So the probability that Angela gets to go to the meeting is 2/5.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.
Here,
There are a total of 5 people in the club, so there are 10 possible pairs of people that could be chosen to go to the meeting. Since each pair is equally likely to be chosen, the probability of any particular pair being chosen is 1/10.
To determine the probability that Angela gets to go to the meeting, we need to count the number of pairs that include Angela. There are 4 other people in the club, so there are 4 possible pairs that include Angela. Therefore, the probability that Angela gets to go to the meeting is:
P(Angela) = number of pairs that include Angela / total number of pairs
= 4 / 10
= 2 / 5
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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 feet up. The ladder makes an angle of 71 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Answer:
30.7
Step-by-step explanation:
sin(71) = 29/x
x = 29/sin71
≈ 30.7
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
A) The completed table is given as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
B) the graph is attached accordingly.
C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
What is the explanation for the above response?a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.
We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.
D(L) = ceil(L/6)
Using this formula, we can complete the table as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).
b) The graph is attached.
c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.
So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.
In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
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The quadrilateral on the graph below is rotated about the point (0, 0). What are the new coordinates of Point B and Point C after a 90 degree clockwise rotation?
A 90 degree clockwise rotation about the point (0,0), the new coordinates of Point B are (3, -1) and the new coordinates of Point C are (1, -2).
How do you check if a quadrilateral is a rectangle on a graph?A quadrilateral can be proven to be a rectangle in a number different ways. Here are the three simplest methods: 1. Establish that all angles are 90 degrees; 2. Establish that two opposed angles are 90 degrees; and 3. Establish that the diagonals are equally long and intersect one another.
The following transformation matrix can be used to rotate a point (x,y) 90 degrees clockwise with respect to the origin (0,0):
|0 1|\s|-1 0|
This transformation matrix can be applied to each point to determine its new coordinates upon rotation.
Point B is the first point, and its initial coordinates are (-1, 3). The transformation matrix in use:
|0 1| |-1| |3|
|-1 0| x |3| = |-1|
After rotating Point B 90 degrees clockwise, the new coordinates are: (3, -1).
The transformation matrix is then applied to Point C, whose initial coordinates are (2, 1):
|0 1| |2| |1|
|-1 0| x |1| = |-2|
After rotating in a clockwise direction by 90 degrees, Point C's new coordinates are (1, -2).
As a result, after rotating 90 degrees in a clockwise direction around Point 0, Point B's new coordinates are (3, -1), while Point C's new coordinates are (1, -2).
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what is the answer of 10.9% of $8.85
Answer:
To find 10.9% of $8.85 we can convert the percentage into a decimal:
10.9% = 0.109
0.109x8.85 = $0.964
=$0.96 (Rounded to 2 decimal places)
Are quadrilaterals LMNO and PQRS similar?
Yes, quadrilaterals LMNO and PQRS are similar because a translation and a dilation map quadrilateral LMNO onto PQRS.
Yes, quadrilaterals LMNO and PQRS are similar because a rotation and a dilation map quadrilateral LMNO onto PQRS.
Yes, quadrilaterals LMNO and PQRS are similar because a reflection and a dilation map quadrilateral LMNO onto PQRS.
No, quadrilaterals LMNO and PQRS are not similar because their corresponding segments are not proportional.
The correct answer is (d) No, quadrilaterals LMNO and PQRS are not similar because their corresponding sides are not proportional.
What are quadrilaterals?A quadrilateral is a geometric shape with four sides and four corners.
To be classified as a quadrilateral, its shape must be a closed figure with four straight sides and four interior angles.
To determine quadrilaterals are similar, we need to check if corresponding angles are congruent and corresponding sides are proportional.
Checking corresponding angles are congruent:
∠ L to ∠P.
∠M to ∠Q.
∠ N to ∠ R.
∠O to ∠S.
All corresponding angles are congruent. Therefore, quadrilaterals have the same shape.
Check if corresponding sides are proportional.
