Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average of the survival times of the 16 batteries is computed. If the claim is true, the average life of 16 batteries should EXCEED what value for 99% of the time?

Answer:

  ±320

Step-by-step explanation:

You want the 4th term of the geometric progression that has first and third terms 5 and 80.

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

for first term a1 and common ratio r.

We are given the 1st and 3rd terms, so we can find the common ratio from ...

  80 = 5·r^(3-1) . . . . . use a3 = 80, a1 = 5, n = 3

  16 = r^2 . . . . . . divide by 5

  ±4 = r . . . . . . . . take the square root

The 4th term will be the product of the 3rd term and the common ratio:

  a4 = a3·(±4) = 80·(±4) = ±320

The fourth term is -320 or +320.

The solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.

2x² + 6 = - 36

2x² = - 36 - 6 { subtract 6 from both sides of the equation }

2x² = - 40

x² = -40/2 {divide through by the coefficient of x² which is 2}

x² = -20

we take the square root of both sides

x = ± √-20

√-20 = √20 x √-1 { -1 = I an imaginary number}

so;

x = √20i or x = -√20i

Therefore, the solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.

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I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. This is worth playing game.

Let's assume that player A wins if both sets of coins are fair and have an equal number of heads.

The likelihood of this = (1/8)^2 + (3/8)^2 + (3/8)^2 + (1/8)^2

The likelihood of this = 1/64 + 9/64 + 9/64 + 1/64

The likelihood of this = (1 + 9 + 9 + 1)/64

The likelihood of this = 20/64

The likelihood of this = 5/16

If the two sets are different, let's say B triumphs.

The likelihood of this = 1 - 5/16 = 11/16

Therefore, if A wins 3 dollars and loses 1 dollar, then A's predicted net gain is

= 3 × 5/16 - 1 × 11/16

= 15/16 - 11/16

= (15 - 11)/16

= 4/16

So this game is defiantly worth playing game.

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The complete question is:

I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. Is this game worth playing?

The complete solution to the system of equations in this problem is given as follows:

x = [-14; 5; 0; 2]

The system Ax = b is given in augmented matrix form, hence it is defined as follows:

Inserting the system into a calculator, the homogeneous solution is given as follows:

[tex]x_1 = -14, x_2 = 5, x_3 = 0, x_4 = 2[/tex]

The system has no given inputs, hence the particular solution is of zero.

Hence the complete solution in matrix form is given as follows:

x = [-14; 5; 0; 2]

(the ; separator means a new line).

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Answer:

=$64.78

Step-by-step explanation:

If. 50 copies. = $2.05

than. 1,580 copies = ?

1580/50 × $2.05

=3239/50

=64.78

Therefore if the cost of 50 copies is $2.05 than the cost of 1,580 copies is $64.78.

Answer:

$64.78

Step-by-step explanation:

 Proportions:

 50 copies >>>> $2.05

1580 copies >>>> $C

C = 1580"2.05/504

C = 64.78

In the given case- An inverse of a Laplace transform, which is the sum of two distinct components, is the sum of the inverse transforms of each term separately.

What does inverse Laplace transform refer to?

A Laplace transform that is the sum of two different terms has an inverse that is the sum of the inverse transforms of each term taken separately. A Laplace transform, which also has an inverse of the constant multiplied by the inverse of the function, is produced when a constant is multiplied by a function.

A given derivative function with a real variable (t) is transformed into a complex function with a variable (s) by the Laplace transform, which is an integral transformation. Assuming that f(t) complies with a number of later-explained conditions,

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Answer:

Step-by-step explanation:

Given two segment measures in a right triangle diagram, you want the values of the other measures.

The Pythagorean theorem can be used to find y:

  BC² = BD² +CD²

  65² = y² +25²

  y² = 65² -25² = 3600

  y = √3600 = 60

The proportionality of corresponding sides in similar triangles can be used to find the remaining measures.

  short side/hypotenuse = 25/65 = 65/(25+x)

  25 +x = 65²/25 = 169

  x = 144

And for z, we can use ...

  long side/hypotenuse = AB/AC = BD/BC

  z/169 = 60/65

  z = 169(12/13) = 156

The triangle measures are ...

The probabilities for this problem are given as follows:

a) At least five: 0.4909 = 49.09%.

b) Less than five: 0.4091 = 40.91%.

c) Between five and ten: 0.585 = 58.5%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are given as follows:

n = 100, p = 0.05.

