The probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
What is Bayes' theorem?Bayes' theorem is used to update probabilities of a hypothesis or an event in light of new data or evidence. It is used to calculate the conditional probability of an event based on prior knowledge of the conditions that might be relevant to the event.In the given problem, we have to find the probability that the response indicated that the dog is small-sized given that they enjoyed the treat.
The probability that the dog is small-sized given that they enjoyed the treat is the conditional probability P(S|T), where S is the event that the dog is small-sized and T is the event that they enjoyed the treat. To find the value of P(S|T), we will use Bayes' theorem. Bayes' theorem states that P(S|T) = P(T|S) * P(S) / P(T) where P(T|S) is the probability that they enjoyed the treat given that the dog is small-sized, P(S) is the prior probability that the dog is small-sized, and P(T) is the probability that they enjoyed the treat.
P(S) = 3/7P(T|S) = 2/3P(T) = (2/3 * 3/7) + (1/4 * 4/7) = 18/84 + 4/28 = 1/3
(adding the probabilities of T given S and T given L)Therefore, P(S|T) = (2/3 * 3/7) / (1/3) = 2/7 = 0.285714...Rounding off to the nearest millionth, the probability is 0.286. Therefore, the probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
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You are dealt five cards from a standard deck of 52 playing cards (A full house consists of three of one kind and two of another. For example, A A A 5-5 and K-K-K 10-10 are full houses) (a) in how many ways can you get a full house? ______ Ways (b) in how many ways can you get a five card combination containing two jacks and three aces ___ ways
The 32 ways to get a five-card combination containing two jacks and three aces.
(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.
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write down the name of shape W
A hexagon with two lines
hope helped you please make me brainalist and keep smiling dude
I hope you are form India
Alfonso wants to purchase a pool membership
for the summer. He has no more than y dollars to
spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.
The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y
Identifying the system of inequalitiesLet's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,
Let S represent the total cost of purchasing a pool membership from the Swimming Hole.
Then we can write the following system of inequalities:
A = 75 + 20x (total cost of Aquatics Club membership)
S = 15 + 65x (total cost of Swimming Hole membership)
Alfonso has no more than y dollars to spend
So, we have
75 + 20x ≤ y
15 + 65x ≤ y
Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y
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using the net below find the area of the triangular prism
6 cm
3 cm
4 cm
6 cm
5 cm
2 cm
Answer:153
Step-by-step explanation:
when performing regression, why would you want to have a quadratic term? group of answer choices you never want to add a quadratic term when performing regression to better fit a scatterplot with too many outliers to better fit a scatterplot that shows a curve in the data to better fit linear data
So, the right response is that, in order to more accurately fit the scatterplot that depicts a curve in the data, you need add a quadratic component while performing regression.
What is the quadratic term count?As ax² +bx + c, a quadratic equation can be expressed. In a quadratic equation, the largest exponent is 2, which limits the number of terms to a maximum of 3. These terms are exponent 2 (ax²) and exponent 1 (bx) fixed term.
Regression can be improved by including a quadratic component to better match scatterplots of data that display curves. This is so that the independent and dependent variables can have a nonlinear connection, which is made possible by a quadratic term. A quadratic component can assist capture inherent curvature of a data and enhance the fit of a regression model in cases where the connection between both the variables isn't really strictly linear.
A quadratic term may not be appropriate or required, though. A quadratic factor would not increase the model's fit if the variables' relationships are strictly linear and might even result in overfitting. In addition, if the scatterplot contains too many anomalies or the data is not consistent, adding a quadratic factor might not be beneficial.
In order to properly fit a scatter plot graph that depicts a curve in the data, the correct response is you would like to add a quadratic term while performing regression.
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A sandwich shop owner observed the first 100 sandwich orders of the day. The data that the owner obtained is given in the table.
Type of Sandwich Number of Customers
Vegetarian 30
Turkey 20
Ham 35
Chicken 15
Which of the following circle graphs correctly represents the data in the table?
a circle graph with four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent
a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent
a circle graph with four sections, labeled chicken 30 percent, vegetarian 20 percent, turkey 35 percent, and ham 15 percent
a circle graph with four sections, labeled ham 30 percent, chicken 20 percent, vegetarian 35 percent, and turkey 15 percent
Question 6(Multiple Choice Worth 2 points)
The circle graphs which correctly represents the data in the table is "a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent"
The correct answer choice is option B.