LM =√((-1 - (-2))² + (4 - 2)²) = √(2² + 2²) = 2√2
MN = √((3 - (-1))² + (4 - 4)²) = √(4²) = 4
NO = √((4 - 3)² + (2 - 4)²) = √(2² + 2²) = 2√(2)
OL = √((-2 - 4)² + (2 - (-6))²) = √(6² + 8²) = 10
PQ = √((4 - 2)² + (-2 - (-6))²) = √(2² + 4²) = 2√5
QR = √((12 - 4)² + (-2 - (-2))²) = √(8²) = 8
RS = √((15 - 12)² + (-6 - (-2))²) = √(3² + 4²) = 5
SP = √((2 - 15)² + (-6 - (-6))²) = √(13²) = 13
LM / PQ = (2√2) / (2√5) = √(8/5)
MN / QR = 4 / 8 = 1/2
NO / RS = (2√(2)) / 5√(1) = (2/5)√(2)
OL / SP = 10 / 13
The corresponding sides are not proportional because they are not all equal or proportional to each other. Therefore, we can conclude that the quadrilaterals LMNO and PQRS are not similar.
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COMM 291C Applications of Statistics in Business
Winter 2023
Assignment 07
1. A fish tank is filled with the fish of three different species, and each fish comes in three sizes. The
counts of all the fish are summarized in the following contingency table:
Small Medium Large Total
Goldfish 48 45 19 112
Guppy 70 42 19 131
Gourami 40 9 10 59
Total 158 96 48 302
a. If I randomly catch any one fish from this tank, what is the probability that the caught
fish is medium-sized? Show your calculations. (1)
b. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
medium-sized guppy? Show your calculations. (1)
c. If I randomly catch one medium-sized fish from this tank, what is the probability that the
caught fish is a guppy? Show your calculations. (1)
d. If I randomly catch one guppy from this tank, what is the probability that the caught fish
is medium-sized? Show your calculations. (1)
e. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
not a goldfish? Show your calculations. (1)
f. Are two events, randomly catching a guppy and randomly catching a medium-sized fish,
independent? Explain how you know. (2)
a) If I randomly catch any one fish from this tank, the probability of catching a medium-sized fish from the tank is 0.3182.
b) the probability of catching a medium-sized guppy from the tank is 0.1391.
c) the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d) the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e) the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f) 0.1384 is not equal to 0.1391, which indicates that the two events are not independent
Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.
The explanation to the above probability answer are given below:
a)
From the contingency table, we can see that the total number of medium-sized fish is 96. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized fish is:
Probability of catching a medium-sized fish = Total number of medium-sized fish / Total number of fish
Probability of catching a medium-sized fish = 96 / 302
Probability of catching a medium-sized fish = 0.3182
Therefore, the probability of catching a medium-sized fish from the tank is 0.3182
b)
From the contingency table, we can see that the total number of medium-sized guppies is 42. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized guppy is:
Probability of catching a medium-sized guppy = Total number of medium-sized guppies / Total number of fish
Probability of catching a medium-sized guppy = 42 / 302
Probability of catching a medium-sized guppy = 0.1391
Therefore, the probability of catching a medium-sized guppy from the tank is 0.1391.
c)
From the contingency table, we can see that the number of medium-sized guppies is 42, and the number of medium-sized fish is 96. Therefore, the probability of catching a guppy if we randomly select a medium-sized fish is:
Probability of catching a guppy given a medium-sized fish = Number of medium-sized guppies / Total number of medium-sized fish
Probability of catching a guppy given a medium-sized fish = 42 / 96
Probability of catching a guppy given a medium-sized fish = 0.4375
Therefore, the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d)
To calculate the probability of catching a medium-sized guppy if we randomly select a guppy from the tank, we need to find the number of medium-sized guppies in the tank and divide it by the total number of guppies in the tank.
From the contingency table, we can see that the number of medium-sized guppies is 42, and the total number of guppies is 131. Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is:
Probability of catching a medium-sized guppy given a guppy = Number of medium-sized guppies / Total number of guppies
Probability of catching a medium-sized guppy given a guppy = 42 / 131
Probability of catching a medium-sized guppy given a guppy = 0.3206
Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e)
From the contingency table, we can see that the total number of non-goldfish is 190 (45 medium goldfish + 70 small guppy + 42 medium guppy + 9 medium gourami + 10 large gourami + 14 small gourami). The total number of fish in the tank is 302. Therefore, the probability of catching a fish that is not a goldfish is:
Probability of catching a fish that is not a goldfish = Total number of non-goldfish / Total number of fish
Probability of catching a fish that is not a goldfish = 190 / 302
Probability of catching a fish that is not a goldfish = 0.6291
Therefore, the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f)
From the contingency table, we can see that the probability of randomly catching a guppy is 131/302, which is approximately 0.4344. Similarly, the probability of randomly catching a medium-sized fish is 96/302, which is approximately 0.3182.
Now, let's consider the joint probability of randomly catching a medium-sized guppy, which we calculated earlier to be 42/302, or approximately 0.1391. To determine if the events are independent, we need to compare the product of the probabilities of the individual events (catching a guppy and catching a medium-sized fish) to the joint probability of the events occurring together.
If the events are independent, then the product of their individual probabilities should be equal to the joint probability:
P(catching a guppy) x P(catching a medium-sized fish)
= P(catching a medium-sized guppy)
0.4344 x 0.3182 = 0.1391
0.1384 is not equal to 0.1391, which indicates that the two events are not independent.
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(1 − cos 0) (1 + cos 0)= 1/csc²0
Step-by-step explanation:
lol sorry for untidy work
Answer the question below
Answer:
Step-by-step explanation:
This question's answer is 'c'. In the first function here we put the value of x=0, then y =3 but in the second function if we put the value of x=0 then y =2. so c is the correct answer.
GIVING BRAINLIST WHOEVER GETS IT RIGHT!!!!!!!!!!!!!!!!!!!! Select the correct answer.
Sam's height is 15 centimeters less than 2 times Martha's height. If Sam is 185 centimeters tall, and Martha's height is x, the relationship between the heights can be represented by the equation 2x − 15 = 185. What is Martha's height?
Step-by-step explanation:
The equation 2x − 15 = 185 represents the relationship between Sam's and Martha's heights. We can solve for x, which represents Martha's height, by isolating x on one side of the equation:
2x − 15 = 185
Add 15 to both sides of the equation:
2x = 200
Divide both sides of the equation by 2:
x = 100
Therefore, Martha's height is 100 centimeters.
If i have a 97% grade and i get a 75% on a quiz that counts 7% of my grade, how much is my grade? (37 points)
Answer: 90.32%
Step-by-step explanation:
To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:
New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)
Plugging in your values, we get:
New grade = (97 * (100 - 7)) + (75 * 7)
New grade = (97 * 93) + (5.25)
New grade = 903.16
Therefore, your new grade is 90.32%.
Answer: The sum of the weight of all your coursework plus your final is equal to 14.00
Step-by-step explanation:
not sure
the length of a rectangle is 9 centimeters less than its width. what are the rectangles dimension if its area is 90.
Length of rectangle in cm:
Width of rectangle in cm:
Let the width of the rectangle be "X". Then the length of the rectangle will be (X-9).
Formula to find the area of a rectangle is given by-
[tex] \small \underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} = Length\times Width }}}}\\[/tex]
On substituting the values-
[tex] \:\:\:\:\:\:\longrightarrow \sf {Area_{(rectangle)} = X \times \bigg(X-9\bigg)}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {90 = X^2 -9X}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X =90}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-15X+6X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X\bigg(X-15\bigg) +6\times \bigg(X-15\bigg)=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {\bigg(X-15\bigg) \times \bigg(X+6\bigg) =0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{X = 15\: Or,\: -6}}}}\\[/tex]
Since,width cannot be (Negative) , so the width will be 15cm.And the length will be (X-9)= (15-9)=6cm.
1/4 x5/3 as a fraction
The product of the fraction 1/4 x5/3 is 4/12
What are fractions?Fractions are defined as the part of a whole number, variable or element.
The different types of fractions in mathematics are;
Simple fractions.Proper fractions.Improper fractions.Complex fractions.Mixed fractions.Examples of simple fraction; 1/4, 2/3
Examples of improper fractions; 3/2. 4/3
Examples of proper fractions; 1/2, 2/3
From the information given, we have that;
1/4 x5/3
To determine the product, we need to multiply the numerator, then multiply the denominator
5/12
We can no longer divide the values as there is no common divisor.
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Jacque bought 2.5 pounds of dark chocolate covered pecans at $0.30 per ounce. In dollars and cents, what was the cost of these pecans?
Answer:
$12.00
Step-by-step explanation:
We know that 1 pound = 16 oz. Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:
[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]
Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:
40 * 0.30 = $12.00
what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Therefore , the solution of the given problem of unitary method comes out to be enable the current to travel, a connection, such as a wire or conductor, is required.
What is a unitary method?Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.
Here,
D. In order for a current to move, there must be an energy source, a recipient, and a connection.
Current is the movement of charged ions through a conductor, most frequently electrons.
The energy required to transport the charged particles is provided by an energy source, such as a battery or generator.
The current has a route through a recipient, which can be a machine or a circuit.
In order to finish the circuit and enable the current to travel, a connection, such as a wire or conductor, is required.
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In a recent survey, 60% of the community favored building a supermarket in their neighborhood. If 25 citizens are chosen, what is the variance of the number favoring the supermarket?
The variance of the number of citizens favoring the supermarket is 6.
To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:
Variance = n × p × (1 - p)
where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.
Plugging in the values, we get:
Variance = 25 × 0.6 × (1 - 0.6)
Variance = 25 × 0.6 × 0.4
Variance = 6
The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.
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Compute the probability that a randomly selected person does not have a birthday on the 1st day of the month.
Answer:
0.9973 or 364/365
Step-by-step explanation:
Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.
Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:
P(not on 1st day) = 1 - P(on 1st day)
P(not on 1st day) = 1 - 1/365
P(not on 1st day) = 364/365
So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.
what is the average allowance for each student?
$7,$12,$8.50,$10,$7,$8,$10.50,$11
The average allowance for each student is $9.25.
What is the average allowance for each student?To find the average allowance for each student, we need to add up all the allowances and divide by the total number of students.
Adding up the allowances:
$7 + $12 + $8.50 + $10 + $7 + $8 + $10.50 + $11 = $74
There are 8 students, so we divide the total allowance by 8 to get:
$74 / 8 = $9.25
Therefore, the average allowance for each student is $9.25.
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On a field trip, the ratio of adults to students is 1:8. Which of the following statements about the field trip must be true? (A) A total of 9 people went on the field trip. B. The total number of people on the trip is a multiple of 8. C. There were 7 more students than adults on the field trip. D. There were 8 times as many students as adults on the field trip.
Answer:
B
Step-by-step explanation:
The correct answer is B. The total number of people on the field trip must be a multiple of 9 (1 adult and 8 students).
A is not true because if there were only 9 people, there could not be both an adult and 8 students, and the ratio would not be 1:8.
C is not necessarily true. It is possible that there were more adults than students on the field trip, or that the ratio was not an exact 1:8.
D is not true because if there were 8 times as many students as adults, the ratio would be 1:64, not 1:8
Simplify the expression below.
5^2 + 9^2
To simplify the expression 5^2 + 9^2, we can evaluate the squares of 5 and 9 and then add the results:
5^2 = 5 x 5 = 25
9^2 = 9 x 9 = 81
So, 5^2 + 9^2 = 25 + 81 = 106
Therefore, the simplified form of the expression 5^2 + 9^2 is 106.
Select all that apply.
Graphs of parabolas can be found in:
Quadrant III
Quadrant II
Quadrant IV
Quadrant I
PLS HELP MEEEEEEEEEEEEEEEEEE I CAN'T ANSWER
A. Tell whether distance, speed, or time is asked in each given situation.
_____1. How long will it take Zihann to arrive at school if she walks a constants 2 kilometers per hour?
_____2. How far do you need to travel at an average speed for 5 hours?
_____3. How fast should you travel to arrive at your destination that is 2.5 hours away?
_____4. If Carla travels a distance of 150 kilometers and arrive after 3 hours, how fast did she drive?
_____5. If Alwyn drove at an average speed to travel a certain distance, how long did it take him to travel?
A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
Which of the following completes the equation 30 100 + 9 10 ?
The expression that completes the equation the result of 30/100 + 9/10 is 1.2.
What fundamental equation format is used?The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. When attempting to solve problems containing two linear equations, this form is also quite helpful.
We must multiply the values of 30 and 100, then add the resulting product to the resulting product of the values of 9 and 10 in order to complete the equation 30 100 + 9 10.
The result of multiplying 30 by 100 is:
30 x 100 = 3000
The result of adding 9 and 10 is:
9 x 10 = 90
Thus, we must combine these two items to finish the equation:
3000 + 90 = 3090
30100 + 910 = 3090, which is the expression that completes the equation.
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the complete question is:
complete the equation
[tex]\frac{30}{100}+\frac{9}{10}[/tex]
Answer:
The answer is 39/100
Step-by-step explanation: Nothing more.
Just curious to know
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
what is percentage ?Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.
given
If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.
You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:
1000 x 67% = 670
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
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The complete question is :-
Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?
Possible Answers:
3,700
57,000
67
None of the given answers
670
PLEASE HELP! Find missing side lengths of B and C. Explain
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
In PQR, PQ= 5.4, QR= 3.6, and PR=6.2. To the nearest Tenth, what is M∠R
Therefore , the solution of the given problem of angles comes out to be M∠R measured at 45.4 degrees, to the closest tenth.
An angle meaning is what?The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.
Here,
To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:
=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)
=> cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)
=> cos(R) = 0.6960917
When we calculate the inverse cosine of both sides, we obtain:
=> R = cos⁻¹(0.6960917)
=> R equals 45.4 degrees
Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.
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13. The profit, in thousands of dollars, from the sale of x kilogram of coffee bean can be modelled by the function () = 5−400 +600 . a) State the asymptotes and the intercepts. Then, sketch a graph of this function using its key features. (5 pts) b) State the domain and range in this context. (2 points) c) Explain the significance of the horizontal asymptote. (1 point) d) Algebraically, find how much amount of tuna fish, in kg, should be sold to have a profit of exactly $4000? (4 points) SOLUTION
Answer: a) The profit function can be written as:
P(x) = 5x - 400x + 600
To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:
5x - 400x + 600 = 0
Solving for x, we get:
x = 1.5 and x = 2.5
Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.
b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.
The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:
x = -b/(2a) = -(-400)/(2(-200)) = 1
Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:
P(1) = 5(1) - 400(1) + 600 = 205
Since the coefficient of x^2 is negative, the range is (-∞, 205].
c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.
d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:
5x - 400x + 600 = 4000
Simplifying, we get:
-395x = -3400
Dividing both sides by -395, we get:
x ≈ 8.61
Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.
Step-by-step explanation:
rx+sy=24
4x+16y=120
In the system of equations above, r and s are
constants. If the system has an infinite number of
solutions, what is the value of rs
?
The values of r and s, considering that the system has an infinite number of solutions, are given as follows:
r = 4/5.s = 16/5.How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The number of solutions of a system of two linear functions is given as follows:
Infinity solutions: same slope and intercept.Zero solutions: same slope, difference intercepts.One solution: different slopes.For this problem, the system has an infinite number of solutions, meaning that the equations are multiples, thus the values of r and s are given as follows:
120/24 = 5.r = 4/5.s = 16/5.More can be learned about linear functions at https://brainly.com/question/24808124
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You pick a card at random. 6 7 8 9 What is P(less than 8)?
Answer:
50% chance
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