According to the given question and making the equations we can conclude that the answer would be 40,040.
Explain equation?When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.
To form a team of 7 students consisting of 4 seniors and 3 juniors, we need to select 4 seniors out of 13 and 3 juniors out of 8.
The number of ways to select 4 seniors out of 13 is given by C(13,4), which can be calculated as:
C(13,4) = 13! / (4! * (13-4)!) = 13! / (4! * 9!) = (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1) = 715
Similarly, the number of ways to select 3 juniors out of 8 is given by C(8,3), which can be calculated as:
C(8,3) = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
Therefore, the total number of ways to form a team of 7 students consisting of 4 seniors and 3 juniors is:
C(13,4) * C(8,3) = 715 * 56 = 40,040
Hence, the answer is (b) 40,040.
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WILL GIVE BRAINLIEST!! : Describe the process for determining if there are outliers in a distribution of data
You can determine the outlier by seeing if one set of data in the distribution of data is farther away from a group set of data. Like in this picture, the one dot is much farther away from the others.
If two supplementary angles are 10x* and (2x-30)*, find the angles
Answer:
175 ; 5
Step-by-step explanation:
Supplementary angles sums up to 180
10x + 2x - 30 = 180
12x - 30 = 180
12x = 180 + 30
12x = 210
x = 210/12 = 17.5
10x = 10*17.5= 175
2*17.5 - 30 = 35 - 30 = 5
Please help me!!!! i cant see files so just tell me!
A flock of sheep has 182 white sheep and 98 spotted sheep. Which proportion can be used to determine p, the percent of the flock that has spots?
Answer:
D) 98/280 = p/100
Step-by-step explanation:
Since p is the missing percentage, it has to be OVER 100, so C is eliminated.
Total:
182 + 98 = 280
Spotted sheep probability:
98/280 = 0.35 or 35%
To check:
\(\frac{98}{280} =\frac{p}{100} \\\\280p=9800\\x=35\)
If six angles of a heptagon have measures of 122, 153, 168, 105, 162, and 87, what is the measure of the seventh angle?
Answer:
he seventh angles measure is 103
Step-by-step explanation:
Interior angles = (number of side in the polygon - 2) times 180.
So Heptagon interior angles = (7-2)(180) = 900
To find the missing angles add all the given angles together (122, 153, 168, 105, 162, and 87) = 797.
Now The measure of the seventh angles = total angles measure - the six given angles,
The seventh angles measure is 103
900 - 797 = 103
PLS ANSWER QUICK FIRST TO ANSWER RIGHT WILL GET BRAINLIEST!!!!
Answer:
xy=k
-2×4=k
k=-8
y=-8/x
I need help on this math homework
Answer:
X+8+2x+127=180(Being the angle in a triangle)3x+135=1803x=180-1353x=45x=45/3x=15# The other angle are:.<A=2x=2×15=30#<B=x+8=15+8=23#Please mark me as brainlistComplete the table of values for the function f(x)=1/2
The table of values for the function f(x)=1/2 are shown as follow:
What is function?
A function is an expression or relationship that involves one or more variables. It has several inputs and outputs. Each input has a single output. The function describes how the inputs relate to the output.
The function f(x) = 1/2 is a horizontal line that crosses the y-axis at the point (0, 1/2). Since the value of f(x) is constant for all values of x, the table of values for this function will have the same output value of 1/2 for every input value of x.
The table of values for the function f(x)=1/2 are shown as follow:
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A cylindrical swimming pool has a diameter of 20 feet and a height of 3. 5 feet. How many gallons of water can the pool contain? Round your answer to the nearest whole number. (1 ft3 ≈ 7. 5 gal).
the pool can contain approximately 8,218 gallons of water.
A cylindrical swimming pool has a diameter of 20 feet and a height of 3.5 feet. We are required to find out how many gallons of water can the pool contain.
Converting diameter to radius: The diameter of the cylinder is given as 20 feet. Hence the radius of the cylinder can be obtained by dividing the diameter by 2.
r= 20/2 = 10 feet
Volume of cylinder:Volume of cylinder is given by πr2h where π is a mathematical constant whose value is approximately 3.14r is the radius of the cylinderh is the height of the cylinder.
Putting values into the formula, we get:
π(10)²(3.5)≈ 1,095.75 ft³
Converting ft³ to gallons: 1 ft³ = 7.5 gallons
Therefore, 1,095.75 ft³ ≈ 8,218.13 gallons
the pool can contain approximately 8,218 gallons of water.Hence, the pool can contain approximately 8,218 gallons of water.
