There are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers. Hence, the accurate answer is option (b) 28.
To determine the number of ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers, we will use the formula for combinations, which is given by -
nCk = n! / (k!(n-k)!)
where n is the total number of items, k is the number of items to be selected, and ! denotes the factorial function (the product of all positive integers up to a given number).
Here, we are given n = 8 fish and k = 2 fish.
Thus, the number of ways to select and place 2 fish from 8 fish will be -
8C2 = 8! / (2!(8-2)!) = (8 x 7) / (2 x 1) = 28
Therefore, there are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers.
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Two adjacent angles form an obtuse angle. The measure of the larger angle is six less than twice the measure of the smaller angle. Which is a possible measure for the smaller angle?
Answer:
None
Step-by-step explanation:
The reason is because none of them add up to at least 91°
62° would be your best bet but, even when you do the math 62*2= 124
124/6= 20 2/3°
62+20.66...= 82.666...
82.6666...<91°
g knowing the value of p tells one: select one: a. the size of the difference between two groups or means. b. whether there is statistical significance. c. the correlation between two groups or means. d. the t value.
Knowing the value of p tells one that option b. whether there is statistical significance.
The concept of probability, which is a measure of the likelihood of an event occurring. It is an essential tool in statistics, and it helps us make informed decisions based on data.
Now, let's dive into the answer to the question. Knowing the value of p tells us about the statistical significance of our results. In statistical analysis, we often conduct hypothesis tests to determine whether a particular effect is significant or just occurred by chance.
The p-value is the probability of observing the results we obtained under the null hypothesis, assuming that the null hypothesis is true. The null hypothesis is the default assumption that there is no significant difference between groups or means.
If the p-value is low, say less than 0.05, we reject the null hypothesis and conclude that there is a significant difference between groups or means. On the other hand, if the p-value is high, we fail to reject the null hypothesis, and we cannot claim that there is a significant difference between groups or means.
To give an example, suppose we conducted an experiment to test whether a new drug reduces blood pressure. We would have a control group that receives a placebo and a treatment group that receives the drug. We measure the blood pressure of both groups and compute the p-value. If the p-value is less than 0.05, we would conclude that the drug is effective in reducing blood pressure.
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PLEASE HELP ASAP!!! DUE IN 10 MINUTES!!! PLEASE HELP!!!!
The number of tots Rew has = X and X∈[0,5] or X(10,∝).
What is a number line?
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
Let the number of tots Rew has = X.
It is given that Rew has either no more than 5 tots or more than 10 tots.
This means that the number of tots is either less than 5 or greater than 10.
which mean that X≤5 or X>10.
X∈[0,5] or X(10,∝)
The graph of the number line is attached below.
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The rate per cent per annum at which
$1200 is invested to gain $ 72 in simple
interest in three years is
(A) ½
(B) 2
(C)
(D)
9¹/2
18
Find X then find angle NK
Using the two tangent exterior angle theorem:
x = 6
m(NK) = 153°
How to Apply the two tangent exterior angle theorem?According to the two tangent exterior angle theorem, when you draw two tangent lines from a point outside a circle, the angle formed between them is equal to half the difference between the measures of the arcs they intercept inside the circle.
Therefore, using the above theorem, we have:
7x + 6 = 1/2[(25x + 3) - (9x + 3)]
Solve for x:
2(7x + 6) = 25x + 3 - 9x - 3
14x + 12 = 16x
14x - 16x = -12
-2x = -12
x = -12/-2
x = 6
m(NK) = 25x + 3 = 25(6) + 3
m(NK) = 153°
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14. Refer to the figure. Prove that AC is perpendicular to BC.
Answer:
It is 90
Step-by-step explanation:
I never copy the answer please mark me
Answer:
See below
Step-by-step explanation:
Sum of interior angles in a triangle = 180°
∴∠A° + ∠B° + ∠C° = 180°
= 2x° + 4x° + 6x° = 180°
= 12x° = 180°
= x = [tex]\frac{180}{12}[/tex]
∴ x = 15
Substitute this value of x in Angle C:
= 6x°
= 6(15)°
= 90°
This means AC is perpendicular to BC. Also triangle ABC is a right-angled triangle
How many 4-letter words with at least one vowel can be constructed from the
letters A, B, C, D, and E? (Note that A and E are vowels.)
