Ms. Dowsing discovered that her leaky faucet was leaking 1.25 cups of water an hour. At this rate, how many gallons a day were leaking?

Answer:

2

Step-by-step explanation:

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Answer:

m=0.8

Step-by-step explanation:

Answer:

0.8

Step-by-step explanation:

1.4-0.6=m

The expression (g∘f)(0) evaluates to 4.

To evaluate the expression (g∘f)(0), we need to find the composition of functions g and f, and then evaluate it at x = 0.

In function composition, the output of one function becomes the input for the other. In this case, we start with function f and then apply function g to its output. Looking at the given graphs, we can determine the values of f(x) and g(x) at various points.

Let's start with function f. By following the graph, we can see that when x = 0, f(x) = 2. So the output of f at x = 0 is 2.

Next, we need to apply function g to the output of f at x = 0. From the graph of g, we can see that when x = 2, g(x) = 4. Therefore, we substitute 2 as the input for g and obtain g(2) = 4.

Finally, we have (g∘f)(0) = g(f(0)) = g(2) = 4.

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Answer:

B. 3408pi

Step-by-step explanation:

formula volume of cone = 1/3 x pi x r x r x h

volume = 1/3 x pi x 12 x 12 x 71

= 3408pi

The volume of the cone is approximately 10,224 cubic units.

Option C is the correct answer.

It is a shape of a christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is V = (1/3)πr²h,

We have,

The formula for the volume of a cone is V = (1/3)πr²h,

where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.

Substituting the given values, we get:

V = (1/3)π(12²)(71)

V = (1/3)π(144)(71)

V = (1/3)(3.14)(144)(71)

V = 10,223.04

Rounding this answer to the nearest whole number, we get:

V ≈ 10,224

Therefore,

The volume of the cone is approximately 10,224 cubic units.

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Using the Pythagorean theorem, we know that the string needed to go from D to C is 3 inches and from E to D is 2.7 inches.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, according to the given information:

We know that:
CE = 1.1 in

EC = 2.7 in

Then,

The string needed to go from E to D is 2.7 in (Given).

String needed to go from D to C:

Using the Pythagorean theorem: c = √a² + b²

Now, calculate DC as follows:

DC = √a² + b²

DC = √1.1² + 2.7²

DC = 2.91548

Rounding off DC: 3 in

Therefore, using the Pythagorean theorem, we know that the string needed to go from D to C is 3 inches and from E to D is 2.7 inches.

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Answer:

I hope this helps! The answer is 9. I solved this by using “sin” to find y.

Step-by-step explanation:

Answer:

56 degrees

Step-by-step explanation:

Hello there!

Remember the sum of the angles in a triangle is equal to 180

so to find the missing angle we subtract the given angles from 180

180 - 34 - 90 = 56

so we can conclude that the measure of the missing angle is 56 degrees

Note: the little square at the bottom left of the triangle indicates that the angle is a right angle. The measure of a right angle is 90 degrees so thats where the 90 came from

Answer:

hope it help you

Answer:

Step-by-step explanation:

Select one or more rows and columns

Or click on any cell in the row and then press Shift + Space. To select non-adjacent rows or columns, hold Ctrl and select the row or column numbers.

This is a linear first-order ordinary differential equation in the form:

\(\(\frac{dy}{dx} - \frac{y}{x} = xe^x\)\)

To solve the given differential equation \(\(y' - \frac{y}{x} = xe^x\)\), we can use the method of integrating factors.

First, let's rewrite the equation in standard form:

\(\(\frac{dy}{dx} - \frac{y}{x} = xe^x\)\)

The integrating factor (IF) is given by the exponential of the integral of the coefficient of y with respect to x:

\(IF = \(e^{\int \left(-\frac{1}{x}\right)dx} = e^{-\ln|x|} = \frac{1}{x}\)\)

Now, multiply the entire equation by the integrating factor:

\(\(\frac{1}{x} \cdot \frac{dy}{dx} - \frac{1}{x} \cdot \frac{y}{x} = \frac{1}{x} \cdot xe^x\)\)

\(\(\frac{1}{x} \cdot \frac{dy}{dx} - \frac{y}{x^2} = e^x\)\)

\(\(\frac{d}{dx} \left(\frac{y}{x}\right) = e^x\)\)

Integrating both sides with respect to x:

\(\(\int \frac{d}{dx} \left(\frac{y}{x}\right) dx = \int e^x dx\)\)

Using the fundamental theorem of calculus, the integral on the left-hand side simplifies to:

\(\(\frac{y}{x} = e^x + C\)\\\(y = xe^x + Cx\)\)

Therefore, the general solution to the given differential equation is \(\(y = xe^x + Cx\)\), where C is the constant of integration.

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Complete Question:

Given differential equation \(\(\frac{dy}{dx} - \frac{y}{x} = xe^x\)\). This is a linear differential equation in the form?

Answer:

Choose 0 to substitute in for x to find the ordered pair. Remove parentheses. Simplify 3(0)−10 3 ( 0 ) - 10 .

Step-by-step explanation:

The distance between the starting point and the second obstacle is 13 meters.

And the total length of one lap is equal to the perimeter of the triangle, which measures 30 meters.

We can see that this distance is equal to the hypotenuse of the triangle on the image.

The two legs measure:

5 meters and 12 meters.

Then using the Pythagorean theorem we can write:

d^2 = 5^2 + 12^2

d = √(5^2 + 12^2) = 13

So the distance between the starting point and obstacle 2 is 13 meters.

b) This will be the perimeter of the triangle, it is:

P = 13 m + 12m + 5m = 30m

One full lap has a length of 30 meters.

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Answer:

14

Step-by-step explanation:

Ok, 60! is a really big number

\(x!=x(x-1)(x-2)...1\)

So we have 60*59*58...*1

2 times 5 is 10 which makes a terminal zero (ending zero)

We need to count how many fives and twos are in 60!

There are 60/5=12 5^1's

There are 60/25=2 5^2's

So 12+2=14

There are way more 2's than fives so we take the lesser number

So the answer is 14

*Note that 60/25 is not 2, we need an integer rounded down

Step-by-step explanation:

3.5x pi=38.48

38.48^2=1,480.7104

38.48x8.2=315.536

315.536+1,480.7104=

1,796.2464cm^2

The value of the sample statistic is used to estimate the value of the population parameter.

The sample statistic is the value that is calculated from the sample data, which is used to make inferences about the population parameter. Sample statistics are used to estimate population parameters. A sample statistic is an estimate of a population parameter that is obtained from a sample, whereas a population statistic is a value that is computed from a population.

Therefore, the correct answer is a. sample statistic.

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The required, D. A study of the popularity of a new sneaker conducted by the sneaker manufacturer is more likely to produce results that are skewed by bias.

This is because the sneaker manufacturer has a vested interest in promoting the new sneaker and may use biased methods to ensure that the study produces favorable results. For example, the manufacturer may selectively sample individuals who are more likely to be interested in the sneaker or use leading questions to bias the responses in favor of the sneaker. In contrast, the other studies listed are less likely to be influenced by bias because they rely on random sampling or objective measurements.

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Answer:

This will work i put a graph image here

Step-by-step explanation:

Answer: The attachment I added is actually the correct answer. The green line is the right one.

Conversion:

12 inches = 1 foot

Divide:

48 / 12 = 4

Therefore, Hailey has 4 feet of ribbon.

Best of Luck!

Answer: 4 foot of ribbon

Step-by-step explanation: there is 12 inches in one foot so this means to get the answer you must divide 48 by 12 to get 4 so 4 feet is the answer

hope this helps and mark me brainliest if it did hope you have a great day

Even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

Let R be a relation that is reflexive and transitive. We want to prove that R2 = R for any relation R with these two properties.

To prove this, we need to show that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R.

First, let's consider (a, b) ∈ R2. By definition, (a, b) ∈ R2 means that there exists an element c such that (a, c) ∈ R and (c, b) ∈ R.

Since R is reflexive, we know that (a, a) ∈ R and (b, b) ∈ R.

By the transitivity of R, if (a, c) ∈ R and (c, b) ∈ R, then (a, b) ∈ R.

Therefore, (a, b) ∈ R2 implies (a, b) ∈ R.

Now, let's consider (a, b) ∈ R. Since R is reflexive, we have (a, a) ∈ R and (b, b) ∈ R.

By the definition of R2, (a, a) ∈ R2 and (b, b) ∈ R2.

Since R is transitive, if (a, a) ∈ R2 and (a, b) ∈ R2, then (a, b) ∈ R2.

Therefore, (a, b) ∈ R implies (a, b) ∈ R2.

We have shown that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R. Hence, R2 = R.

If the relation R is anti-reflexive, it is not necessarily true that R2 is anti-reflexive.

To understand why, let's consider an example. Let R be a relation defined on the set of integers such that R contains the ordered pairs (a, b) where a < b.

In this case, R is anti-reflexive because for any integer a, (a, a) is not in R.

Now, let's consider R2. R2 is the composition of R with itself. If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R2.

In our example, if we take a = 1, b = 2, and c = 3, we have (1, 2) ∈ R and (2, 3) ∈ R. Therefore, (1, 3) ∈ R2.

However, (1, 1) is not in R2 because (1, 1) is not in R. Therefore, R2 is not anti-reflexive in this case.

This example demonstrates that even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

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The solution to the problem is: d/dx ∫_1ˣ sec(t)dt = sec(x)tan(x) . To solve this problem, we first need to apply the fundamental theorem of calculus, which states that:

d/dx ∫_aˣ f(t)dt = f(x)

In other words, the derivative of an integral with respect to its upper limit is equal to the integrand evaluated at the upper limit.

Applying this theorem to the given integral, we get:

d/dx ∫_1ˣ sec(t)dt = sec(x)

Now we need to apply the chain rule to the right-hand side to find the derivative of the integral with respect to x:

d/dx ∫_1ˣ sec(t)dt = d/dx sec(x) = sec(x)tan(x)

Therefore, the solution to the problem is: d/dx ∫_1ˣ sec(t)dt = sec(x)tan(x)

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a and b.

a unit rate has a certain value per 1 thing

Answer:

10

Step-by-step explanation:

5+10=15

15×2=30

so the answer to your question is 10

Answer:

x = 10.

Step-by-step explanation:

Given: Two times the sum of 5 and some number is 30. What is the number?

First, write the equation:

2(5 + x) = 30

Simplify the brackets with distribution property:

10 + 2x = 30

Then collect like terms:

2x = 30 - 10

Finally, calculate:

2x = 20   (Divide both sides by 2)

x = 10

The third root of f(x) is x = 4, and it must also be a root of the polynomial.

Since 0 and 4 are already roots of f(x), we can write the factors of the polynomial as (x - 0) and (x - 4).

Multiplying these factors gives us f(x) = x(x - 4).

To find the third root, we set f(x) = 0 and solve for x.

Substituting f(x) = x(x - 4) = 0, we see that either x = 0 or x - 4 = 0.

The second equation gives us x = 4.

Therefore, the third root of f(x) is x = 4, and it must also be a root of the polynomial.

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9514 1404 393

Answer:

  2)  f(x) = log3(x -1) +1

Step-by-step explanation:

The vertical asymptote of the log function is normally x=0. In this function, it is moved to the right 1 unit. That is accomplished by replacing the function argument x with (x-1). Only one answer choice matches:

  f(x) = log3(x -1) +1

When interest compounded continuously so the amount after 10 years the amount will be $18819.75, when n = 365 and t = 10 years amount will be $18819.22, when n = 12 and t = 10 years amount will be $18803.91.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

\(A = P (1 + \frac{r}{n} )^{nt}\)

Where A = Final amount

         P = Principal amount

         r  = annual rate of interest

         n = how many times interest is compounded per year

         t = How long the money is deposited or borrowed (in years)

If the interest compounded continuously:

P = $12000, r = 4.5% = 0.045%

⇒ \(A (t) = 12000 (e)^{0.045t}\)

When t = 10 years, plug this value in the above expression and calculating, we get;

A(10) = $18819.75

When interest compounded daily:

\(A(t) = 12000 (1 + \frac{0.045}{365} )^{365t}\)

Plug t = 10 years:

We get;

A(10) = $18819.22

Similarly, If interest is compounded monthly:

n = 12 and t =10, we get:

A(10) = $18803.91

Thus, when interest compounded continuously so the amount after 10 years the amount will be $18819.75, when n = 365 and t = 10 years amount will be $18819.22, when n = 12 and t = 10 years amount will be $18803.91.

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The time complexity of this algorithm is O(n), where n is the number of nodes in the linked list. The space complexity is O(1), since we are only using two pointers to traverse the list.

The problem can be solved using Floyd's cycle-finding algorithm, also known as the "tortoise and hare" algorithm. The algorithm uses two pointers, a slow pointer and a fast pointer, to traverse the linked list. The slow pointer moves one step at a time, while the fast pointer moves two steps at a time. If there is a cycle in the linked list, the fast pointer will eventually catch up to the slow pointer, and they will meet at some node.

Here's a Python implementation of the algorithm:

```
class ListNode:
   def __init__(self, val=0, next=None):
       self.val = val
       self.next = next

def hasCycle(head):
   if not head:
       return False
   slow = head
   fast = head.next
   while slow != fast:
       if not fast or not fast.next:
           return False
       slow = slow.next
       fast = fast.next.next
   return True
```

We start by initializing two pointers, slow and fast, to the head of the linked list. We then move the slow pointer one step at a time and the fast pointer two steps at a time. If there is a cycle in the linked list, the fast pointer will eventually catch up to the slow pointer, and they will meet at some node. If there is no cycle, the fast pointer will reach the end of the list and the loop will terminate.

The time complexity of this algorithm is O(n), where n is the number of nodes in the linked list. The space complexity is O(1), since we are only using two pointers to traverse the list.

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4 per a minute

Step-by-step explanation: