The area of the trapezoid is solved and height h = 2A / ( a₁ + b₁ )
Given some information, the formula for a trapezoid's area is:
Area = (1/2) (base₁ + base₂) height
where base₁ and base₂ are the lengths of the parallel sides of the trapezoid, and height is the perpendicular distance between the parallel sides.
So, to calculate the area of a trapezoid, you need to know the lengths of the two bases and the height.
Let's say base1 = b1, base2 = b2, and height = h.
Then, the formula for the area becomes:
Area = (1/2) x (b1 + b2) x h
b = longer base of trapezium
h = height of trapezium
Now , on solving for height of trapezium , we get
A = ( ( a₁ + b₁ ) h₁ ) / 2
Multiply by 2 on :
2A = ( a₁ + b₁ ) h
Divide by ( a + b ) :
h = 2A / ( a₁ + b₁ )
Hence , the height is h = 2A / ( a₁ + b₁ )
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please help fast with my assignment
if 63 adults represent 87.5% of the people who visited a museum over a noon hour,
how many people visited the museum during the noon hour
A.72
B.86
C.135
D.151
Answer:
A. 72
Step-by-step explanation:
63/x = 87.5/100
x = 6300 divided by 87.5
x = 72
In a random sample of 144 observations, P = 0.6. The 95% confidence interval for P is 0.52 to 0.68 0.144 to 0.200 0.60 to 0.70 0.50 to 0.70
The correct answer is: In a random sample of 144 observations, with a sample proportion of 0.6, the 95% confidence interval for the true population proportion is estimated to be between 0.52 and 0.68.
This means that if we were to repeat this sampling process many times and construct a confidence interval each time, we would expect 95% of those intervals to contain the true population proportion. The other options given are not correct as they do not accurately reflect the information given in the question.
In a random sample of 144 observations, with P = 0.6, the 95% confidence interval for P can be calculated using the following steps:
1. Identify the sample proportion (p) and the sample size (n): p = 0.6 and n = 144.
2. Calculate the standard error (SE) of the sample proportion using the formula: SE = sqrt[(p * (1 - p))/n]. In this case, SE = sqrt[(0.6 * (1 - 0.6))/144] = sqrt[(0.6 * 0.4)/144] = sqrt[0.24/144] = 0.04.
3. Find the critical value (z) for the 95% confidence interval using a z-table or a calculator. For a 95% confidence interval, the critical value is approximately 1.96.
4. Calculate the margin of error (ME) using the formula: ME = z * SE. In this case, ME = 1.96 * 0.04 = 0.0784.
5. Determine the lower and upper bounds of the 95% confidence interval by adding and subtracting the margin of error from the sample proportion: Lower Bound = p - ME = 0.6 - 0.0784 = 0.5216; Upper Bound = p + ME = 0.6 + 0.0784 = 0.6784.
So, the 95% confidence interval for P is approximately 0.52 to 0.68.
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a game is played by drawing one card at random from a standard 52-card deck. if the card is a diamond, the player wins. if the card is not a diamond, the player loses $52. in order for this to be a fair game, when the player wins, how much should they win?
To determine the fair amount the player should win, we need to calculate the probability of drawing a diamond from a standard 52-card deck. There are 13 diamonds in a deck, and 52 total cards, so the probability of drawing a diamond is 13/52, or 1/4. This means that there is a 25% chance of winning the game.
To make the game fair, the expected value of the game must be zero. The expected value is calculated by multiplying the amount won by the probability of winning, and subtracting the amount lost by the probability of losing. In this case, the amount lost is $52, and the probability of losing is 75%, or 3/4.
So, the expected value equation would be:
0 = (amount won)(1/4) - ($52)(3/4)
Solving for the amount won, we get:
Amount won = $208/1 = $208
Therefore, in order for this game to be fair, the player should win $208 when they draw a diamond. This makes the expected value of the game zero, ensuring that it is a fair game for both the player and the house.
Answer more than 100 words: To summarize, the amount the player should win in order for the game to be fair is $208. This calculation is based on the probability of drawing a diamond from a standard 52-card deck, which is 1/4 or 25%. By calculating the expected value of the game, we can determine the amount the player should win in order for the game to be fair. The expected value equation takes into account both the probability of winning and the amount lost when losing. By setting the expected value equal to zero and solving for the amount won, we can determine the fair amount the player should win. This ensures that the game is fair for both the player and the house, as the expected value is zero.
In a fair game, the expected value of the game should be zero, meaning the player neither wins nor loses money on average. To determine the winning amount, let's analyze the probabilities and outcomes of the game.
A standard 52-card deck has 13 diamonds and 39 non-diamond cards. The probability of drawing a diamond is 13/52 or 1/4, and the probability of drawing a non-diamond is 39/52 or 3/4. If the player loses, they lose $52.
Let X be the winning amount if the player draws a diamond. The expected value (EV) is given by:
EV = (probability of winning) * (winning amount) + (probability of losing) * (losing amount)
Since the game is fair, EV = 0. Therefore:
0 = (1/4) * X + (3/4) * (-52)
To solve for X, multiply both sides by 4:
0 = X - 3 * 52
Now, add 3 * 52 to both sides to find the winning amount:
X = 3 * 52
X = $156
In order for this game to be fair, the player should win $156 when they draw a diamond.
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if you always test whether the number is positive or negative, big endian is more easy to use than little endian. true false
the statement "if you always test whether the number is positive or negative, big endian is more easy to use than little endian" is incorrect.
Endianness refers to the way in which a computer stores data in memory. In big endian, the most significant byte is stored at the smallest address and the least significant byte is stored at the largest address. In little endian, the least significant byte is stored at the smallest address and the most significant byte is stored at the largest address.
The choice between big endian and little endian has no impact on testing whether a number is positive or negative. Both endianness formats can store positive and negative numbers in the same way.
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Which of the following is equal to the rational expression when x + 1 or -1?
5(x-1)
(x+1)(x-1)
Ο Α.
OB.
5
(x-1)(x + 1)
5
X+1
OC. 5(x-1)
X+1
OD 5
x-1
We can see here that the expression that is equal to the rational expression when x doesn’t equal 1 or -1 is 5/(x+1).
What is a rational expression?A fraction with a polynomial in the numerator and denominator is referred to as a rational expression. No numerator can be 0. A polynomial is an expression that only supports the operations of addition, subtraction, multiplication, and non-negative integer exponents. It can also contain constants, variables, and exponents.
The given expression is: 5(x-1)/(x+1)(x-1) where x doesn’t equal 1 or -1.
Thus, if we cancel out numerator and denominator, we will have: 5/(x+1).
Thus, 5/(x+1) is the correct answer.
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The complete question is:
Which of the following is equal to the rational expression when x doesn’t equal 1 or -1? 5(x-1)/(x+1)(x-1).
PLEASE HELP ME!!! THIS IS TIMED!! BRAINLIEST & 15 POINTS
Answer: I think the answer is A
Step-by-step explanation:
If all are equally likely, find the number of possible outcomes
4 play dates, 3 show times
There are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.
For each play date, you have 3 options for the show time.
Since the events are independent and all options are equally likely, you can multiply the number of options together to find the total number of possible outcomes.
Number of possible outcomes
= Number of play dates × Number of show times
= 4 × 3
= 12
Therefore, there are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.
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how should a firm record an impairment in the value of property, plant, or equipment?
A firm should record an impairment in the value of property, plant, or equipment by reducing the carrying amount of the asset and recognizing the impairment loss as an expense in the financial statements.
When the value of property, plant, or equipment is impaired, meaning its recoverable amount is lower than its carrying amount, a firm should recognize this impairment in its financial statements. The impairment is recorded by reducing the carrying amount of the asset to its recoverable amount, which is the higher of its fair value less costs to sell or its value in use. The difference between the carrying amount and the recoverable amount is recognized as an impairment loss and recorded as an expense in the income statement. This adjustment reflects the decrease in the value of the asset and allows the firm to accurately report its financial position and performance.
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pls help Jiya is renting a truck to move into her college dorm. The rental company charges $55 for the first hour and then $10 per hour after that. If it will take Jiya 7 hours to move, which explicit formula describes how much it will cost her to rent the truck?
a.a7=55+(7+1)10
b.a7=10+(7-1)55
c.a7=10+(7-1)7
d.a7=55+(7-1)10
Use an Explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours .The correct answer is option (d) a7=55+(7-1)10
The rental company charges $55 for the first hour and then $10 per hour after that, we can use an explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours.
The explicit formula for the total cost of renting the truck for a given number of hours can be written as:
a(n) = c + (n-1)d
where a(n) is the total cost of renting the truck for n hours, c is the cost of the first hour, and d is the additional cost per hour.
Using this formula, we can find the cost of renting the truck for 7 hours:
a(7) = 55 + (7-1)*10
Simplifying the expression in the parentheses, we get:
a(7) = 55 + 6*10
Multiplying 6 by 10, we get:
a(7) = 55 + 60
Adding 55 and 60, we get:
a(7) = 115
Therefore, the explicit formula that describes how much it will cost Jiya to rent the truck for 7 hours is:
a7=55+(7-1)10
Simplifying the expression, we get:
a7 = 55 + 6*10
a7 = 55 + 60
a7 = 115
Therefore, the correct answer is option (d) a7=55+(7-1)10.
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there were 375 books sold last week at Sid's Bookstore. The table below summarizes these books by genre. This information is also presented as a circle graph.
Find the central angle measure, x° for the Self-Help slice in the circle graph. Do not round.
The central angle formed by the Self Help slice is 86.4°.
A circle is formed when you draw a point and connect it from end to end forming a complete revolution.
We have to find the central angle formed by the Self Help slice
One revolution equals 360°.
Therefore, each piece of pie for each type of book is a fraction of one revolution.
The fraction can be determined by dividing the number for a specific type of book to the total number of books.
Specifically, the fraction for the Self Help slice would be 90/375 which is equal to 0.24 or 24%.
Then, 24% of 360 is 86.4.
Therefore, the central angle formed by the Self Help slice is 86.4°.
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There are 375 books sold at Sid's Bookstore. The table below summarizes these books by genre. This info is presented in circle graph. Find the central angle measure for Self Help slice in graph. Mystery 99, romance 81, self help 90, cooking 57, biography 48.
If a balloon contains 25 cubic centimeters of air, and if you can further add a maximum of 15 cubic centimeters of air to the balloon, what is the maximum capacity of the balloon?
The approximate surface area of the balloon is 199 cm².
The approximate volume of the balloon is 262 cm³
Here, we have,
the surface area and the volume of the balloon:
Radius of the balloon = circumference / 6.2832
25 / 6.2832 = 3.98cm
we know that,
Surface area = 4πr²
4 x 22/7 x 3.97² = 199 cm²
we have,
Volume = 4/3πr³
4/3 x 22/7 x 3.97³ = 262.20 cm³
Hence, The approximate surface area of the balloon is 199 cm².
The approximate volume of the balloon is 262 cm³
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complete question:
A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic centimeter?
If xy + 4ey = 4e, find the value of y'' at the point where x = 0. y'' = Need Help? Read It Chat About It Submit Answer Save Progress Practice Another Version
We cannot find the value of y'' at the point where x = 0 using this method.
To find y'' at the point where x = 0, we need to differentiate the given equation twice with respect to x.
First, we take the derivative of both sides with respect to x:
y + xy' + 4ey' = 0
Next, we take the derivative of this equation with respect to x:
y' + xy'' + y' + 4ey'' = 0
Simplifying this expression, we get:
2y' + xy'' + 4ey'' = 0
We are given that xy + 4ey = 4e. Differentiating this equation with respect to x, we get:
y + xy' + 4ey' = 0
Substituting y' = -(y + 4ey')/x from this equation into the previous equation, we get:
2y' - (y + 4ey') + 4ey'' = 0
Simplifying this expression, we get:
y'' = (y + 4ey' - 2y')/(4e)
When x = 0, we have y = 4e/4e = 1 and y' = -(1 + 4e*y')/0, which is undefined.
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Pls help, thankssssss
30 points
Answer:option c is the answer
Step-by-step explanation:
Helppppppppp pleaseeeeee
The amount of wrapping paper that is needed to cover the package is 1625 sq cm.
How to determine the amount of wrapping paperTo determine the amount of wrapping paper that is required to cover the package, we will be determining the surface area of a triangle with the formula: A = 1/2 × b × h.
To find this surface area, we will go around the triangle while considering the bases and heights as follows:
((20 + 5) * 5 /2) * 2 + (20 * 30) + (17 * 30) + (5 * 30) + (8 * 30)
125 + 600 + 510 + 150 + 240
1625 sq cm
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Could someone explain this to me???
For vector arithmetic, vector addition (adding two vectors) and scalar multiplication (multiplying a vector by a scalar) is "component-wise". So when adding two vectors you add each component in the first vector to the corresponding one in the second to get the resulting vector. In scalar multiplication you multiply each vector component by the scalar and that gives the resulting vector.
So if u = <3,-2> and v = <-1,4>,
3u = <3*3,-2*3> = <9,-6>
2v = <-1*2,4*2> = <-2,8>
3u + 2v = <9,-6> + <-2,8> = <9+(-2),-6+8> = <7,2>
Calculate the length of ED and BE
Which model represents the sum of 5/3 and 2/3?
The model that represents the sum of 5/3 and 2/3 is 7/3.
to find the sum of 5/3 and 2/3, we need to add the numerators (top numbers) together and keep the same denominator (bottom number). so, we have:
5/3 + 2/3 = (5+2)/3 = 7/3 to represent this visually, you could imagine a number line with 0 on the left and increasing values to the right. each whole number is divided into three equal parts. the model for 5/3 would be a point 5/3 of the way from 1 to 2, and the model for 2/3 would be a point 2/3 of the way from 0 to 1. to find the model for 7/3, we would locate the point 7/3 of the way from 2 to 3 on the number line.
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Select the correct answer.
The graphs represent functions f and g.
-10.
10
-10
9
Which ordered pair represents (fg)(2) on the graph of the combined function?
OA. (4,42)
OB. (2,9)
O C. (2,81)
OD. (4,81)
PLS HELP IM TIMED TY
Solve the equation. Enter your answer as an equation that shows the value of
the variable (like s= 2/3, or 4= w).
-7x-3=-31
The solution to the equation -7x - 3 = -31 is x = 4.
To solve the equation -7x - 3 = -31, we will isolate the variable x.
Step 1: Begin by moving the constant term to the other side of the equation.
-7x - 3 + 3 = -31 + 3
Simplifying, we get:
-7x = -28
Divide both sides of the equation by -7 to solve for x.
(-7x) / -7 = (-28) / -7
Simplifying, we have:
x = 4
Therefore, the solution to the equation -7x - 3 = -31 is x = 4.
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Writing unit fractions with a common denominator to add or subtract
finding 1/4-1/2 pls help
1/4 - 1/2 = -1/4. Don't forget to include the negative sign in your answer, which indicates that the result is less than 0. it's important to find a common denominator so that you can add or subtract them easily.
To subtract unit fractions like 1/4 and 1/2, you need to find a common denominator. A common denominator is a number that both denominators can divide into evenly. In this case, the smallest common denominator is 4, since 4 can be divided evenly by both 4 and 2.
To get both fractions to have a denominator of 4, you need to multiply 1/4 by 1 and 1/2 by 2/2, which equals 2/4.
Now that both fractions have the same denominator, you can subtract the numerators:
1/4 - 2/4 = -1/4
Overall, when working with unit fractions,
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Trapezoid ABCD is congruent to trapezoid A′′B′′C′′D′′ . Which sequence of transformations could have been used to transform trapezoid ABCD to produce trapezoid A′′B′′C′′D′′ ? Responses Trapezoid ABCD was reflected across the y-axis and then across the x-axis. , , trapezoid A B C D, , , , was reflected across the y -axis and then across the x -axis. Trapezoid ABCD was reflected across the y-axis and then translated 7 units up. , , trapezoid A B C D, , , , was reflected across the y -axis and then translated 7 units up. Trapezoid ABCD was translated 7 units up and then 12 units left. , , trapezoid A B C D, , , , was translated 7 units up and then 12 units left. Trapezoid ABCD was reflected across the x-axis and then across the y-axis. , , trapezoid A B C D, , , , was reflected across the x -axis and then across the y -axis.
The correct sequence of transformations that could have been used to transform Trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.
To transform trapezoid ABCD into trapezoid A''B''C''D'', we need to apply a sequence of transformations that will result in the same size and shape of the two trapezoids, which means that they are congruent.
One possible sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is:
Trapezoid ABCD was reflected across the y-axis and then across the x-axis.
This sequence of transformations would result in the same size and shape of the two trapezoids, which means that they are congruent. Let's see why this is true.
When we reflect trapezoid ABCD across the y-axis, each point on the trapezoid is reflected across the y-axis, which means that its x-coordinate is multiplied by -1 while its y-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the y-axis.
Next, when we reflect the trapezoid across the x-axis, each point is reflected across the x-axis, which means that its y-coordinate is multiplied by -1 while its x-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the x-axis.
The resulting trapezoid is now in the same position and orientation as trapezoid A''B''C''D'', but it may not be in the same location. However, since the trapezoid is congruent, we can translate it to match the position of trapezoid A''B''C''D''.
Therefore, the correct sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.
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Find the distance between the points A and B given below.
(That is, find the length of the segment connecting A and B.)
Round your answer to the nearest hundredth.
Answer:
Measure the distance between those 2 points, A and B. Then when you get your answer, round it to the second number after your decimal. (The hundredth place) It is explained more below:
Step-by-step explanation:
After measuring, you should get a decimal number. With that number, you need to round to the nearest hundredth.
-Meaning you need to check the 2nd number right after the decimal. The second number right after the decimal will be 2 in this example.
If the number after 2 is less than five, you can just remove all the numbers after 2, leaving everything else the same. If the number after 2 is more than five or is exactly 5, you would change 2 to one number higher. (In this example, you would make it 3) Then you can remove all numbers after the 2 (which turned into 3 now)I hope this helped. <3
complete the point-slope equation of the line through (-5 4) and (1 6)
Answer:
y - 4 = 1/3(x + 5)
Step-by-step explanation:
The general equation for the point-slope form of a line is given by:
y - y1 = m(x - x1), where
(x1, y1) is a point on the line, and m is the slope of the line.Step 1: To find the equation of the line through (-5, 4) and (1, 6), we first need to find the slope of the line using the slope formula, which is:
m = (y2 - y1) / (x2 - x1), where
(x1, y1) are one point on the line,and (x2, y2) are another point on the lineWe can allow (-5, 4) to be our (x1, y1) point and (1, 6) to be our (x2, y2) point:
m = (6 - 4) / (1 - (-5))
m = 2 / (1 + 5)
m = 2/6
m = 1/3
Now we can use the point-slope form of the equation with either of the two points.
Since we already used (-5, 4) as our (x1, y1) point, let's use it for the point-slope form:y - 4 = 1/3(x - (-5))
y - 4 = 1/3(x + 5)
Thus, the point-slope equation of the line through (-5, 4) and (1, 6) is:
y - 4 = 1/3(x + 5)
How do I solve this?
The trigonometric identity 1 + cot⁴θ = cosec⁴θ - 2cot²θ
What are trigonometric identities?Trigonometric identities are mathematical equations that contain trigonometric ratios in which one side is equal to the other.
Given the trigonometric identity
1 + cot⁴θ = cosec⁴θ - 2cot²θ, we need to show that the Left hand side L.H.S equals the Right Hand side R.H.S. we proceed as follows.
So, L.H.S = 1 + cot⁴θ
Now using the trigonometric identity
1 + cot²θ = cosec²θ
Making cot²θ subject of the formula, we have that
cot²θ = cosec²θ - 1
So, substituting this into the equation, we have that
1 + cot⁴θ = 1 + (cot²θ)²
= 1 + (cosec²θ - 1)²
Expanding the bracket, we have that
= 1 + cosec⁴θ - 2cosec²θ + 1
= cosec⁴θ - 2cosec²θ + 1 + 1
= cosec⁴θ - 2cosec²θ + 2
= cosec⁴θ + 2 - 2cosec²θ
= cosec⁴θ + 2(1 - cosec²θ)
= cosec⁴θ + 2cot²θ
= R.H.S
Since L.H.S = R.H.S
1 + cot⁴θ = cosec⁴θ - 2cot²θ
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the ratio of children to adults on a school trip is initially 10:1 this does not meet government regulations, so 5 more children and 5 more adults join the trip so that the ratio is now 9:1 how many children are there now
The number of children are there in the given scenario are 400.
Given that, the ratio of children to adults on a school trip is initially 10:1.
Here, the given ratio can be written as 10x:1x
5 more children and 5 more adults join the trip so that the ratio is now 9:1
10x+5:1x+5
The new ratio is (10x+5)/(x+5) = 9/1
10x+5=9(x+5)
10x+5=9x+45
10x-9x=45-5
x=40
So, the number of children =10x=400
Therefore, the number of children are there in the given scenario are 400.
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g a biker is riding along a trail at 13ft/s . she spots an aspen tree that is 15 feet away from a traffic cone located along the trail at the shortest distance from the trail to the aspen tree (see diagram). how fast is the angle between her line of sight and the trail changing when she is 25 feet away from the tree?
Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.
To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:
tan(θ) = x/15
We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:
d^2 = x^2 + 25^2
Taking the derivative of both sides with respect to time t, we get:
2d (dd/dt) = 2x (dx/dt)
Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):
tan(θ) = x/15
sec^2(θ) (dθ/dt) = (1/15) (dx/dt)
(dθ/dt) = (1/15) (dx/dt) sec^2(θ)
We can use the equation for d to solve for x:
x^2 = d^2 - 25^2
2x (dx/dt) = 2d (dd/dt)
(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)
(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)
Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):
(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))
(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))
(dθ/dt) = (13/375) sec^2(arctan(15/25))
(dθ/dt) ≈ 0.039 radians per second
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Mr.Pham assigns a quiz that will have at most 15 questions. Write an inequality that shows how many questions, q, will be on the quiz.
Correct inequality that shows number of questions, q, will be on the quiz is,
⇒ q ≤ 15
Since, A relation by which we can compare two or more mathematical expression is called an inequality.
Here, We have to given that;
Mr. Pham assigns a quiz that will have at most 15 questions.
Since, Symbol of at most is, ( ≤ )
Hence, Correct inequality that shows number of questions, q, will be on the quiz is,
⇒ q ≤ 15
Thus, Correct inequality that shows number of questions, q, will be on the quiz is,
⇒ q ≤ 15
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2. Given the regular polygon below, what is the measure of each measured angle? *
12
Om<1 = 72; m>2 =
108
m<1 = 36; m>2 = 72
Om<1 = 72; m>2 = 54
Om<1=36; m>2 = 144
The measure of the angles m∠1 and m∠2 for the polygon are 72° and 54° respectively.
How to calculate for the interior angles of a polygonTo calculate the sum of interior angles of a polygon, you can use the following formula:
Sum of interior angles = (n-2) x 180 degrees
Where "n" represents the number of sides (or vertices) of the polygon.
Given the 5 sided polygon;
(5 - 2) × 180 = 540
one interior angle = 540/5 = 108°
m∠2 = 108°/2
m∠2 = 54°
m∠1 = 180 - [2(54°)]
m∠1 = 180 - 108
m∠1 = 72°
Therefore, the measure of the angles m∠1 and m∠2 are 72° for the polygon and 54° respectively.
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Need Help ASAP! Please
A nervous kicker usually makes 71% of his first field goal attempts. If he makes his first attempt, his success rate rises to 89%. What is the probability that he makes his first two kicks?
Answer: 0.632
The probability that the kicker makes his first two kicks is 63.21%. This means that out of 100 attempts, the kicker is likely to make both kicks 63 times.
To solve this problem, we need to use conditional probability. We know that the kicker usually makes 71% of his first field goal attempts. So, the probability that he makes his first kick is 0.71. If he makes his first attempt, his success rate rises to 89%. So, the probability that he makes his second kick given that he made his first kick is 0.89.
Now, to find the probability that he makes his first two kicks, we need to multiply the probability of him making his first kick by the probability of him making his second kick given that he made his first kick. This can be represented as:
P(2 successful kicks) = P(1st kick is successful) x P(2nd kick is successful | 1st kick is successful)
P(2 successful kicks) = 0.71 x 0.89
P(2 successful kicks) = 0.6321 or 63.21%
Therefore, the probability that the kicker makes his first two kicks is 63.21%. This means that out of 100 attempts, the kicker is likely to make both kicks 63 times.
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