13) Which value is equivalent to the expression 7^2 - 3^4
A) -32
B)-19
C) 16
D) 32

Rahab originally had 165 oranges.

Let total number of oranges Rahab had be x.

John got 1/3 of x, which is (1/3)x.

Sarah got 5% of x, which is (5/100)x = (1/20)x.

The remaining fruit after John and Sarah got their share is:

= (1 - 1/3 - 1/20)x

= (16/60)x

= (4/15)x.

Peter got 2/3 of this remainder, which is:

(2/3)*(4/15)x

= (8/45)x.

The total number of oranges Rahab originally had is:

x = (1/3)x + (1/20)x + (8/45)x + 60

Multiplying through with 135 gives:

135x = 45x + 9x + 32x + 8100

We will simplify it

135x - 45x - 9x - 32x = 8100

49x = 8100

x = 8100/49

x = 165.306122449

x = 165.

Note we assumed some figures that were missing:

Rahab shared oranges among her three children John, Sarah and Peter, John got 1/3 of the fruit, Sarah got 5% of the fruit and Peter got 2/3 of the remainder. If she was left with 60 fruits, how many oranges had she before?

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The domain of g(x) is [9,15] and the range is [4,64]. The domain is the same as the original function f(x), while the range is obtained by multiplying the range of f(x) by 4.

The function g(x) = 4(f(x)) is obtained by applying a transformation to the original function f(x). Since f(x) has a domain of [9,15] and a range of [1,16], we need to determine the domain and range of g(x).

The domain of g(x) is determined by the values of x that can be plugged into f(x) without any restrictions. Since the domain of f(x) is [9,15], and g(x) applies a transformation to f(x) without affecting the domain, the domain of g(x) will also be [9,15].

The range of g(x) is determined by the values that the transformed function g(x) can take. In this case, g(x) is obtained by multiplying f(x) by 4. Multiplying f(x) by a positive constant like 4 will stretch the range of f(x) vertically. Since the range of f(x) is [1,16], multiplying it by 4 will stretch it to [4,64]. Therefore, the range of g(x) is [4,64].

In summary, the domain of g(x) is [9,15], same as the domain of f(x), and the range of g(x) is [4,64], obtained by stretching the range of f(x) by multiplying it by 4.

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Answer:

119 degrees

Step-by-step explanation:

All triangles have a sum of 180 degrees for all of their angles

so 180= 24+37+ x

x= 119

Answer:

119

Step-by-step explanation:

Answer: 12.5% is 1/8

Answer: 25/2 would be your answer, as it is already in it's simplest form.  I hope this helps! :)

Step-by-step explanation:

To represent the proportional relationship between the number of apples, x, and the amount of cinnamon, y, we can set up a proportion based on the given information which will be 2 * x = 3 * y.

The recipe states that there are 2 teaspoons of cinnamon for every 3 apples. Using this information, we can set up the following proportion:

2 teaspoons of cinnamon / 3 apples = y teaspoons of cinnamon / x apples

To express this proportion as an equation, we can cross-multiply:

2 * x = 3 * y

This equation represents the proportional relationship between the number of apples, x, and the amount of cinnamon, y. It states that the product of the number of apples and the amount of cinnamon is equal to a constant value, which indicates that the two quantities are in a proportional relationship.

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The dimensions of the box that maximize the volume are x = √700 and h = 100 / √700.

To find the largest possible volume of the box, we need to optimize the dimensions of the box. Let's denote the length of each side of the square base as x and the height of the box as h.

The surface area of the box consists of the area of the square base (x^2) and the four sides of the box (4xh). Since the box has an open top, we do not consider the top surface. The total surface area is given as 2100 square centimeters, so we have:

x^2 + 4xh = 2100

To maximize the volume, we need to express the volume of the box (V) in terms of a single variable. The volume of a rectangular prism is given by V = x^2h.

We can rewrite the equation for the surface area to solve for h:

h = (2100 - x^2) / (4x)

Now we can substitute this expression for h in the volume equation:

V = x^2 * [(2100 - x^2) / (4x)]

Simplifying, we have:

V = (1/4) * (2100x - x^3)

To find the maximum volume, we need to find the critical points of this function. We take the derivative of V with respect to x and set it equal to zero:

dV/dx = 2100/4 - (3/4)x^2 = 0

Solving this equation, we find:

2100/4 = (3/4)x^2

x^2 = 700

x = √700

Substituting this value back into the equation for h, we find:

h = (2100 - 700) / (4 * √700) = 1400 / (4 * √700) = 100 / √700

Therefore, the largest possible volume of the box is:

V = (1/4) * (2100 * √700 - 700 * √700) = 350√700 cubic centimeters.

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Answer:No

Step-by-step explanation:

The horizontal line test is used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value.

A function that is one-to-one can be inverted, meaning that it has an inverse function. Inverse functions are important in many areas of mathematics, such as solving equations, finding derivatives, and studying geometric transformations.

The horizontal line test is used because it provides a simple and easy way to determine if a function is one-to-one without having to solve for the inverse function. By drawing a horizontal line through the graph of a function and seeing if the line intersects the graph at most once, it is possible to determine if the function is one-to-one without the need for complex calculations or algebraic manipulations.

Another reason is that the horizontal line test can be applied to functions that are defined on a closed interval or on all real numbers and it is a visual way to understand if a function is one-to-one.

In conclusion, the horizontal line test is used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.

The test is simple and easy to apply, and it provides a visual way to understand if a function is one-to-one without the need for complex calculations or algebraic manipulations. It can be applied to functions that are defined on a closed interval or on all real numbers.

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The defendant was charged with aggravated assault. During the trial, the victim testified that the defendant beat her savagely.

In this case, aggravated assault refers to a more severe form of assault that involves the intentional causing of serious bodily harm to another person. The victim's testimony plays a crucial role in providing evidence and establishing the defendant's guilt. The prosecution will likely present other evidence, such as medical reports or eyewitness testimonies, to support the victim's claim.

It's important to note that the final verdict will depend on the judge or jury's assessment of the evidence presented during the trial. The defense will have an opportunity to cross-examine the victim and present their own evidence or witnesses to challenge the victim's testimony. The defendant's attorney may also argue for a lesser charge or attempt to establish that the defendant acted in self-defense. Ultimately, the court will weigh all the evidence and decide whether the defendant is guilty of aggravated assault based on the standard of proof beyond a reasonable doubt.

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Answer:

3x-5y

Step-by-step explanation:

⇒13x+2y-10x-7y

arrange the like terms together

⇒13x-10x-7y+2y

⇒3x-5y ...answer

hope that helps...

Answer:

7 1/3 inches

Step-by-step explanation:

2 (1 3/4 + 1 11/12)

9+11

3/4+11/12= -------------

12

20/12

=1 2/3+ 2

2(3 2/3)

= 7 1/3

Answer:

$758 per week

Step-by-step explanation:

15.16 x 50 = 758

Answer:$758 per week

Step-by-step explanation:Answer:15.16 x 50 = 758

Answer:

\(\dfrac{1}3\)

Step-by-step explanation:

When rolling a die successively, the probability of rolling a certain number(s) does not change because the die stays the same.

In this problem, we need to find the probability that a die roll will produce a number less than 3. First, we can list out those numbers:

all numbers:

numbers less than 3:

We can see that there are 6 total numbers and 2 numbers less than 3.

Therefore, we can represent the probability of rolling a number less than 3 as:

\(\dfrac{2}{6}\)

\(\boxed{=\dfrac{1}3}\)

First, we'll find the probability that a die is rolled only once.

There are 2 numbers that are less than 3, which are 1 and 2.

This makes the fraction 2/6, or simplified to 1/3.

The probability is 1/3.

Answer:

So, the correct answer is (30.104, 32.896).

Step-by-step explanation:

To find the 95% confidence interval for the mean number of pounds of trash per person per week, we can use the following formula:

CI = X + Zα/2 * (σ/√n)

σ = population standard deviation = 7.8 pounds

n = sample size = 120

Plugging in the values, we get:

CI = 31.5 ± 1.96 \times(7.8/√120)

CI = 31.5 ± 1.96 \times 0.711

CI = 31.5 ± 1.39

Therefore, the 95% confidence interval for the mean number of pounds of trash per person per week is (30.11, 32.89).

So, the correct answer is (30.104, 32.896).

Answer:

R y-axis (x,y) to (-x,y)

Step-by-step explanation:

The  rule for reflection is \(r_y\) axis (x, y) -> (-x, y).

A transformation is a broad phrase covering four distinct methods of changing the shape and/or position of a point, line, or geometric figure.

The original shape of the object is known as the Pre-Image, and the final shape and location of the object is known as the Image during the transformation.

As per the figure. the coordinates of Triangle LMN are

L(-6, 2),

M(-5, 4)

N(-3, 2)

and, the coordinates of Triangle L'M'N' are

L'(6, 2),

M'(5, 4)

N'(3, 2)

Here, the y coordinate is same only the sign of x coordinate change.

So, the rule for reflection is r y- axis (x, y) -> (-x, y).

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Answer:

11.4

Step-by-step explanation:

19.948-8.57=11.378

approximately 11.4

The correct number of significant figures is found as 1.1378 x 10⁻¹ .

To demonstrate the accuracy of measurements and calculations in the fields of math, chemistry, and other sciences, significant figures are essential.

The following five rules can be used to assess whether a number is significant.

The equation is given as:

=  19.948 - 8.57

On subtracting.

= 11.378

On converting in the significant figures:

= 1.1378 x 10⁻¹

Thus, the correct number of significant figures is found as 1.1378 x 10⁻¹ .

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820

Step-by-step explanation:

because 800+20 is 820

The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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Answer:

We can define a horizontal dilation/contraction of scale factor A, as:

g(x) = f(x*A)

if A > 1, this will be a contraction (it will be steeper)

if  0 < A < 1, this will be a dilation. (it will be less steep)

Then if we have:

g(x) = f(6*x) we have a contraction of scale factor 6, this means that the graph of the parent function will be contracted.

Below, you can see how the graphs change, where:

Blue is f(x)  =x

green is g(x) = f(6*x) = 6*x

Answer:

f(x)=x+6

-2+6

4

when x=0

0+6

6

when x=5

5+6

11

Step-by-step explanation:

The probability that the sample mean will be within plus minus 2 of the population mean if the sample size is n = 100 between z-scores of 0 and 2.5 using a z-table.

The standard deviation of the sample distribution, commonly known as the standard error, can be computed using the formula given that the population mean is 100 and the standard deviation is 16:

Standard Error = Standard Deviation / sqrt(sample size)

Let's determine the likelihoods for sample sizes of n = 100 and n = 400:

For n = 100:

Standard Error = 16 / sqrt(100) = 16 / 10 = 1.6

We can determine the z-scores for the upper and lower boundaries to establish the likelihood that the sample mean will be within plus or minus 2 of the population mean:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 1.6

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 1.6

Upper Bound z-score = 4 / 1.6

Upper Bound z-score = 2.5

We can calculate the region under the normal distribution curve between z-scores of 0 and 2.5 using a z-table or statistical software. This shows the likelihood that the sample mean will be within +/- 2 standard deviations of the population mean.

For n = 400:

Standard Error = 16/√400

Standard Error = 16/20

Standard Error = 0.8

We determine the z-scores by following the same procedure as above:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 0.8

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 0.8

Upper Bound z-score = 4 / 0.8

Upper Bound z-score = 5

Once more, we may determine the region under the normal distribution curve between z-scores of 0 and 5 using a z-table or statistical software.

A larger sample size, like n = 400, has the benefit of a lower standard error. The sampling distribution of the sample mean will be more constrained and more closely resemble the population mean if the standard error is less.

As a result, there is a larger likelihood that the sample mean will be within +/- 2 of the population mean. In other words, the estimate of the population mean gets more accurate and dependable as the sample size grows.

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The required solution of the linear programming problem for the given objective function and subject to constraints are,

Linear programming problem is Maximize 15x1 + 2x2

Subject to:

7x1 + x2 < 23

3x1 - x2 < 5

x1, x2 > 0

Objective function value for rounding up fraction 1/2 solution is 53

Objective function value for rounding up all fraction solution is 23.

Optimal objective function value 53 is lower than optimal value 95.5.

Optimal objective function value is always less than or equal to the LP's optimal objective function value as ILP problem is a more constrained version.

To solve the problem as an LP,

we can ignore the integer constraints

And solve the problem as a continuous linear program.

The problem can be written as,

Maximize 15x1 + 2x2

Subject to:

7x1 + x2 < 23

3x1 - x2 < 5

x1, x2 > 0

Rounding up fractions greater than or equal to 1/2,

The following feasible solution is,

x1 = 3, x2 = 4

The objective function value for this solution is 53.

However, this is not the optimal integer solution since both x1 and x2 are not integers.

Rounding down all fractions, we get the following feasible solution,

x1 = 1, x2 = 4

The objective function value for this solution is 23, which is less than the LP's optimal objective function value of 95.5.

This is not the optimal integer solution either.

Optimal objective function value for the ILP is lower than that for the optimal LP, solve the ILP problem.

In any one constraints

When x1 = 0 ⇒ x2 = 23

x2 = 0 ⇒ x1 = 3.3

Optimal value is ,

15(3.3) + 2(23)

= 49.5 + 46

= 95.5

Optimal objective function value is lower than optimal value.

The optimal objective function value for the ILP problem is always less than or equal to the corresponding LP's optimal objective function value .

Because the ILP problem is a more constrained version of the linear programming problem.

The ILP problem restricts the variables to be integers, which reduces the feasible region and makes the problem more difficult to solve.

The optimal objective function values for the LP and ILP problems are equal.

If the LP problem has an optimal solution that satisfies the integer constraints.

In general, the optimal objective function value of the MILP problem can be better or worse than that of the LP or ILP problem.

It depends on the specific problem instance.

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The above question is incomplete, the complete question is :

Given the following all-integer linear program:

Max 15x1 + 2x2

s. t.

7x1 + x2 < 23

3x1 - x2 < 5

x1, x2 > 0 and integer

a. solve the problem as an lp, ignoring the integer constraints.

b. what solution is obtained by rounding up fractions greater than or equal to 1/2? is this the optimal integer solution?

c. what solution is obtained by rounding down all fractions? is this the optimal integer solution? explain.

d. show that the optimal objective function value for the ilp (integer linear programming) is lower than that for the optimal lp.

e. why is the optimal objective function value for the ilp problem always less than or equal to the corresponding lp's optimal objective function value? when would they be equal? comment on the optimal objective function of the milp (mixed-integer linear programming) compared to the corresponding lp and ilp.

You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The relationship between the two variables in a bivariate data set is graphically represented by a scatter plot. Consider them to be the graphic depiction of two data sets that have been combined by allocating each axis in the plot to a distinct variable.

Due to the presence of two variables, this type of data is known as bivariate data. Only 1 variable may be displayed on a line plot. You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The standard deviation of each variable and the covariance between them must first be determined in order to calculate the Pearson correlation. Covariance is subtracted from the product of the standard deviations of the two variables to get the correlation coefficient.

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a. The PMF (Probability Mass Function) for X is:

PMF(X) = {}

0.1, for X = 0

0.2, for X = 1

0.25, for X = 2

0.2, for X = 3

0.15, for X = 4

0.06, for X = 5

0.03, for X = 6

0.01, for X = 7

b. The mean (μ) is 2.54; the Variance (σ²) is 1.6484

c. The CDF is a valid CDF because it is a non-decreasing function and it approaches 1 as x approaches infinity.

a) The PMF (Probability Mass Function) for X, the number of goals scored in a World Cup soccer match, is given by the following:

PMF(X) = {}

0.1, for X = 0

0.2, for X = 1

0.25, for X = 2

0.2, for X = 3

0.15, for X = 4

0.06, for X = 5

0.03, for X = 6

0.01, for X = 7

This PMF is valid because it assigns probabilities to each possible value of X (0 to 7) and the probabilities sum up to 1. The probabilities are non-negative, and for any value of X outside the range of 0 to 7, the probability is zero.

b) To compute the mean and variance of X, we can use the following formulas:

Mean (μ) = Σ(X * PMF(X))

Variance (σ^2) = Σ((X - μ)² * PMF(X))

Using the PMF values given above, we can calculate:

Mean (μ) = (0 * 0.1) + (1 * 0.2) + (2 * 0.25) + (3 * 0.2) + (4 * 0.15) + (5 * 0.06) + (6 * 0.03) + (7 * 0.01) = 2.54

Variance (σ²) = [(0 - 2.54)² * 0.1] + [(1 - 2.54)² * 0.2] + [(2 - 2.54)² * 0.25] + [(3 - 2.54)² * 0.2] + [(4 - 2.54)² * 0.15] + [(5 - 2.54)² * 0.06] + [(6 - 2.54)² * 0.03] + [(7 - 2.54)² * 0.01] ≈ 1.6484

c) The CDF (Cumulative Distribution Function) of X is a function that gives the probability that X takes on a value less than or equal to a given value x.

The CDF can be obtained by summing up the probabilities of X for all values less than or equal to x.

CDF(x) = Σ(PMF(X)), for all values of X ≤ x

For example, the CDF for x = 3 would be:

CDF(3) = PMF(0) + PMF(1) + PMF(2) + PMF(3)

CDF(3) = 0.1 + 0.2 + 0.25 + 0.2

CDF(3) = 0.75

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a) The PMF for X is valid because it assigns non-negative probabilities to each possible value of X and the sum of all probabilities is equal to 1.

b) The mean of X is 2.55 and the variance is 2.1925.

c) The CDF of X is a valid cumulative distribution function as it is a non-decreasing function ranging from 0 to 1, inclusive.

a) The PMF (Probability Mass Function) for X, the number of goals scored in a randomly selected World Cup soccer match, can be represented as follows,

PMF(X) = {

 0.1, if X = 0,

 0.2, if X = 1,

 0.25, if X = 2,

 0.2, if X = 3,

 0.15, if X = 4,

 0.06, if X = 5,

 0.03, if X = 6,

 0.01, if X = 7,

 0, otherwise

}

This PMF is valid because it satisfies the properties of a valid probability distribution. The probabilities assigned to each value of X are non-negative, and the sum of all probabilities is equal to 1. Additionally, the PMF assigns a probability to every possible value of X within the given distribution.

b) To compute the mean (expected value) and variance of X, we can use the formulas,

Mean (μ) = Σ (x * p(x)), where x represents the possible values of X and p(x) represents the corresponding probabilities.

Variance (σ^2) = Σ [(x - μ)^2 * p(x)]

Calculating the mean,

μ = (0 * 0.1) + (1 * 0.2) + (2 * 0.25) + (3 * 0.2) + (4 * 0.15) + (5 * 0.06) + (6 * 0.03) + (7 * 0.01)

  = 0 + 0.2 + 0.5 + 0.6 + 0.6 + 0.3 + 0.18 + 0.07

  = 2.55

The mean number of goals scored in a World Cup soccer match is 2.55.

Calculating the variance,

σ^2 = [(0 - 2.55)^2 * 0.1] + [(1 - 2.55)^2 * 0.2] + [(2 - 2.55)^2 * 0.25] + [(3 - 2.55)^2 * 0.2]

      + [(4 - 2.55)^2 * 0.15] + [(5 - 2.55)^2 * 0.06] + [(6 - 2.55)^2 * 0.03] + [(7 - 2.55)^2 * 0.01]

    = [(-2.55)^2 * 0.1] + [(-1.55)^2 * 0.2] + [(-0.55)^2 * 0.25] + [(-0.55)^2 * 0.2]

      + [(-1.55)^2 * 0.15] + [(2.45)^2 * 0.06] + [(3.45)^2 * 0.03] + [(4.45)^2 * 0.01]

    = 3.0025 * 0.1 + 2.4025 * 0.2 + 0.3025 * 0.25 + 0.3025 * 0.2

      + 2.4025 * 0.15 + 6.0025 * 0.06 + 11.9025 * 0.03 + 19.8025 * 0.01

    = 0.30025 + 0.4805 + 0.075625 + 0.0605 + 0.360375 + 0.36015 +          0.357075 + 0.198025

    = 2.1925

The variance of the number of goals scored in a World Cup soccer match is 2.1925.

c) The CDF (Cumulative Distribution Function) of X can be calculated by summing up the probabilities of X for all values less than or equal to a given x,

CDF(X) = {

 0, if x < 0,

 0.1, if 0 ≤ x < 1,

 0.3, if 1 ≤ x < 2,

 0.55, if 2 ≤ x < 3,

 0.75, if 3 ≤ x < 4,

 0.9, if 4 ≤ x < 5,

 0.96, if 5 ≤ x < 6,

 0.99, if 6 ≤ x < 7,

 1, if x ≥ 7

}

The CDF is valid because it satisfies the properties of a valid cumulative distribution function. It is a non-decreasing function with a range between 0 and 1, inclusive. At x = 0, the CDF is 0, and at x = 7, the CDF is 1. The CDF is right-continuous, meaning that the probability assigned to a specific value of x is the probability of x being less than or equal to that value.

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(a) The head loss through straw is 0.007 m

(b) The pressure drop if the flow is horizontal up is 1974 Pa

(c) The pressure drop if the flow is vertically up 0.007 m

(a) For turbulent flow (high Re), the friction factor depends on the roughness of the straw's walls and can be calculated using the Colebrook equation. Since the straw is smooth, we can assume laminar flow.

Substituting the values into the Reynolds number equation, we get:

Re = (1000 kg/m³ x 0.0955 m/s x 0.002 m) / (0.001 kg/ms) = 191,000

Therefore, the friction factor is:

f = 64 / 191,000 = 0.000334

Finally, substituting all the values into the Darcy-Weisbach equation, we get:

h_L = (0.000334 x 0.2 m x 0.0955 m/s²) / (2 * 9.81 m/s² x 0.002 m) = 0.007 m

(b) In this case, the change in height is the height of the straw, which is 20 cm. Substituting the values, we get:

ΔP = 1000 kg/m³ x 9.81 m/s² x 0.2 m = 1962 Pa

Therefore, the total pressure drop when the flow is horizontal upward is:

P_drop = h_L + ΔP = 0.007 m + 1962 Pa = 1974 Pa

(c) If the flow is vertical upward, there is no change in elevation of the fluid, so the pressure drop is solely due to the head loss calculated in part (a). Therefore, the pressure drop is:

P_drop = h_L = 0.007 m

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Answer:

4 x 20 - X

Step-by-step explanation:

4 times 20 - X

x is the unknown variable

Unknown variable = what you are trying to find.

9514 1404 393

Answer:

  (3, -2)

Step-by-step explanation:

Given:

  y = -2x +4

Find:

  the value of x for y=-2

Solution:

  Put the value of y into the equation and solve for x:

  -2 = -2x +4 . . . . use -2 for y

  -6 = -2x . . . . . . . subtract 4

  3 = x . . . . . . . . . .divide by -2

The solution of interest is (3, -2).

Answer:

a. Cube Root

I hope this helps!

Answer:

7ft; 8 minutes

Step-by-step explanation:

a. to find the height the person boarded at, plug in t=0 since this is right when the person got on the Ferris wheel. we then get:

h(0) = -45 * cos ((pi/4)*0) + 52 = 7 ft

b. to find the period, we have pi/4 * t = 2*pi, solve for t to get t=8