The sum of three numbers is 154
The second number is 8 times the first.
The third number is 16 less than the second.
What is the third number?

The first integral becomes ∫∫\(R u^5 v^4 (2uv^2) \sqrt{(4u^2v^2 + 1) du}\)

To compute the flux of the vector field F through the surface S, we can use the surface integral formula:

flux = ∬s F · dA

where dA is the differential area element of the surface S and the double integral is taken over the entire surface.

In this case, the vector field F is given by:

F = −xz i − yz j + \(z^2 k\)

And the surface S is the cone \(z = x^2 y^2\)for 0 ≤ z ≤ 9, oriented upward. To find the differential area element dA, we can use the parametrization of the surface in terms of u and v:

x = u

y = v

\(z = u^2 v^2\)

where (u, v) ranges over the region R = {(u, v) | 0 ≤ u ≤ 3, 0 ≤ v ≤ 3}.

The partial derivatives of the parametrization are:

∂x/∂u = 1, ∂x/∂v = 0

∂y/∂u = 0, ∂y/∂v = 1

∂z/∂u = \(2uv^2, ∂z/∂v = 2u^2v\)

Using these, we can find the cross product of the partial derivatives:

∂r/∂u x ∂r/∂v = \((-2uv^2) i + (2u^2v) j + k\)

and the magnitude of this vector is:

|∂r/∂u x ∂r/∂v| = \(\sqrt{((2uv^2)^2 + (2u^2v)^2 + 1) } = \sqrt{(4u^2v^2 + 1)}\)

Therefore, the differential area element is:

dA = |∂r/∂u x ∂r/∂v| du dv = sqrt(4u^2v^2 + 1) du dv

Now we can compute the flux of F through S using the surface integral formula:

flux = ∬s F · dA

= ∫∫R F(u, v) · (∂r/∂u x ∂r/∂v) du dv

Substituting in the expressions for F and the cross product, we have:

flux = ∫∫\(R (-uxz -vyz + z^2) (-2uv^2 i + 2u^2v j + k) \sqrt{(4u^2v^2 + 1) du dv}\)

The limits of integration are u = 0 to u = 3 and v = 0 to v = 3. We can break this up into three separate integrals:

flux = ∫∫\(R (-uxz) (-2uv^2) \sqrt{ (4u^2v^2 + 1) du dv}\)

+ ∫∫\(R (-vyz) (2u^2v) \sqrt{(4u^2v^2 + 1) du dv}\)

+ ∫∫\(R z^2 \sqrt{(4u^2v^2 + 1) du dv}\)

The first integral can be simplified using the equation for the cone z = \(x^2 y^2:\)

\(uxz = u(-u^2 v^2)(u^2 v^2) = -u^5 v^4\)

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The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.

The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.

The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.

It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.

Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.

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Answer:

Step-by-step explanation:

x=y-3 this is your main formula to find x

first  y=4-3=1 , x=1

second y=8-3=5  , x=5

third  y=5-3=2,  x=2

Answer:

.

Step-by-step explanation:

The possible triangle orientations are given below -

The relation is that the sum of the two sides of the triangle is greater than the third side. Mathematically -

a + b > c

Given are the sides of a triangle as shown in the triangle.

{ 1 } -

2 yd , 7 yd , 8 yd

7 + 2 > 8

9 > 8    {true}

It forms a triangle.

{ 2 } -

1.5 cm, 2.3 cm, 3.8 cm

2.3 + 1.5 > 3.8

3.8 > 3.8    {false}

It does not form a triangle.

{ 3 } -

3 in. , 4 in. , 5in.

4 + 3 > 5

7 > 5  {true}

It forms a triangle.

{ 4 } -

5 m , 9 m , 14.5 m

9 + 5 > 14.5

14 > 14.5   {false}

It does not form a triangle.

{ 5 } -

14 ft , 15.8 ft , 33 ft

15.8 + 14 > 33

29.8 > 33    {false}

It does not form a triangle.

{ 6 } -

2.8 mm , 7.1 mm , 9.5 mm

7.1 + 2.8 > 9.5

9.9 > 9.5 {true}

It forms a triangle.

Therefore, the possible triangle orientations are given below -

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Answer:

Is there a full question??

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perimeter of ABCD is 30cm

The Sum of the perimeter of three rectangles at the corner is 20cm.

following the variables as the same as you assigned

large rectangle: u by v

rectangle center A: 2a by 2b

rectangle center B: 2c by 2d

rectangle center D: 2e by 2f

2 equations (from the givens):

2u+2v=30

2(a + b + c + d + e + f )= 20

now to find the length

a+b+a/2+b/2+(v-b/2-d/2)+c/2+d+c+d/2+(u-c/2)+(v-f/2)+e/2+f+e+f/2+(u-e/2-a/2)

which is (a+b+c+d+e+f)+u+v+u+v = 10+30=40

Her employer's contribution to the 401(k) was $2,500.

Given that for the first 3% of Pam's salary, her employer matches 100% of her 401(k) contributions, and from 3% to 12%, Pam's employer matches 50% of her 401(k) contributions, and Pam's salary is $30,000 , and last year, she contributed $4000 to her 401(k) plan, to determine what was her employer's contribution to the 401(k) the following calculation must be made:

Therefore, her employer's contribution to the 401(k) was $2,500.

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Answer: C. $2250

Step-by-step explanation: took the quiz.

The maximum clearance of the underpass ahead is 12 feet and 6 inches.

Based on the information provided, the sign indicates that there is an underpass ahead with a clearance of 12 feet and 6 inches. The sign further mentions that the train in question is also 12 feet and 6 inches long, and it highlights the presence of a narrow median, which is only 6-12 inches wide.

In this context, the sign serves as a warning to drivers approaching the underpass. The clearance measurement of 12 feet and 6 inches informs drivers of the maximum height of vehicles that can safely pass through the underpass without any risk of collision. Since the train length matches the clearance, it implies that vehicles longer than the underpass clearance may not be able to pass through safely if the train is present.

The mention of a narrow median emphasizes the limited space available between the opposing lanes of traffic. With a width of only 6-12 inches, the median may not provide sufficient room for larger vehicles to maneuver, particularly when encountering oncoming traffic or passing through the underpass while the train is present.

Overall, the sign conveys important information regarding the underpass clearance, the train length, and the narrow median, all of which should be considered by drivers to ensure safe passage through the upcoming area.

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The sign indicates the clearance height of an underpass, warns of a narrow median, and mentions the length of a train.

The sign in question is indicating that there is an underpass ahead with a clearance of 12 feet and 6 inches. This means that any vehicle taller than that would not be able to pass through without hitting the underpass ceiling. Additionally, the sign mentions that the train itself is also 12 feet and 6 inches long, so it is important for drivers to be cautious and aware of the height restrictions. The narrow median mentioned refers to the strip of land or barrier between lanes, which in this case is only 6-12 inches wide.

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The area of the running track to the nearest tenth of a yard is 1456 yards

The length of the field is 100 yards with a width of 40 yards.

Notice that the two semicircles on both ends form a circle with diameter 40 yards. Since it's diameter is 40, then it's radius is 20. We can get the length of the rectangle by subtracting two 20 from 100 or subtracting it's diameter to the entire length 100:

= 100-20-20

=100-40

=60

Since we formed a rectangle with two semicircles on both ends, we have the length of the rectangle 60 yards and the width 40 yards.

We first get the circumference of the circle.

C=πd

=(3.14)(40)=125.6

Then we get the measure of the two lengths of the rectangle which is 60

60+60=120

We multiply 145.6 by 10 and we get 1456

Therefore, the area of the running track to the nearest tenth of a yard is 1456 yards.

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Answer:

3570 square yards.

Step-by-step explanation:

A=  ℓh-ℓh+πr square-πr square

A=60 * 100 - 40 * 100 + π(30) square - π(20) square

A= 6000-4000+900π-400π

A=2000+500π

A=2000+500*3.14

A=3570 square yards.

Answer:

t = 4

Step-by-step explanation:

1. 2*t = 2t

2. 2*1 = 2

3. 2t+2 = 10

4. 10-2 = 8

5. 2t = 8

6. 8/2 = 4

7. t = 4

Answer:

t = 4

Step-by-step explanation:

2(t + 1) = 10

2t + 2 = 10

2t = 10 - 2

2t = 8

t = 8 ÷ 2

t = 4

-TheUnknownScientist

Aw that's really nice of you thanks

thank you <3 appreciate it loads

The values of the trigonometric identities are;

1. tan X = 10/17

2.  tan X = 29/25

3. sin A = 24/25

4. tan C = 15/17

5. sin A = 8/17

6. cos A = 9/41

7. cos Z = 3/4

Note that fractions are the part of a whole number.

Also,

sin θ = opposite/hypotenuse

cosθ = adjacent /hypotenuse

tan θ = opposite/adjacent

1. tan X = opposite/ adjacent

tan X = 30/21 = 10/7

2. tan X = 29/25

3. sin A = opposite/hypotenuse

sin A = 24/25

4. tan C = opposite/adjacent

tan C = 30/34

tan C = 15/17

5. sin A = 16/34

sin A = 8/17

6. cos A = adjacent/hypotenuse

cos A = 9/41

7. sin A = 21/35

8. cos Z = 21/28

cos Z = 3/4

Hence, the fractions takes the function of the trigonometric identities.

