find the length of each side of a square field whose area is 608 sq.m

Answer:

r=30

Step-by-step explanation:

r/30=-2+3

r/30=1

r=1×30

r=30

The number of ways to divide 10 players into two teams of 5 with Steve and Danny on different teams is -3668, implying that it's impossible to divide the teams as such. This result shows that the probability of both players being on the same team is one, and is related to the complement of the probability of them being on opposite teams.

We have our basketball team has 10 players, including Steve and Danny, and we need to divide them into two teams of 5 for an intrasquad scrimmage.

The number of ways of selecting r objects out of n is given by ⁿCr where,

ⁿCr = (n!) / [(n - r)! r!]

Here, the number of ways to choose 5 players out of 10 is ¹⁰C₅.

¹⁰C₅ = (10!) / [(10 - 5)! 5!]

¹⁰C₅ = (10 x 9 x 8 x 7 x 6) / (5 x 4 x 3 x 2 x 1)

¹⁰C₅ = 252

There are 252 ways to divide the 10 players into two teams of 5.

Using complementary probabilities, we can find the number of ways in which the teams can be picked such that Steve and Danny are on the same team.

For that, we need to calculate the number of ways in which Steve and Danny can be together, and then subtract this from the total number of ways.

Using the same logic, the number of ways to choose 4 more players out of 8 is ⁸C₄.

⁸C₄ = (8!) / [(8 - 4)! 4!]

⁸C₄ = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1)

⁸C₄ = 70

There are 70 ways to choose 4 players from the remaining 8 (excluding Steve and Danny).

We can consider Steve and Danny as one player, so we need to select 3 more players from the remaining 8 (excluding Steve and Danny).

The number of ways to do this is ⁸C₃.

⁸C₃ = (8!) / [(8 - 3)! 3!]

⁸C₃ = (8 x 7 x 6) / (3 x 2 x 1)

⁸C₃ = 56

There are 56 ways to select 3 players from the remaining 8 to join Steve and Danny.

Using the multiplication principle, we get the number of ways to select the entire team as 70 x 56 = 3920.

There are 3920 ways to choose the teams so that Steve and Danny are on the same team.

Now, using the complement rule, the number of ways to select the teams so that Steve and Danny are on opposite teams is given by the total number of ways minus the number of ways in which Steve and Danny are on the same team.

Using this, we can say that the number of ways to divide the 10 players into two teams of 5 such that Steve and Danny are on opposite teams is given by 252 - 3920 = -3668.

However, the answer is negative which means that there is no way to divide the teams such that Steve and Danny are on opposite teams.

Hence, the solution to the problem is related to the complement of the probability.

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In this case, The critical numbers are x = 1.

To find the critical numbers of g(y) = (y-2)/(y^2-2y+4), we first find the derivative g'(y) and then set it equal to zero or find where it's undefined.

g'(y) = (2y-2)/((y^2-2y+4)^2).

The critical numbers are y = 1. 2.

For f(x) = x^(-2)ln(x), you probably meant f(x) = x^(-2)ln(x).

In this case, find the derivative f'(x) and set it equal to zero or find where it's undefined.

f'(x) = -2x^(-3)ln(x) + x^(-2)(1/x).

The critical numbers are x = 1.

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Answer: 4,375 rs

Step-by-step explanation:

25% × 17,500 = 4,375

Answer:

$4375

Step-by-step explanation:

25 percent *17500 =

(25:100)*17500 =

(25*17500):100 =

437500:100 = 4375

Now we have: 25 percent of 17500 = 4375

Answer:

20

Step-by-step explanation:

x^2 -y +1

Let x =5 and y = 6

5^2 -6+1

25-6+1

19+1

20

Answer:

diameter 12mm

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(f + g) (x) = f(x) + g(x)

= ( |3x + 4| + 4) + (2)

= |3x + 4| + 4 + 2

= |3x + 4| + 6

Answer:

Option B: \(y=\left \{ {{x^2+6,x<3} \atop {-x+6,x\geq3}} \right.\)

Step-by-step explanation:

We can see that the first part of the piecewise function is a parabola with a y-intercept of (0,6) where the domain is restricted for all values of x less than 3 given the open circle at x=3.

The second part of the piecewise function is a linear function with a negative slope where the domain is restricted for all values of x greater than or equal to 3 given the closed circle at x=3.

Essentially, the piecewise function has a jump discontinuity at x=3 where the first part of the function goes to the second part of the function at one point by "jumping".

The algebraic expression for the given phrase would be: c + 6, where c represents the unknown quantity (number of cars in the garage) and 6 represents the number of cars outside.