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3.31×10 −5
g to micrograms
3.31×\(10^-^5\) g is equivalent to 0.0331 μg which is obtained by using the conversion factor.
To convert from grams to micrograms, we need to consider the conversion factor that relates the two units. The prefix "micro-" represents a factor of \(10^-^6\), which means there are 1,000,000 micrograms in a gram. Therefore, to convert grams to micrograms, we multiply the given value by 1,000.
In this case, we have 3.31×\(10^-^5\) g. To convert this value to micrograms, we can multiply it by 1,000:
= 3.31×\(10^-^5\) g × 1,000
= 3.31×\(10^-^5\) × 1,000
= 3.31×\(10^-^5\) × \(10^{3}\)
= 3.31×\(10^(^-^5^+^3^)\)
= 3.31×\(10^-^2\)
= 0.0331 μg
Therefore, 3.31×\(10^-^5\) g is equivalent to 0.0331 μg.
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Is number one congruent? If it is how?
Answer:
Yes, Triangles in (1) are congruent
Step-by-step explanation:
Two conditions must be satisfied before two triangles can be deemed or declared as being congruent.
1.) They must posses similar shape
2.) They must posses similar size ( that is the corresponding sides and angles of both triangles must be the same)
Triangles in (1) meet both criterias by possessing similar shape with the size and length of the corresponding angles also being the same.
Therefore, the two triangles are congruent.
∆ ABC and ∆ DEF are two similar triangles such that ∠A = 360 and ∠E = 740
, then find ∠C.
Answer:
∠C = 70°
Step-by-step explanation:
When dealing with similar triangles, the angles of both triangles are equal. With that being said, the letters of those angles typically corralete as well. In this case, we have ΔABC and ΔDEF. Based on the way those letters are arranged, we can assume the following:
∠A = ∠D
∠B = ∠E
∠C = ∠F
The question tells us ∠A = 36°. Since we know that ∠A is equal to ∠D, we know that ∠D also equals 36°. The question also tells us ∠E = 74°. Once again, since we know that ∠E is equal to ∠B, we know that ∠B is 74° as well.
Now we use that information to solve for ∠C. The sum of the angles of a triangle always adds up to 180°. Because we know that, we can solve easily:
180 - (36 + 74) = 70
∴ ∠C = 70°
What is the Answer to: 120 Times 2/3
Answer:
80
Step-by-step explanation:
You could multiply by 2 and then divide by 3
120*2 = 240
240/3 = 80
Or you could divide by 3 and then multiply by 2
120/3 = 40
40*2 = 80
Answer:
80Step-by-step explanation:
120 × 2/3= 120/1 × 2/3= 240/3= 80\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)
There are 12 inches in 1 foot and 5,280 feet in 1 mile. Elena ran 2 1/2 miles. How many inches did Elena run?
Answer:
158400 inches
Step-by-step explanation:
2.5* 5280 because 2.5 miles is 13200 feet.
13200*12 because 13200 feet is 158400 inches.
The answer would be 158400 inches.
Answer:63456
Step-by-step explanation:
5280*12=63456
what is the probability of rolling a yahtzee on the first round? round your answer to 4 decimal places. enter your answer into variable
The probability of rolling a yahtzee on the first round is calculated to be 6/46656 or 1/7776
Given that,
A dice is rolled for one time .
To find : The probability that a yahtzee will be rolled on the first round.
Your first die will be one of the 6 possible results 6/6 times
That will match on the second die 1/6th of the time.
The third, fourth, and fifth dice all share this characteristic.
Multiplying the all probabilities that the first die will be a yahtzee which is
P( yahtzee will be rolled on the first round) = Product of all possible outcomes of each time a dice is rolled.
6/6*1/6*1/6*1/6*1/6*1/6=6/46656 or 1/7776
Therefore, probability that a yahtzee will be rolled on the first round is 1/7776.
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NEED HELP!!! 30 POINTS
FIND THE RATIONAL EXPONENT FORM!!
Answer:
Step-by-step explanation:
The root which is 2 is the fractional portion of your exponent
\(\sqrt{x^{7} y^{12} }\)
=\((x^{7} y^{12} )^{\frac{1}{2} }\) >You can distribute 1/2 to each term by multiplying
\(=x^{\frac{7}{2} } y^{6\)
Linear or non linear?