Hence the mean and the standard deviation of the approximation are given as follows:

Then the probability of at least five successes, using continuity correction, is P(X > 4.5), which is one subtracted by the p-value of Z when X = 4.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (4.5 - 5)/2.18

Z =  -0.23.

Z = -0.23 has a p-value of 0.4091. (probability of less than five successes).

1 - 0.4091 = 0.4909 = 49.09%.

The probability of between five and ten successes is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 4.5, hence:

Z = (10.5 - 5)/2.18

Z =  2.52

Z = 2.52 has a p-value of 0.9941.

Z = (4.5 - 5)/2.18

Z =  -0.23.

Z = -0.23 has a p-value of 0.4091.

Hence:

0.9941 - 0.4091 = 0.585 = 58.5%.

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Answer:

(a) The number of tiles Jon will use to cover the worktop is 6 * 15 = 90 tiles.

(b) To find the length of the worktop, we first need to find the length of each tile, which is 20 cm = 0.2 m.

The length of the worktop is then 0.2 m * 6 tiles = 1.2 m.

The width of the worktop is 0.2 m * 15 tiles = 3 m.

So, the length of the worktop is 1.2 m and the width is 3 m.

Step-by-step explanation:

I'm not sure if there were answer choices, but the smallest possible positive integers for x/y=2 is x=2 and y=1

If we plug those in to the other equation

(x^2+y^2)=z

(2^2+1^2)=z

(4 + 1) = z

5=z

Indicating that any number less than 5 cannot equal Z

Answer: 24.35333333

Step-by-step explanation:

Answer:

the correct answer is A

Step-by-step explanation:

A correspond to Note La

Probability on cards.

(a) P(Jack or five or King) = 12/52 = 3/13

(b) P(heart or club or spade) = 39/52 = 3/4

(c) P(Ace or Queen or heart) = 19/52

(d) P(seven or Queen or heart or diamond) = 30/52 = 15/26

Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

A single card is drawn from a standard 52-card deck. Find the probability that the card is either

a) a Jack, or a five, or a Jing?

b) a heart, or a club, or a spade?

c) an Ace, or a Queen, or a heart?

d) a seven, or a Queen, or a heart, or a diamond?

The four suits for a standard deck of 52 cards are hearts, diamonds, clubs, and spades of 13 cards each. The hearts and diamonds are red. While, the clubs and spades are black. The 13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

The total number of events is n(S) = 52.

Let's count each number of favorable outcomes, then the probability of the event!

(a) The number of Jack is 4, five is 4, and King is 4. They are 12.

P(Jack or five or King) = 12/52 = 3/13

(b) The number of hearts is 13, clubs is 13, and spade is 13. They are 39.

P(heart or club or spade) = 39/52 = 3/4

(c) The number of hearts is 13, other Aces is 3, other Queens is 3. They are 19.

P(Ace or Queen or heart) = 19/52

(d) The number of diamonds is 13, hearts is 13, other seven is 2, other Queen is 2. They are 30.

P(seven or Queen or heart or diamond) = 30/52 = 15/26

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No. The determinant doesn't show that the matrix will reduce to an identity matrix.

The determinant of a matrix is a scalar value that can be used to determine whether a matrix is invertible or not. If the determinant is non-zero, the matrix is invertible and can be reduced to an identity matrix through row operations. If the determinant is zero, the matrix is not invertible and cannot be reduced to an identity matrix.

In this case, the determinant of the matrix [3 0 5 1] is equal to 3 * 1 - 0 * 5 = 3, which is non-zero. Therefore, this matrix can be reduced to an identity matrix through row operations, but the determinant does not indicate this directly.

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Step-by-step explanation:

The answer is do ur homework ur self

Answer:

16.625 miles

Step-by-step explanation:

The time elapsed between 4:45 pm and 12 noon is 4 hours and 45 minutes

45 minutes is equivalent to 45/60 = 0.75 hour

Total elapsed time = 4.75 hours

At a speed of 3.5 mph the distance that can be covered

= 3.5 x 4.75 = 16.625 miles

The amounts of each solution that he should use are given as follows:

The amounts of each solution are obtained by a system of equations, for which the variables are given as follows:

The total solution is of 18 liters, hence:

x + y = 18.

x = 18 - y.

The final concentration is of 80%, hence:

0.3x + 0.9y = 0.8 x 18

0.3x + 0.9y = 14.4.

As x = 18 - y, the value of y is obtained as follows:

0.3(18 - y) + 0.9y = 14.4

0.6y = 9

y = 9/0.6

y = 15.

Hence the value of x is obtained as follows:

x = 18 - y

x = 18 - 15

x = 3.

