Answer:can you copy and paste it?
Step-by-step explanation:
when the base and leg side of right triangle are the same what is the angel measure fo the hypotenuse?
the measure of the hypotenuse angle must be 180 - (45 + 45) = 90 degrees .The angle measure of the hypotenuse in this case would be 45 degrees.
In right triangles, the angles of the triangle always add up to 180 degrees. Since the base and leg side of the triangle have the same measure, the two angles opposite of them must both be 45 degrees. Thus, the measure of the hypotenuse angle must be 180 - (45 + 45) = 90 degrees.In right triangles, the sum of the angles is always 180 degrees. The base and leg of a right triangle have the same measure, thus the angles opposite of them must both be equal. This means that the two angles add up to 90 degrees. Subtracting 90 from 180 degrees gives us the angle measure of the hypotenuse, which is 90 degrees.
180° - (45° + 45°) = 90°
Therefore, the angle measure of the hypotenuse in this case is 90°
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A rectangular prism made is 3 units high, 2 units wide, and 5 units long. What is its surface area in square units? Explain or show your reasoning.
Answer:
62 square units
Step-by-step explanation:
You want the surface area of a rectangular prism 3 units high, 2 units wide, and 5 units long.
AreaThe surface area of a rectangular prism is given by the formula ...
SA = 2(LW +H(L +W))
ApplicationUsing the given dimensions, L=5, W=2, H=3, the area is ...
SA = 2(5·2 +3(5 +2)) = 2(10 +3(7)) = 2(31)
SA = 62 . . . square units
The surface area of the prism is 62 square units.
Determine which answers in in the solution that will make the equation true
Answer:
9
Step-by-step explanation:
3p + 6 = 5p – 12
6 + 12 = 5p – 3p
18 = 2p
p = 18/2
p = 9
rate as brainliest
thank you
Answer:
The answer would be 9.
Step-by-step explanation:
If you plug in 18 for both of them, the answer would be:
60=78
If you plug in 9 for both of them, the answer would be:
33=33
If you plug in 0 for both of them, the answer would be:
6=-12
If you plug in -9 for both of them, the answer would be:
-21=-57
So, 9 would be the best choice.
Hope this helps! :D
You are refilling your inventory of welcome packets for new customers. For each packet, it takes 5 minutes to print, 2 minutes to organize, and 5 minutes to proofread. The ink in the printer will need to be changed every 5 packets, which takes 3 minutes. You have 3 hours to dedicate to this task. Assume thathe ink in the printer was already changed before beginning and that you have to complete each packet before completing any steps for the next one. How many welcome packets will you be able to fully complete in the time allotted?
Answer:
5x + 2x + 5x + (3/5x) = 180
12x + 0.6x = 180
12.06x = 180
x = 14
14 packetsStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Exercises 57 and 58 refer to the following setting. In Exercises 14 and 18 of Section we examined the probability distribution of the random variable the amount a life insurance company earns on a 5 -year term life policy. Calculations reveal that and Life insurance If four 21 -year-old men are insured, the insurer's average income is
where is the income from insuring one man. Assuming that the amount of income earned on individual policies is independent, find the mean and standard deviation of . (If you compare with the results of Exercise 57 , you should see that averaging over more insured individuals reduces risk.)
the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective
Mean: $2,000
Standard Deviation: $741.42
The mean of the random variable X is calculated by taking the sum of the products of the probability of each outcome and the corresponding value of X. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. Thus, the mean of X is calculated as:
Mean =[tex]$\sum_{i=1}^{N} P(X = x_i)*x_i[/tex]
= 0*1000 + 0.38*2000 + 0.59*3000 + 0.03*4000
= 2000
The standard deviation of the random variable X is calculated by taking the square root of the sum of the products of the probability of each outcome and the square of the difference between the corresponding value of X and the mean. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. The mean of X is 2000. Thus, the standard deviation of X is calculated as:
Standard Deviation = [tex]$\sqrt{\sum_{i=1}^{N} P(X = x_i)(x_i - \mu)^2}[/tex]
= [tex]\sqrt{(0(1000-2000)^2[/tex] + [tex]0.38*(2000-2000)^2[/tex] + [tex]0.59*(3000-2000)^2 + 0.03*(4000-2000)^2)}[/tex]
= [tex]\sqrt{741.42} = 27.22$[/tex]
Therefore, the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective
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you are dealt three cards without replacement from a standard 52-card deck. a) Find the probability of being dealt no hearts. b) Next, use complements to find the probability of being dealt at least one heart.
The the probability of being dealt no hearts is 0.75 and probability of being dealt at least one heart is 0.25 .
Total number of cards = 52
A : the probability of being dealt no hearts
B: the probability of being dealt with hearts
P( A ) = 1 - P( B)
= 1 - 13/52
= 1 -0.25
=0.75
C : probability of being dealt at least one heart
P(C) = 13C1 / 52C1
= 13 / 52
=0.25
Probability is a way to tell or calculate the possibility of an event to occur. Using it, we can make predictions about the likelihood of an event happening, or how likely it is , it helps to make predictions more clear .
The probability can be between 0 and 1 here , P being 0 means a failure and P being 1 means a success.
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Problem 2 (D.16 Exercise 5, p 511). Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still. All possibilities are equally likely. So, here is the transition matrix: [1/3 1/4 0 1/5 ] 1/3 1/4 1/4 1/5 0 1/4 1/4 2/5 1/3 1/4 1/2 1/5 Predict the long-term distribution of rats. What is the long-term probability that a given marked rat is in room 4? You must use the method of eigenvalues and eigenvectors.
The long-term probability that a given marked rat is in room 4 is 1/3
What is meant by probability?
In statistics, probability is defined as the measure of the likelihood of an event to happen and it measures the certainty of the event.
Here we have given that Forty rats are placed at random in a house having 4 rooms. There is one door between rooms 1 and 2, one door between rooms 1 and 4, one door between rooms 2 and 4, one door between rooms 2 and 3, and two doors between rooms 3 and 4 see the book for a picture). There are no doors between rooms 1 and 3. After each minute, a rat may change rooms, or stay still.
And we need to find the the long-term probability that a given marked rat is in room 4.
By using the eigenvalues method, we know that
Room 4 has the 3 exits that is from Room 1, Room 2 and Room 3.
So, here we have 3 possibilities for the exit so, the rat can choose any one these three ways,
So, the probability can be written as,
=> 1/3
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A student made a mistake while using similar triangles to find the missing side length indicated by the letter z in the diagram Analyze the student's work and find the state. Explain what was done incorrectly and find the correct solution Student's work to find the value of x
The students ratio expressed in fraction as 6/4 = 4/x is incorrect for the similar triangles, and the correct ratio is x : 3 = 10 : 6 expressed in fraction as x/3 = 10/6. The value for x = 5.
How to calculate for x for the similar trianglesSince the triangles are similar, it implies that the length 3 of the smaller triangle is similar to the length x of the larger triangle,
Also the length 6 of the smaller triangle is similar to the length of the larger triangle (4 + 6 = 10).
So it will be wrong to write 6/4 = 4/x, rather the correct fraction will be;
x : 3 = 10 : 6
which when expressed as fraction, we get;
x/3 = 10/6
x = (10 × 3)/6
x = 30/6
x = 5
Therefore, the students expression 6/4 = 4/x is incorrect representation for the lengths of the similar triangles. And the correct expression is x/3 = 10/6, which gives us the value of x equal to 5.
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Leslie gathered this data revealing the distance traveled and the cost of ticket when taking a commuter train between six different pairs of stations
The cost for two stations that are 10 miles apart will be $8.21.
What is cost?
Cost denotes the amount of money that a company spends on the creation or production of goods or services. It does not include the markup for profit. From a seller's point of view, cost is the amount of money that is spent to produce a good or product.
Given equation is;
y = 0.354x+4.669
Where x represents the number of miles traveled.
For measuring the cost for two stations that are 10 miles apart;
x=10
Putting in given equation
y=0.354(10)+4.669
y=3.54+4.669
y=8.209
Rounding off to nearest hundredth;
y=$8.21
The cost for two stations that are 10 miles apart will be $8.21
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Select all irrational numbers.