Which of the following circle graphs correctly represents the data in the table?Type of Sandwich Number of Customers
Vegetarian 30
Turkey 20
Ham 35
Chicken 15
Total number of customers = 30 + 20 + 35 + 15
= 100
Percentage of each sandwich:
Vegetarian = 30/100 × 100
= 30%
Turkey = 20/100 × 100
= 20%
Ham = 35/100 × 100
= 35%
Chicken = 15/100 × 100
= 15%
Therefore, a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent represents the table.
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What is an equation for the quadratic function represented by the table shown?
Find the value of 2 - 3x when x = 7
2 - 3x is a(n)__________.
Therefore, when the equation x = 72 - 3x, the value of 2 - 3x is -52.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.
Here,
When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:
x + 3x = 72
Combining like terms, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Now that we know x = 18, we can substitute this value into the expression 2 - 3x:
2 - 3x = 2 - 3(18)
2 - 3x = 2 - 54
2 - 3x = -52
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machines at a factory produce circular washers with a specified diameter. the quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. the null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. the alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. which of the following describes a type i error that could result from the test? responses the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. a type i error is not possible for this hypothesis test.
Answer:
the test does not provide convincing evidence that the proportion is greater than 90%
the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. what is the effect on the weight when the distance is multiplied by 2?
The weight becomes 1/4 of its original value when the distance is multiplied by 2.
According to the question, "the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth." We need to determine the effect on the weight when the distance is multiplied by 2.
Let w be the weight of a body, d be the distance from the center of the earth, and k be the constant of variation. According to the question,
w = k / d²
When the distance is multiplied by 2, the new distance is 2d. Therefore, the new weight is given by:
w' = k / (2d)²
w' = k / 4d²
w' = w / 4
Therefore, the weight becomes 1/4 of its original value when the distance is multiplied by 2.
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I NEED HELPP PLEASEEEEEEEE
The slope between the points (-3, 0) and (0, -1) is -1/3.
What is slope?The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.
Let us consider the first two points (-3, 0) and (0, -1).
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the values we have:
m = (-1 - 0) / (0 - (-3)) = -1/3
Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.
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Round the answer to the nearest hundredth
Using trigonometric functions, the value of the side AC = 2.85 units.
What are trigonometric functions?The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.
The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.
Now in the given figure,
The angle is a right-angled triangle.
Now as per the trigonometric functions,
Sin 35° = AC/AB
⇒ 0.57 = x/5
⇒ x = 0.57 × 5
= 2.85.
The length of the opposite side AC is 2.85 units.
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Factor completely.
7b^2-63
Thank you :DDD
Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=b[/tex] and [tex]b=3[/tex]
Answer:[tex]7(b+3)(b-3)[/tex]Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than coin B?
The probability that more heads are tossed using coin A than coin B is 5/16.
The given data is: Coin A is tossed three times and coin B is tossed two times. We have to find the probability that more heads are tossed using coin A than coin B.
P(E) = Number of favorable outcomes/ Total number of possible outcomes
Coin toss:
There are two possible outcomes in a coin toss, Head or Tail. The probability of getting a head in a coin toss is
1/2 = 0.5.
Therefore, the probability of getting a tail in a coin toss is also 1/2 = 0.5.
Let's calculate the possible outcomes when coin A is tossed three times.
There are 2 possible outcomes when one coin is tossed.
Number of possible outcomes when three coins are tossed = 2 * 2 * 2 = 8
Likewise, the possible outcomes when coin B is tossed two times are:
The number of possible outcomes = 2 * 2 = 4
Therefore, the total number of possible outcomes = 8 * 4 = 32
Now, we will find out the cases where the number of heads is more when coin A is tossed three times.
HHH HHT HTH HTT THH THT TTH TTT HHT HTT THT TTT TTH TTT HTT TTT THT TTT TTT TTT
Therefore, the number of times when more heads are obtained when coin A is tossed three times is 10. (We have to exclude the case when there is an equal number of heads.)
Therefore, the required probability is: P = Number of favorable outcomes/ Total number of possible outcomes
P = 10/32P = 5/16
Therefore, the probability that more heads are tossed using coin A than coin B is 5/16.