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Answer:

The total cost of groceries if the state sales tax of 6.4% added $9.60 to the original cost would be $159.60. To calculate this, multiply the original cost by 1.064, which is the amount of the sales tax in decimal form. For example, if the original cost was $150, then the total cost would be $150*1.064 = $159.60.

Answer:

3 hours

Step-by-step explanation:

First, we need to set up an equation with a variable representing the time.

12 + 3x = 15 + 2x

Then you solve.

12 + 3x = 15 + 2x

-2x-12       -2x-12

x = 3

Using the relationships between the angles of a parallelogram, the value of x is 12.55°.

A parallelogram has opposite angles that are equal, and adjacent angles that add up to 180°.

We can start with angles a and c. Since they are both equal to 90°, that means that angle b must also be 90°.

We can now use this information to find the value of x.

We can use the fact that angles a, b, and c add up to 270° to find x.

Since angles a and c are both 90°, that means that angle b must be 90°.

We can then solve for x by subtracting 190° (90° + 100°) from 270° and dividing by 7.

In order to solve for the value of x, we must use the properties of a parallelogram.

Since a parallelogram has four sides and four angles, the sum of the interior angles must equal 360°.

Therefore, we can set up an equation using the given angles and the unknown angle of x to solve for the value.

95° + (7x - 4)° + 90° + (3x + 23)° + (9x - 6)° = 360°

20x + 109° = 360°

20x = 251°

x=12.55°

Therefore,  the value of x is 12.55°.

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Answer:

To find 26% of an amount, you would use the percentage multiplier of 0.26.

Step-by-step explanation:

To use the multiplier, you would simply multiply the amount by 0.26.

For example:

26% of $100 = $100 x 0.26 = $26.

Alternatively, you can also express the percentage as a decimal by moving the decimal point two places to the left. In this case 26% is equal to 0.26

So, to find 26% of an amount you would multiply the amount by 0.26

For example:

26% of $100 = $100 x 0.26 = $26.

Answer:

Below

Step-by-step explanation:

Circumf = pi * 2 r

Circumf/(2pi ) = r

area = pi r^2

       = pi * (circumf/2pi)^2    

        = circumf^2 / 4 pi =

                24^2 / (4 pi) = 45. 8  units^2  

Answer:

45.84 units^2

The probability that all 3 selected guinea pigs are pregnant is 0.033.

Let's consider the event "A" as "3 guinea pigs selected are all pregnant". The number of ways to choose 3 guinea pigs from the 4 pregnant ones is C(4,3) = 4. The total number of ways to choose 3 guinea pigs from the 10 is

C(10,3) = 120.

The probability of event "A" is given by

P(A) = C(4,3) / C(10,3) = 4 / 120 = 1/30.

Therefore, the probability that all 3 guinea pigs selected are pregnant is 1/30 or 0.033 rounded to 3 decimal places.

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Answer: We can set up an equation to represent the given information:

4.563 = 4B + 127

where B is the number of residents in Town B.

To solve for B, we can first subtract 127 from both sides:

4.563 - 127 = 4B

Then divide both sides by 4:

B = (4.563 - 127) / 4

B = 1.140775

So Town B has approximately 1.140775 residents.

Step-by-step explanation:

Answer:

A ≈ 83.34 cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{195}{360}[/tex] ( r is the radius of the circle )

  = 3.14 × 7² × [tex]\frac{13}{24}[/tex] ( cancelling by 15 )

 = [tex]\frac{3.14(49)(13)}{24}[/tex]

 ≈ 83.34 cm² ( to the nearest hundredth )

There are indefinitely many solutions to the system.

[x(1), x(2), x(3)] = [-t, 0, t]

The matrix is:

[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]

The system of equations' equivalent augmented matrix is

[tex]\left [ \left.\begin{matrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0 \end{matrix}\right|\begin{matrix}0\\0 \\0 \end{matrix} \right ][/tex]

The following matrix has been reduced and transformed into a set of equations.

x(1) + x(3) = 0

Subtract x(3) on both side, we get

x(1) = -x(3)

x(1) = -t

x(2) = 0

Let x(3) = t

[tex]\begin{bmatrix}x(1)\\ x(2)\\ x(3)\end{bmatrix}=\begin{bmatrix}-t\\ 0\\ t\end{bmatrix}[/tex]

There are indefinitely many solutions to the system.

[x(1), x(2), x(3)] = [-t, 0, t]

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The complete question is:

Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)

[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]

(x1, x2, x3) =