√3/16
√4/16
√9/16
√3/4
√9/4
From the given numbers root (3/4) and root (9/4) irrational numbers.
What are irrational numbers?
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.
Here,
root(3/16) is a rational number
root(9/16) is a rational number.
Therefore, from the given numbers root(3/4) and root(9/4) are the irrational numbers.
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In 2012, James Cameron descended to the bottom of Challenger Deep in the Marianas Trench; the deepest point in the ocean. The vessel he rode in was called DeepSea Challenger. Challenger Deep is 35,814 feet deep at its lowest point. The ascent can be modeled by a different proportional relationship y =kx. What is the value of k in this case?
What the value of k means in the proportional relationship y =kx is; the change in depth per second of the ascent.
How to Interpret Proportional Relationships?We are told that;
James Cameron descended to the bottom of Challenger Deep in the Marianas Trench; the deepest point in the ocean.
The vessel he rode in called DeepSea Challenger was 35,814 feet deep at its lowest point.
Now, if the time spent is denoted as x in seconds and the depth is denoted as y, the the relationship will be;
y = -kx
where -k is the constant of proportionality which is the change in depth per second of descent.
Now, if the ascent can be modeled by a different proportional relationship y = kx, then it means that k here will be the change in depth per second of the ascent.
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Find the measure of
Answer:
<MON = 102°
Step-by-step explanation:
Alternative Interior Angles so both of those angle equal to each other.
(12x + 30) = (9x + 48)
Get x to one side by subtracting.
12x - 9x + 30 = 48
3x + 30 = 48
Subtract 30 to both side to get x by itself.
3x = 18
Divide 3 to both side to solve for x.
x = 6
Plug x = 6 into <MON = (9x + 48)
9*6 + 48 = 54 + 48 = 102°
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. TRUE or FALSE​
Answer:
True
Step-by-step explanation:
This is true by definition.
in the graph, y represents the money collected from the sale of adult tickets, and x represents the number of adult tickets sold. which equation describes the proportional relationship between the amount of money collected and the number of adult tickets sold?
On solving the question we got to know that - Answer: For every ticket sold, 52$ is made, 1 : 52
What is a graph?A diagram or graphical representation that organizes the depiction of data or values is known as a graph. The relationships between two or more items are frequently represented by the points on a graph.
What is the structure of a graph?A graph is a type of non-linear data structure that consists of nodes and links. While the vertices are often sometimes referred to as nodes, in a graph the edges are the lines or arcs that connect any two nodes. The vertices (V) and edges (E) that make up a graph are what constitute it most rigorously ( E ). The prefix "G" appears in the graph (E, V).
y = mx - rise/run = 208/4, m = 52
The proportion is that for every ticket sold, 52 $ is made, 1 : 52
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Luke invests $800 into an account with a 2.9% interest rate that is compounded semiannually.
How much money will he have in this account if he keeps it for 5 years?
Round your answer to the nearest dollar.
The money he will have in this account if he keeps it for 5 years is $358.
What is meant by compound interest?Compound interest is the term used to describe interest on savings that is calculated using both the initial principal and interest that has accrued over time. You can earn interest on interest, which is known as compound interest.
WE have given $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year.
Given,
P = $800
Time t=5 years
Interest rate= 2.9%
Hence, the amount will have in his account is:
=[tex]P(1 + 10 / 2000)^{2t}[/tex]
Here, the interest is compounded semiannually.
[tex]800 (1 + 2.9 / 200)^{10}[/tex]
=$358
Therefore, if the interest rate is compounded semiannually then the money he will have in this account if he keeps it for 5 years is $358.
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a satellite traveling in a circular orbit 1,000 miles above the earth passes directly over a tracking station at noon. assume that the satellite takes 2 hours to make an orbit and that the radius of the earth is 4,000 miles. find the distance between the satellite and tracking station at 12:03 p.m. draw a picture (using the idea of orbits like above), then solve.
The distance between the satellite and tracking station at 12:03 p.m is 1271.55 miles.
Given that :
TS = 1000 miles
Orbital time = 2 hours
Let T be tracking station.
S be satellite position.
