So the measures of the angles in the isosceles obtuse triangle are 20 degrees, 80 degrees, and 80 degrees.
What is triangle ?
Three straight ends and three angles make up a closed triangle, a two-dimensional geometric object. A triangle's angles add up to 180 degrees in all cases. Based on their side lengths and angle measurements, triangles can be categorized in a variety of ways. Typical categorizations comprise: Triangle having no equal sides is referred to as a scalene triangle. Isosceles triangle: A triangle with two sides of equal length. A triangle having an equilateral shape is one with three equal sides. Triangle that has all angles that are less than 90 degrees is referred to as an acute triangle. Triangle with one angle that is precisely 90 degrees is referred to as a right triangle. A triangle that has a side that is more acute than 90 degrees is said to be obtuse.
given
In the isosceles obtuse triangle, let x represent the measurements of each equal angle.
One of the equal angles is bigger than 90 degrees since the triangle is obtuse. As a result, we have:
x + x + 20 = 180 (sum of angles of a triangle) (sum of angles in a triangle)
When we simplify this equation, we obtain:
2x + 20 = 180
2x = 160
x = 80
Hence, each of the equal angles is 80 degrees in length. As a result, there are three different ways to measure the angles in the isosceles obtuse triangle, which has one angle that is 20 degrees, as follows:
20-80-80 degree range
80-20-80 degree range
80-80-20 Celsius
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Learning task 3: translate each problem into a mathematical equation then solve
The mathematical equations of each problem is 24 = 2x - 2, y + 16 = 85, 56 = (1/2)x - 6, x = 1/3 * 12600 and 120 + 50x = 270 and their solution are Sister is 13 years old, Arvin sold 69 cakes yesterday, You have 124 stamps, Chiz earned P4,200 this month and The horse ride lasted for 60 minutes, with 30 minutes being the initial ride and 30 minutes for the additional ride, respectively.
The translation of each problem into a mathematical equation then solution is.
Let x be the age of the sister.
Then, we have the equation:
24 = 2x - 2
Adding 2 to both sides gives:
26 = 2x
Dividing both sides by 2 gives:
x = 13
Therefore, the sister is 13 years old.
Let y be the number of cakes Arvin sold yesterday.
Then, we have the equation:
y + 16 = 85
Subtracting 16 from both sides gives:
y = 69
Therefore, Arvin sold 69 cakes yesterday.
Let x be the number of stamps you have.
Then, we have the equation:
56 = (1/2)x - 6
Adding 6 to both sides gives:
62 = (1/2)x
Multiplying both sides by 2 gives:
x = 124
Therefore, you have 124 stamps.
Let x be the amount Chiz earned this month.
Then, we have the equation:
x = 1/3 * 12600
Simplifying gives:
x = 4200
Therefore, Chiz earned P4,200 this month.
Let x be the number of 10-minute blocks for the additional horse ride time.
Then, we have the equation:
120 + 50x = 270
Subtracting 120 from both sides gives:
50x = 150
Dividing both sides by 50 gives:
x = 3
Therefore, the additional horse ride time was 3 blocks of 10 minutes, or 30 minutes in total. Adding this to the initial 30 minutes gives a total ride time of 60 minutes.
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_____The given question is incomplete, the complete question is given below:
Learning Task 3: Translate each problem into a mathematical equation then
solve:
1. i am 24 years old. My age is 2 less than twice my sister's age.
2. Arvin has a bake shop. He sold 85 cakes today. That is 16 cakes
fewer than yesterday. How many cakes did he sell yesterday?
3. Ann has 56 stamps that is 6 less than one-half of my stamps. How
many stamps do I have
4. This month Chiz eamed only of his earnings last month. If his
eaming last month is P12,600. How much did he earn this month?