To translate the following phrase into an algebraic expression, we need to use the variable c to represent the unknown quantity. The phrase is "the total of the number of cars in the garage and the 6 cars outside."

So, the algebraic expression is: c + 6Where "c" represents the number of cars in the garage.

The expression c + 6 represents the total number of cars, which is the sum of the number of cars in the garage and the 6 cars outside.

Example: If there are 10 cars in the garage, then the total number of cars would be: c + 6= 10 + 6= 16.

So, there would be 16 cars in total.

The expression c + 6 would always give us the total number of cars, regardless of the value of "c."

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The value of k that would make the system consistent is k = 30.

To find the value of k that would make the system consistent, we can solve the system of equations:

{-9x - 6y = 15

{-18x - 12y = k

{-12x - 8y = 20

We'll use the first equation to eliminate x in the other equations. Multiply the first equation by -2 and the third equation by -1:

{18x + 12y = -30

{-18x - 12y = k

{12x + 8y = -20

Adding the modified equations (1) and (2):

{18x + 12y + (-18x) - 12y = -30 + k

0 = -30 + k

Simplifying the equation, we get:

k = 30

Therefore, the value of k that would make the system consistent is k = 30.

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If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.

An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.

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Answer:

-1/24 < x < 0

Step-by-step explanation:

We are asked to interpret the meaning of r'(3), which is the derivative of the leak rate function at three hours after the leak is discovered.

r'(3) represents the instantaneous rate of change of the leak rate function at three hours after the leak is discovered. More specifically, it tells us how fast the leak rate is changing with respect to time at that particular moment. If r'(3) is positive, it means that the leak rate is increasing at that moment, whereas if it is negative, it means that the leak rate is decreasing.

For example, if r'(3) = 2, it means that the leak rate is increasing at a rate of 2 gallons per hour per hour (or 2 gallons per hour squared) at three hours after the leak is discovered. In other words, the leak rate is accelerating at that moment. Similarly, if r'(3) = -1, it means that the leak rate is decreasing at a rate of 1 gallon per hour per hour (or 1 gallon per hour squared) at three hours after the leak is discovered. In this case, the leak rate is decelerating at that moment.

Therefore, r'(3) provides us with valuable information about the behavior of the leak rate function at a particular moment in time.

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The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

a) The probability that in any given hour zero new visitors will arrive at the website is given by;P(X = 0) = (e^-λ λ^0)/0!Where λ = 2.3Thus;P(X = 0) = (e^-2.3 2.3^0)/0!P(X = 0) = (0.1003)/1P(X = 0) = 0.1003b) The probability that in any given hour exactly one new visitor will arrive at the website is given by;P(X = 1) = (e^-λ λ^1)/1!Where λ = 2.3Thus;P(X = 1) = (e^-2.3 2.3^1)/1!P(X = 1) = (0.2303)/1P(X = 1) = 0.2303c) The probability that in any given hour two or more new visitors will arrive at the website is given by;P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)Thus;P(X ≥ 2) = 1 - 0.1003 - 0.2303P(X ≥ 2) = 0.6694d) The probability that in any given hour fewer than three new visitors will arrive at the website is given by;P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)Thus;P(X < 3) = 0.1003 + 0.2303 + 0.2642P(X < 3) = 0.5948Therefore,The probability that in any given hour zero new visitors will arrive at the website is 0.1003.The probability that in any given hour exactly one new visitor will arrive at the website is 0.2303.The probability that in any given hour two or more new visitors will arrive at the website is 0.6694.The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

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Answer:

The answer is C

Step-by-step explanation:

All I did was try to match C with F. Count how many lines you went to the right and thats your x value. Same for Y but down. Down forgot to add integers.

Answer:

Volume

For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3

For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, \(\pi\) = 3.14
V = radius^2 x height x \(\pi\)
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)

Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3

Surface Area

Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2

A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)

Semi-circular prism:
A = 2\(\pi\)rh + 2\(\pi\)r^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2

Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2

Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.

To find the component of vector v = 3a - 2b over vector w = 2a + 3b, we can use the formula for the projection of one vector onto another. The projection of v onto w is given by the formula:

Proj_w(v) = (v . w) / ||w||^2 * w where . denotes the dot product and ||w|| denotes the magnitude of vector w. First, let's calculate the dot product of v and w: v . w = (3a - 2b) . (2a + 3b)

Expanding this using the distributive property, we get: v . w = 6(a . a) - 4(a . b) + 9(b . b) Next, we need to find the magnitudes of a and b to calculate ||w||: ||w|| = ||2a + 3b|| = sqrt((2a + 3b) . (2a + 3b)) Expanding this using the distributive property, we get: ||w|| = sqrt(4(a . a) + 6(a . b) + 9(b . b))

Now, substitute the values we have calculated into the projection formula: Proj_w(v) = (v . w) / ||w||^2 * w Proj_w(v) = (6(a . a) - 4(a . b) + 9(b . b)) / (4(a . a) + 6(a . b) + 9(b . b))^2 * (2a + 3b) After simplifying, we get: Proj_w(v) = (18(a . a) - 12(a . b) + 27(b . b)) / (4(a . a) + 6(a . b) + 9(b . b))^2 * (2a + 3b)

Now, plug in the values of a = (4, -2, 1) and b = (2, -1, 4) into the formula to get the component of v over w.