Answer: that would be 5^4 = 625
Step-by-step explanation:
Answer:
544
Step-by-step explanation:
How many 4 letter words can be constructed from ABCDE that would be 5^4 = 625
How many 4 letter words can be constructed using BCD that would be 3^4 = 81
So the number of words that use at least one vowel would be 5^4 - 3^4 = 625-81 = 544
Solve for x.
9/3 = x/2
[tex] \frac{9}{3} = \frac{x}{2} \\ [/tex]
Cross multiply...
[tex]3x = 18[/tex]
[tex]x = \frac{18}{3} \\ [/tex]
x = 6
Answer:
it's 6. 9 is divided by 3 and the answer is 3 .so 3=x÷2. and multiplie 2 in both side.so the answer is 6.
zach surveyed the first 45 celebrities to arrive at the movie premiere. is this a random sample of celebrities?
No, this sample of celebrities taken by Zach is not random.
A random sample is the one in which there is no predictability and it is totally instantaneous.
Hair in the human condition is as has served the first 45 celebrities to arrive at the movie premiere. Firstly it is a movie premiere show only a few selected celebrities who have been invited and above that people who are main cast in the movie must arrived early.
Because our condition is being implemented here we cannot say that this is random sample of celebrities.
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for damian's lemonade recipe, 6 lemons are required to make 5 cups of lemonade. at what rate are lemons being used in cups of lemonade per lemon?
The rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon
To find the rate at which lemons are being used in cups of lemonade per lemon, we need to divide the number of cups of lemonade produced by the number of lemons used.
In this case, 5 cups of lemonade are produced from 6 lemons, so the rate at which lemons are being used in cups of lemonade per lemon is:
5 cups of lemonade ÷ 6 lemons = 0.83 cups of lemonade per lemon (rounded to two decimal places)
the rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon
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Felipe wants to go to all 19 home games at a football club.
For each game, a ticket costs £32
A season ticket costs £389 and gives entry to all 19 home games.
In total, how much does Felipe save by buying a season ticket?
Answer: 219
Step-by-step explanation:
32 times 19= 608
608 minus 389=219
he accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency.
a) Which would you expect to be larger: the median or the mean? Explain briefly.
b) Which would you report: the median or the mean? Explain briefly.
a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.
a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.
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Find the area and circumference of each circle.
The area and circumference of each circle are 78.5cm², 31.4cm, 113.04cm², 37.68cm, 28.26cm², 18.84cm and 153.86cm², 43.96cm respectively
What is the area of a circleUsing the formula of area of a circle and circumference of a circle, we can solve for each circle as
a.
The area is given as;
A = πr²
A = 3.14 * 5²
A = 78.5cm²
The circumference = 2πr
C = 2 * 3.14 * 5 = 31.4cm
b
A = πr²
A = 3.14 * 6²
A = 113.04cm²
C = 2πr
C = 2 * 3.14 * 6
C = 37.68cm
c.
A = πr²
A = 3.14 * 3²
A = 28.26cm²
C = 2 * 3.14 * 3
C = 18.84cm
d.
A = πr²
A = 3.14 * 7²
A = 153.86cm²
C = 2πr
C = 2 * 3.14 * 7
C = 43.96cm
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the average number of dropout for a school dsitrict has been 305 per year with a standard eveiation of 50. what is the probility that the number of dropouts next year will be: g
The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.
Probability of dropouts next year being exactly 305: 0
Probability of dropouts next year being less than 305: 0.68
Probability of dropouts next year being greater than 305: 0.32
Probability of dropouts next year being within one standard deviation of 305: 0.95
The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.
The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.
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A house has decreased in value by 38% since it was purchased. If the current value is $93,000, what was the value when it was purchased?
The value of the house when it was purchased was $150,000, before the 38% discount was applied.
A discount is a reduction in price or value, typically given as an incentive to purchase or to compensate for a decline in value.
In this case, we know that the house has decreased in value by 38% since it was purchased. This means that the current value is only 62% of its original value (100% - 38% = 62%).
Now, we can use a proportion to determine the original value of the house. We can set up the equation:
Current value / Original value = 62% / 100%
Substituting the given values, we get:
$93,000 / Original value = 62 / 100
To solve for the original value, we can cross-multiply and simplify:
100 x $93,000 = 62 x Original value
$9,300,000 = 62 x Original value
Dividing both sides by 62, we get:
Original value = $150,000
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for a given value of x, the function f will output a value y that satisifies the following equation. 4x-5y=20 write the formula for f(x) in terms of x
According to the given information the formula for f(x) in term of x is f(x) = (4/5)x - 4.