5. In Baguio City a horse ride costs P120.00 per person for the first 30
minutes and P50.00 for every additional 10 minutes. If you spent
P270.00 for a horse ride, for how long did you ride?
kristiana went to yoga class at 12:30 after class she went to lunch whith her friends for 1hr and 35 minutes she finshed lunch at 2:50 how long was her yoga class
Answer:
45 minutes
Step-by-step explanation:
We Know
Kristiana went to a yoga class at 12:30.
She went to lunch with her friends for 1hr and 35 minutes
She finished lunch at 2:50
How long was her yoga class?
We take
12:30 + 1:35 = 2:05
Then we take
2:50 - 2:05 = 45 minutes
So, her yoga class was 45 minutes.
A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.07
0.07
.
If 310
310
are sampled, what is the probability that the sample proportion will be less than 0.04
0.04
? Round your answer to four decimal places.
Assume that the actual ratio is 0.07. If 310 people are sampled, there is a 0.0716 percent chance that the sample percentage and population proportion will deviate by more than 0.04.
The sample proportion, denoted by p', is an estimate of the population proportion p. The formula for the standard error of p' is:
SE = [tex]\sqrt{[p(1-p)/n]}[/tex]
where n denotes sample size and p denotes population proportion.
In this case, p = 0.07 and n = 310. Therefore, the standard error of p' is:
SE = [tex]\sqrt{[0.07(1-0.07)/310]}[/tex] = 0.019
To find the probability that the sample proportion will differ from the population proportion by more than 0.04, we need to find the probability that |p' - p| > 0.04. We can use the normal distribution to approximate this probability since the sample size is large (n = 310).
The z-score for a difference of 0.04 is:
z = 0.04 / 0.019 = 2.1053 (rounded to four decimal places)
Using a standard normal distribution table, the probability of a z-score being greater than 2.1053 or less than -2.1053 is approximately 0.0358. where n denotes sample size and p denotes population proportion.
P(|p' - p| > 0.04) = 2(0.0358) = 0.0716
Rounding to four decimal places, the probability is 0.0716.
The complete question is;-
A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.07. If 310 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.04? Round your answer to four decimal places.
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what is the probability of a defect when the lower and upper specification limits are 3 standard deviations away from the mean?
The probability of having an error when confidence limits are 3 standard deviations far from the mean is approximately 0.27.
Assume that the data is normally distributed. For a normal distribution, approximately 99.7% of the data is within 3 standard deviations of the mean.
As a result, if the lower and upper specification limits are 3 standard deviations away from the mean, they encompass 99.7% of the data.
As a result, there is only a 0.3% chance of an error. Since this is a two-tailed test, the probability of an error on each side is 0.15%
As a result, the probability of an error when the lower and upper specification limits are 3 standard deviations away from the mean is approximately 0.27.
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Error Analysis: Your friend concluded that because two discriminants are equal, the solutions to the two equations are the same. Explain your friend's error. Give an example of two quadratic equations that disprove this conclusion.
HELP PLEASE (50 points)
Answer:
Your friend's error is that having two equal discriminants doesn't necessarily mean that the two quadratic equations will have the same roots. The discriminant of a quadratic equation determines whether the roots are real, complex, or equal. If two quadratic equations have the same discriminant, then they have the same nature of roots, but that does not mean that their roots are equal.
As an example, consider the following two quadratic equations:
1. x^2 + 4x + 4 = 0
2. x^2 + 6x + 9 = 0
Both equations have the same discriminant: (b^2 - 4ac) = 16 - 16 = 0, but their roots are different. The first equation has one real root: x = -2, while the second equation has only one root, which is repeated twice: x = -3.
Therefore, it is incorrect to conclude that two quadratic equations have the same roots just because they have the same discriminants.
The data in the table describes the preferred type of exercise of 9th graders.
Cycling Running Swimming Row Totals
Boy 12% 18% 16%
Girl 14% 21% 19%
Column Totals 100%
Find the marginal relative frequency for students who prefer swimming as their preferred type of exercise.
39%
35%
19%
16%
The frequency for boys is 16% and the frequency for girls is 19%. Adding these two values together gives us the marginal relative frequency of 16%.
The marginal relative frequency of students who prefer swimming as their preferred type of exercise is 16%. Marginal relative frequency is a measure of the proportion of a certain group in relation to the total population. In this case, the marginal relative frequency of students who prefer swimming as their preferred type of exercise is 16%, which means that out of the total population of students, 16% prefer swimming as their preferred type of exercise.To calculate this, we need to add up the frequency of swimming for boys and girls. The frequency for boys is 16% and the frequency for girls is 19%. Adding these two values together gives us the marginal relative frequency of 16%.
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please help me with this !!!
A total of 336 tubs of cookie dough were sold in all.
What is a percentage?A ratio or figure stated as a fraction of 100 is called a percentage. The sign "%" is frequently used to indicate it as a percentage or a component of a total.
So, the number of tubs sold in each week can be represented by the following sequence:
Week 1: 100
Week 2: 0.8(100) = 80
Week 3: 0.8(80) = 64
Week 4: 0.8(64) = 51.2 ≈51
Week 5: 0.8(51) = 40.8≈41
To find the total number of tubs sold in all 5 weeks, we can add up the number of tubs sold in each week:
Total = 100 + 80 + 64 + 51 + 41
Total = 336
Therefore, a total of 336 tubs of cookie dough were sold in all.
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Justine gets dressed in the dark and decides to do an experiment to determine what color sock she will randomly grab from her sock drawer. She drew pairs of socks twelve times to determine the frequency of the occurrences. She then drew pairs of socks a large number of times and calculated the experimental probability based on the frequencies she found. Determine the correct values to complete the rest of the table. The data from her experiment is displayed in the table below.
Answer: Well look at it closely so it will help you understand more of it.
Step-by-step explanation: I read it over and over and over again and I think this will help.
What is the volume of Box A?
(The box is a rectangular prism.)
Box A
32 cm
25 cm
16 cm
Answer: 12800 cm³
Step-by-step explanation:
Area of Rectangular Prism = [tex]lwh[/tex]
A = 32 x 25 x 16
A = 12800
The price of a box of pencils has been steadily increasing by $1.10 per year. The cost of a box of pencils is now $2.19. (3 pts)
Answer:
Step-by-step explanation:
We can use algebra to determine how many years it has been since the cost of a box of pencils was $0.00, and therefore calculate how many years the price has been increasing by $1.10 per year.
Let's say that x is the number of years since the cost of a box of pencils was $0.00.
If the price of a box of pencils is increasing by $1.10 per year, then the cost of a box of pencils x years after it cost $0.00 would be:
$0.00 + ($1.10 * x)
We know that the current cost of a box of pencils is $2.19. Setting this equal to the expression above, we can solve for x:
$0.00 + ($1.10 * x) = $2.19
$1.10 * x = $2.19
x = $2.19 / $1.10
x = 1.99
So, it has been approximately 1.99 years (or just under 2 years) since the cost of a box of pencils was $0.00, and the price of a box of pencils has been steadily increasing by $1.10 per year during that time.
Match the reasons with the statements in the proof to prove AB || DC , given that AD is parallel to BC and AD = CB .
Given:
AD || BC
AD = CB
Prove:
AB || DC
1 .
CPCTE (Corresponding Parts of Congruent Triangles are Equal)
AD || BC , AD = CB
2 .
Reflexive Property of Equality
AC = AC
3 .
If Alternate Interior Angles are Congruent, then Lines are Parallel.
2 = 3
4 .
If Lines are Parallel, then Alternate Interior Angles are Equal.
ACD = CAB
5 .
Given
1 = 4
6 .
SAS (Side-Angle-Side)
AB || DC
Triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:
AB || DC, as required.
What is the congruent angle?
When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.
Corresponding Parts of Congruent Triangles are Equal
AD || BC, AD = CB
Given
1 = 4
From statements 1 and 5, we can conclude that:
ACD is congruent to CAB because they are corresponding angles of parallel lines AD and BC.
