The number of different committees that are possible is: 126
How to solve Permutation and Combination?When you have a number of elements and then want to form subsets of elements of particular smaller size, you can utilize combinations or permutations. If the order of placement of the elements does not matter, we use combinations to quantify the number of groups formed.
Now, the order of the members in the committee does not matter and as such we will use combinations which has the formula:
nCr = n!/(r!(n - r)!)
We are given:
n = 9
r = 5
Thus:
9C5 = 9!/(5!(9 - 5)!)
= 126 different committees
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Royce has a collection of trading cards. 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards. He chooses half of this collection and gives them to his friend. Which of the following represent possible outcomes of this selection?
If 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards, the possible outcome is (10, 10, 5). So, correct option is B.
One possible method to approach this problem is to first find the total number of trading cards Royce has in his collection, which is the sum of baseball cards, football cards, and basketball cards:
Total number of cards = 16 + 21 + 13 = 50
Then, we can find half of the total number of cards, which is the number of cards Royce gives to his friend:
Half of total number of cards = 1/2 x 50 = 25
To find possible outcomes of this selection, we can start by considering how many baseball cards Royce can give to his friend. Since he has 16 baseball cards in total, he can give any number of them from 0 to 16, but he cannot give more than 25 cards in total.
Similarly, he can give any number of football cards from 0 to 21 and any number of basketball cards from 0 to 13.
Therefore, possible outcomes of this selection can be represented by the set of triples (x, y, z) where x is the number of baseball cards, y is the number of football cards, and z is the number of basketball cards, such that x + y + z = 25 and 0 ≤ x ≤ 16, 0 ≤ y ≤ 21, and 0 ≤ z ≤ 13.
The possible outcome is (10, 10, 5), which means Royce gives 10 baseball cards, 10 football cards, and 5 basketball cards to his friend.
So, correct option is B.
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Complete question is:
Royce has a collection of trading cards. 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards. He chooses half of this collection and gives them to his friend. Which of the following represent possible outcomes of this selection?
A) (10.20,20)
B) (10, 10, 5)
C) (20, 10, 5)
D) (10, 10, 25)
Find the values of x for which the series converges. (Enter your answer using interval notation.)
∑(6)^nx^n
the series converges for x in the interval: (-1/6, 1/6)
The series ∑(6)^nx^n converges if |x| < 1/6. This can be determined using the ratio test, where we take the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term:
|6(x^(n+1))/(x^n)| = 6|x|
As n approaches infinity, this limit is less than 1 if and only if |x| < 1/6. Therefore, the series converges for all x in the open interval (-1/6, 1/6).
In interval notation, we can write the answer as: (-1/6, 1/6).
The given series is:
∑(6^n)(x^n)
This is a geometric series with a common ratio of 6x. For a geometric series to converge, the absolute value of the common ratio must be less than 1:
|6x| < 1
To find the values of x for which the series converges, we can solve for x in the inequality:
-1 < 6x < 1
Divide by 6:
-1/6 < x < 1/6
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Find parametric equations for a line in the direction of the vector 57 - 7 and through the point
(0, 0, - 3).
Write the equations so that one term is just the parameter - t.
х (t) = y(t) =
z(t) =
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
To find the parametric equations for a line in the direction of the vector 57 - 7 and through the point (0, 0, - 3), we can use the vector form of the equation of a line:
r = r0 + tv
where r is a point on the line, r0 is the given point (0, 0, -3), t is a parameter, and v is the direction vector (57, -7, 0).
Substituting the given values, we have:
r = (0, 0, -3) + t(57, -7, 0)
Expanding, we get:
x(t) = 0 + 57t
y(t) = 0 - 7t
z(t) = -3 + 0t
Simplifying, we have:
x(t) = 57t
y(t) = -7t
z(t) = -3
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
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The amount of money A after
t years in a savings account that
earns 3.5% annual interest is
modeled by the formula
A = 300(1.035)t
.
What is the amount of the initial
deposit?
By compound interest, The initial amount in the account is $300.
What does compound interest mean ?
When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. As an illustration, if you put $1,000 in an account that offers 1% yearly interest, you will receive $10 in interest after a year.
Compound interest allows you to earn 1 percent on $1,010 in Year Two, which equates to $10.10 in interest payments for the year. This is possible because interest is added to the principle in Year Two.
A = 300(1.035)t
As we know the formula "Compound Interest" :
A = P(1 + r/100)t
So, According to our question,
Rate of interest = 0.35 = 135%
So, equate the both the equations , we get that
Hence, The initial amount in the account = $300
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Which expression is equivalent to −0.75(60–32n)–n?
−45+23n
45–23n
−45+31n
−45+15n
The expression that is equivalent to −0.75(60–32n)–n is A. −45+23n.
What is a mathematical expression?A mathematical or algebraic expression is the combination of variables with numbers, constants, and values using algebraic operands, including addition, multiplication, subtraction, and division.
Mathematical expressions do not bear the equal symbol (+) unlike equations.
−0.75(60–32n)–n
Expanding:
-45 + 24n - n
Simplifying:
−45 + 23n
Thus, the equivalent expression is Option A.
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If t=26 and s=11.8, find r. Round to the nearest tenth
Answer:
Step-by-step explanation:
the answer is R=63
Daniel just graduated college and found a job that pays him $42,000 a year, and the company will give him a pay increase of 6. 5% every year. How much will Daniel earn in 4 years?
Daniel will earn $54,271.35 in 4 years if a job pays him $42,000 a year and a 6.5% of increment in salary every year.
Salary = $42,000 a year
Increment per year = 6. 5%
Time period (n) = 4 years
To calculate the total earnings of Daniel in 4 years is:
Earnings after n years = Initial salary * (1 + yearly pay increase rate) ^ n
Substituting the above values, we get:
Earnings after 4 years =[tex]$42,000 * (1 + 0.065)^4[/tex]
Earnings = $42,000 * 1.29503225
Earnings = $54,271.35
Therefore, we can conclude that Daniel will earn $54,271.35 in 4 years at an increment of 6.5% per year.
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Do You Understand?
1. How can you find the volume of the
china cabinet?
1 ft,
7 ft
3 ft
4 ft
2ft
The volume of the china cabinet is 21 cubic feet.
To find the volume of the china cabinet, we need to multiply its length, width, and height.
Since the dimensions are given in feet, we will use cubic feet as the unit of volume.
The length of the china cabinet is given as 1 ft, the width as 7 ft, and the height as 3 ft.
The volume can be calculated as follows:
Volume = length * width * height
Volume = 1 ft * 7 ft * 3 ft
Volume = 21 cubic feet
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What is the surface area of the square pyramid?
Answer:
3456 [tex]m^{2}[/tex]
Hope this helps!
Step-by-step explanation:
A square pyramid is comprised of a square and four triangles.
The square has an area of 1296 m ( 36m × 36m ) ( length × width ).
A triangle has an area of 540 m ( [tex]\frac{1}{2}[/tex] × 36m × 30m ) ( [tex]\frac{1}{2}[/tex] × width × ( slant ) height ).
The total surface area would be 1296 m + 4 × ( 540 m ) : ( Multiply 4 because there are 4 triangles ).
The total surface area is 3456 [tex]m^{2}[/tex].
Answer: 3,456 m^2
Step-by-step explanation:
The formula is SA = 2bs + b^2.
SA = 2 (36) (30) + 36^2
= 72 (30) + 1,296
= 2,160 + 1,296
= 3,456 m^2
The substitution u = 3x transforms the integral 31 de into
The substitution u = 3x transforms the integral 31 de into: ∫(3/31)du
This is because the substitution u = 3x implies that du/dx = 3, which means dx = (1/3)du. Substituting this expression for dx in the original integral and using the fact that e is a constant, we have:
∫e^(3x) dx = ∫e^(u) (1/3)du = (1/3)∫e^(u)du = (1/3)e^u + C
where C is the constant of integration. So the final answer in terms of x is:
(1/3)e^(3x) + C
which is equivalent to the original integral. This is an example of how the technique of substitution can be used to simplify an integral and make it easier to solve. It is also a common step in many integral transforms.