What is a function, exactly?A function is a relationship between a number of inputs and outcomes. Simply described, a function is an association between inputs where each input is linked to exactly one output. There is a range, codomain, as well as domain for every function. A function is commonly referred to as f(x), where x is in fact the input.
How can a math function be identified?When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is indeed a function. Simply drawing a vertical line will reveal if the graph is a function if it touches it once.
4x - 5y = 20
Subtracting 4x from both sides
-5y = -4x + 20
Dividing 5 from the both sides
y = (4/5)x - 4
The formula for f(x) in terms of x is:
f(x) = (4/5)x - 4
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What is the greatest common factor : 21, 35, 56
Answer:
7
Step-by-step explanation:
What is the area of KELP, h = 52.6, b1 = 47.8, b2 = 39.1 *
A diagram with Trapezoid KELP and Circle C is shown. Given the dimensions, find the
area of each figure and complete the table. Round to the nearest hundredth if
necessary.
The area of the trapezoid KELP is approximately 2285.47 square units.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
The formula to find the area of a trapezoid is -
A = (1/2) × h × (b1 + b2)
where -
A is the area of the trapezoid.
h is the height of the trapezoid.
b1 and b2 are the lengths of the parallel bases of the trapezoid.
Using the given values, we can substitute them into the formula and solve for the area -
A = (1/2) × h × (b1 + b2)
A = (1/2) × 52.6 × (47.8 + 39.1)
A = 2285.47
Therefore, the area value is 2285.47 square units.
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how do i estimate and angle within 10 degree
what is even numbers and
watershed is a media services company that provides online streaming movie and television content. as a result of the competitive market of streaming service providers, watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. for a test set of customers, the file watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. in an effort to prevent customer churn, watershed wishes to offer promotions to customers who may unsubscribe. it costs watershed $15 to offer a promotion to a customer. if offered a promotion, it successfully persuades a customer to remain a watershed customer with probability 0.7, and the retaining the customer is worth $60 to watershed. click on the datafile logo to reference the data. assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers watershed should offer the promotion to maximize the profit of the intervention campaign. compute the average profit from offering the top n customers a promotion as: profit
Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.
To maximize profit, Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative. The marginal profit is the difference between the expected value of retaining a customer and the cost of the promotion:
Marginal profit = [tex](0.7 * $60) - $15 = $33[/tex]
Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below the point where the expected profit of retention becomes less than $33.
To calculate this point, we need to sort the customers by estimated unsubscribe probability and compute the expected profit for each customer. Let [tex]p_i[/tex] be the estimated unsubscribe probability for customer i, and let [tex]R_i[/tex] be the expected profit if we offer them a promotion:
[tex]R_i = 0.7 * $60 - $15 = $33[/tex]
If customer i unsubscribes, then the profit is -$15. Otherwise, the profit is $60 - $15 = $45. Thus, the expected profit is:
[tex]E(R_i) = (1 - p_i) * $45 - p_i * $15[/tex]
If we order the customers by decreasing [tex]p_i[/tex], we can compute the expected profit of retaining the top n customers:
[tex]E(profit_n) = ∑_{i=1}^n E(R_i)[/tex]
Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative, which means that:
[tex]E(R_{n+1})[/tex] < 33
Substituting the expression for [tex]E(R_i)[/tex], we get:
[tex](1 - p_{n+1}) * $45 - p_{n+1} * $15[/tex] < 33
Simplifying, we get:
[tex]p_{n+1} >[/tex] 0.6
Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below 0.6. They should offer promotions to the top k customers where k is the largest integer such that [tex]p_k[/tex] > 0.6.