If Lines are Parallel, then Alternate Interior Angles are Equal.
ACD = CAB
From statement 4, we know that angles ACD and CAB are equal because AD is parallel to BC. Therefore:
ACD = CAB
Reflexive Property of Equality
AC = AC
From statement 2, we know that segment AC is equal to itself because of the reflexive property of equality. Therefore:
AC = AC
If Alternate Interior Angles are Congruent, then Lines are Parallel.
2 = 3
From statement 3, we know that if alternate interior angles are congruent, then the lines are parallel. Therefore, since ACD = CAB (statement 4) and AC = AC (statement 2), we can apply the SAS (Side-Angle-Side) congruence theorem to triangles ACD and CAB to conclude that they are congruent.
SAS (Side-Angle-Side)
AB || DC
Hence, As a result, since triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:
AB || DC, as required.
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What is the missing value for x on the diagram below?
Angle in a semi-circle is a right angle then, angle x is 90°, Z is 100° and y is 53° (refer below figure)
Define the term Circle identities?The six trigonometric functions of an angle in a right-angled triangle are connected by a set of fundamental identities known as the "Circle identities" in trigonometry.
In a semicircle AGE, angle at the circumference is 90 degree.
then, angle x = 90°
and arc Z° from the center of circle is a triangle AOB, see below figure,
40° + Z° + 40° = 180°
Then, Z° = 100°
Similarly, arc 74° from center of circle is a triangle EOG;
74°+ y° + y° = 180°
Then, y° = 53°
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Within this population, what is the probability that a student likes rap music?
(Each dot represents 1 person)
Group of answer choices
4/21
9/21
4/17
5/17
Answer:
i think the right answer is 9/21
Step-by-step explanation:
hope it will help you!!
a bag has 10 blue,12 green,8 yellow,11 pink, and 10 orange pieces of candy. what is the probability of reaching in the bag, without looking, and choosing either a blue or a yellow piece of candy
The probability of reaching into the bag and choosing either a blue or yellow piece of candy is 38/60 or 56%.
What is probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: a bag has 10 blue,12 green,8 yellow,11 pink, and 10 orange pieces of candy.
The probability of reaching into the bag and choosing a blue piece of candy is 5/10 or 50%.
The probability of reaching into the bag and choosing a yellow piece of candy is 3/5 or 60%.
Hence, the probability of reaching into the bag and choosing either a blue or yellow piece of candy is 38/60 or 56%.
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David went to the farmers market in san pedro and bought 3 churros for $2. 1. He then went to the swap meet on saturday and bought 5 churros for $3. 20. Which is the better buy for david
The better buy for david is churro at the swap
To determine which is the better buy for David, we need to compare the cost per churro for each purchase.
For the farmers market purchase, David bought 3 churros for $2.1, so the cost per churro is:
Cost per churro at farmers market = 2.1/3 = 0.7
For the swap meet purchase, David bought 5 churros for $3.20, so the cost per churro is:
Cost per churro at swap meet = 3.2/5 = 0.64
Since the cost per churro at the swap meet is lower than the cost per churro at the farmers market, buying churros at the swap meet is the better buy for David.
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For each of the following, write down whether
the data would be discrete or continuous:
a) Height of a building
b) Population of a country
c) Number of seats in a cinema
d) Mass of an apple
Answer:
a) discrete ; only from a particular building that stays the same
b) continuous ; the population of a country fluctuates and therefore shows trends
c) discrete ; information of a particular place
d) continuous ; there are trends of apple masses because there are different types of apples
Step-by-step explanation:
What is the value of f^{-1}(4)f
−1
(4)f, start superscript, minus, 1, end superscript, left parenthesis, 4, right parenthesis?
The function f with its inverse function [tex]f^{-1}[/tex] is equal to the identity function. The value of [tex]f^{-1}(4)f[/tex] is equal to 4.