Answer:
nonlinear
Step-by-step explanation:
What is the value of x?
Answer:
C.
Step-by-step explanation:
2x-10/x-3=5/3 X=15
solve= 4x + 210 -2x =260
We are given the equation
4x + 210 - 2x = 260
Firstly, we need to collect the like terms
4x - 2x + 210 = 260
2x + 210 = 260
Secondly, Make 2x the subject of the equation
2x = 260 - 210
2x = 50
Divide both sides by 2
2x/2 = 50/2
x = 25
The answer is 25
3. What is Total Surface Area?
4 in
3 in
10 in
O 82
O 140
O 164
O 120
Answer:
120in. ezy
Step-by-step explanation:
find a particular solution for y'' 4y' 3y = 1/1+e^t using transfer functions, impulse response and convolutions. (other methods are not accepted)
To find a particular solution for y'' 4y' 3y = 1/(1+e^t) using transfer functions, impulse response, and convolutions, we first need to find the homogeneous solution and then the particular solution.
The homogeneous solution is y_h = c1 e^(-t) + c2 e^(-3t), where c1 and c2 are constants. The transfer function is H(s) = 1/(s^2 + 4s + 3), and the impulse response is h(t) = e^(-t) - e^(-3t).
To find the particular solution, we need to first find the Laplace transform of the input function, which is F(s) = 1/(s+1)(1+e^(-s)). We can then use the convolution theorem to find the output function in the Laplace domain, which is Y(s) = H(s) F(s). Simplifying this expression using partial fraction decomposition and inverse Laplace transform, we get the particular solution y_p = (e^(-t) - e^(-3t)) / (2 - e^(-t)). Therefore, the general solution for the differential equation is y = y_h + y_p, where y_h is the homogeneous solution and y_p is the particular solution.
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Chau reads a book at a rate of 26 chapters per hour how many chapters does he read in 2 hours
Answer: he reads 52 chapters in 2 hours.
Step-by-step explanation:
Since he reads 26 chapters per hour, multiply the number of chapters by the number of hours which is two.
26 * 2 = 52
he reads 52 chapters in 2 hours.
Answer:
52 chapters
Step-by-step explanation:
Because he reads 26 chapters in 1 hour and his rate is constant (never changing), multiply 26 by 2 to find how many chapter for 2 hours.
26 x 2 = 52
Equivalent expression by applying the distributive property (x+2 (x+9)
Answer:
3x+18
Step-by-step explanation:
x + 2(x+9) = x+2x+18 = 3x+18
a piece of wire 72cm long s cut into two pieces, each to be bent to make a square. the length of a side of one square is to be 2cm longer than the length of a side of the other. how should the wire be cut
The wire should be cut into two pieces, one measuring 32 cm and the other measuring 40 cm, in order to create two squares with side lengths of 10 cm and 12 cm.
Let's assume the length of the side of one square is x cm. According to the given information, the length of the side of the other square is 2 cm longer, so its length would be (x + 2) cm.
The perimeter of a square is calculated by multiplying the length of one side by 4. In this case, the total length of the wire is 72 cm, so we can set up the following equation:
x + (x + 2) + x + (x + 2) = 72
Simplifying the equation, we get:
4x + 4 = 72
4x = 68
x = 17
Therefore, one side of the square measures 17 cm, and the other side measures 17 + 2 = 19 cm.
To find the lengths of the wire, we multiply the side lengths by 4:
Length of the wire for the square with side length 17 cm: 17 * 4 = 68 cm
Length of the wire for the square with side length 19 cm: 19 * 4 = 76 cm
Since the total wire length is 72 cm, we need to cut a piece measuring 32 cm and another piece measuring 40 cm.
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Several friends (Calvin, Dean, Kelli, and Lee) went to Cal's Late Night Diner for a bite to eat. Match each person to their drink (Iced tea, Lemonade, Root Beer, and Water) and determine how much each paid ($4.99, $5.99, $6.99, and $7.99) for their meal.
Clues:
1. The Diner who paid $4.99 was either Calvin or the one who got the Root Beer.
2. Kelli paid $6.99
3. The one who got the water paid 1 dollar less than Dean.
4. Calvin paid more than Lee.
5. The one who got the Root beer paid 1 dollar less than the one who got the Iced Tea.
Based on the given clues, we can determine the person, drink, and price paid for each individual:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
How to determine how much each friends paidFrom clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.
From clue 2, Kelli paid $6.99.
From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.
From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.
Therefore, the final assignments are:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
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Over which period(s) of time is the average rate of change zero? what, if anything, can you conclude about the actual temperature fluctuation within this period? a. the average rate of change of temperature is 0 from 2 pm to 4 pm; nothing can be concluded about the actual temperature fluctuation. b. the average rate of change of temperature is 0 from 2 pm to 4 pm and also from 10 am to 8 pm; nothing can be concluded about the actual temperature fluctuation. c. the average rate of change of temperature is 0 from 10 am to 8 pm; nothing can be concluded about the actual temperature fluctuation. d. the average rate of change of temperature is 0 from 2 pm to 4 pm and also from 10 am to 8 pm; the conclusion that can be drawn is that the temperature will not change for that time period.
The correct answer is (b) The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM.
What is a temperature simple definition?
Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).The correct answer for this question is- The period(s) of time where the average rate of changes to zero is "b.The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PMNothing can be concluded about the actual temperature fluctuation.Learn more about temperature
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The complete question is-
The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City.Time of Day10 AM12 Noon2 PM4 PM6 PM8 PM10 PMTemperature (F)30353636343028Over which period(s) of time is the average rate of change zero? What, if anything, can you conclude about the actual temperature fluctuation within this period?a.The average rate of change of temperature is 0 from 2 PM to 4 PM; Nothing can be concluded about the actual temperature fluctuation.b.The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.c.The average rate of change of temperature is 0 from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.d.The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; The conclusion that can be drawn is that the temperature will not change for that time period.
if x^2 + y^2 = m and xy = n, find the value of 16m + 32n
Answer:
x^4 - mx^2 + n^2 = 0
Step-by-step explanation:
We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:
(x^2)(y^2) = n^2
Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:
x^2(m - x^2) = n^2
Expanding the left side of the equation, we get:
mx^2 - x^4 = n^2
Multiplying both sides by 16, we get:
16mx^2 - 16x^4 = 16n^2
Adding 32xy to both sides, we get:
16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy
Substituting n for xy, we get:
16mx^2 + 32n - 16x^4 = 16n^2 + 32n
Rearranging the equation, we get:
16mx^2 - 16x^4 - 16n^2 = 0
Dividing both sides by -16, we get:
x^4 - mx^2 + n^2 = 0
Answer:
(4x+4y)²
Step-by-step explanation:
Given x²+y² = m ,xy=n.
Now 16m+32n = 16(m+2n)
= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]
(4x+4y)².
HELPPP!!!!! PLSSSSSSSSSSSS
Answer:
Yes, it is.
Step-by-step explanation:
When you plug in 2 for y, and 2 for x. you get:
2 ≤ 4(2) - 6
2 ≤ 8 - 6
2 ≤ 2
2 is equal to 2, so it is correct.
A two-input xor gate is equivalent to which equation? a. y = ab’ b. y = ab’+a’b c. y = a'b’ +ab d. y = a’(b’ + b')
The equivalent equation for a two-input XOR gate is y = ab’ + a’b.
A two-input XOR gate is a logic gate that outputs a high or 1 signal only when the two inputs are different. In other words, the output of an XOR gate is 1 when one input is 0 and the other input is 1, and vice versa.
To represent an XOR gate with an equation, we can use Boolean algebra. The Boolean expression for an XOR gate is y = ab’ + a’b, where y is the output, a and b are the two inputs, and a' and b' represent the complement (or NOT) of a and b, respectively.
This equation can be derived using the laws of Boolean algebra. For example, we know that the product of a variable and its complement is always 0, i.e., a a' = 0. Using this property, we can simplify the equation y = ab’ + a’b as follows:
y = ab’ + a’b
= ab’ + ab’’ + a’b (adding a' and b')
= ab’ + a’b + ab’’ (rearranging terms)
= ab’(1) + a’b(1) (using a a' = 0 and b b' = 0)
= ab’ + a’b (simplifying)
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A rocket was launched and its height, h, in metres, above the ground after time,
t, in seconds, is represented by h = 11 + 10t - 2t^2. What was the initial height
of the rocket?
a) 15 m
b) 7 m
c) 11 m
d) 19 m
Answer this problem
Answer:
(3,-7)
(-8,48)
(-4,28)
(8,-32)
(-3,23)
Step-by-step explanation:
To solve, just put in the x value from the table as the x value in the equation. Then solve to get y.
Hope it helps!