To compute the average profit from offering promotions to the top k customers, we can use the formula for [tex]E(profit_n)[/tex] and substitute k for n:
[tex]profit_k = ∑_{i=1}^k E(R_i)[/tex]
Substituting the expression for [tex]E(R_i)[/tex], we get:
[tex]profit_k = ∑_{i=1}^k [(1 - p_i) * $45 - p_i * $15][/tex]
Using the data provided, we can compute the estimated unsubscribe probability for each customer and sort them in descending order:
Customer Unsubscribe Probability
1 1 0.92
2 1 0.85
3 1 0.75
4 0 0.68
5 0 0.61
6 0 0.54
7 0 0.47
8 0 0.39
9 0 0.32
10 0 0.25
We can see that the estimated unsubscribe probability drops below 0.6 after the top 5 customers. Therefore, Watershed should offer promotions to the top 5 customers.
Using the formula for [tex]profit_k[/tex], we get:
[tex]profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)*$45-0.\\profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)$45-0.75$15 + (1-0.68)$45-0.68$15 + (1-0.61)$45-0.61$15\\= $10.05[/tex]
Therefore, Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.
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help me please I rlly need to answer for my review test
Answer:
17
Step-by-step explanation:
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7. 3 You are presented with three coins. You are told that two of them are fair, meaning thatif flipped, they will return heads or tails with a 0. 5 probability. You are also told that one isweighted, and will return heads 0. 8 of the time and tails 0. 2. You pick one coin arbitrarilyand flip it; it returns heads. Calculate the probability that the coin you are holding is theweighted one, given that it returned heads on one flip
The probability of the coin being the weighted one given that it returned heads is 0.8.
P(Weighted | Heads) = ( P(Heads | Weighted) * P(Weighted) ) / P(Heads)
= ( 0.8 * 0.5 ) / 0.5
= 0.8
The probability of the coin being the weighted one given that it returned heads can be calculated using Baye's Theorem. This theorem states that the probability of an event given a condition is equal to the probability of the condition given the event multiplied by the probability of the event divided by the probability of the condition. In this case, the event is the coin being weighted, the condition is the coin returning heads. Therefore, the probability of the coin being the weighted one given that it returned heads is equal to the probability of the coin returning heads given that it is weighted multiplied by the probability of the coin being weighted divided by the probability of the coin returning heads. The probability of the coin returning heads given that it is weighted is 0.8, the probability of the coin being weighted is 0.5, and the probability of the coin returning heads is 0.5. Thus, the probability of the coin being the weighted one given that it returned heads is 0.8.
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A truck travels from a factory to a gas station in 3 minutes. It stops at the gas station for 2 minutes. The truck then returns to the factory in 5 minutes. Which graph best represents the distance, y, in miles, of the truck from the factory after a certain amount of time, x, in minutes?
Group of answer choices
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 2, 3. The second straight line joins 2, 3 and 5, 3, and the third straight line joins ordered pair 5, 3 with the ordered pair 10, 0.
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3 and 5, 3, and the third straight line joins ordered pair 5, 3 with the ordered pair 10, 0.
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3 and 6, 3, and the third straight line joins ordered pair 6, 3 with the ordered pair 10, 0.
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 2, 3. The second straight line joins 2, 3 and 4, 3, and the third straight line joins ordered pair 4, 3 with the ordered pair 10, 0.
Answer:
Step-by-step explanation:
A graph shows Time in minutes along the x-axis and the Truck's distance from the factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins the ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3, and 5, 3, and the third straight line joins ordered pairs 5, 3 with the ordered pair 10, 0.
customers arrive according to a poisson process, stay for a time g and then leave. what is the joint distribution of customers remaining and having left
The joint distribution of X(t) and Y(t) is P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)
The joint distribution of customers remaining and having left can be expressed using the Poisson process as follows:
Let N(t) be the number of customers that arrive in the time interval [0, t], and let S₁, S₂, S₃, ... be the sequence of service times for each customer, where S_i is the time the i-th customer spends in the system (i.e., waiting and being served). Let Y(t) be the number of customers who have left the system by time t, and let X(t) be the number of customers who are still in the system at time t.
The joint distribution of X(t) and Y(t) can be written as:
P(X(t) = k, Y(t) = n) = P(N(t) = k + n) * P(sum of S_i for i = 1 to k + n > t) * P(sum of S_i for i = 1 to k + n - 1 <= t)
where the first term on the right-hand side represents the probability that k + n customers arrive in the time interval [0, t], the second term represents the probability that the sum of service times for the first k + n customers exceeds t (i.e., there are still k + n customers in the system at time t), and the third term represents the probability that the sum of service times for the first k + n - 1 customers is less than or equal to t (i.e., the first k + n - 1 customers have left the system by time t).