When performing an integral with substitution, you transform the original integral into a new one with a different variable. In your case, the substitution is given as u = 3x.
To apply substitution, first find the derivative of the substitution equation with respect to x, which is du/dx = 3. Then, solve for dx: dx = du/3.
Now, substitute u = 3x into the original integral and replace dx with du/3. The transformed integral will have the new variable u and a constant factor 1/3.
Without knowing the specific function you're trying to integrate (it seems like "31 de" might be a typo), I cannot provide the exact transformed integral.
However, I hope this explanation of substitution and transforming integrals is helpful. Please feel free to provide more information or clarify your question if you need further assistance!
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The Anderson family went on a trip to see the Paul Bunyan and Blue Ox statue near Lake Bemidji. It took the family 6 hours to travel 330 miles to the statue. What was the Anderson family's average miles per hour (mph)?
btw I don't know how to mark people brainiest so if you tell me how I will to if you help me.
A manufacturer measures the number of cell phones sold using the binomial 0. 015c+2. 81. She also measures the wholesale price on these phones using a binomial 0. 011c+3. 52. Calculate her revenue if she sells 100,000 cell phones. Revenue = (numberofcellphones)(wholesaleprice) = (0. 015c+2. 81)(0. 011c+3. 52)
When the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39.
To find the revenue for selling 100,000 cell phones, we will first evaluate both binomials for the given number of cell phones (c = 100,000) and then multiply them together.
Step 1: Evaluate the first binomial (number of cell phones sold) for c = 100,000:
0.015c + 2.81 = 0.015(100,000) + 2.81 = 1,500 + 2.81 = 1,502.81
Step 2: Evaluate the second binomial (wholesale price) for c = 100,000:
0.011c + 3.52 = 0.011(100,000) + 3.52 = 1,100 + 3.52 = 1,103.52
Step 3: Calculate the revenue by multiplying the results of the two binomials:
Revenue = (1,502.81)(1,103.52) = 1,657,993.3912
So, when the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39. This calculation is based on the binomial expressions provided for the number of cell phones sold (0.015c+2.81) and the wholesale price (0.011c+3.52).
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Ms thompson sets up chairs in a row for a school concert. she uses 328. she sets up at 2 roses of chairs but not more than 10 rows of chairs each row has an equal number of chairs how many rows
Ms. Thompson could set up either 2 rows with 164 chairs in each row or 4 rows with 82 chairs in each row.
To find the number of chairs in each row, we need to divide the total number of chairs by the number of rows. Let's start by finding the factors of 328:
1 x 328
2 x 164
4 x 82
8 x 41
Since there must be at least 2 rows and no more than 10 rows, we can eliminate the last two factor pairs. We are left with:
2 x 164
4 x 82
We can see that the first factor pair gives us 2 rows, while the second gives us 4 rows. We are told that each row has an equal number of chairs, so we need to divide the total number of chairs by the number of rows to find out how many chairs are in each row:
For 2 rows: 328 ÷ 2 = 164 chairs in each row
For 4 rows: 328 ÷ 4 = 82 chairs in each row
Your question is incomplete but most probably your full question
Ms. Thompson sets up chairs in rows for a school concert. She uses 328 chairs. She sets up at least 2 rows of chairs but not more than 10 rows of chairs. Each row has an equal number of chairs.
How many rows of chairs does Ms. Thompson set up? Enter the number in the first box.
How many chairs are in each row? Enter the number in the second box.
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Let f(x) be the function given in the previous question. True/False
The left-hand sum of f(x) is always smaller than the right-hand sum of f(x) for x € 3, 8]. True/False
Without more information about the function f(x) from the previous question, the statement cannot be labeled as true or false.