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How to graph it on a coordinate plan to the right 5x-3y=18
Tο shift the graph tο the right, we can simply add a pοsitive cοnstant tο the x values οf each pοint befοre plοtting them. Fοr example, if we want tο shift the graph tο the right by 2 units.
What is cοοrdinate plan?The intersectiοn οf twο number lines creates a twο-dimensiοnal plane knοwn as a cοοrdinate plane. The x-axis, a hοrizοntal number line, and the y-axis, a vertical number line, are twο examples οf these number lines.
Tο graph the equatiοn 5x - 3y = 18 οn a cοοrdinate plane, we can fοllοw these steps:
1. Sοlve fοr y in terms οf x:
5x - 3y = 18
-3y = -5x + 18
y = (5/3)x - 6
2. Chοοse sοme values fοr x and use the equatiοn tο find the cοrrespοnding y values. Fοr example, we can chοοse x = 0, 3, and 6:
When x = 0: y = (5/3)(0) - 6 = -6
When x = 3: y = (5/3)(3) - 6 = -3
When x = 6: y = (5/3)(6) - 6 = 2
3. Plοt the pοints (0, -6), (3, -3), and (6, 2) οn the cοοrdinate plane.
4. Draw a straight line passing thrοugh these three pοints. This line represents the graph οf the equatiοn 5x - 3y = 18.
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PLEASE HELP WILL GIVE BRAINLIEST.
Given f(x)=sin x and g(x)=cos x show that f(g(pi/2))=0. Show all your steps.
Answer:
Step-by-step explanation:
xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc
First, we need to find the value of g(pi/2):
g(pi/2) = cos(pi/2) = 0
Now we can substitute this value into f(x):
f(g(pi/2)) = f(0) = sin(0) = 0
Therefore, f(g(pi/2)) = 0.
Luke bought 4 kilograms of apples and 0.29 kilograms of oranges. How much fruit did he buy
in all?
He bought 4.29 Kilos of fruit.
4+0.29=4.29
Luke bought 4.29 kilograms of fruit in all
Step-by-step explanation:
Simple addition will be used to find the total fruit Luke bought.
Given
Amount of apples he bought = 4 kilograms
Amount of oranges he bought = 0.29 kilograms
so the total fruit will be:
[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]
[tex]=4+0.29[/tex]
[tex]=4.29[/tex]
So,
Luke bought 4.29 kilograms of fruit in all
Keywords: Measurement, addition
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Let A, B, and C be subsets of some universal set U. (a) Draw two general Venn diagrams for the sets A, B, and C. On one, shade the region that represents A - (B nC), and on the other, shade the region that represents (A -B) U (A C). Based on the Venn diagrams, make a conjecture about the relationship between the sets A-(BnC) and (A -B)U (A -C). (b) Use the choose-an-element method to prove the conjecture from Exer- cise (5a). (c) Use the algebra of sets to prove the conjecture from Exercise (5a).
In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.
To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].
This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).
To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).
We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).
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cala used 4 2/3 cups of watermelon and 2 1/6 cups of cherries to make a fruit bowl how many cups of watermelon and cherries were used in all
Answer:
6 5/6 cups
Step-by-step explanation:
Add.
4 2/3 = 4 4/6
4 4/6 + 2 1/6 gives 6 5/6 cups were used in all.
Hope this helps!
Which choice is an exponential function?
Of(x)=x²+6
Of(x)=5(3)*
Of(x) = 3x + 7
Of(x) = |2x+ 41
Answer:1st one
Step-by-step explanation:
an equation of a circle is given by (x+3)^2+(y_9)^2=5^2 apply the distributive property to the square binomials and rearrange the equation so that one side is 0.
The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].
Given:
Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]
Expand the equation
[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]
[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]
[tex]5^2 = 25[/tex]
Then, substitute the expanded expressions into the equation
[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]
Simplify and combine like terms
[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]
Rearrange the equation so that one side is 0
[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.
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What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.
According to the question:
To find the zeros of the function
f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.
So we start with the equation:
x² + 7x - 60 = 0
Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:
x² + 7x - 60 = (x + 12)(x - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 12 = 0 or x - 5 = 0
Solving for x, we get:
x = -12 or x = 5
The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.
