a random variable x is exponentially distributed with a mean of 25. what is the probability that x is between 25 and 30?

The highest score obtained in this group of 12 scores is 19

What is the distribution in statistics?

In statistics, a distribution refers to the way in which a variable is spread out or distributed across different values. A distribution describes the probability of different outcomes for a variable, and can be visualized using graphs such as histograms, box plots, and probability density functions.

The distribution in Table 2-3 shows frequency (f) for different score ranges (x). Without knowing the exact scoring system, we can't say for certain what the highest score obtained in this group of 12 scores is. However, we can determine the upper limit of the highest score range by multiplying the upper limit of the range by its frequency:

Upper limit of 20-24 range = 24

Frequency of 20-24 range = 2

Upper limit of 15-19 range = 19

Frequency of 15-19 range = 5

Upper limit of 10-14 range = 14

Frequency of 10-14 range = 4

Upper limit of 5-9 range = 9

Frequency of 5-9 range = 1

To find the highest score, we need to determine the upper limit of the score range that has the highest frequency. In this case, the highest frequency is 5, which corresponds to the range 15-19.

Hence, the highest score range is 15-19, and the highest score within that range is the upper limit of that range, which is 19. So, the highest score obtained in this group of 12 scores is 19 (assuming the scoring system is such that higher scores correspond to higher ranges).

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Answer:

yes

Step-by-step explanation:

All of the opposite sides are parallel  to each other.  

Answer:Correct option is

A

10

Given y=(x−11)  

2

⇒y=x  

2

−22x+121

After substitute y=25. we get,

x  

2

−22x+121−25=0

⇒x  

2

−22x+96=0

⇒(x−16)(x−6)=0

⇒x=16,x=6

∴ two points are  A,B are (16,25),(6,25).

Distance between A and B is  

(16−6)  

2

−(25−25)  

2

​

=10

Hence, option A is correct.

Answer: 1080

Step-by-step explanation:

Heres why:

SA is L*W*H as the same formula as volume.

Answer:

2.3333333333

Step-by-step explanation:

2+1/3

= 2.3333333333

= 233.33333333%

Using long division:

As you can see, the quotient is 2.8, therefore:

Answer:

80.456 is a 9.6% decrease of 89.

Step-by-step explanation:

Answer:

Step-by-step explanation:

 89×(1-9.6%)

=89×(1-0.096)

=89×0.904

=80.456

≈80

the answer is 80 if you have to round it.

The rate of change of the population, measured in people per year, is 200.

The rate of change of the population, measured in people per year, can be modeled by using the concept of population growth or decline. If we assume that the population of the town is increasing, we can use the formula:

Rate of Change = (Final Population - Initial Population) / Time

In this case, the initial population is 10,000 in 1990. To find the final population, we need additional information, such as the year we are interested in. Let's say we want to find the rate of change in 2000. If the population in 2000 is 12,000, we can substitute the values into the formula:

Rate of Change = (12,000 - 10,000) / (2000 - 1990) = 200 people per year

So, the rate of change of the population, measured in people per year, is 200.

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The interpretation of the expression (5x-2)×3 is 15x-6

A linear expressions is an algebraic expressions of the form mx+b. involving only a constant and a first-order (linear) term, Occasionally, the above is called a "linear expressions of one variables," where x is the variable and m is the coefficient of x and b is a constant.

For example 5x+2

In this case( 5x-2) 3;has only one variable which is x.

By opening the parenthesis, we multiply 3 by all the terms in the parentheses.

Therefore( 5x-2)×3 = 15x-6

This means the interpretation of the expression 5x-2)×3 is 15x-6

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A vector space is a mathematical structure with closure under addition and scalar multiplication, while the rank of a matrix refers to the maximum number of linearly independent rows or columns, and a matrix is singular if its determinant is zero, otherwise, it is non-singular.

We have,

a)

A vector space is a mathematical structure that consists of a set of vectors along with operations of addition and scalar multiplication.

It satisfies certain properties, including closure under addition and scalar multiplication, associativity of addition and scalar multiplication, existence of additive identity and inverses, and distributive properties.

b)

To express M as a linear combination of N, Q, and 2, we need to find scalars a, b, and c such that:

M = aN + bQ + c(2)

Given:

M = (2, 2, 4)

N = (2, 0, 2)

Q = (3, 1, -2)

2 = (0, 1, -3)

Let's solve for the scalars:

M = aN + bQ + c(2)

(2, 2, 4) = a(2, 0, 2) + b(3, 1, -2) + c(0, 1, -3)

Comparing the components, we can set up a system of equations:

2 = 2a + 3b

2 = b + c

4 = 2a - 2b - 3c

Solving this system of equations, we find:

a = 1

b = 0

c = 2

Therefore, M can be expressed as a linear combination of N, Q, and 2 as follows:

M = 1N + 0Q + 2(2)

M = N + 2(2)

M = (2, 0, 2) + 2(0, 1, -3)

M = (2, 0, 2) + (0, 2, -6)

M = (2, 2, -4)

c)

(i) Rank of a matrix:

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix.

It represents the dimension of the vector space spanned by the rows or columns of the matrix.

(ii) Singular and non-singular matrices:

A matrix is said to be singular if its determinant is zero. In other words, a square matrix is singular if it does not have an inverse.

On the other hand, a non-singular matrix is one that has a nonzero determinant and an inverse, meaning it is invertible or non-degenerate.

Non-singular matrices have full rank, whereas singular matrices have rank less than the number of rows or columns.

Thus,

A vector space is a mathematical structure with closure under addition and scalar multiplication, while the rank of a matrix refers to the maximum number of linearly independent rows or columns, and a matrix is singular if its determinant is zero, otherwise, it is non-singular.

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Answer: Solution In photo

Answer:

50/120 =12:5

Step-by-step explanation:

First we are divide 50/120

answer is 12:5

Answer: 0.05 : 120. OR

50 : 120000 or 1:2400

Step-by-step explanation:

Speed of garden snail

= 50 meters per hour = 0.05 kph

Speed of cheetah

= 120 km per hour or 120000 mph

Ratio of snail : cheetah

= 0 05 : 120

The number of petals that the flower should have is of:

8 petals.

A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.

In this problem, we want the flower to have a rotation symmetry of 45 degrees.

The total angle measure of the flower is given as follows:

360º.

Then the number of petals needed for the flower to have a rotational symmetry of 45º is calculated as follows:

360/n = 45.

Applying cross multiplication, we have that:

45n = 360

n = 360/45

n = 8 petals.

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To calculate the cost of building a house of any size, you can use the formula: Cost = 5000 + (500 * Area), where Area represents the total square meters of the house.

Cost = 5000 + (500 * 100) = 5000 + 50000 = 55000.

The formula Cost = 5000 + (500 * Area) provides a way to estimate the cost of building a house based on its size. The fixed cost of 5000 represents the base cost that the builder charges, which includes expenses like labor, permits, and other overhead costs. The term (500 * Area) calculates the additional cost based on the area of the house in square meters.

By multiplying the area by 500, the formula accounts for the builder's charge of 500 per square meter. This variable cost component ensures that larger houses, which have more square meters, will incur higher construction costs. Adding the fixed cost to the variable cost yields the total cost of building the house.

For example, if you want to calculate the cost of building a house with an area of 100 square meters, you can substitute the value of Area into the formula:

Cost = 5000 + (500 * 100) = 5000 + 50000 = 55000.

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In slope-intercept form:

a. The parallel equation is: y = -4x + 19.

b. The perpendicular equation is: y = 1/4x + 2.

When writing the equation of lines that are parallel to each other, take note that they will have the same slope (m), while if they are perpendicular, they will have slopes that are negative reciprocal.

First, find the slope of the line in the graph:

Slope (m) = rise/run = -4/1 = -4.

The line that is parallel to the line in the graph will have the same slope, m = -4, while the line that is perpendicular to the line would have a slope, m = 1/4.

Substitute m = -4 and (x, y) = (4, 3) into y = mx + b, to find the value of the y-intercept (b):

3 = -4(4) + b

3 = -16 + b

3 + 16 = b

b = 19

To write the equation of the parallel line, in slope-intercept form, substitute m = -4 and b = 19 into y = mx + b:

y = -4x + 19 (equation of the line parallel to the line in the graph)

Substitute m = 1/4 and (x, y) = (4, 3) into y = mx + b, to find the value of the y-intercept (b):

3 = 1/4(4) + b

3 = 1 + b

3 - 1 = b

b = 2

To write the equation of the perpendicular line, in slope-intercept form, substitute m = 1/4 and b = 2 into y = mx + b:

y = 1/4x + 2 (equation of the line perpendicular to the line in the graph)

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The after-school club collected 136 items per day for the food bank.

We'll need to use division to solve this problem.
Identify the total number of items collected (2,720) and the number of days items were collected (20).
Divide the total number of items (2,720) by the number of days (20) to find the number of items collected per day.
2,720 items ÷ 20 days = 136 items
To determine how many items were collected per day, we can divide the total number of items collected (2,720) by the number of days (20):

2,720 ÷ 20 = 136

Therefore, the after-school club collected an average of 136 items per day for 20 days.

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Yes, the equation y = 5x represents a proportional relationship

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=5x.

In a proportional relationship, the ratio of y to x is constant.

In the given equation the variable x and y has a proportional relationship.

The equation is in the form of y=mx+b

the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.

Hence,  Yes, the equation y = 5x represents a proportional relationship

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Step-by-step explanation:

Slope intercept form is   y = mx + b  

Re-arrange given equation  to

2y = 4x-6        divide by 2

y = 2x -3          done.

Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

A parking sign is in the shape of a square. The area in square centimeters, is given by the equation: l^(2)=400 The length, l, of one side of the sign is  20 centimeters.

The equation l^2 = 400 represents the relationship between the length of one side of the square (l) and its area. To find the length of one side, we need to solve for l. In this case, we can take the square root of both sides of the equation to isolate l.

Taking the square root of 400, we get l = √400 = 20.

Therefore, the length of one side of the parking sign is 20 centimeters.

By substituting the value of l back into the equation, we can verify that it satisfies the equation: (20)^2 = 400, which is true.

Hence, the length of one side of the square parking sign is 20 centimeters.

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The exercise has to do with the Graphing of a Cosecant Function. From the graph, the completed statements have been indicated below.

The completed statements are:

It is to be noted that the graph is of the function 2Sec (3x) – 1.

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Answer:

2pi/3

corresponding cosine function is 2.

1 unit down.

graph 2sec(3x) – 1

Step-by-step explanation:

There is a 20% chance that a risky stock investment will end up in a total loss. If you invest in 25 independent risky stocks, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.

Given data:

Probability of getting a total loss in one investment = 20% = 0.20

Probability of not getting a total loss in one investment = 1 - 0.20 = 0.80

Number of investments = 25

We need to find the probability that fewer than six out of these 25 risky investments end up in total losses.

We will use the binomial distribution formula here:P(X < 6) = Σp(x) (from x = 0 to x = 5)

Here, Σ is the summation signp(x) = probability of x successes in 25 trials, which is given by the formula:

p(x) = [ nCx * p^x * (1-p)^(n-x)]

Where, n = number of trial

s = 25

p = probability of success = 0.80

q = probability of failure = 1 - p = 0.20n

Cx = n! / (x! × (n-x)!) = combination of n items taken x at a time

We need to substitute these values in the formula and calculate the probability:

P(X < 6) = Σp(x) (from x = 0 to x = 5)

P(X < 6) = p(0) + p(1) + p(2) + p(3) + p(4) + p(5)

P(X < 6) = \([25C0 * (0.80)^0 * (0.20)^25] + [25C1 * (0.80)^1 * (0.20)^24] + [25C2 * (0.80)^2 * (0.20)^23] + [25C3 * (0.80)^3 * (0.20)^22] + [25C4 * (0.80)^4 * (0.20)^21] + [25C5 * (0.80)^5 * (0.20)^20]\)

P(X < 6) ≈ 0.91

Therefore, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.

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Answer:

3.25

Step-by-step explanation:

Divide 104 by 32

Answer:

3.25 or 3 1/4

Step-by-step explanation:

"By what number must I multiply 32 to get 104?"

Divide 104 by 32:  3.25 or 3 1/4

Answer: B. h = 2

Step-by-step explanation:

Given

5 + h = 11 - 2h

Add 2h on both sides

5 + h + 2h = 11 - 2h + 2h

5 + 3h = 11

Subtract 5 on both sides

5 + 3h - 5 = 11 - 5

3h = 6

Divide both sides by 3

3h / 3 = 6 / 3

h = 2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B) h=2

Step-by-step explanation:

5+h=11-2h

5+h-(-2h)=11

5+h+2h=11

5+3h=11

3h=11-5

3h=6

h=6/3

h=2

Answer: Triangle FGH is an equilateral with values of x as 9.

Step-by-step explanation: The triangle given is an equilateral because all the given side are equal.  The value of x is 9.

Answer:

x = 9

Step-by-step explanation:

if x = 2 then

If x = 22.25 then

if x = 180 then

If x = 9 then

Answer:

(fg)(x) = x^3-4x^2-16x+64, D: All Real Numbers

Step-by-step explanation:

(fg)(x) = f(x) x g(x)

= 16-x^2(4-x)

=64-16x-4x+x^3

(fg)(x) = x^3-4x^2-16x+64

Domain is all real numbers because you can substitute any real number for x and the function would still work.

Thus the value of \((fg)(x) = x^3 -4x^2 -16x -64\) , and the domain is a set of real numbers.

The domain is a set of all real numbers because by substituting any value in the equation we only get real numbers.

The function is defined as a relationship between two variables a dependent and an independent variable. A function consists of a domain and a co-domain.  The set of codomains is called a range.

      Example : \(f(x) = 4x+ 3\)

All those values of a set for which a function is defined are called a domain.

According to the question :

\(f(x) = 16 - x^2\\ g(x) = 4 - x.\)

\((fg)(x) = (16- x^2) (4-x)\\(fg)(x) = [16(4-x) -x^2(4- x)]\\\(fg)(x) = [64- 16x -4x^2+x^3]\\(fg)(x) = x^3 -4x^2 -16 x -64\)

Thus the value of \((fg)(x) = x^3 -4x^2-16x-64.\)

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I assume that the "d2" was a typo as a problem such as this with 2 variables would require a system of equations.

I also assume that the ? is a typo and will replace it with 0, however you can repeat my steps with whatever it actually it.

I assume that the correct form is 2 + 3a + 6 + a = 0

2 + 3a + 6 + a = 0

Combine like terms

8 + 3a + a = 0

8 + 4a = 0

move 8 to other side

4a = -8

a= -8/4

a = -2*

plug this value of a into the original equation

2 + 3(-2) + 6 + (-2) = 0

The statement is true!

* This probably isn't your answer!  Repeat my steps with whatever the value of "?" is.

yep

it just simplifies to 1/7 since 4 and 4 cancel out each other

Answer:

1) Pr(all three) = 0.064

2) Pr(none) = 0.216

3) Independent event

Step-by-step explanation:

Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)

Where Pr = probability

This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure

Where p = success, q = failure

For n trials,

Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)

Pr (security) = 40% = 0.4

p = 0.4

q = 1-p = 1-0.4 = 0.6

Numbers selected at random = n = 3

See attachment for more details on the workings.

1) Probability all three of the selected homes have a security system = Pr(all three)

Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³

= 0.4×0.4×0.4

Pr(all three) = 0.064

2) Probability none of the three selected homes have a security system

= Pr(none)

Pr(none) = 1 × (0.4)^0 × (0.6)³

= 0.6³ = 0.6×0.6×0.6

Pr(none) = 0.216

3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.