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The events A and B are not independent.

Given that,

                  P(A|B) = 0.4

                  P(A) = 0.5

                  P(B) = 0.8

Two events A and B are said to be independent, if P(A∩B) = P(A) P(B)

We have, P(A|B) = P(A∩B)/P(B)

Therefore, P(A∩B) = P(A|B) P(B) = 0.4 x 0.8 = 0.32

Now P(A) P(B) = 0.5 x 0.8 = 0.4

So P(A∩B) ≠ P(A)P(B)

Therefore, the events A and B are not independent.

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Answer:

Step-by-step explanation:

7(i)

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=\frac{dx}{dx} *(3x-5)^\frac{5}{3}+x*\frac{d}{dx} \{(3x-5)^\frac{5}{3} \}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=1*(3x-5)^\frac{5}{3} +x*\frac{5}{3}*(3x-5)^{\frac{5}{3} -1}*\frac{d}{dx} \{(3x-5)\}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +\frac{x*5*(3x-5)^{\frac{2}{3}}*3 }{3} \\\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +5x*(3x-5)^\frac{2}{3} \\\\[/tex]

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3}*((3x-5)^{\frac{5}{3}-\frac{2}{3}} + 5x)\\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5)^\frac{3}{3}+5x) \\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5+5x)\\\ \frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(8x-5)*(3x-5)^\frac{2}{3}[/tex]

7(ii)

[tex]\int\limits {(x*(3x-5)^\frac{2}{3}) } \, dx \\Let\ \sqrt[3]{3x-5} =u\\Hence,\\(\sqrt[3]{3x-5})^3=u^3\\ 3x-5=u^3\\3x-5+5=u^3+5\\3x=u^3+5\\[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=\frac{u^3+5}{3}\\\\dx=\frac{d}{du} \{\frac{u^3+5}{3}\} \\dx=\frac{3u^2}{3} du=\\\\dx=u^2du\\Hence,\\\\\int\limits {\frac{u^3+5}{3}* u^2*u^2} \, du =\\\\\int\limits {\frac{u^3+5}{3} *u^4} \, du =\\\\\int\limits {\frac{u^7+5u^4}{3} } \, du =\\\\\frac{1}{3} \int\limits {u^7} \, du +\frac{1}{3}\int\limits {5u^4} \, dxu =\\\\[/tex]

Answer: 18

Step-by-step Explanation:

Subtract: 5 from 41 | 41-5= 36

Divide: by 2 | 36/2= 18

Answer:18

Step-by-step explanation:

SUBTRACT41 FROM 5

THAT GIVES YOU 38

THEN DIVIDE 38/2 AND IT WILL GIVES 18

a) The distance of the plane from the airport is approximately 781.025 miles.

b) The bearing of the airplane in standard position is approximately 320.194°.

Let the location of the airport be the origin and the orthogonal axes are oriented to the east and north, respectively. Beside, let consider that the plane moves at constant speed. a) Thus, the distance of the plane can be found by using the Pythagorean Theorem:

d = √[[(240 mi / h) · (2.5 h)]² + (500 mi)²]

d ≈ 781.025 mi

b) And the bearing in standard position is determined by the following inverse trigonometric function:

θ = tan⁻¹ [(- 500 mi) / [(240 mi / h) · (2.5 h)]]

θ ≈ 320.194°

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The perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

We are given the vertices:

A(-4,4), B(2,-2), and C(-4,-2).

We need to find the perimeter of ABC.

AB = √ ( 2 + 4)² + (-2 - 4)²

AB = √ 6² + 6²

AB = √72

AB = 6 √2 units

BC = √ (-4 - 2)² + ( -2 + 2)²

BC = √ 6²

BC = 6 units

AC = √ ( -4 + 4)² + (-2 - 4)²

AC = √ 6²

AC = 6 units.

Perimeter = AB + BC + AC

Perimeter = 6 √2 + 6 + 6 units

Perimeter = 12 + 6 √2 units.

Perimeter = 12 + 6(1.414) units

Perimeter = 12 + 8.848 units

Perimeter = 20.848 units

Therefore, the perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

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Answer:

Step-by-step explanation:

12 = 12 + v - (8/2)

12 = 12 + v - 4

12 - 12 = v - 4

v = 4

Answer: The approximately percent uncertainty for the measurement is 0.62%.

Step-by-step explanation:

The given parameters:

Area of the measurement, A = 1.59 m²

The uncertainty in the measurement of the area = ±0.01 m²

The approximately percent uncertainty for the measurement is calculated as follows;

[tex](0.01/1.59)*100[/tex] %

=0.62%

Thus, the approximately percent uncertainty for the measurement is 0.62%.