To determine the value of [tex]f^{-1}[/tex](4)f−1(4)f, we would need to know the function f and its inverse function [tex]f^{-1}[/tex].
In this case, we are asked to find [tex]f^{-1}[/tex](4)f−1(4)f, start superscript minus 1, end superscript, left parenthesis 4, right parenthesis. This means we need to find [tex]f^{-1}(4)[/tex] and then plug that value into the original function f.
Now, [tex]f(f^{-1}(4))[/tex] can be simplified as follows:
[tex]f(f^{-1}(4)) = 4[/tex]
This is because [tex]f^{-1}(4)[/tex] is the input that produces an output of 4, and then f is applied to that input to produce the same output.
Multiplying [tex]f^{-1}(4)[/tex] by f is equivalent to evaluating the function f at the point [tex]f^{-1}(4)[/tex]. Thus, we have:
[tex]f(f^{-1}(4)) = 4[/tex]
This means that the composition of the function f with its inverse function [tex]f^{-1}[/tex] is equal to the identity function. Therefore, the value of [tex]f^{-1}(4)f[/tex] is equal to 4.
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BEFORE solving an equation, how do you know if it is a 1-step or Multi-step
equation?
Solve the following equation
-4(x + 5)-2 = 6x
Explain how you solved the equation above./
Answer:
Step-by-step explanation:
if an equation needs only one step to isolate the variable, it is 1-step. For example, 4x=16, which means x=4. Generally I’m not sure of a way other than that to know if an equation is one step or multi-step.
-4(x+5)-2=6x
So, use distributive property.
-4x-20-2=6x
Add 4x to both sides.
-20-2=10x
Solve -20-2.
-22=10x
Divide 10 from both sides.
x=-10/22
Simplify
x=-5/11
what is the image of (-3,0) after a dilation by a scale factor of 2 centered at the origin
Step-by-step explanation:
A dilation is a transformation that enlarges or reduces an object by a certain scale factor, and it is centered at a fixed point. In this case, we want to dilate the point (-3, 0) by a scale factor of 2, and the center of dilation is at the origin (0, 0).
To perform the dilation, we first need to find the distance between the point (-3, 0) and the center of dilation (0, 0), which is simply the magnitude of the vector (-3, 0), or 3.
Next, we need to multiply this distance by the scale factor of 2 to get the new distance after dilation, which is 6.
Finally, we need to find the point that is 6 units away from the origin along the same line that passes through the origin and the original point (-3, 0). This can be done by multiplying the direction vector of this line by the distance of 6 and adding the result to the center of dilation (0, 0). The direction vector is (-3, 0), normalized to have unit length, which is (-1, 0).
So the image of (-3, 0) after dilation by a scale factor of 2 centered at the origin is:
(-1 * 6, 0 * 6) + (0, 0) = (-6, 0)
Therefore, the image point is (-6, 0).
What is the vertex of g(x) = 3x2 − 12x 7? (−6, −5) (−2, −5) (2, −5) (6, −5)
The vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).
The vertex of a parabola in the form of y = a[tex]x^{2}[/tex] + bx + c can be found using the formula x = -b/2a for the x-coordinate of the vertex and then substituting this value into the equation to find the y-coordinate.
For the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7, we can see that a = 3 and b = -12. We can use the formula to find the x-coordinate of the vertex:
x = -b/2a = -(-12)/(2*3) = 2
So the x-coordinate of the vertex is 2. To find the y-coordinate, we can substitute x = 2 into the equation:
g(2) = 3 [tex](2)^{2}[/tex]- 12(2) + 7 = -5
Therefore, the vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).
So the correct answer is (c) (2, −5).
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An astronaut who weighs 180 pounds on Earth would weigh 30 pounds on the Moon. If an object weighs 7 pounds on the Moon, how much would it weigh on Earth?
The object would weight 42 pounds on Earth.