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Answer:

10. _. 4

Step-by-step explanation:

5 5 10 _. + _ = _ 4. 4. 4

Answer:

45

Step-by-step explanation:

it's very easy to do if u know

Step-by-step explanation:

to find the area more easily, you can divide the figure.

make a small rectangle from the upper part (a 5×6 rectangle) then a square from the lower part (a 5×5 square).

now you have a small rectangle, a big rectangle and a square.

small rectangle: 5×6=30

big rectangle: 15×5=75

square:5×5=25

30+75+25=130

if anything is unclear, ask freely.

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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Answer: 0.512

Step-by-step explanation:

256/32=8

8*(0.4)^3=

8*0.064=0.512

y=0.512

The value of y is 0.8 when x is 256.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

x is directly proportional to the cube of y.

Implies that,

x ∝ y³

Or x = k . y³        (1)

Here, k is a constant.

Substitute x = 32 and y = 0.4 in equation (1),

32 = k (0.4)³
32 = k (64/1000)

k = 1000/2

k = 500

To find the value of y when x = 256 and k = 500,

From equation (1)

256 = 500 y³

y³ = 256 / 500

y³ = 64/ 125

y = 4/5

y = 0.8

The required value of y is 0.8 when x = 256.

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Answer:

n + 6 > 31

Step-by-step explanation:

We can't flip a coin a fractional number of times, we round up to the nearest whole number, which gives us a minimum sample size of 385 flips. We would need to flip the coin at least 385 times in order to obtain a 95% confidence interval of width at most 0.05 for the probability of flipping a head.

To determine how many times we would need to flip the coin, we can use the formula for the margin of error for a confidence interval:
Margin of error = z* * (standard deviation / sqrt(sample size))
Here, z* is the z-score corresponding to the desired level of confidence (95% in this case), and the standard deviation is equal to sqrt(p*(1-p)), where p is the true probability of flipping a head. Since we suspect the coin is fair, we can use p = 0.5.
Rearranging the formula to solve for sample size, we get:
Sample size = (z* / margin of error)^2 * p * (1-p)
Plugging in the values we have, with a desired margin of error of 0.05 and a z-score of 1.96 for 95% confidence, we get:
Sample size = (1.96 / 0.05)^2 * 0.5 * (1-0.5) = 384.16
Since we can't flip a coin a fractional number of times, we round up to the nearest whole number, which gives us a minimum sample size of 385 flips. Therefore, we would need to flip the coin at least 385 times in order to obtain a 95% confidence interval of width at most 0.05 for the probability of flipping a head.

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Here is a diagram of the points described:

(2,3)      (2, -3)

  |             |

  |             |

  c----------d

Based on the given points, let's consider the following:

Point A: A (2, 3)

Point B: B (2, -3)

Points A and B have the same x-coordinate, indicating that they lie on a vertical line. The y-coordinate of A is greater than the y-coordinate of B, suggesting that A is located above B on the y-axis.

Now, you mentioned that points C and D are collinear. Collinear points lie on the same line. Assuming that points C and D lie on the same vertical line as A and B, but at different positions.

The points A (2,3) and B (2, -3) are collinear, but the points A, B, C, D, and F are not. This is because the points A and B have the same x-coordinate, so they lie on the same vertical line. The points C and D also have the same x-coordinate, so they lie on the same vertical line. However, the point F does not have the same x-coordinate as any of the other points, so it does not lie on the same vertical line as any of them.

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Answer:

x= 67, y= 113 , z= 67........... ...........

Answer:

c

Step-by-step explanation:

it moves virticly across

Answer:

-4x + 6

Step-by-step explanation:

The equation is 2(-2x + 3). We need to do distributive property to solve this. 2 times -2x = -4x. 2 x 3 = 6. Therefore, the final answer will be -4x + 6. We cannot simplify the equation any further because -4x and 6 are not like terms.

Hope this helps! Thanks for brainliest! :D

Answer:

-4x + 6

Step-by-step explanation:

2(-2x + 3) = -4x + 6

Solution given.

Volume of rectangular prism=2400cm³

area of base*height=2400cm³

For A

satisfied for all

for B

not satisfied for all

for C

not satisfied for all

for D.

not satisfied for all

Option A.is your answer.

The probability that one item is defective is 32.4%.

Here we have two possibilities for each of the 3 items, it is defective or it is not.

Where the probability that the item is defective is equal to 15% (or 0.15 in decimal form)

Now, if only one is defective, this means that the other two are not, so the probabilities (at random) are 15%, 85% and 85%.

Then the joint probability, equal to the product of those 3 probabilities, is:

p = 0.15*0.85*0.85

= 0.108

But we have 3 possible permutations (in which different options are the defective one) so the probability is 3 times that number:

P = 3p = 3*0.108 = 0.324

So the probability, in percentage form, is 32.4%

Hence we get the required answer.

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Answer:

Step-by-step explanation:

1. 1 3/4

2. 3 3/8