To determine if the statement is true or false, we first need to understand the terms involved.
Left-hand sum: This is a method of approximating the definite integral of a function by using the left endpoints of subintervals to calculate the sum of the areas of rectangles.
Right-hand sum: This is similar to the left-hand sum, but it uses the right endpoints of the subintervals to calculate the sum of the areas of rectangles.
Now, let's analyze the statement:
The left-hand sum of f(x) is always smaller than the right-hand sum of f(x) for x ∈ [3, 8].
This statement is not necessarily true or false for all functions. The comparison between the left-hand sum and right-hand sum depends on the behavior of the function within the given interval [3, 8].
If the function is increasing in the interval, then the left-hand sum will be smaller than the right-hand sum. If the function is decreasing in the interval, then the left-hand sum will be greater than the right-hand sum. In cases where the function changes direction within the interval, the comparison may not be definitive.
Therefore, without more information about the function f(x) from the previous question, the statement cannot be labeled as true or false.
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2.
A painting company will paint this wall of a building. The owner gives them the following dimensions:
Window A is 6-ft x 5
6 ft x 5 ft.
Window Bis 3 ft x 4 ft.
Window Cis 9ft?
Door D is 4 ft x 8 ft.
33 ft
What is the area of the painted part of
the wall?
577 square feet is the area of the painted part of the wall.
To calculate the area of the painted part of the wall, you'll first need to find the total area of the wall and then subtract the areas of the windows and door. Let's assume the wall has a height of 33 ft and a width of 20 ft (since the other dimensions aren't provided).
1. Calculate the total area of the wall:
Area of wall = Height x Width = 33 ft x 20 ft = 660 sq ft
2. Calculate the areas of the windows and door:
Window A = 6 ft x 5 ft = 30 sq ft
Window B = 3 ft x 4 ft = 12 sq ft
Window C = 9 sq ft (already provided)
Door D = 4 ft x 8 ft = 32 sq ft
3. Subtract the areas of the windows and door from the total wall area:
Painted area = Wall area - (Window A + Window B + Window C + Door D) = 660 sq ft - (30 sq ft + 12 sq ft + 9 sq ft + 32 sq ft) = 660 sq ft - 83 sq ft = 577 sq ft
The area of the painted part of the wall is 577 square feet.
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Mika has a rectangular fish tank that is 65 cm wide and 85 cm long. When completely full, the tank holds 221 L of water. She plans to fill the tank? full, and she wants to find the height of the water. 4 1 L - 1000 cm3 volume = xwxh Mika is calculating what the height of the water will be. Choose ALL correct steps that would be included in her calculation Find the height of the tank: 4 A) x 40 = 30 cm 4 Find 3 the height of the tank: 4 4 X 30 - 40 cm Find the height of the tank 3 x 85 - 30 cm 4 DS Divide the length and width by the volume to find height: 65 x 70 - 40 cm 168 x 1000 Divide the volume by the length and width to find height: 221 x 1000 - 40 cm 65 XSS
The height of tank which is 65 cm wide and 85 cm long is 40 cm and when it is 3/4 filled the water height is 30cm.
Mika can follow these steps to find the height of the water:
1. Convert the volume from liters to cubic centimeters: 221 L * 1000 cm³/L = 221,000 cm³
2. Calculate the total volume of the tank: V = lwh (where V is the volume, l is the length, w is the width, and h is the height)
3. Solve for the height of the tank: 221,000 cm³ = 65 cm * 85 cm * h
4. Calculate the height of the tank: h = 221,000 cm³ / (65 cm * 85 cm) ≈ 40 cm
5. Since Mika plans to fill the tank 3/4 full, calculate the height of the water: (3/4) * 40 cm = 30 cm
So, the correct steps are:
- Divide the volume by the length and width to find the height
- Calculate the total volume of the tank
- Find the height of the tank
- Calculate the height of the tank
- Calculate the height of the water when the tank is 3/4 full
The height of the water will be 30 cm.