Define weightIn physics, weight is a measure of the force exerted on an object due to gravity. It is a vector quantity, which means that it has both magnitude (numerical value) and direction.
Let's denote the weight of the object on Earth as W and set up a proportion:
Weight on Earth / Weight on Moon = Gravitational force on Earth / Gravitational force on Moon
Using the given information, we can substitute the weights and simplify:
W / 7 = 180 / 30
W / 7 = 6
Multiplying both sides by 7, we get:
W = 7 ×6 = 42
Therefore, the object would weigh 42 pounds on Earth.
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20. You decide to invest some of your summer money earned to help buy
yourself a Can-Am Spyder when you turn 20 years old - some teacher you
remember fondly had a ripping cool black matte one that inspired you. You
earn this money when you are 16 years old and the investment vehicle
chosen takes a full 4 years to financially mature. You invest $2,500 that
compounds weekly at a 4.5% rate. How much do you have as a down
payment on that bad-boy motorcycle when the time comes?
if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.
How to solve investment?
If you invest $2,500 at a 4.5% weekly compounding rate, it will grow to a considerable amount in 4 years. To calculate this, we need to use the compound interest formula:
A = P(1 + r/n)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $2,500
r = 4.5% = 0.045
n = 52 (since compounding is weekly)
t = 4 years
Plugging in these values, we get:
A = $2,500(1 + 0.045/52) in power (52*4) = $3,157.22
So, if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.
It's important to note that this calculation assumes that the investment vehicle will have a steady and reliable return rate for the entire 4 years. There is always some level of risk involved with investing, so it's important to do your research and make informed decisions about where to put your money.
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Mikey would like to save more than $200 for a new bike. If he earns $25 per week, how many weeks until he can buy the bike?
Mikey needs to save for at least 9 weeks to buy the bike.
What is inequality?
An inequality is a mathematical statement that compares two values, indicating that they are not equal. It uses symbols such as <, >, ≤ (less than or equal to), or ≥ (greater than or equal to) to express the relationship between the two values.
Let's call the number of weeks that Mikey needs to save "w". We can set up an equation using the given information:
$25 x w > $200
Simplifying this inequality, we get:
w > 8
This means that Mikey needs to save for more than 8 weeks to have more than $200. Since the number of weeks has to be a whole number, Mikey needs at least 9 weeks to save enough money to buy the bike.
Therefore, Mikey needs to save for at least 9 weeks to buy the bike.
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what is an obtuse triangle
Answer:An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Step-by-step explanation:basically its more than 90 degrees
Answer:
An obtuse triangle is a triangle where one of the interior angles measures more than 90°
classify the statement as an example of classical probability, empirical probability, or subjective probability. the probability of an earth-impacting asteroid causing a person's death is .
The given statement "the probability of an earth-impacting asteroid causing a person's death" is empirical probability, which is based on observations and data.
Empirical probability, also known as experimental probability, is based on observations or data. It involves collecting data through repeated trials of an experiment and calculating the probability of an event based on the frequency of its occurrence.
Subjective probability, also known as personal probability, is based on personal judgment or belief. It reflects an individual's degree of belief in the likelihood of an event occurring, based on their own knowledge and experience.
Now, let's classify the statement in the prompt. The statement is "the probability of an earth-impacting asteroid causing a person's death is." We can see that the statement does not specify which type of probability is being used.
In conclusion, probability is a crucial concept in mathematics and science, and there are different types of probability, including classical, empirical, and subjective probability.
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Triangle AABC has side lengths of a = 16, b= 16 5, and c = 32 inches.
Part A: Determine the m/A. (5 points)
Part B: Show how to use the unit circle to find tan A. (2 points)
Part C: Calculate the area of AABC. (3 points)
Answer/Step-By-Step Explanation:
Part A:
To determine the measure of angle A (m/A), we can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab*cos(A)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
Substituting the given values, we have:
(32)^2 = (16)^2 + (16√5)^2 - 2(16)(16√5)*cos(A)
Simplifying:
1024 = 256 + 1280 - 512√5*cos(A)
512√5*cos(A) = 512
cos(A) = 1/√5
Using a calculator, we find:
A ≈ 63.43 degrees
Therefore, m/A ≈ 63.43 degrees.