R be a satellite position at 12:03 p.m
Time = 12:03 - 12:00 = 3 min
SR = Satellite speed × time
Orbital distance = 2πR
= 2π(4000 + 1000)
= 10000 π miles
Orbital speed = [tex]\frac{satellite distance}{satellite time}[/tex]
= [tex]\frac{10,000\pi }{2}[/tex]
= 5000 π miles/hour
= [tex]\frac{5000 \pi }{60}[/tex] miles/min
Distance SR = Orbital speed × time
= [tex]\frac{5000 \pi }{60}[/tex] × 3
= 250 π miles
Using pythagoras theorem in triangle TSR
[tex]TR^{2}[/tex] = [tex]TS^{2} + SR^{2}[/tex]
= [tex]\sqrt{TS^{2} + SR^{2} }[/tex]
= [tex]\sqrt{1000^{2} + 250 \pi ^{2} }[/tex]
TR = 1271.55 miles
Therefore, the distance between the satellite and tracking station at 12:03 p.m is 1271.55 miles.
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Omar has a classic car valued at $24275. It has been appreciating in value at the rate of 4.05% per
year. How much can he expect the car to be worth in 10 years?
The computation of the future value is $92,691.08
How to calculate the future value?As we know that
Future value = Present value × (1 + interest rate)^number of years
where, the Present value is $24275
The Interest rate is 4.05%
And, the number of the year is 10 years
Now placing these values to the above formula;
So, the future value is;
Future value = Present value × (1 + interest rate)^number of years
= $24275× (1 + 0.0405)^10
= $24275× 1.448298166
= $92,691.08
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Divide 25 by 5,
then add 7.
Answer:
The answer would be 12.
The equation would be (25/5)+7
Step-by-step explanation:
To solve this problem, first divide 25 by 5.
25/5=5
Now, add 7 to 5 for your answer.
The answer would be 12.
The equation would be (25/5)+7
Hope this helps! Have a great day! :D
25÷5=5
5+7=12
12 is your answer
Select the values that make the inequality h < 2 true.
(Numbers written in order from least to greatest going across.)
The inequality is: h less than equal to 2 That is the Numbers written in order from least to greatest going across
To find:
The values that make the given inequality true.
We have,
h less than equal to 2
It means the value of h must be less than or equal to 2.
In the given options, the list of numbers which are less than or equal to 2 is
-6, -3, -1, 1, 1.9, 1.99, 1.999, 2
The list of numbers which are greater than 2 is
2.001, 2.01, 2.1, 3, 5, 7, 10
Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
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1
You are told that 56% of the pupils in a class are girls.
What is the smallest number of pupils the class could contain?
The smallest number of pupils the class could contain is 25.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100
Since we are told that 56% of the pupils in a class are girls, the smallest number of pupils the class could contain is 25. This will be:
= 14 / 25 × 100
= 56%
This is correct as indicated above.
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(please explain :))A 35 foot ladder is set against the side of a house so
that it reaches up 21 feet. If Elijah grabs the ladder at its
base and pulls it 4 feet farther from the house, how far up
the side of the house will the ladder reach now? (The
answer is not 17 ft.) Round to the nearest tenth of a foot.
Answer:
21.4
Step-by-step explanation:
If the ladder originally reaches up 21 feet on the side of the house, and Elijah pulls it 4 feet farther away from the house, the distance from the base of the ladder to the side of the house will increase by 4 feet. This means that the new distance from the base of the ladder to the side of the house will be 21 feet + 4 feet = 25 feet.
Since the height of the ladder is the same, and the base of the ladder is now 25 feet from the side of the house, the ladder will still reach up 21 feet on the side of the house. Therefore, the new distance from the top of the ladder to the ground will be 25 feet - 21 feet = <<25-21=4>>4 feet.
To find the new distance from the top of the ladder to the side of the house, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have a right triangle with legs of lengths 21 feet (the height of the ladder) and 4 feet (the distance from the top of the ladder to the ground), and we want to find the length of the hypotenuse (the distance from the top of the ladder to the side of the house). We can use the formula c^2 = a^2 + b^2 to find the length of the hypotenuse:
c^2 = 21^2 + 4^2
= 441 + 16
= 457
c = sqrt(457)
= 21.37
Therefore, the distance from the top of the ladder to the side of the house is 21.37 feet, and the ladder will reach up 21.37 feet on the side of the house after Elijah pulls it 4 feet farther away. Round to the nearest tenth of a foot, the ladder will reach up 21.4 feet on the side of the house.