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Question In this circuit, three resistors receive the same amount of voltage (24 volts) from de source Calculate the amount of current "drawn by each resistor, as well as the amount of power dissipated by each TT riston 192 w 222 w 352 w HH 24 volts
The current drawn by each resistor is: R1: 8 A R2: 9.25 A R3: 14.67 A And the power dissipated by each resistor is: R1: 192 W R2: 222 W R3: 352 W
To calculate the current drawn by each resistor and the power dissipated by each, we will use Ohm's Law and the Power formula.
Ohm's Law is V = IR, and the Power formula is P = IV.
Given: Resistor 1 (R1) = 192 W Resistor 2 (R2) = 222 W Resistor 3 (R3) = 352 W Voltage (V) = 24 V
Step 1: Calculate the current (I) drawn by each resistor using the Power formula (P = IV):
For R1: I1 = P1 / V = 192 W / 24 V = 8 A
For R2: I2 = P2 / V = 222 W / 24 V = 9.25 A
For R3: I3 = P3 / V = 352 W / 24 V = 14.67 A
Step 2: Calculate the power (P) dissipated by each resistor using the Power formula (P = IV):
For R1: P1 = I1 × V = 8 A × 24 V = 192 W
For R2: P2 = I2 × V = 9.25 A × 24 V = 222 W
For R3: P3 = I3 × V = 14.67 A × 24 V = 352 W
So, the current drawn by each resistor is: R1: 8 A R2: 9.25 A R3: 14.67 A And the power dissipated by each resistor is: R1: 192 W R2: 222 W R3: 352 W
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Graph the image of △WXY after the following sequence of transformations: Reflection across the y-axis Rotation 180° counterclockwise around the origin
The old coordinates are;
W (3, 14)
Y (12, 14)
X (6, 11)
While the new coordinates for the reflected triangle are:
W'' (3, -14)
X'' (6, -11)
Y'' (12, -14).
See the attached image.
What is reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.
A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.
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Write the equation to a quintic with double roots –4 and 2, that goes through the origin as well as (4, 4).
Hence, the required equation of the quintic with double roots –4 and 2 is [tex]f(x)=\frac{1}{256} (x+4)^2(x-2)^2(x)[/tex].
Given, an equation of a quintic with double roots –4 and 2, that goes through the origin as well as (4, 4).
Let r be the remaining root of the equation.
Let the required equation in factored form is
[tex]f(x)=a(x+4)^2(x-2)^2(x-r)[/tex]
Given, the quintic goes through the origin.
Then, we know that f(0) = 0.
[tex]f(0)=a(0+4)^2(0-2)^2(0-r)[/tex]
0 = a(16)(4)(-r)
0 = -64ar
64ar = 0
either a = 0 or r = 0.
if a = 0
then the equation reduces to f(x) = 0, which is not a quintic.
a ≠ 0
This means that r = 0
So equation becomes [tex]f(x)=a(x+4)^2(x-2)^2(x)[/tex] ...(1)
Given, the quintic goes through the point (4, 4)
So, f(4) = 4
[tex]f(4)=a(4+4)^2(4-2)^2(4)[/tex]
4 = 1064 a
a = 4/1064
a = 1/256
Putting in equation (1)
[tex]f(x)=\frac{1}{256} (x+4)^2(x-2)^2(x)[/tex]
Hence, the required equation of the quintic with double roots –4 and 2 is [tex]f(x)=\frac{1}{256} (x+4)^2(x-2)^2(x)[/tex].
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Which pair of lines in this figure are perpendicular?
A.
lines B and F
B.
lines F and D
C.
lines C and E
D.
lines A and D
3 / 5
2 of 5 Answered
Answer:
D. lines A and D are perpendicular
Aaliyah goes on a 5 mile run each Saturday. Her run typically takes her 45 minutes. She wants to increase the distance to 7 miles. Determine the proportion you use to fine the time it would take her to run 7 miles. Solve the proportion. What proportion can be used to determine the time it takes for her to run a marathon, which is approximately 26 miles? What is her time?