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Answer: 0.6 percent.

Step-by-step explanation:   to find the uncertainty , we will take that absolute uncertainty _0.01 divided by the measurement of 1.59 _ times by a hundred percent and we get 0.6 percent.

Answer:

49

Step-by-step explanation:

The ratio of three numbers = 2:5:7

Then the numbers are 2x,5x and 7x

Given that the LCM of these numbers  = 490

LCM of 2x,5x,7x is 2×5×7×x = 70x

Then, we have 70x = 490

x  = 7

Hence, the numbers are 14, 35 and 49

Largest number = 49

∴The square root of the largest number = 7

A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to  foot/hour

2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to  miles/minute

1 mile=5280 feet

22 miles/hour=22 × 5280 foot/hour

22 miles/hour=116,160 foot/hour

1 hour=60 minute

125 miles/hour= 125/60 miles/minutes

125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes

Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

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Answer:

1) 1/2 × 3/5 = 45/150

2) 5/5 × 3/5 = 90/150

3) 2 2/3 × 3/5 = 1 90/150

Explanation below

Explanation belowHope this helps :)

Step-by-step explanation:

1/2 × 3/5 = 3/10

2 2/3 × 3/5 = 8/3 × 3/5 = 24/15

5/5 × 3/5 = 15/25

We need to find the Least Common Multiple (LCM) to order them from least to greatest.

The LCM is 150.

3/10 = 45/150

24/15 = 1 9/15 = 1 90/150

15/25 = 90/150

So the order from least to greatest is ...

1) 1/2 × 3/5 = 45/150

2) 5/5 × 3/5 = 90/150

3) 2 2/3 × 3/5 = 1 90/150

The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]

Here,

The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]

The velocity of a particle = [tex]\frac{d r(t)}{dt}[/tex]

[tex]r (t ) = ti + t^{2} j +2k[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

The acceleration of a particle = [tex]\frac{d^{2} r(t)}{dt^{2} }[/tex]

[tex]r (t ) = ti + t^{2} j +2k[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

[tex]\frac{d^{2} r(t)}{dt^{2} }= 2j[/tex]

The speed of a particle = [tex]| \frac{d r(t)}{dt}| = |v(t)|[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

[tex]|v(t)|=\sqrt{1 + 4t^{2} }[/tex]

Hence, The velocity of a particle = [tex]i + 2t j[/tex]

The acceleration of a particle = [tex]2 j[/tex]

The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]

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The relationship between the length of a side and the area is non proportional.

The answer is non proportional because the side length is x,

so is the other side lengths.

The side lengths are all equal and to find area you do x squared or x times x.

So they are not proportional because there will be different numbers for each.

For example. X= 2, area ( x squared ) is 4.

Hence, The relationship between the length of a side and the area is non proportional.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a square, we need to find the relationship between the length of a side and the area.

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The set of all such points is a sphere center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9

what is the sphere?

The standard form of the equation of a sphere with center (a ,b ,c) and radius r is

( x -a)² + ( y-b)² + ( z - c)² = r²

We let P = ( x, y,z ) be an arbitrary point which satisfies the given conditions. Then

[tex]\sqrt{(x - 1)^{2} + ( y - 5)^{2} + (z - 3)^{2} } = 2 \sqrt({x - 6)^{2} + ( y - 2 )^{2} +( z - 3)^{2} }[/tex]

Squaring both sides of this equation and simplifying yields

( x - 1)² + ( y - 5)² + ( z -3)² = 4 [ (x - 6)² + ( y- 6 )² + ( z - 3)²

( 3x² - 46x + 143 ) + ( 3y² - 38y + 119 ) + ( 3z² - 18z + 27 ) = 0

Next, we complete the square for each variable to obtain

( x - 23/3)²  + ( y - 19/3)² + ( z - 3 )² = 332/9

Thus the set of all such points P forms a sphere, with

center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9

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Answer: Im not sure

Step-by-step explanation:

You didnt list the options therefore i cant answer this for you. :I

Answer:

11

Step-by-step explanation:

Plug 4 into the x, 6(4) = 24

24 - 13 = 11

Answer:

-15w+9y+6

Step-by-step explanation:

I think that you are asking to simplify the expression.  An equation has an equal sign and I do not see one.

We need to distribute the -3 to everything inside of the parentheses.  

A negative times a negative is a positive.

A negative times a positive is a negative.

-3(5w-3y-2)

-3(5w) -3(-3y) -3(-2)

-15w + 9y + 6

Hi!

