a complex electronic system is built with a certain number of backup components in its subsystems. one subsystem has four identical components, each with a probability of 0.45 of failing in less than 1,000 hours. the sub system will operate if any two of the four components are operating. assume that the components operate independently. (round your answers to four decimal places.) (a) find the probability that exactly two of the four components last longer than 1,000 hours. (b) find the probability that the subsystem operates longer than 1,000 hours.

Perimeter of rectangle is 208p² - 160p + 272 centimeters

Given:

Width of rectangle = (10p+6)(10p+6) centimeters

Length of rectangle = (2p-10)(2p−10) centimeters

Find:

Perimeter of rectangle

Computation:

Width of rectangle = (10p+6)(10p+6)

Width of rectangle = 100p² + 120p + 36

Length of rectangle = (2p-10)(2p−10)

Length of rectangle = 4p² - 40p + 100

Perimeter of rectangle = 2(l + b)

Perimeter of rectangle = 2[(4p² - 40p + 100) + (100p² + 120p + 36)]

Perimeter of rectangle = 2[104p² - 80p + 136]

Perimeter of rectangle = 208p² - 160p + 272 centimeters

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The type of sampling that requires giving every part an equal chance of being selected for the sample is called "simple random sampling."

Simple random sampling is a method of selecting a sample from a population where each member has an equal probability of being chosen. In this type of sampling, every part or element of the population is assigned a number or label, and a random process, such as a lottery or a random number generator, is used to select the sample. The main characteristic of simple random sampling is that each member of the population has an equal and independent chance of being selected, without any bias or preference.

This sampling method ensures that every part of the population has an equal opportunity to be included in the sample, making it a fair representation of the entire population. By giving each part an equal chance of being selected, simple random sampling helps to minimize sampling errors and increase the generalizability of the findings to the larger population. It is often used in research studies and surveys when the goal is to obtain an unbiased and representative sample.

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Answer:

12

Step-by-step explanation:

12+3=15

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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Answer:

no

Step-by-step explanation:

Answer:

26.411

Step-by-step explanation:

In 3a+bc-c you have to substitute

a=8.6, b=2.3, c=0.47

3*8.6 + 2.3*0.47 - 0.47 first do the multiplication then addition and subtraction

25.8 + 1.081 - 0.47=

26.411

Answer:

the length of chicken coop and the garden is of 40 feet.

Explanation:

Given that the garden is the length of the chicken coop, equal length

→ 3x + 12 = 6x – 16

→ 3x - 6x = -16 - 12

→ -3x = -28

→  \(x = \frac{-28}{-3}\)

→ \(x= 9\frac{1}{3}\)

→ x = 9.33 feet.

Solution:

Note that:

Solve the equation (3x + 12 feet = 6x - 16 feet) to find the length of the garden and the chicken coop.

Now, substitute the value of x into the equation to find the length of the garden and the chicken coop.

The length of the chicken coop and the garden is 40 feet.

Answer:

\(x^{5}\) - 25x³

Step-by-step explanation:

Given

(x + 5)(x - 5)x³ ← expand the factors using FOIL

= (x² - 25)x³ ← distribute

= \(x^{5}\) - 25x³

Answer:

(x+5)(x−5)x3

=x5−25x3

Step-by-step explanation:

(x+5)(x−5)x3

=x5−25x3

Answer: − 2 ± √ 13

Step-by-step explanation:

(-b±√(b²-4ac))/(2a)

Plug in and solve.

Answer:

y = (x + 2)² - 13

Step-by-step explanation:

y = x² + 4x - 9

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

y = x² + 2(2)x + 4 - 4 - 9

  = (x + 2)² - 13 ← in vertex form

Answer:

m = 2

Step-by-step explanation:

m - 2 = 2 - m

2m = 4

m = 2

Hello,

Answer: m = 2

Step-by-step explanation:

       m - 2 = 2 - m

⇔ m - 2 + m = 2 - m + m

⇔ 2m - 2 = 2

⇔ 2m - 2 + 2 = 2 + 2

⇔ 2m = 4

⇔ 2m/2 = 4/2

⇔ m = 2

The answer is -8

This was too easy

The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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the more compact hospital. The Law of Large Numbers, which makes intuitive sense, states that when there are more observations, the experimental average tends to approach the true proportion. Large hospitals have more observations, therefore their results are less likely to deviate from 50% or have a wide range of results.

An equation that states that two ratios are equal is a genuine proportion. You can utilise information about one ratio in a proportion to determine values in the other equal ratio.

The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) follows..

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Answer: answer for what?

Step-by-step explanation: oh I see it appeared iN wrong catogory I’m browsing History sorry

The number of new phone sold is 1 and the number of old phone sold is 5, if the sales for the day totals $625.

It is given that

A new phone sells for $250

and a used one sells for $75

Let number of new phone is sold = x

and number of old phone is sold = y

Here the total profit for the day is $625

So, 250x + 75y = 625

or 10x + 3y = 25

Now the value of x  and y satisfy the above equation, if we take x = 2 and more than 2, it is clear that it not satisfy the above equation. So we made a conclusion here x must be equal to 1 here.

Now, if x = 1

10(1) + 3y = 25

3y = 15

y = 5

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Hope it helps.

Don't forget to click the Brainliest button if you like my answer and if you have any query, feel free to ask in the comment section.

Answer:

New radius(r) = 3.65 (Approx)

Step-by-step explanation:

Given:

Radius of sphere(R) = 8

Find:

New radius(r)

Computation:

Volume of sphere = (4/3)πR³

Volume of sphere = (4/3)π(6)³

Volume of sphere = 288π

Volume of ring = (4/3)π(R²-r²)³/²

Half volume of sphere = Volume of ring

288π / 2 = (4/3)π(R²-r²)³/²

144 = (4/3)(6²-r²)³/²

108 = (6²-r²)³/²

New radius(r) = 3.65 (Approx)

option A

To detrmine the correct graph, let's find the factors of the function given:

To get the factors equate the function to zero, that is y = 0

The graph with two x intercepts as 2 and -6 will be the correct quadratic function

Each unit on the graph is 4 units

From the options, option A has x intercepts as 2 and -6

Answer:

\({x}^{2} - 10x + 25\)

Step-by-step explanation:

For this problem, we can break the equation into (x - 5) use FOIL. First, Outer, Inner, Last.

(x - 5) (x - 5)

First, multiply the two Xs together.

X * X =

\( {x}^{2} \)

Now, the outer numbers and values.

X * -5 =

\( - 5x\)

Then, it's the inner numbers and values.

-5 * x =

\( - 5x\)

Finally, multiply the last numbers.

-5 * -5 =

\( 25\)

Now that we have multiplied all of the values, we can put the answers from FOIL together.

\( {x}^{2} - 5x - 5x + 25\)

Now, add any like terms.

\( - 5x - 5x = - 10x\)

The answer is

\( {x}^{2} - 10x + 25\)

a) i) The construction 5A - B can be calculated as [8 12 -7][-13 -18 -25].

ii) The construction BA does not exist because the number of columns in matrix B (3) does not match the number of rows in matrix A (2).

a) i) To calculate 5A - B, we perform scalar multiplication on matrix A by multiplying each element by 5 and then subtract matrix B element-wise.

ii) To calculate BA, we perform matrix multiplication by multiplying the rows of matrix B with the columns of matrix A.

iii) To calculate A², we multiply matrix A with itself by performing matrix multiplication.

b) i) To show that I + 2A + A² equals the zero matrix, we multiply A with itself to obtain A², perform scalar multiplication on matrix A by multiplying each element by 2, and add the resulting matrices element-wise with the identity matrix I. If the resulting matrix is the zero matrix, then the equation is satisfied.

ii) Using the equation I + 2A + A² = 0, we can rearrange the equation to get A² + 2A + I = 0. Multiplying both sides by A⁻¹, we get A⁻¹(A² + 2A + I) = A⁻¹ * 0, which simplifies to A + 2I + A⁻¹ = 0. Rearranging the equation, we find that A⁻¹ = -A - 2I.

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Jadi, ada 35 siswa yang memilih Hidayat sebagai ketua kelas.

Jika pemilihan ketua kelas melibatkan 250 siswa dan persentase pemilih Hidayat adalah 14%, kita dapat menghitung jumlah siswa yang memilih Hidayat sebagai berikut:

Jumlah siswa yang memilih Hidayat = Persentase pemilih Hidayat × Jumlah siswa

= 0.14 × 250

= 35

Jadi, ada 35 siswa yang memilih Hidayat sebagai ketua kelas.

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The process of finding h'(2) and h(2) is important in calculus as it helps us understand the behavior of a function at a particular point. It also helps us find the maximum and minimum values of a function as well as the points of inflection.

The given integral is: S = ∫sin(x) cos²(x) + cos cos(x) - 6 dx

Let's use the following trigonometric identity:cos²(x) = 1 - sin²(x)

Substituting this into the integral gives: S = ∫sin(x) (1 - sin²(x)) + cos cos(x) - 6 dx

Simplifying: S = ∫sin(x) - sin³(x) + cos cos(x) - 6 dx Integrating term by term,

we have: S = (-cos(x)) - (1/4)cos³(x) + (1/2)sin²(x) - 6x + C Where C is the constant of integration. In conclusion, we were given the integral S sin(x) cos²(x)+cos cos(x)-6 dx and we solved it by using the trigonometric identity cos²(x) = 1 - sin²(x) which then resulted in S = ∫sin(x) - sin³(x) + cos cos(x) - 6 dx.

After simplifying, we got S = (-cos(x)) - (1/4)cos³(x) + (1/2)sin²(x) - 6x + C where C is the constant of integration.

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The value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

Let's simplify the addition within the parentheses:

8 1/5 + 4 1/5 = (8 + 4) + (1/5 + 1/5) = 12 + 2/5 = 12 2/5

Next, let's simplify the subtraction within the parentheses:

6 6/8 - 6 2/4 = (6 - 6) + (6/8 - 2/4) = 0 + (3/4 - 1/2) = 0 + 1/4 = 1/4

Now, we can substitute the simplified terms back into the original expression:

(8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) = 12 2/5 - 1/4

To subtract mixed numbers, we need to find a common denominator. The common denominator for 5 and 4 is 20. Converting both terms:

12 2/5 = 12 * 5/5 + 2/5 = 60/5 + 2/5 = 62/5

1/4 = 1 * 5/5 * 5/20 = 5/20

Now we can subtract:

62/5 - 5/20 = (62 * 4)/(5 * 4) - 5/20 = 248/20 - 5/20 = (248 - 5)/20 = 243/20

Therefore, the value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

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There is no linear combination of the first two vectors that is as close as possible to [0, 0, 5].

To find the linear combination of the first two vectors that is as close as possible to the third vector [3, -1, 0], we need to find coefficients x and y such that the linear combination x*[i, 2, 1] + y*[2, 0, -1] is as close as possible to [3, -1, 0].

Let's set up the system of equations:

x*[i, 2, 1] + y*[2, 0, -1] = [3, -1, 0]

This system can be rewritten as:

x + 2y = 3

2x - y = -1

Solving this system of equations, we find x = 1 and y = 1. Therefore, the linear combination that is as close as possible to [3, -1, 0] is [i, 2, 1] + [2, 0, -1] = [3, 2, 0].

(b) To find the linear combination of the first two vectors that is as close as possible to the third vector [0, 0, 5], we set up the system of equations:

x*[1, 0, 1] + y*[0, 1, 1] = [0, 0, 5]

This system can be rewritten as:

x + y = 0

x + y = 0

x + y = 5

Since the third equation is inconsistent with the first two equations, there is no solution that satisfies all three equations. Therefore, there is no linear combination of the first two vectors that is as close as possible to [0, 0, 5].

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Using the perimeter and side length table the value for equation is option B: P = 5s.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

Let the perimeter be denoted by P.

Let the side length be denoted by s.

The first value for P is 5 and for s is 1.

The equation will be -

P/s = 5/1

P = 5s

The second value for P is 10 and for s is 2.

The equation will be -

P/s = 10/2

P/s = 5/1

P = 5s

The third value for P is 15 and for s is 3.

The equation will be -

P/s = 15/3

P/s = 5/1

P = 5s

Therefore, the equation is obtained as P = 5s.

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The table shows the relationship between the side lengths of a regular pentagon and its perimeter.

Which equation shows the relationship between the side length and the perimeter of a regular pentagon?

A. P = s + 5

B. P = 5s

C. P = 1/5s

D. P= 5s + 5

Answer:

length is 6 and breadth is 3

Step-by-step explanation:

A=L×B

18=3B×B

18=3B

DIVIDE BOTH SIDES BY 3

B=6

THEREFORE L=6

B=6÷2=3