The answer would not be 17 feet because the height of the ladder and the distance from the base of the ladder to the side of the house are two separate and independent quantities. The height of the ladder is a fixed distance and does not change, regardless of the position of the base of the ladder. Therefore, even if Elijah pulls the ladder 4 feet farther away from the house, the height of the ladder will still be 21 feet and the ladder will still reach up 21 feet on the side of the house. The only change will be the distance from the base of the ladder to the side of the house, which will increase by 4 feet.
Sunset Lake is stocked with 2800 rainbow trout and after 1 year the population has grown to 7000. Assuming logistic growth with a carrying capacity of 28000, find the growth constant kk, and determine when the population will increase to 14600.
The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.
How to find the increase of population?The increase of population can be found by using the logistic equation. It is
[tex]P(t) = \frac{K}{1 + Ae^{-kt} }[/tex]
Where
P(t) = population at time t (in years)K = carrying capacityA = (K- P₀)/P₀k = growth constant of proportionalityt = time (in years)Sunset Lake is stocked with the rainbow trout. We have
P₀ = 2800P(1) = 7000K = 28000Find the growth constant k and time t when P(t) = 14600!
A = (K - P₀)/P₀
A = (28000 - 2800)/2800
A = 25200/2800
A = 9
After 1 year, we have 7000 rainbow trout. The growth constant is
[tex]7000 = \frac{28000}{1 + 9e^{-k(1)} }[/tex]
[tex]1 + 9e^{-k} = 4[/tex]
[tex]9e^{-k} = 3[/tex]
[tex]e^{-k} = \frac{1}{3}[/tex]
k = - ln (1/3)
k = 1.0986
Use k value to find the time when the population will increase to 14600!
[tex]14600 = \frac{28000}{1 + 9e^{-1.0986t} }[/tex]
[tex]1.9178 = 1 + 9e^{-1.0986t}[/tex]
[tex]0.9178 = 9e^{-1.0986t}[/tex]
[tex]\frac{0.9178 }{9} = e^{-1.0986t}[/tex]
[tex]t = \frac{ln \: 0.10198}{-1.0986}[/tex]
t = 2.078
t ≈ 2.1 years
It is in another 1.1 years after t = 1.
Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.
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A regular hexagon has a perimeter of 120 m. Find its area. Express your answer in the simplest radical form.
A) 1800√3m^2
B) 5√3m^2
C) 600√3m^2
D) 3600√3m^2
The area of the regular hexagon value calculated using given perimeter of the regular hexagon is equal to option C. 600√3 square meters.
As given in the question,
Perimeter of the regular hexagon is equal to 'P' = 120m
Relation between the area of the regular hexagon 'A' and the perimeter of the regular hexagon 'P is given by :
A = √3 × ( P²/24 )
= √3 × [(120)²/ 24]
= √3 × ( 14400 / 24 )
= √ 3 × 600
= 600√3 square meters
Therefore, the area of the regular hexagon using the perimeter of the regular hexagon is equal to Option C. 600√3 square meters.
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consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. the possible outcomes of the sample space s are listed as follows, where in each case the die on the left is blue and the one on the right is gray. s = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in roster notation. Enter EMPTY or o for the empty set.) The event that the sum of the numbers showing face up is at least 9. E Compute its probability.
The set of events that the sum of the numbers showing face up is at least 9 is E = {36, 45, 46, 54, 55, 56, 63, 64, 65, 66} and the probability is 5/18.
In the roster form, the elements (or members) of a set are listed in a row between curly brackets. For the event that the sum of the numbers showing face up is at least 9 and is written as a set, look at the sum of values of blue and gray dies that has values greater than equal to 9.
