Three water pumps can move a total 1700 gallons of water per minute from a flooded mineshaft. If engineers
wnat to remove at least 5500 gallons per minute, how many pumps will they need to be operating? The answer choices are:
9.7 water pumps
9 water pumps
10 water pumps
93 water pumps

To find the z-score on a TI-84 calculator with the mean and standard deviation, use the "invNorm" function.

The z-score measures how many standard deviations a data point is away from the mean. On a TI-84 calculator, you can find the z-score using the "invNorm" function, which calculates the inverse of the cumulative distribution function (CDF) for the standard normal distribution.

To find the z-score, follow these steps:

1. Press the "2nd" button, followed by the "Vars" button to access the DISTR menu.

2. Scroll down or press "3" to select "invNorm(" and press "Enter".

3. Enter the desired area under the normal curve (probability), followed by a comma.

4. Enter the mean (μ) followed by another comma.

5. Enter the standard deviation (σ) and close the parentheses by pressing ")".

6. Press "Enter" to calculate the z-score.

The result displayed on the calculator will be the z-score corresponding to the given area, mean, and standard deviation. The z-score helps in understanding the relative position of a data point within a normal distribution by indicating the number of standard deviations it is above or below the mean.

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Answer:

See below.

Step-by-step explanation:

Solving :-

#1

#2

They both have the numerator in both solutions to be 5 and -3 respectively. I believe this is because both equations have the constant term, c, to be -15 and 5 and -3 are factors of -15.

Answer:

1.5

Step-by-step explanation:

I did it

Answer:

B: Horizontal Assymptote

Step-by-step explanation:

A horizontal asymptote is defined as a horizontal line in a graph that gives us an idea of its x-values. It's either approaching away to the right of the origin or to the left.

In this case, the W-axis is also the x-axis and thus can be said to be the horizontal assymptote

Answer:

Top:(4r⁹+3r³-5)

Bottom: r⁵

Step-by-step explanation:

The f(5) for the given function f(x) is equal to 29.

We have,

f(x) = {x³     x< -3

         2x² -9   -3≤x<4

          5x+ 4       x≥4}

To determine f(5) for the function f(x), we need to evaluate the function at x = 5.

Let's consider the different cases based on the given piecewise definition of f(x):

For x < -3:

Since 5 is not less than -3, this case does not apply to the value we are evaluating.

For -3 <= x < 4:

Again, 5 does not fall within this range. Therefore, this case also does not apply.

For x >= 4:

Since 5 is greater than or equal to 4, this case applies. In this case, the function is defined as 5x + 4. So, substituting x = 5 into this equation, we get:

f(5) = 5(5) + 4

f(5) = 25 + 4

f(5) = 29

Therefore, f(5) for the given function f(x) is equal to 29.

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In an MDP (Markov Decision Process), the following statements are true:

The optimal policy for a given state s is unique.

The problem of determining the value of a state is solved recursively by the value iteration algorithm.

The optimal policy for a given state in an MDP refers to the best course of action to take from that state in order to maximize expected rewards or outcomes. This policy is unique because, given a specific state, there is a single action or set of actions that yields the highest expected value.

The value iteration algorithm is a dynamic programming method used to determine the value of each state in an MDP. It starts with an initial estimate of the state values and then iteratively updates them until convergence. This recursive process involves considering the immediate rewards and expected future rewards obtained by transitioning from one state to another, following the optimal policy. Through this algorithm, the values of states are refined and converge to their optimal values.

The third statement, "V* (s) = 25, T (s, a, s') [R (s, a, s') + yV* (s')]," represents the equation for calculating the value function V*(s) of each state in an MDP. It states that the value of a state is determined based on the transition probabilities T(s, a, s'), immediate rewards R(s, a, s'), discount factor y, and the value of the next state V*(s'). This equation allows us to compute the value of a state by considering the expected rewards and future values.

The fourth statement, "Q* (s, a) = ∑T (s, a, s') [R (s, a, s') + yV* (s')]," represents the equation for calculating the action-value function Q*(s, a) in an MDP. It calculates the expected value of taking action a in state s, considering the transition probabilities, immediate rewards, discount factor, and the value of the next state. However, the specific notation given in the statement, with "2,," is incomplete or incorrect, making it an invalid equation.

In summary, the optimal policy for a given state in an MDP is unique, and the value of each state is determined recursively using the value iteration algorithm. The value function V*(s) and the action-value function Q*(s, a) play key roles in evaluating the expected rewards and future values in an MDP.

The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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The mean is represented by a line that divides the box plot into two equal parts. It is placed at the center of the box plot, between the lower and higher quartiles.

The mean is represented by a line in the box plot, which divides the box plot into two equal parts. This line is placed in the center of the box plot, between the lower and higher quartiles. The mean is the average of all the values within the data set, and is represented by the line in the box plot. It is the midway point between the highest and lowest values of the data set. The mean can help to give a better understanding of the data set by providing an overall average of the data. It can be used to compare the data set to other sets of data, as well as to identify outliers within the data set. The mean can be used to identify trends within the data set, and to make predictions about future data sets or events.

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Answer:

v-at/m

Step-by-step explanation:

v=mu+at

change of subject of the formula

mu=v-at

u=v-at/m

We are given the expression for the velocity of a moving vehicle, \(v=mu+at\) and asked to rewrite the expression in terms of "u."

To complete this, we simply need to use our knowledge of algebra.

\(\Longrightarrow v=mu+at\)

\(\Longrightarrow v-at=mu\\\) - Subtracted "at" from both sides of the equation

\(\Longrightarrow \frac{v-at}{m} =u\\\) - Divided both sides by "m"

\(\Longrightarrow \boxed{u=\frac{v-at}{m} \\} \therefore Sol.\)

(3) the segment is half the length of the third side and parallel to it.

The midpoint theorem is a geometric theorem which states that if a line segment connects the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length.

This theorem is also known as the midsegment theorem or the triangle midsegment theorem. The midpoint theorem has various applications in geometry, particularly in relation to triangles and quadrilaterals.

Statement (3) is correct. Statements (1), (2), and (4) are not true for a midpoint

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Answer:

A 0.6

Step-by-step explanation:

The arc length of the polar curve `r = e^(2θ)` where `0 ≤ θ ≤ 2π` is `0`.

To find the arc length of the polar curve `r = e^(2θ)` where `0 ≤ θ ≤ 2π`, we use the formula:

`L = int_a^b sqrt[r^2 + (dr/dθ)^2] dθ`

where `a` and `b` are the limits of integration, and `r` and `dr/dθ` are the polar coordinates of the curve.

First, we find `dr/dθ`:

`dr/dθ = d/dθ (e^(2θ)) = 2e^(2θ)`

Then, we plug in `r` and `dr/dθ` to the formula for arc length and integrate:

`L = int_0^(2π) sqrt[e^(4θ) + 4e^(4θ)] dθ`

`L = int_0^(2π) sqrt[5e^(4θ)] dθ`

`L = sqrt(5) int_0^(2π) e^(2θ) dθ`

Using integration by substitution with `u = 2θ`, we get:

`L = sqrt(5) int_0^(4π) (1/2) e^u du`

`L = sqrt(5) [ (1/2) e^u ]_0^(4π)`

`L = sqrt(5) [(1/2) e^(8π) - (1/2) e^0]`

`L = sqrt(5) [(1/2) (1) - (1/2) (1)]` (since `e^(8π) = 1`)

`L = 0`

Therefore, the arc length of the polar curve `r = e^(2θ)` where `0 ≤ θ ≤ 2π` is `0`.

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The sum of 8 + 2 ¹ / ₂ would be c. 10 ¹ / ₂.

To calculate the sum of mixed fractions and whole numbers, you can convert the mixed fraction into an improper fraction by adding the numerator to the product of the denominator and the whole number. Then determine a common denominator for both the whole number and the improper fraction.

Finally, simplify the resulting fraction by dividing its numerator and denominator by their greatest common factor.

This means that the sum of 8 and 2 ¹ / ₂ would therefore be :

= 8 + 2

= 10

Then involve the fraction :

= 10 + 1 / 2

= 10 ¹ / ₂

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Answer:

D

Step-by-step explanation:

6% of 40 is 2.4, 40.00+ 2.40=42.40

Answer:

42.50

Step-by-step explanation:

40X1.06

42.40

Answer:

Step-by-step explanation:

Let the invested amount is x

Using the interest formula and solving for x:

The amount invested is AED 3000

Answer:

The value of 14(n+1) is 112.

Step-by-step explanation:

14n=98

n=98/14

n=7

-------------

14(n+1)=14(7+1)=14(8)=112

Answer:

m = 16

Step-by-step explanation:

304 = 19 m      ( / 19)

16 = m

Answer:

y = -1/2x + 7/2  

Step-by-step explanation:

y = -1/2x + b

3 = -1/2(1) + b

3 = -1/2 + b

7/2 = b

y = -1/2x + 7/2  

There are 362,880 possible permutations of the letters in the word HISTOGRAM.

To find the number of permutations of these letters, first count all the letters on the word histogram.

Since it has 9 distinct letters, we can solve for its permutation using the formula:

P = n!

which represents the number of ways to arrange n distinct objects in a line.

Therefore, the number of permutations of the letters in the word HISTOGRAM is:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

Thus, in the word HISTOGRAM, there are 362,880 possible permutations of the letters.

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The amount of feet of border that she needs to purchase is given as follows:

20 feet.

The perimeter of a square of side length s is given by the multiplication of four and the side length s, as follows:

P = 4s.

All the sides measure 5 feet, hence the parameter s is given as follows:

s = 5.

Then the perimeter of the square plot is given as follows:

P = 4 x 5

P = 20 feet.

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730

bought at x

x + 50 - 20 = 760

x = 760 - 30 = 730

The statement given "regression equations are usually used to predict values of unavailable data. if the data do not closely model a particular type of function, then that type of function is not appropriate to use in statistical regression. the more closely data fit a model, the more predicted values will be." is true because regression equations are indeed employed for predicting values of unavailable data.

Regression equations are commonly utilized to make predictions for unavailable data. When the data does not closely conform to a specific type of function, that function is deemed inappropriate for statistical regression. The accuracy of predicted values is contingent on the degree of resemblance between the data and the chosen model. Hence, a strong fit between the data and the model enhances the reliability of predicted values, ensuring that regression analysis is effectively applied for making accurate predictions.

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Answer:

y = \(\frac{1}{3}\) (x - 1)

Step-by-step explanation:

9y - 3x = - 3 ( add 3x to both sides )

9y = 3x - 3 ← factor out 3 from each term

9y = 3(x - 1) ← divide both sides by 9

y = \(\frac{3}{9}\) (x - 1) = \(\frac{1}{3}\) (x - 1)

Answer:

Step-by-step explanation:

Given parabola:

Its transformations from the parent function g(x) = x² are:

Correct choice is C

To answer this question, we'll use the range rule of thumb for unusual values. The range rule of thumb states that an outcome is considered unusual if it falls more than 2 standard deviations away from the mean.

Step 1: Calculate the probability of guessing a question correctly.
Since each question has 5 possible answers, the probability of guessing correctly is 1/5 or 0.20.

Step 2: Find the mean and standard deviation for the binomial distribution.
Mean (μ) = n * p, where n is the number of questions (20) and p is the probability of guessing correctly (0.20).
μ = 20 * 0.20 = 4

Standard deviation (σ) = √(n * p * q), where q is the probability of guessing incorrectly (1 - p).
σ = √(20 * 0.20 * 0.80) ≈ 1.79

Step 3: Determine the unusual range.
Using the range rule of thumb, we consider values unusual if they are more than 2 standard deviations away from the mean.
Unusual range = μ ± 2σ
Lower limit: 4 - 2 * 1.79 ≈ 0.42
Upper limit: 4 + 2 * 1.79 ≈ 7.58

Since we're looking for the number of questions correct by guessing alone, we round the upper limit to the nearest whole number: 8.

So, it would be unusual to get 8 or more questions correct by guessing alone on a 20-question test with 5 possible answers for each question.

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Answer:

32

Step-by-step explanation:

The answer would be 32:);)

The approximate value of the expression \(log_{5}\) ( \(\frac{4}{7}\) ) is -0.3477.

A Logarithm is just another way to express an exponent. Logarithmic properties are used to compress or expend the existing log expression.

Here we use log property for the expansion i.e.,

\(log_{b}\) \(\frac{x}{y}\) = \(log_{b}\) x + \(log_{b}\) y

(Note that \(log_{b}\)x = \(\frac{ log x} {log \\b}\) )

Given,

\(log_{5}\) ( \(\frac{4}{7}\) )

can be written as:

\(log_{5}\) ( \(\frac{4}{7}\) ) =  \(log_{5}\) (4) -  \(log_{5}\) (7) = \(\frac{log 4 - log 7}{log 5}\) =  \(\frac{0.6020 - 0.8450}{0.69897}\) = - 0.3477

Hence the expression value is -0.3477.

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