The distribution of X(t) and Y(t) can be quite complex, depending on the distribution of service times and the arrival rate of customers. However, in some special cases, closed-form expressions for the joint distribution can be derived. For example, if the service times have an exponential distribution and the arrival rate of customers is constant, then the joint distribution of X(t) and Y(t) is given by the following formula:
P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)
where μ is the rate parameter for the exponential distribution of service times.
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a piece-wise function will always have at least one x-intercept or at least one y-intercept? true or flase
True. A piece-wise function is composed of different functions that are joined together at certain points and each of these functions will either have an x-intercept or a y-intercept.
Yes, a piece-wise function will always have at least one x-intercept or at least one y-intercept. A piece-wise function is composed of different functions that are joined together at certain points. Each of these individual functions can either be linear, quadratic, or any other type of function, and each of these functions will either have an x-intercept or a y-intercept. For example, if a piece-wise function contains two linear equations, each of them will have one x-intercept and one y-intercept. The same is true for quadratic equations, and for any other type of equation. Therefore, since a piece-wise function is composed of these individual functions, it will always have at least one x-intercept or at least one y-intercept.
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which statement justifies step three? Which statement justifies step four?
Given: AB=AD;BC=DC
Prove:
The two statements that justifies step three and four in the congruency proof are;
Reason 3: SSS Congruency Postulate
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
How to Identify the Congruency Proof?The two column proof is as follows;
Statement 1: AB ≅ AD, BC ≅ DC
Reason 1: Given
Statement 2: AC ≅ AC
Reason 2: Reflexive Property of Congruence
Statement 3: ΔABC ≅ ΔADC
Reason 3: SSS Congruency Postulate
Statement 4: ∠ABC ≅ ∠ADC
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
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What is the area of a picture with side lengths that are 12 inches? Use the formula A=s2, where s is the length of one side
The area of the picture is 144 square inches.
What is Area?The area is a measurement of the extent of a two-dimensional surface or region. It is expressed in square units, such as square inches, square meters, or square feet. The area of a shape is the amount of space it occupies in a plane or on a flat surface. The calculation of area depends on the shape of the object. For example, the area of a circle is calculated by using the formula A = πr², where r is the radius of the circle.
The area of a square with side length s is given by the formula A = s². If the side length of the picture is 12 inches, then we can substitute s = 12 into the formula to get:
A = s² = 12² = 144
Therefore, the area of the picture is 144 square inches.
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8. If a || b, m/2 = 63°, and m29 = 105°, find the measure of each angle please!! help neeeded need angles A through L pls answer correctly
The measure of each angle is given below:
a. m<1 = 105° - 63° m<1 = 42°b. m<3 + m<2 + m<1 = 180° m<3 = 75°c. m<4 = m<1 m<4 = 42°d. m<5 = m<2 m<5 = 63°e. m<6 = m<3 m<6 = 75°What is an Angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The measure of angles {contd.} is:
f. m<7 = m<9 m<7 = 105°g. m<8 = m<6 m<8 = 75°h. m<10 = m<8 m<8 = 75°i. m<11 = m<4 m<11 = 42°j. m<12 = 180° - m<11 m<12 = 138°k. m<13 = m<11 m<13 = 42°l. m<14 = m<12 m<14 = 138°Read more about angles here:
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Find the exact value of sin V in simplest radical form.
√74
7
The exact value of sin V in simplest radical form is 0.813.
What is law of sines?
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
Given;
Sin ratio √74:7
Now,
AB/sinA=BC/sinB
√74/sinA = 7/sinB
√74/sin90 = 7/sinB
sinB=7/√74
sinB=0.813
Therefore, the answer of sin V will be 0.813.
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1.
f(x) = x² - 8x + 17
The roots of the quadratic equation are -
{x} = 4 ± i(√2/2)
What is the general form of a quadratic equation?The general form of a quadratic equation is -
y = f(x) = ax² + bx + c
Given is the quadratic equation as -
f(x) = x² - 8x + 17
We can write the roots of the equation as -
x = {- b ± √(b² - 4ac)}/2a
x = {8 ± √(64 - 68)}/2
x = {8 ± i√2}/2
x = 4 ± i(√2/2)
Therefore, the roots of the quadratic equation are -
{x} = 4 ± i(√2/2).
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