Part B:
To use the unit circle to find tan A, we first draw a unit circle with its center at the origin of a coordinate plane. We then draw a ray from the origin through the point (1,0) on the circle, which corresponds to the angle of 0 degrees.
Next, we draw another ray from the origin through the point on the circle that corresponds to angle A. This ray intersects the circle at a point (x,y), where x = cos(A) and y = sin(A).
Since cos(A) = 1/√5, we have:
x = cos(A) = 1/√5
To find y, we use the Pythagorean theorem:
x^2 + y^2 = 1
Substituting x = 1/√5, we get:
(1/√5)^2 + y^2 = 1
y^2 = 4/5
y = ± 2/√5
Since angle A is in the first quadrant, we take y = 2/√5.
Therefore, tan(A) = y/x = (2/√5)/(1/√5) = 2.
Part C:
To calculate the area of triangle AABC, we can use Heron's formula, which states that:
Area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, given by:
s = (a+b+c)/2
Substituting the given values, we have:
s = (16+16√5+32)/2 = 24+8√5
Using this value of s, we can calculate the area:
Area = √[(24+8√5)(8√5-8)(8√5)(24-8√5)]
Simplifying:
Area = √[4096] = 64
Therefore, the area of triangle AABC is 64 square inches.
In this problem, we use the tangent function to solve for angle A, understand that the unit circle cannot be directly used to find the tangent of A, and finally find the area of the triangle using the formula 1/2*base*height.
Explanation:Part A: Assuming triangle AABC is a right triangle, we can determine m∠A by using the tangent function (tan ∠A = opposite side / adjacent side). Here, the opposite side is 'b' and the adjacent side is 'a'. So, m∠A = tan⁻¹ (b/a) = tan⁻¹ (16 5/16). To get the correct result, we then use a calculator with the inverse tangent or arctan function.
Part B: The unit circle is a fundamental tool in trigonometry. But in this case, having calculated m∠A in Part A, we cannot directly use the unit circle to find tan A as tan A is not represented on the unit circle.
Part C: The area of a triangle can be calculated using the formula 1/2*base*height. In a right triangle, this can be represented as 1/2*a*b: 1/2*16*16 5 = 130 square inches.
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I ready write and solve multiplication equations
Answer:
45x261
Step-by-step explanation:
261
x45
---------
11745
Harper ordered at a set of beads she recieved 20 beads and 60% of them were green how many green beeds did harper receive
Answer:
12
Step-by-step explanation:
Green beads
=60/100x20
=12
probabilities for parametric probability distribution models are expressed as what kind of probability?
The it is used to understand the likelihood of getting a particular outcome or event from a population.It is important to note that the probabilities for parametric probability distribution models are expressed as cumulative probabilities. Cumulative probabilities are used to evaluate the probability of a particular event or outcome.
Probabilities for parametric probability distribution models are expressed as cumulative probabilities.Parametric probability distribution refers to a type of probability distribution in which the probability distribution is defined by the probability distribution's parameters. The parameters are usually numeric values that define the distribution's probability density function (PDF) or probability mass function (PMF).The probability distribution is usually used to model a population's characteristics.
It is used to help understand the probability of obtaining a particular set of results from a population.Cumulative probabilities Cumulative probability refers to the probability of obtaining a score equal to or lower than a particular value in a given distribution. It is a probability value that is used in statistical analysis, which is usually represented by the area under the probability distribution's curve.The cumulative probability can be expressed as follows:P(X ≤ x)Where;X: random variablex: score or valueCumulative probabilities are used to evaluate the probability of a particular event or outcome.
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-2x + 14 >84 HELP PLEASE
Answer: x < -35
Step-by-step explanation: