if
\(f(x) = \sqrt{x} + 12\)
and
\(g(x) = 2 \sqrt{x} \)
what is the value of
\((f - g)(144)\)
?​

the probability that at least 3 phones are defective in a random sample of 37 phones is approximately 0.7889

To calculate the probability that at least 3 phones are defective in a random sample of 37 phones, we can use the binomial probability formula. The formula for the probability of at least a certain number of successes in a binomial distribution is:

P(X ≥ k) = 1 - P(X < k)

Where:

P(X ≥ k) is the probability of at least k successes

P(X < k) is the probability of less than k successes

In this case, "success" refers to a defective phone, and the probability of a phone being defective is 11% or 0.11. The sample size is 37 phones.

To calculate the probability, we need to sum up the probabilities of having 3, 4, 5, ..., up to 37 defective phones. We can use this formula:

P(X < k) = Σ (n choose i) * p^i * (1 - p)^(n - i)

Where:

n is the sample size (37)

i is the number of defective phones (ranging from 0 to k-1)

p is the probability of a defective phone (0.11)

Let's calculate the probability:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the formula above, we can calculate each term:

P(X = 0) = (37 choose 0) * 0.11⁰ * (1 - 0.11)³⁷

P(X = 1) = (37 choose 1) * 0.11¹ * (1 - 0.11)³⁷

P(X = 2) = (37 choose 2) * 0.11² * (1 - 0.11)³⁵

Now, let's calculate each term and sum them up:

P(X = 0) = (1) * (1) * (0.89)³⁷ = 0.0134

P(X = 1) = (37) * (0.11) * (0.89)³⁶ = 0.0613

P(X = 2) = (666) * (0.11)² * (0.89)³⁵ = 0.1364

Finally, calculate the probability:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.0134 + 0.0613 + 0.1364

= 0.2111

P(X ≥ 3) = 1 - P(X<3)

= 1 - 0.2111

=  0.7889

Calculating this value, the probability that at least 3 phones are defective in a random sample of 37 phones is approximately 0.7889

Learn more about probability here

https://brainly.com/question/32733835

#SPJ4

The domain of the function is all negative real number and zero.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The given function

ƒ(x) = √−2x

The domain of the expression is all real numbers except where the expression is undefined.

And here, when x is positive real number then field changes to complex.

That means the function is undefined in real field when x is not negative or zero.

Therefore, the domain of the function is all negative real number and zero.

To learn more about the function;

brainly.com/question/28303908

#SPJ1

Answer:

$23.18

Step-by-step explanation:

you have to subtract 238.32 from 562.84 and then divide by 14 to get $23.18

Given the following inequality:

To solve it, you need to solve for "a" by applying the Subtraction property of Inequalities and subtract 18 from both sides, as you can see below:

To graph it on a number line we must put a dot or a circle where -11 is.

Since the symbol of the inequality is <, the dot or the circle must be unfilled and the line must go from -11 to the left (because it is the direction of the numbers that make the given inequality true).

Then, you get:

Answer:

8411.67 m³

Step-by-step explanation:

The volume of a pyramid is one third its height times the area of its base. The Louvre pyramid has a height of 20.6 meters and a square base with sides of 35 meters. Find its volume, rounded to the nearest hundredth. Include units in your answer.

Volume of a pyramid is given as:

1/3 × Height × Area of it's base

= 1/3 × 20.6m × (35 m)²

= 8411.6666667 m³

Approximately = 8411.67 m³

Therefore, the volume of the pyramid = 8411.67 m³

No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.

An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.

To estimate a few terms of the sequence in order to obtain a feel how it looks like.

In our case, the definition is that \($\forall$\) (for all) \($n > 1: a_n=a_{n-1} a_{n+1}-1$\).

This can be rewritten as \($a_{n+1}=\frac{a_n+1}{a_{n-1}}$\).

We have \($a_1=x$\) and \($a_2=2000$\), and we estimate:

\($& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\\)

\($& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\\)

\($& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\\)

\($& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\\)

\($& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000\)

At this point we see that the sequence will become periodic: we contain \($a_6=a_1, a_7=a_2$\), and each subsequent term exists uniquely determined by the previous two.

Hence 2001 appears, it contains to be one of \($a_1$\) to \($a_5$\).

As \($a_2=2000$\), we only have four possibilities left.

Clearly \($a_1=2001$\) for x = 2001, and \($a_3=2001$\) for x = 1.

The equation \($a_4=2001$\)

solves to \($x=\frac{2001}{2000 \cdot 2001-1}$\), and the equation \($a_5=2001$\) to \($x=2000 \cdot 2001-1$\)

There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.

Therefore, the correct answer is option (D) 4.

The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........  in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?

(A) 1

(B) 2

(C) 3

(D) 4

(E) more than 4

To learn more about sequences refer to:

https://brainly.com/question/1109502

#SPJ4

The length of side m is, 5.08 inches.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔMNO,

⇒ o = 8 inches, m ∠M = 28° and m ∠O = 48°.

Now, Let the length of side m = x

So, By sine rule, we get;

⇒ sin M / m = Sin O / o

Substitute all the values, we get;

⇒ sin28°/  x = sin 48° / 8

⇒ 0.47 / x  = 0.74 / 8

⇒ x = 0.47 × 8 / 0.74

⇒ x = 5.08 inches

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer:

200 miles

Step-by-step explanation:

Let's say that our variable is x, where x equals the amount of miles

Company A: a(x)=0.6x+130

Company B: b(x)=0.9x+70

For the first equation, you are charged 130 dollars, in addition to the 0.60 cents that you are charged per mile.

For the second equation, you are charged 70 dollars, in addition to the 0.90 cents that you are charged per mile.

You want to find how many miles it takes to make the two equations equal:

0.6x+130 = 0.9x+70 (Set them equal to each other because you are trying to find when the miles are equal and the cost is equal)

130=0.3x+70 (Subtract 0.6x from both sides)

60=0.3x (Subtract 70 from both sides)

x=200 (Divide both sides by 0.3 to find x)

Remember that x is the amount of miles, so, Company A and B would charge the same if you drove 200 miles.

Answer:I believe it’s 200 miles

Step-by-step explanation: let x represent the mileage you are trying to find and set the two equations equal to one another to find the mileage and which the rental cost would be the same.

130 + 0.60x = 70 + 0.90x

130-70 = 0.90x - 0.60x

60 = 0.30x

X= 60/0.03

X= 200 miles

To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.

In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.

To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.

Let's consider a graph:

     A

    / \

   B---C

  / \ / \

 D---E---F

In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.

    A

    / \

   B---C

  / \ / \

 D---E---F

Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.

To know more about graph here.

https://brainly.com/question/17267403

#SPJ4

The property of adding to complete the second step of the equation is identity (0).

Hence, the correct answer is option d. Identity.

The property of add to complete the second step of the equation -

(7/9) + (2/3) = (-1/9) + (-2/3) + 2/3 is identity (0).

When we add -7/9 and 2/3, we first have to get the common denominator.

This would give us -7/9 = -6/9 - 1/9 and 2/3 = 6/9.

The equation would then become -(6/9) - 1/9 + 6/9 = (-1/9) + (-2/3) + 6/9.

Now we can simply add -1/9 and 6/9, which gives us 5/9.

The equation now becomes -(6/9) + 5/9 = (-2/3) + 6/9.

We can simplify this further to give us -1/9 = -2/3 + 6/9.

We can now add 2/3 to both sides to get rid of the -2/3 on the right side.

This gives us -(1/9) = 0.

Therefore, the property of adding to complete the second step of the equation is identity (0).

Hence, the correct answer is option d. Identity.

To know more about property refer here:

https://brainly.com/question/29528698

#SPJ11

6

6 multiplied by 12 =72

72 multiplied by 2 =144

Answer:

its 12 because its 23 then 34 then i dont know

Step-by-step explanation:

they look like school

The scatterplot between a predictor variable and an outcome with a non-linear relationship would not form a straight line, but rather a curved or nonlinear shape.

In linear regression, we assume that there is a linear relationship between the predictor variable and the outcome. However, this assumption may not hold in all cases, and there may be cases where the relationship between the two variables is not linear.

In such cases, a straight line may not be a good fit for the data, and a non-linear model may be more appropriate. In a scatterplot, a non-linear relationship would be indicated by a curve or a nonlinear shape rather than a straight line.

Examples of non-linear relationships include exponential, logarithmic, and polynomial relationships. It is important to identify and account for non-linear relationships when modeling data to ensure accurate and valid results.

To know more about variable, refer here:

https://brainly.com/question/2466865#

#SPJ11

Covariance matrix of the noise vector term in the ZF MIMO detector can be written as covn′​=σn2​(HHH)−1. We will start by expanding varn′​ which is as follows:varn′​=E[n′n′H]=E[(y−HX)(y−HX)H]=E[yyH]−E[yXH]−E[XyH]+E[XHXH],where y is the received signal vector and X is the MIMO channel matrix.

Let's start with the first term which is as follows:

\(E[yyH]=E[HXn′(HXn′)H]=H(E[n′n′H])H=H(covn′​)H...Equation [1].\)

The second term is as follows:

\(E[yXH]=HE[XXH]−−→HE[HH−1XXH]H=(HHH−1HHH−1)HE[HH−1XXH]H=(HHH−1)H...Equation [2].\)

Similarly, the third term can be calculated as:

\(E[XyH]=E[XHXH]H=HHH−1Equation [3].\)

Finally, the last term is as follows:

\(E[XHXH]=E[XXH]−E[XXH]HHH−1HHH−1=σ2pI−σ2p(HHH−1)Equation [4].\)

Here, σ2p is the signal power. Let's use equations 1, 2, 3, and 4 to get the final result.

Therefore,

\(varn′​=E[n′n′H]=H(covn′​)H+HHH−1+HHH−1+(σ2pI−σ2p(HHH−1))=H(covn′​)H+σ2pI...Equation [5].\)

Finally, let's use the given formula of ZF MIMO detector:n^(ZF)=argmin‖y−Hx‖22=xH(HH)−1HTy..

In this case, if the eigenvalues of HH are very small or zero, the inverse of HH becomes very large or infinity and it creates noise enhancement.

ZF (zero-forcing) is a popular MIMO (multiple-input, multiple-output) technique for signal detection. It is a simple and effective method to increase system capacity and performance in wireless communication systems. In ZF MIMO, the received signal is detected by using the inverse of the channel matrix.

This allows the system to remove interference and extract the signal from noise. However, ZF MIMO is sensitive to noise and it can create noise enhancement, which is an unwanted increase in noise power due to the matrix inversion process.

Covariance matrix of the noise vector term in the ZF MIMO detector can be written as covn′​=σn2​(HHH)−1. We have shown that the covariance of the noise term is given by this expression using the expansion of varn′​. The noise enhancement occurs in ZF MIMO when the eigenvalues of the channel matrix are very small or zero.

In this case, the inverse of the matrix becomes very large or infinity and it creates noise enhancement. Therefore, ZF MIMO is not an optimal technique for noise-limited systems, and other methods such as MMSE (minimum mean square error) can be used to reduce noise enhancement.

We have shown how to calculate the covariance of the noise vector term in the ZF MIMO detector. We have also explained analytically how noise enhancement takes place for zero-forcing receivers. ZF MIMO is a useful technique for increasing system capacity and performance, but it can create noise enhancement in certain situations. Therefore, it is important to choose the appropriate signal detection technique based on the system requirements and limitations.

To know more about eigenvalues  :

brainly.com/question/29861415

#SPJ11

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

To know more about ratio visit:

https://brainly.com/question/13419413

#SPJ11

Answer:

not equal because 2+5=7 and 1+5=6

Step-by-step explanation:

An easy way to find the surface area of a composite figure is to divide the composite figure up into smaller shapes whose area it is easier to find. It is best to divide a composite figure up into a figure composed of many triangles and rectangles. Then, one will find the area of each of these smaller figures and add the value up to find the total surface area of the composite figure.

Answer:

The second option

Step-by-step explanation:

Since root 16 is an integer (4), the second option produces the fraction 4/5 which is rational.

Answer:

h≈2.86

Step-by-step explanation:

Multiplication and division of regular numbers are the same as fractions and we will learn them with the multiplication and division of rational numbers worksheet.

To do the multiplication, first find the greatest common divisor of the numerator and the denominator. The factors are then grouped together so that the score equals one. Then multiply by the remaining factors. To divide, first rewrite the division as multiplication by the inverse of the denominator.

Cuemath's interactive math worksheets contain visual simulations to help your child visualize the concepts being taught, "see things as they really are, and reinforce learning from them". The Rational Numbers Multiplication and Division Worksheet follows a step-by-step learning process that helps students better understand concepts, identify errors, and eventually develop strategies for solving future problems.

Learn more about Multiplication:

https://brainly.com/question/5992872

#SPJ4

Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

The center of the circular track with the equation x² - 18x + y² - 22x = -177 is (20, 0). See below for other solutions

The equation of a circle that passes through the origin is represented as

x² + y² = r²

Where

r = radius

For circle 13, we have

Point = (0, 6)

So, the radius is

0² + 6² = r²

r = 6

This gives

x² + y² = 6²

For the point (√11, 5), we have

(√11)² + 5² = 6²

36 = 36 --- true

The point (√11, 5) is on the circle

For circle 14, we have

Point = (-7, 0)

So, the radius is

-7² + 0² = r²

r = 7

This gives

x² + y² = 7²

For the point (√14, 6), we have

(√14)² + 6² = 7²

50 = 49 --- falsee

The point (√14, 6) is not on the circle

Andy's error is that he did not square 12 in (√23)² + (11)² ≠ 12

The correct solution is

(√23)² + (11)² = 12²

144 = 144

The point (√23, 11) is on the circle

The equation of a circle is represented as

(x - a)² + (y - b)² = r²

For circle 16, we have

Center = (-1, 5)

Radius, r = 4

So, we have

Equation: (x + 1)² + (y - 5)² = 4²

For circle 17, we have

Center = (2, 0)

Point = (-2, 3)

So, we have

Equation: (x - 2)² + (y - 0)² = (-2 - 2)² + (3 - 0)²

Equation: (x - 2)² + y² = 25

Given that

x² - 18x + y² - 22x = -177

This gives

x² - 40x + y² = -177

Factorize

(x - 20)² + y² = -177 + 400

Evaluate

(x - 20)² + y² = 223

From the above, we have

Center = (20, 0)

Read more about circle equations at

https://brainly.com/question/1506955

#SPJ1

To paint 70 ornaments, he will need 70 bottles of paint.

To find the total surface area of one ornament, we need to find the lateral area of each cone and add them together.

The lateral area of a cone can be found using the formula:

L = πrℓ

where L is the lateral area, r is the radius, and ℓ is the slant height.

Since the two cones are identical, we only need to find the lateral area of one cone and then multiply it by two.

For each cone, we have:

r = 3.9 cm

ℓ = 8.4 cm

Using the formula, we get:

L = π(3.9)(8.4) ≈ 103.45 cm²

So the lateral area of both cones is:

2L = 2(103.45) = 206.9 cm²

The total surface area of one ornament is the sum of the lateral area and the area of the circular base:

A = πr² + 2L

A = π(3.9)² + 2(103.45)

A ≈ 235 cm²

Since one bottle of paint covers an area of 235 cm², Tim will need one bottle of paint for each ornament.

To learn more about the cone;

brainly.com/question/16394302

#SPJ1

The complete question is given in the attached image.

Answer:

If 25 is 40% of a value, what is that value?

A. 85

B. 12.5

D. 60

Step-by-step explanation:

You're welcome.

Answer:

C) 62.5

Step-by-step explanation:

Write the expression:

40% of x = 25

Then calculate:

4x/10 = 25

4x = 250

x = 62.5

The 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

To calculate the 95.44% confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's determine the critical value. Since the confidence level is 95.44%, we need to find the z-score that corresponds to a tail probability of (1 - 0.9544)/2 = 0.0228. Looking up this value in the standard normal distribution table or using a statistical calculator, we find that the z-score is approximately 2.17.

Next, we need to determine the standard deviation of the population. Since we don't have that information, we'll use the sample standard deviation as an estimate. Let's assume the sample standard deviation is 5 minutes.

Now we can calculate the confidence interval:

Confidence Interval = 22.3 ± (2.17) * (5 / sqrt(20))

Calculating the expression inside the parentheses:

= 22.3 ± (2.17) * (5 / sqrt(20))

= 22.3 ± 2.17 * (5 / 4.472)

= 22.3 ± 2.17 * 1.118

Calculating the confidence interval:

Lower Limit = 22.3 - (2.17 * 1.118)

Upper Limit = 22.3 + (2.17 * 1.118)

Lower Limit = 22.3 - 2.42706 ≈ 19.87294

Upper Limit = 22.3 + 2.42706 ≈ 24.72706

Therefore, the 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

To know more about confidence interval check the below link:

https://brainly.com/question/15712887

#SPJ4