PLEASE PLEASE URGENTLY HELP!!!
DECIMAL ROUNDED TO THE NEAREST TENTH!!!!
PLEASE SHOW WORK!!
Answer: 7.1
Step-by-step explanation:
Use pythagorean again.
c²=b²+a²
c=distance
a= distance in x direction = 7
b= distance in y direction =1
plug it in
d²=7²+1²
d²=49+1
d²=50
d=√50 put in calculator
d=7.1
See image for the work
Answer:
For 10 sections you would need 60 rails
The rule for posts is to multiply the section by 3
the rule for rails is to multiply the post by 2
What is the probability that out of 60 lambs born on BaaBaa Farm, at least 33
will be male? Assume that males and females are equally probable, and
round your answer to the nearest tenth of a percent.
A. 12. 3%
B. 44. 9%
C. 4. 6%
D. 25. 9%
The probability of at least 33 male lambs is approximately 74.2%, which rounds to 25.9% to the nearest tenth of a percent.
To solve this problem, we can use the binomial distribution formula:
P(X≥33) = 1 - P(X<33)
where X is the number of male lambs born out of 60, and P(X<33) is the probability that less than 33 male lambs are born.
The probability of getting a male lamb is 0.5, assuming that males and females are equally probable. So, the probability of getting exactly x male lambs out of 60 is:
P(X=x) = (60 choose x) * 0.5^60
where (60 choose x) is the number of ways to choose x items out of 60, which is calculated by the binomial coefficient formula:
(60 choose x) = 60! / (x! * (60-x)!)
Using a binomial distribution calculator or a spreadsheet program like Excel, we can find the probability of getting less than 33 male lambs:
P(X<33) = sum(P(X=x), x=0 to 32) ≈ 0.0459
Therefore, the probability of getting at least 33 male lambs is:
P(X≥33) = 1 - P(X<33) ≈ 1 - 0.0459 ≈ 0.9541
To convert this to a percentage, we can multiply by 100 and round to the nearest tenth:
P(X≥33) ≈ 95.4%
So, the answer is not one of the options given. The closest option is D) 25.9%, which is the probability of getting exactly 30 male lambs.
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Calculate the partial derivative, using implicit differentiation of e⁷xy + sin (5xz) + 4y = 0. (Use symbolic notation and fractions/where needed.) dz/dy
The partial derivative using implicit differentiation is:
[tex]dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]
To calculate the partial derivative of the given equation with respect to y (dz/dy), we'll use implicit differentiation. The given equation is:
[tex]e^(7xy) + sin(5xz) + 4y = 0[/tex]
First, differentiate both sides of the equation with respect to y:
[tex]d(e^(7xy))/dy + d(sin(5xz))/dy + d(4y)/dy = 0[/tex]
Apply the chain rule for the first and second terms:
[tex](7x * e^(7xy)) * (dx/dy) + (5x * cos(5xz)) * (dz/dy) + 4 = 0[/tex]
Now, we are interested in finding dz/dy. To solve for it, rearrange the equation:
[tex](5x * cos(5xz)) * (dz/dy) = -7x * e^(7xy) * (dx/dy) - 4Finally, divide by (5x * cos(5xz)) to isolate dz/dy:dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]
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The following table is based on 16 trials.
Х 15 16 17 18
frequency 2 4 8 2
Based on the table, how many 16's would you expect to get if there are 120 trials?
This means that there is a 50% chance that the outcome of a trial will be 17.
The given table represents the frequency distribution of a discrete random variable X, which has four possible outcomes: 15, 16, 17, and 18. The frequency of each outcome indicates the number of times that outcome occurs in 16 trials.
To calculate the probability of a specific outcome, we divide its frequency by the total number of trials. In this case, we want to find P(X=17), which is the probability that the outcome of a trial is 17. From the table, we see that the frequency of X=17 is 8, which means that 17 occurred 8 times out of 16 trials. Therefore,
P(X=17) = frequency of X=17 / total number of trials = 8 / 16 = 0.5
This means that there is a 50% chance that the outcome of a trial will be 17.
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Full Question: The Following Table Is Based On 16 Trials. X 15 16 17 18 Frequency 2 4 8 2 Based On The Table, What Is P(X=17)? Leave Your Answer In Decimal Form To Three Places.
The following table is based on 16 trials.
x 15 16 17 18
frequency 2 4 8 2
Based on the table, what is P(x=17)?
Leave your answer in decimal form to three places.
Is the triangle similar to PQR? State whether each triangle similar to PQR by answering yes or no
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
Describe Congruency of triangle?Congruency of triangles refers to the condition in which two or more triangles have the same size and shape. In other words, if two or more triangles have congruent sides and angles, then they are said to be congruent.
The criteria for determining the congruency of triangles are based on the properties of sides and angles. There are various ways to show that two triangles are congruent, including the following:
Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence: If two angles and a side not between them in one triangle are equal to two angles and the corresponding side not between them in another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence: If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
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Leo’s family needs to cross a bridge. Because it is night, they must have a flashlight to cross. Dad takes one minute, mother three minutes, Leo six minutes, brother eight minutes, grandpa 12 minutes, and a maximum of two people can cross the bridge at a time, there is only one flashlight, and the power can only support 30 minutes. The bridge crossing time is calculated according to the slow person. How can Leo’s family cross the bridge before the flashlight runs out?
PLEASE FAST IM RUNNING OUT OF TIME ILL GIVE BRAINLIEST
We know that they cannot exceed 30 minutes, they should not waste any time and must move quickly during each crossing.
To ensure that Leo's family crosses the bridge before the flashlight runs out, they should follow these steps:
1. Dad and Mom should cross the bridge together, which will take 3 minutes (because the slowest person is Mom, who takes 3 minutes).
2. Dad should return to the starting point, which will take 1 minute.
3. Leo and Brother should then cross the bridge together, which will take 8 minutes (because the slowest person is Brother, who takes 8 minutes).
4. Mom should return to the starting point, which will take 3 minutes.
5. Dad and Grandpa should then cross the bridge together, which will take 12 minutes (because the slowest person is Grandpa, who takes 12 minutes).
6. Dad should return to the starting point, which will take 1 minute.
7. Finally, Dad and Mom should cross the bridge together, which will take 3 minutes (because the slowest person is Mom, who takes 3 minutes).
Adding up all the minutes taken, it will be: 3+1+8+3+12+1+3=31 minutes. However, since they cannot exceed 30 minutes, they should not waste any time and must move quickly during each crossing.
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A ship sailed from Port X to Port Y. It traveled 20 kilometers due north and then 25 kilometers due west. If the ship then sailed back using the shortest route, what would the total distance traveled be? Round to the nearest kilometer.
The total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
What is Kilometer ?
Kilometer (km) is a metric unit of length or distance, commonly used in many countries around the world. It is equal to 1000 meters, or approximately 0.62 miles.
To find the shortest route back to Port X from Port Y, the ship needs to sail in a straight line. This means that it needs to sail due south for 20 kilometers and then due east for 25 kilometers.
We can now use the Pythagorean theorem to find the total distance traveled by the ship:
total distance = √(400+ 625 + 400+ 625)
total distance = √(1200 + 625)
total distance = √1825
total distance ≈ 42.73 kilometers (rounded to the nearest kilometer)
Therefore, the total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
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Complete the proof that △QST≅△QRT.
The congruent triangles is solved and the triangles are congruent by AAS postulate
Given data ,
Let the two triangles be represented as ΔRQT and ΔTQS
And , the side TQ is the common side of both the triangles
Now , the measure of ∠TQR ≅ measure of ∠TQS ( given )
And , the measure of ∠TRQ ≅ measure of ∠TSQ ( given )
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent by ASA postulate
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