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Answer:

Step-by-step explanation:

Let be cost price =Rs.100

Then mark price =Rs.120

∴ Selling price =90% of 120

=

100

120×90

​

=Rs.108

Profit = Selling price− Cost price

=Rs.(108−100)=Rs.8

Profit % =

100

8×100

​

=8%

Answer: $2 per candle

Step-by-step explanation:

Dollars to candles

4 to 2

is equivalent to

2 to 1

$2 per candle

The ratio of candles to dollars is 1/2.

$2 per candle.

Option B is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The following coordinates are from the graph.

(2, 4), (4, 8), (8, 16).

The x-coordinates denote the number of candles.

The y-coordinate denotes the cost.

Now,

(2, 4) means 2 candles cost $4.

(4, 8) means 4 candles cost $8.

(8, 16) means 8 candles cost $16.

The ratio of candles to dollars.

= 2/4

= 1/2

This means,

The cost of one candle is $2.

Thus,

The cost of one candle is $2.

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Answer: b is right angel triangle 90 degrees

b - c is straight line that adds up to 180 degrees

9 is the height for sin, cos and sine

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

Answer:

7(32)=7(30+2)=7*2=210+14=224

Step-by-step explanation:

nd the star is the multiplacations sign bcz i dont have the dot mk.

Answer:

the value would be 49

Answer:

\(2x^{2} + 3y^{2} -17 \\x=3 ; y=4\\\\2*2^{2}+ 3*4^{2}-17\\8+48 -17\\=39\)

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Approximately 1.5% of computer programmers make over $97,800.

The average salary of computer programmers is $71,800 with a standard deviation of $13,000. To determine the percentage of programmers making over $97,800, we need to find the area under the normal distribution curve to the right of this value.

Using the z-score formula, we can find the z-score corresponding to $97,800: z = (x - μ) / σ = (97800 - 71800) / 13000 ≈ 2.145.

Looking up the z-score in a standard normal distribution table, we find that approximately 1.5% of programmers make over $97,800.

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 By multiplying matrices B and A, we obtain the product BA. Using BA, we can solve the system of equations y + 2z = 7, x - y = 3, and 2x + 3y + 4z = 17.the values of x, y, and z are -1, 2, and 1 respectively

To find the product BA, we multiply matrix B with matrix A. The resulting matrix will have the same number of rows as B and the same number of columns as A. The product BA will be used to solve the given system of equations.
The product BA can be computed by multiplying each row of matrix B by each column of matrix A and summing the results. The resulting matrix will be:
Now, we can use the product BA to solve the system of equations:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.

1 -1 2
2 3 1
0 4 2
We can rewrite this system of equations as:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.
By comparing the coefficients of x, y, and z in the system of equations with the entries in the matrix BA, we can determine the values of x, y, and z.
Solving the system of equations using matrix BA, we get:
x = -1,
y = 2,
z = 1.
Therefore, the values of x, y, and z are -1, 2, and 1 respectively.

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The complete question is:
Given A=
⎣2 2 -4|
|-4 2 -4|
|2 -1 5|
, B=
⎣1 -1 0|
⎢2 3 4|
⎢0 1 2|
, find BA and use this to solve the system of equations y+2z=7, x−y=3, 2x+3y+4z=17.

Step-by-step explanation:

I don't know

if this is what. You were trying to look for

y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

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Given:

The value is \(\sqrt{90}\).

To find:

The two consecutive whole numbers such that \(\sqrt{90}\) lies between those numbers.

Solution:

The perfect square numbers between 1 to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

We know that, 90 lies between 81 and 100.

\(81<90<100\)

\(9^2<90<10^2\)

The value of x radical cannot be negative. So taking square root on each side, we get

\(\sqrt{9^2}<\sqrt{90}<\sqrt{10^2}\)

\(9<\sqrt{90}<10}\)

The given number lies between 9 and 10. Therefore, the correct option is (d)

Answer:

10 pounds

Step-by-step explanation:

given ratio weight:added weight=10:1

100:x=10:1

100/x=10/1

solving for x

100=10x

x=10