To simplify this, use the Distributive Property:

Now, let's simplify the given expression:

[tex]\dashrightarrow\sf{-3(5w-2y-2)}[/tex]

Like the property said, We should distribute -3 so that it's multiplied by each term:

[tex]\bullet\dashrightarrow\sf{-15w+9y+6}[/tex]

Therefore,

[tex]\bullet\dashrightarrow\stackrel{\heartsuit}{\boxed{\boxed{\boldsymbol{-15w+9y+6}}}}}\dashleftarrow\bullet[/tex]

- stargazing :')

The numbers have absolute values that differ by 1, and the number with the larger absolute value is positive.

Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula

Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.

Variance = Summation n to i = 1 [tex]\frac{(X_{1-X} )^2}{n-1}[/tex]

        0 = Summation n to i = 1[tex]\frac{(X_{1-X} )^2}{n-1}[/tex]

                Summation n to i [tex]{(X_{1-X} )^2[/tex] = 0

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Answer:

31/35

Step-by-step explanation:

3/5 + 2/7 = (3 × 7) / (5 × 7)  + (2 × 5) / (7 × 5)

= 21/35 + 10/35

= 31/35.

Using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

Given the equation, y - 6 = x/4, we can rewrite the equation as:

y = x/4 + 6

For x = 12, we have:

y = 12/4 + 6 = 3 + 6

y = 9

For x = 0, we have:

y = 0/4 + 6 = 0 + 6

y = 6

For y = 4, we have:

4 = x/4 + 6

4 - 6 = x/4

-2 = x/4

-8 = x

x = -8

For y = -3, we have:

-3 = x/4 + 6

-3 - 6 = x/4

-9 = x/4

-36 = x

x = -36

Thus, using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

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The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

[tex]\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}[/tex]

y = x - 2

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Step-by-step explanation:

did you leave something out ?

(5p + 3)(p + 1) = 5p×p + 5p×1 + 3×p + 3×1 =

= 5p² + 5p + 3p + 3 = 5p² + 8p + 3

at no point do we have 5 terms to sum up. but 4 and then finally 3, yes.

but we always have also additions, not only multiplications (products).

so, none of the 2 options is correct.

we could, of course. start with the initial expression, that shows the product of 2 factors and multiply by 1×1

(5p + 3)(p + 1)×1×1

then we have the expression as product of 4 factors.

in the same way we could bump up the sum scenario by adding one or 2 0s : tadah ! sum of 5 terms.

I strongly suspect there is something missing in the problem description.

Answer:

Neither is correct.

Step-by-step explanation:

The term in the given expression is -3x − 7(x + 4) (A) -3x.

Term:

Therefore, the term in the given expression is (A) -3x.

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The correct question is given below:
Which choice is a term in this expression? -3x − 7(x + 4)

Answer:

21=1×21 or 3×7

Step-by-step explanation:

21 is a composite number.factors of 21:1,3,7,21.

Prime factorization:21=3×7.

since 3 and 7 are the only prime numbers ...

Thanks!!

[tex] \: \Large \mathbb{SOLUTION:}[/tex]

[tex] \: \: \rm{ {7x}^{2} + 4x - {x}^{2}}[/tex]

[tex] \: \: \text{Reorder and gather like terms}[/tex]

[tex] \: \: \rm{( {7x}^{2} - {x}^{2} ) + 4x}[/tex]

[tex] \: \: \text{Collect coeffiecients of like terms}[/tex]

[tex] \: \: \rm{(7 - 1) {x}^{2} + 4x}[/tex]

[tex] \: \: \text{Calculate the sum or difference}[/tex]

[tex] \: \: \rm{ \underline{ \underline{ {6x}^{2} + 4x}}}[/tex]

[tex] \rm{6x {}^{2} + 4x}[/tex]

Collect like terms

[tex] \red{7x {}^{2} } + 4x \red{ - x {}^{2} }[/tex]

[tex] \red{6x {}^{2} } + 4x [/tex]

Ordinal is the answer.

In the given statement is:
A scale that allows one to determine only if there is more, less, or an equal amount of the attribute in comparison to another observation is called a(n) ____ scale.

Ordinal Scale is the 2nd level of measurement that reports the ranking and ordering of the data without actually establishing the degree of variation between them. Ordinal level of measurement is the second of the four measurement scales. "Ordinal" indicates "Order".

Hence, The answer is Ordinal

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Answer:

30 yards

Step-by-step explanation:

9+9+6+6=30yards

Answer:

3/25

Step-by-step explanation: