Save ProjectWhen we create a rectangle in ANSYS in the geometry step, we are not affecting the mathematical model.A) TrueB) FalseThere are three elements needed to define a boundary value problem:
1. Governing equations
2. Domain
3. Boundary conditions
The rectangle in ANSYS defines the domain. Hence we are affecting the boundary value problem (i.e. the mathematical model) when we create the rectangle in ANSYS.

Answer:

7 17/99

Step-by-step explanation:

The height of domino number 10 is 56.9 inches.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

The exponential function:-An exponential function is given by:

y = abˣ

where a is the initial value of y at x = 0, y, x are variables and b is the multiplication factor

Let y represent the height of the number x domino

Since the height of the smallest domino no 0 is 3 inches, hence a = 5. b = 100% + 19% = 1.19

y = 10(1.19)ˣ

For x = 10:

y = 10(1.19)¹⁰= 56.9 inches

Therefore the height of domino number 10 is 56.9 inches.

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Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

200 * 0.06 = 12

It's important to note that the pdf represents the likelihood of observing a particular value of X, while the cdf gives the probability that X takes on a value less than or equal to a given x.

To compute the probability density function (pdf) and cumulative distribution function (cdf) of a continuous random variable X following a uniform distribution on the interval (0,1), we can use the following formulas:

1. Density Function (pdf):The pdf of a uniform distribution is constant within its support interval and zero outside it. For the given interval (0,1), the pdf is:

f(x) = 1,  0 < x < 1

      0,  otherwise

2. Cumulative Distribution Function (cdf):The cdf of a uniform distribution increases linearly within its support interval and is equal to 0 for x less than the lower limit and 1 for x greater than the upper limit. For the given interval (0,1), the cdf is:

F(x) = 0,     x ≤ 0

      x,     0 < x < 1       1,     x ≥ 1

These formulas indicate that the pdf of X is a constant function with a value of 1 within the interval (0,1) and zero outside it. The cdf of X is a linear function that starts at 0 for x ≤ 0, increases linearly with x between 0 and 1, and reaches 1 for x ≥ 1.

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Two parallel lines in the coordinate system share the same slope, this means that if you have two parallel lines:

For the given equations, the slopes are:

The slopes are different, so this lines are not parallel.

Two lines are perpendicular, when the slope of one of them is the negative inverse of the first one, this is for the perpendicular lines:

For the given equations, using y=17x-8 as reference, the slope of a line perpendicular to this one must be:

The slope of a perpendicular line to y=17x-8 is different from the slope of the second given line, so you can conclude that these lines are not perpendicular.

The correct choice is Neither

Answer:

x=1 2/3y-1/3z hope this helps!

Step-by-step explanation:

5y=3x+z

-z        -z

5y-z=3x

/3      /3

1 2/3 - 1/3z=x

x=1 2/3y-1/3z

Answer:

x = \(\frac{5y-z}{3}\)

Step-by-step explanation:

5y = 3x + z ( subtract z from both sides )

5y - z = 3x ( isolate x by dividing both sides by 3 )

\(\frac{5y-z}{3}\) = x

Answer:

Lucas monthly net pay is $1758

Step-by-step explanation:

Lucas works for a salary of $2,396 per month.

His deductions include $360 of federal income tax,

$148 for Social Security,

$35 for Medicare, and

a $95 insurance premium.

Now,

2396 - 360 - 148 - 35 - 95 = 1758

Thus, Lucas monthly net pay is $1758

-TheUnknownScientist

Given :

One cell phone company offers a plan that costs $26.99 and includes unlimited night and weekend minutes.

Another company offers a plan that costs $18.99 and charges $0.35 per minute during nights and weekends.

To Find :

For what numbers of night and weekend minutes does the second company's plan cost more than the first company's plan.

Solution :

Let, after n number of nights and weekends second plan is most costly.

So,

\(18.99+0.35x > 26.99\\\\0.35x > 8\\\\x>22.85\)

Therefore, after 22 night and weekends second plan is  most costly.

Hence, this is the required solution.

Answer:

Step-by-step explanation:

Survey methods A, C, and D are likely to introduce bias in determining customers' preferred toothpaste brand. Option A, C and D

When considering potential biases in survey methods for determining customers' preferred toothpaste brand, there are a few options that could introduce bias. Let's analyze each method individually:

A) A survey is sent to the customers who are on the pharmacy's frequent buyer list.

This method is likely to introduce bias because it only targets customers who are already on the frequent buyer list. This group of customers may not be representative of the entire customer base, as they could have specific preferences or purchasing behaviors that differ from the general population.

C) Three customers who buy toothpaste with a coupon are selected, and the toothpaste brand they purchased is recorded.

This method is also prone to bias. By selecting customers who purchased toothpaste with a coupon, the survey is limited to a specific subgroup of customers.

This subgroup might have different preferences and motivations for purchasing toothpaste compared to the general population. The presence of a coupon could influence their purchasing decisions, making them more likely to choose a particular brand.

D) Every 10th customer who enters the pharmacy on 1 day is selected and asked.

This sampling method is known as systematic sampling. While it might seem unbiased, it could introduce bias if there are any patterns in customer behavior.

B) One hundred people from the pharmacy's customer list are selected at random, called on the phone, and asked.

This method, known as random sampling, is generally considered one of the least biased survey methods. By randomly selecting customers from the pharmacy's customer list and conducting phone interviews, it provides an opportunity to obtain a more representative sample of the customer base and their preferences. Option A, C and D

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The change in total revenue brought about by a 16 unit increase in Q is -1.5.

(a) (i) To differentiate y = 4x⁴ − 2x² + 28 with respect to x, we apply the power rule of differentiation. We have:
dy/dx = 16x³ - 4x

(ii) To differentiate f(x) = 1/x² + √x³ with respect to x, we can apply the chain rule of differentiation. We have:
f(x) = x⁻² + x³/²
df/dx = -2x⁻³ + 3/2x^(3/2)

(iii)(a) The slope of the function y = 3x² − 4x + 5 at x = 4 and x = 6 can be found by differentiating the function with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
At x = 4,
dy/dx = 6(4) − 4 = 20
At x = 6,
dy/dx = 6(6) − 4 = 32

(b) The second-order derivative of the function y = 3x² − 4x + 5 at x = 4 can be found by differentiating the function twice with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
d²y/dx² = 6
The second-order derivative at x = 4 is 6. The slope of the function at x = 4 is positive, so we would expect the second-order derivative to be positive.

(b) (i) The demand equation is given by: P = aQ⁻² + b
The marginal revenue function is the derivative of the total revenue function with respect to Q. The total revenue function is:
R = PQ
Differentiating both sides with respect to Q gives:
dR/dQ = P + Q(dP/dQ)
Since P = aQ⁻² + b,
dP/dQ = -2aQ⁻³
Substituting into the equation for dR/dQ, we have:
dR/dQ = aQ⁻² + b + Q(-2aQ⁻³)
dR/dQ = aQ⁻² + b - 2aQ⁻²
dR/dQ = (b - aQ⁻²)
Therefore, the marginal revenue function is:
MR = b - aQ⁻²

(ii) To calculate the marginal revenue when Q = 3b, we substitute Q = 3b into the marginal revenue function:
MR = b - a(3b)⁻²
MR = b - ab²/9
To find the change in total revenue brought about by a 16 unit increase in Q, we can use the formula:
ΔR = MR × ΔQ
where ΔQ = 16
ΔR = (b - ab²/9) × 16
To show that ΔR = -1.5, we need to use the given relationship a > 0 and b > 0. Since a > 0, we know that ab²/9 < b. Therefore, we can write:
ΔR = (b - ab²/9) × 16 > (b - b) × 16 = 0
Since the marginal revenue is negative (when b > 0), we know that the change in total revenue must be negative as well. Therefore, we can write:
ΔR = -|ΔR| = -16(b - ab²/9)
Since ΔQ = 16b, we have:
ΔR = -16(b - a(ΔQ/3)²)
ΔR = -16(b - a(16b/3)²)
ΔR = -16(b - 256ab²/9)
ΔR = -16/9(3b - 128ab²/3)
ΔR = -16/9(3b - 16(8a/3)b²)
ΔR = -16/9(3b - 16(8a/3)b²) = -16/9(3b - 16b²/9) = -16/9(27b²/9 - 16b/9) = -16/9(3b/9 - 16/9)
ΔR = -16/9(-13/9) = -1.5

Therefore, the change in total revenue brought about by a 16 unit increase in Q is -1.5.

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Answer:

g = -7

I hope this helps!

Answer:

he can rent it for 10 hours

Step-by-step explanation:

35 - 15 = 20

20 divided by 2 equals 10

Answer:

10 hours

Step-by-step explanation:

Say x is the number of hours he can rent the detector at most. Using it, we can set up this equation:

15 + 2x = 35

Subtract 15 from both sides

2x = 20

Divide by 2 on both sides

x = 10

The correct option c. 5/7. The value of cos L is found to be 5 /7.

For the stated right angles triangle:

Cos L = base / hypotenuses

Cos L = 10 / 14

Cos L = 5/7

Thus, the value of cos L is found to be 5/7.

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Answer:

\( \huge{ \boxed{ \bold{ \tt( \: 0 \: ,5 \: )}}}\)

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☞ First, Let's explore about Midpoint :

Midpoint of the segment simply means middle point of a line segment. Formula of Midpoint :

\( \boxed{ \sf{(x _{ \: m \: } ,\: y_{m}) = ( \frac{x_{1} + x_{2}}{2} ,\: \frac{y_{1} + y_{2}}{2} )}}\)

where ,

The Midpoint Formula is used to find the exact center point between two defined points in a line segment.  The Midpoint formula is quite simple , so you should easily be able to remember it. It won't matter which point you pick to be the 'first" point you plug in. Just make sure that you're adding both an x to an x and a y to a y. Hence, keep in mind , in order to find the midpoint of a line segment, the first step is to add both ' x - co-ordinates' and divide it by 2 and then the second step is to add both ' y - co-ordinates ' and divide it by 2.

Now, Let's solve it!

☯ Question :

☯ Step - by - step explanation :

Let P ( x , y ) divide the line joining the points A ( - 2 , 7 ) and B ( 2 , 3 ). Now, let :

Apply midpoint formula , then plug the values and lastly simplify it :

\( \sf{ midpoint \: = \: ( \frac{x _{ \: 1 \: } + x _{ \: 2 \: }}{2} ,  \: \frac{y_{ \: 1 \: } + y _{ \: 2\: }}{2} })\)

➺ \( \sf{midpoint = ( \frac{ - 2 + 2}{2},  \: \frac{7 + 3}{2} )}\)

➺ \( \sf{midpoint = ( \frac{0}{2} ,  \: \frac{10}{2} )}\)

➺ \( \boxed{ \sf{ midpoint = ( \: 0 \: , 5})}\)

Hence , The midpoint of the segment with the end points A ( - 2 , 7 ) and B ( 2 , 3 ) is ( 0 , 5 ) .

Hope I helped!

Have a wonderful time ッ

~TheAnimeGirl ♡

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Answer:

2.95 each

Step-by-step explanation:

We can see that the constant of proportionality between x and y is k = 8, using that we can see that when x = 12 the value of y is 96

We know that x and y vary directly, then we can write the equation that relates these variables as.

y = kx

Where k is a constant

We know that y = 48 when x = 6, then we can write.

48 = k*6

48/6 = k

8 = k

The relation is:

y = 8*x

Then if x = 12, we have.

y = 8*12

y = 96

That is the value of y.

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For the standard normal probability distribution, the area under the probability density function to the left of the mean is 0.5.

This means that half of the distribution lies to the left of the mean, and the other half lies to the right. Since the distribution is symmetric, the area under the curve to the left of the mean is equal to the area under the curve to the right of the mean. Therefore, both areas are 0.5 or 50%.

In a standard normal distribution, the probability density function (PDF) is symmetric about the mean. This means that the area under the curve to the left of the mean is equal to the area under the curve to the right of the mean.

Since the total area under the curve represents the probability of the entire distribution, it sums up to 1. Therefore, when we divide the distribution into two equal parts, each part represents 0.5 or 50% of the total area.

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The dress was sold at a profit of 20%.

Profit percent is the percentage of profit earned on a product or investment, calculated as the profit divided by the cost price multiplied by 100%.

The profit or loss percent can be calculated using the following formula:

Profit/Loss percent = (Profit or Loss / Cost Price) x 100%

Here, the Cost Price (CP) of the dress is Rs. 2500, and the Selling Price (SP) is Rs. 3000.

Profit = SP - CP = Rs. 3000 - Rs. 2500 = Rs. 500

Therefore, the profit percent is

Profit percent = (Profit / CP) x 100%

Substitute the values in the equation

= (500 / 2500) x 100%

= 20%

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I have solved the question in general, as the given question is incomplete.

The complete question is:

A dress was bought for Rs. 2500 and sold for Rs. 3000. Find the profit or loss percent

Answer:

-4+7=3

-4+3=-1

3-4=1

7-4=3

Step-by-step explanation:

Answer:

-4 + 7.

Step-by-step explanation:

Here, we want to get the volume of the box, given its dimensions

Mathematically, the formula for this is as follows;

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

(0, -54)

Step-by-step explanation:

We find the y-intercept by plugging in 0 for x:

\(y=-2(x-3)(x-9)\\y=-2(0-3)(0-9)\\y=-2*-3*-9\\y=6*-9\\y=-54\)

Answer:

5.083

Step-by-step explanation:

\(V=\frac{1}{3}Bh=(1/3)(1/2)(1.7)(3.9)(4.6)=5.083\)

By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.

So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.

Now, solve for y when the value of x is 489.

Rounding off: y = $215

Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.

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