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Two ropes are attached to a tree, and forces of F_1 = 1.31 + 4.6J n and F_2 = 3.2i + 6.8j n are applied. The forces are coplanar (in the same plane). What is the resultant (net force) of these two force vectors (in N)? (Express your answer in vector form.) Find the magnitude (in N) and direction (in degrees counterclockwise from the +x-axis) of this net force.
The magnitude and direction of the net force are found by adding the two forces together as resultant force vectors.
a) 11.82 N
b) 74.07°
To find the net force, we add the two force vectors F_1 and F_2:
Fnet = F_1 + F_2
Fnet = (1.31 + 4.6j) N + (3.2i + 6.8j) N
Fnet = 3.2i + (1.31 + 4.6j + 6.8j) N
Fnet = 3.2i + (1.31 + 11.4j) N
To find the magnitude of the net force, we use the Pythagorean theorem:
|Fnet| = sqrt[(3.2)^2 + (1.31 + 11.4)^2] N
|Fnet| ≈ 11.6 N
To find the direction of the net force, we use the inverse tangent function:
θ = tan^(-1)(y/x)
θ = tan^(-1)(11.4/3.2)
θ ≈ 73.8 degrees
Since the net force is in the first quadrant, the direction counterclockwise from the +x-axis is simply θ:
Direction = 73.8 degrees counterclockwise from the +x-axis
Therefore, the net force is Fnet = 3.2i + (1.31 + 11.4j) N, with a magnitude of approximately 11.6 N and a direction of approximately 73.8 degrees counterclockwise from the +x-axis.
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HELP PLS ILL GIVE U POINTS
Answer:
i think 16 im not sure
Step-by-step explanation:
I need help with these 2 please
Question 7. C (rectangular pyramid)
Question 8. 17 cm
Answer:
Question 7:C rectangular pyramid
Question 8: C 120 in
A=2(wl+hl+hw)=2·(10·2+5·2+5·10)=160
Step-by-step explanation:
The graph shows the velocity, v metres per second, of a car at time t seconds. Work out an estimate for the distance the car travelled for the first 8 seconds. Use 4 strips of equal width. -1-500- -1000- -500 0 V t
please help!!!
To estimate the distance traveled we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.
Define velocity-time graph?A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.
The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.
Using the trapezium rule, the estimated area of each strip is:
Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s
Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s
Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s
Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s
The total estimated area is the sum of the areas of the 4 strips:
Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s
Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:
Estimated distance traveled is = |-4000| = 4000 meters
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Please help quick with this question.
Answer:
b = [tex]\frac{S-2la}{h+l}[/tex]
Step-by-step explanation:
S = bh + lb + 2la ( reversing the equation )
bh + lb + 2la = S ( subtract 2la from both sides )
bh + lb = S - 2la ← factor out b from each term on the left side
b(h + l) = S - 2la ← divide both sides by (h + l)
b = [tex]\frac{S-2la}{h+l}[/tex]
The average between 3. 15 and x is 40 what is x?
The value of x that makes the average between 3.15 and x equal to 40 is 76.85.
In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:
(3.15 + x) / 2 = 40
To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.
To solve for x, we can start by multiplying both sides of the equation by 2:
3.15 + x = 80
Next, we can subtract 3.15 from both sides of the equation:
x = 76.85
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20x50x30x50 = ?
Please answer someone!!
Answer: 1500000
Step-by-step explanation:
use a calculator
Answer:
1,500,000
Step-by-step explanation:
Breaking it up into an easier problem:
20x50 = 1,000
30x50=1,500
1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.
Thus, the answer is 1,500,000
HELP
Given the information in the diagram of circle P below, find:
Based on the information in the diagram of circle P, the magnitude of the missing angle are as follows;
m∠BPC = 80 degrees.
m∠ADC = 205 degrees.
What is the central angle property?In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.
Based on the information provided about circle P, the central angle of circle P is represented by m∠BPC and the measure of arc BC is equals to 80 degrees. Therefore, the magnitude of angle BPC is given by:
m∠BPC = 80 degrees.
Since m∠A is an inscribed angle, its magnitude can be calculated as follows;
m∠A = 1/2(m∠BPC)
m∠A = 1/2(80)
m∠A = 40 degrees.
For the magnitude of m∠ADC, we have:
m∠ADC = 360 - (80 + 75)
m∠ADC = 360 - 155
m∠ADC = 205 degrees.
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