Here, the total outcome S = 36
By doing that, we get,
E = {36, 45, 46, 54, 55, 56, 63, 64, 65, 66} = 10
Then, the probability of getting a sum of at least 9 is calculated as,
[tex]\begin{aligned}P(X\geq 9)&=\frac{\text{Number of favorable outcomes}}{\text{total number of outcomes}}\\&=\frac{n}{S}\\&=\frac{10}{36}\\&=\frac{5}{18}\;\text{or}\;0.28\end{aligned}[/tex]
The answer is 5/18.
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4. Find the length of A B.
Using the Pythagorean triplet, the value of AB is 2.
In the given question we have to find the length of AB.
From the given diagram we can see that;
ED = 2, DC = 8 and BC = 6.
To solve this question we use the Pythagorean Triplet.
Pythagorean triples consist of the three positive numbers a, b, and c, where a^2+b^2 = c^2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.
Since we have to find the value of AB.
So we can write it as
EC^2 = AE^2+AC^2
(ED+DC)^2 = AE^2+(AB+BC)^2
Now putting the value
(2+8)^2 = AE^2+(6+AB)^2
10^2 = AE^2+(6+AB)^2
As we know that triplet (6,8,10).
The value of EC is 10, AE = 6, the value of AC can't be 6 because one part of value of AC is already given 6. So the value of AC is 8. AS BC=6, so AB=2.
Hence, the value of AB is 2.
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In a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.
How many were in math only?
How many were not majoring in computer science?
How many were not math or computer science?
a. The number of students who were in math only is 7 students.
b. The number of students who were not majoring in computer science is 15.
c. The number of students who were not math or computer science is 8
How to calculate the number of students?From the information given, in a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.
It should be noted that the number of math majors only will be:
= 13 - 6
= 7
The number of students not majoring in computer science will be:
= 25 - 10
= 15
Those not math or computer science majors will be:
= 25 - 6 - 7 - (10 - 6)
= 8
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The ______ of an object is a measure of the average kinetic energy of the particles in the object.
a.heat b.temperature c.conductivity d.charge
Answer:
b. temperature
Step-by-step explanation:
It is the measure of average kinetic energy of motion or K.E of a single particle in a system.
Which of the following are solutions to the equation below?
Check all that apply.
x² + 6x + 9 = 20
A. x= 2√5-3
B. x= √3+ 20
C. x= -2√5 +3
D. x = -√3+20
☐ Ex= 2√5 +3
OF x=-2√5-3
The solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
x = [-b± (√b²-4ac )] / 2a
The quadratic equation:
x²+6x+9=20
x²+6x -11 = 0
a = 1, b = 6, c = -11
x₁,₂ = [-6±√6² - 4.1.(-11)]/2(1)
x = -3 + 2√5 , x = -3 - 2√5
Thus, the solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.
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the base of a solid is a circular disk with radius 3. find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.
the base of a solid is a circular disk with radius 3. Therefore, the volume of the solid is 27π.
The volume of a solid is determined using the formula V = πr²h, where r is the radius of the base and h is the height of the solid. In this problem, the base is a circular disk with radius 3, and the cross-sections are isosceles right triangles with hypotenuse lying along the base. Since the cross-sections are isosceles right triangles, the height of each triangle is equal to the radius of the base, which is 3. Therefore, the height of the solid is also 3. Substituting these values into the formula gives V = π(3)²(3), which simplifies to V = 27π.
Therefore, the volume of the solid is:
V = πr²h
V = π(3)²(3)
V = 27π
Therefore, the volume of the solid is 27π.
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34) A company advertises on a website. A worker tracked the number of visits to the website and the number of clicks on the advertisement. The table shows the data for several days. A linear function can be used to model the data.
Based on the table, what is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website?
A) 77 B) 137 C) 83 D) 105
The best prediction of the number of clicks on the advertisement if 1,500 people visit the website is; C: 83
How to interpret Function Tables?
We want to find the best prediction of the number of clicks on the advertisement if 1,500 people visit the website.
Now, we see the coordinates from the table;
(1045, 60)
(1106, 63)
(1500, y)
where y is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website.
By interpolation, we can say that;
(y - 63)/(1500 - 1106) = (63 - 60)/(1106 - 1045)
(y - 63)/394 = 3/39
(y - 63)/394 = 1/13
Cross multiply to get;
y - 63 = 394/13
y = 93
Looking at the options, the closest option is option C.
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