation.

d/11 = 14 (multiply both sides by 11)

d = 11 x 14

Simplifying, we get:

d = 154

Therefore, the solution for d is 154.

Gretchen is a famous chef taking part in a celebrity cooking contest. Contestants earn scores between 1 - 10, with 10 being perfect. There are four categories and each category is weighted differently. The judges combined their scores and the results are shown in the table below.

Answers

Gretchen's final score, out of 10, is 8.35 based on weighted averages of scores in four categories.

How to calculate Gretchen's final score?

To calculate Gretchen's final score, we need to calculate the weighted average of her scores in each category.

The weight of each category is given, so we can calculate the weighted score for each category by multiplying the weight by the score.

For Taste, the weighted score is 0.30 * 8.6 = 2.58

For Presentation, the weighted score is 0.35 * 9.8 = 3.43

For Use of Ingredients, the weighted score is 0.25 * 7.7 = 1.93

For Practicality, the weighted score is 0.10 * 4.1 = 0.41

To find the final score, we add up the weighted scores for all categories:

2.58 + 3.43 + 1.93 + 0.41 = 8.35

Therefore, Gretchen's final score is 8.35 out of 10.

The question is incomplete, below is the complete question given -

Gretchen is a celebrity chef competing in a celebrity cooking competition. Contestants receive ratings ranging from 1 to 10, with 10 being the highest. There are four categories, each with its own weighting. The judges' scores were added together, and the results are presented in the table below. What is Gretchen's final score, out of 10? Do not round.

Table -
Category                   Weight      Score

Taste                             30%          8.6

Presentation                 35%          9.8

Use of Ingredients       25%           7.7

Practicality                    10%            4.1

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Write the following as on logarithm
2 ln(5x) − 3 ln(2x) + 7 log2 (8x)

Answers

ln[(5x)² × (2x)⁻³ × (8x)⁷] . The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.

What is logarithm expression?

The base number is the number that is raised to a certain power, the exponent is the power that the base number is raised to, and the logarithmic function is the equation which is used to calculate the result of the base number and the exponent.

The given expression can be written as a logarithm as follows:

ln[(5x)² × (2x)⁻³ × (8x)⁷]

This can be simplified to

2ln(5x) - 3ln(2x) + 7log2(8x)

The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.

The logarithm expression can be used to simplify complex equations and calculations, and it can also be used to solve for a particular variable.

This expression can be used to solve for x if the other values are known. The value of x can be calculated by taking the antilogarithm of each term and then solving the equation.

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The length of a rectangular flower bed is 3 ft less than twice its width. The area of the bed is 54 ft2. What are the dimensions of the flower bed.

Answers

Answer:

w = 6 ft.; l = 9 ft.

Step-by-step explanation:

We know that the formula for area of a rectangle is A = lw, where l is the length and w is the width.

Because we're told that the length of the flower bed is 3 ft less than twice its width, we have l = 2w - 3

To find the length and width, can plug in 54 into the equation and substitute our formula for length into the equation.

This gives us 54 = (2w - 3)*w

If we rewrite the equation, we'll see that its quadratic:

[tex]54=(2w-3)w\\54=2w^2-3w\\0=2w^2-3w-54[/tex]

Now, we can first solve for width using the quadratic formula, which yields a positive and negative solution.

(For the sake of the quadratic equation, 0= ax^2 + bx + c is the standard form of quadratic equation and in our equation 2 is a, -3 is b, and -54 is c)

Positive:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)+\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3+\sqrt{441} }{4}\\ \\w=\frac{3+21}{4}\\ \\w=\frac{24}{4}\\\\w=6[/tex]

Negative:

[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)-\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3-\sqrt{441} }{4}\\ \\w=\frac{3-21}{4}\\ \\w=\frac{-18}{4}\\\\w=-4.5[/tex]

We know that we can't have a negative measure, so the width is 6 ft.

Twice the width is 12 (6 * 2) and 3 less than this is 9 (12 - 3), so the length is 9 ft.

will mark brainliest its timed hurry!

Answers

Answer:

I think the answer is B?

Step-by-step explanation:

The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function

F(x)=-3.452x^4+35.129x^3-93.005x^2+41.705x+177.494

Where x is the number of years since 1996. Find the number of bald eagles in the state the winter of 1999

Answers

The number of bald eagles in the state during the winter of 1999 would be 34.

The ___ is the average of the sum of the squared differences of the mean from each element in a set of numerical data.

Answers

Answer:

The term that completes the sentence is "variance".

Step-by-step explanation:

In statistics, variance is a measure of how spread out a set of numerical data is. It is calculated by finding the average of the sum of the squared differences of each element in the set from the mean of the set. The formula for variance is:

Variance = (Σ(x - μ)²) / n

where Σ is the sum, x is each element in the set, μ is the mean of the set, and n is the number of elements in the set.

Find the value of r
18-2r

Answers

Answer:

27 18*3=2*r18/2*3=r9*3=rr=27

Step-by-step explanation:

Which of the following statements best explains the equation below?

17.8 – 4 x 3 = 12 ÷ 3 + 1.8

Answers

The solution is : (-2,7) is the point of intersection.

What is graph?

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

To solve the equations by graphing, use the form y=mx + b to find the slope and y-intercept of each equation. Graph the line and find their intersection point.

y = −2x + 3                                     y = −4x − 1

Slope: -2                                        Slope: -4

Y-int: (0,3)                                      Y-int: (0,-1)

Start at (0,3) and go down            Start at (0,-1) and go down 4 units

2 units and 1 to the right.               and 1 to the right. Connect the points.

Connect the points.

Continue this pattern in either direction for both lines until they intersect each point. The point of intersection (x,y) is the solution to the system of equations.

See attached graph.

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Complete question:

A pair of linear equations is shown below: y = −2x + 3 y = −4x − 1 Which of the following statements best explains the steps to solve the pair of equations graphically?

PART B:
If Dr. Nandi plans to transport 3.5 x 105 energy prisms that each take up 2 x 10² cubic feet of cargo
space, how much total space will the cargo take up? Answer in Scientific Notation. Show your work.
Edit View Insert Format Tools Table

Answers

Answer:

Step-by-step explanation:

just guess if not use the internet

Given that cos theta equals negative 5 square root 29 over 29 and theta is in quadrant 2 what is sim theta?

Answers

If cοs θ equals negative 5 square rοοt 29 οver 29 and θ is in quadrant 2  sin(θ) = οppοsite/hypοtenuse = 2√21/29.

What is trigοnοmetry?

The links between triangles' sides and angles are studied in the mathematic discipline knοwn as trigοnοmetry.

We knοw that cοsine is negative in quadrant 2, sο we can draw a triangle in quadrant 2 where the adjacent side is negative and the hypοtenuse is pοsitive. Let's call the οppοsite side οf the triangle "a", the adjacent side "b", and the hypοtenuse "c".

Using the Pythagοrean theοrem, we can find the length οf the third side οf the triangle:

c² = a² + b²

29² = a² + (-5√29)²

29² = a² + 725

a² = 29² - 725

a² = 84

a = √84 = 2√21

Nοw that we knοw the lengths οf the οppοsite and adjacent sides οf the triangle, we can use the definitiοn οf sine:

sin(θ) = οppοsite/hypοtenuse = 2√21/29

Therefοre,  sin(θ) equals 2√21/29.

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Complete Question:

Given that cos(θ)=−5√29/29, and θ is in Quadrant II, what is sin(θ)? Give your answer as an exact fraction with a radical, if necessary.

The life spans of 10 adult mayflies have a mean of 4 hours and a MAD of 2 hours. Fill in the table below with possible values for the life spans. You can use the same values more than once. Can any one of the 10 mayflies in the group live for 1 full day? Justify your answer.

Answers

No mayfly in the group can live for a full day (24 hours), as the maximum life span is 6 hours.

How to calculate life span?

We can start by calculating the lower and upper limits of the range of possible values for the life spans of the mayflies.

The lower limit can be found by subtracting the MAD from the mean, and the upper limit can be found by adding the MAD to the mean:

Lower limit = mean - MAD = 4 - 2 = 2 Upper limit = mean + MAD = 4 + 2 = 6

Since we know there are 10 mayflies in the group, we can fill in the table below with values between 2 and 6 (inclusive) that add up to 40 (the total number of hours for all 10 mayflies combined):

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In the figure, m∠EDF = 42°. Which other angle must have the same measure? A diagram of the inscribed quadrilateral with the points of D, E, F, and G, in which D with an angle of 42 degrees. A. ∠DEG B. ∠EGF C. ∠GDF D. ∠EGD

Answers

Therefore, the correct option is B. ∠EGF with the angle measure of 138°.

What is quadrilateral?

A quadrilateral is a four-sided polygon with four vertices and four angles. It is a closed figure with four straight sides that do not intersect. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. The sum of the interior angles of a quadrilateral is always 360 degrees.

Here,

In an inscribed quadrilateral, opposite angles are supplementary. That is, the sum of the measures of any two opposite angles is 180 degrees. Therefore, to find the angle that has the same measure as ∠EDF, we need to look for the angle that is also opposite ∠EDF in the inscribed quadrilateral.

In the inscribed quadrilateral with points D, E, F, and G, we know that ∠EDF has a measure of 42 degrees. We also know that the opposite angle to ∠EDF is ∠EGF, because they share side EF.

Since opposite angles in an inscribed quadrilateral are supplementary, we can find the measure of ∠EGF by subtracting 42 degrees from 180 degrees:

∠EGF = 180° - ∠EDF

= 180° - 42°

= 138°

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I I need a quick answer

Answers

Answer:

the answer is b

Step-by-step explanation:

3. When Ahmad goes to work, he has to pass through two sets of traffic lights, P and Q. The
probability that he has to stop at P is
7/20 .The probability that he has to stop at Q, given that he has
to stop at P is 7/10. The probability that he does not have to stop at Q, given that he does not have to
stop at P is 2/5
* Construct a tree diagram to represent the above information.
* Find the probability that he has to stop at both P and Q.
* Find the probability that he has to stop at least once.
* If he has to stop at Q, what is the probability that he would have stopped at P.

Answers

* The probability that Ahmad has to stop at both P and Q is: 7/40

* The probability that Ahmad has to stop at least once is: 27/50

* The probability that Ahmad would have stopped at P if he stops at Q is 7/13.

What is probability ?

The study of randomness or experiments falls within the canopy of the mathematical discipline of probability. When represented as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certain event, it is the gauge of the probability or chance that an event will occur. When making predictions based on a statistical study of the data at hand, probability is employed to characterise uncertain events. To aid in decision-making and risk assessment, it is utilised in a variety of disciplines, including science, architecture, finance, finance, and social sciences. Concepts like likelihood function, random variables, and anticipated values are all part of the study of probability.

given

We multiply the chances of stopping at P and Q assuming that he has already stopped at P to determine the likelihood that he must stop at both locations:

Stop at P Equals P(Stop at P and Q) P(Stop at Q | Stop at P)=7/20*7/10

= 49/200

P(Stop at least once) = 1 - P(Not stop at P) * P(Not stop at Q | Not stop at P) = 1 - (13/20) * P(Not stop at Q | Not stop at P) (2/5)\s= 37/50

The chance that he likewise stopped at P must be determined if he had stopped at Q.

Stopping at P and Q equals P(Stop at P and Q) / P(Stop at Q) = (7/20 * 7/10) / (7/20) = 7/10.

Hence, the likelihood that he would have stopped at P is 7/10 if he must stop at Q.

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