ƒ(x) = − x² – 14
-
Find f(6)

Answer:

the second one, ((6 x 5) x 4) +((5 x 4) x 2) = 160

the third one, ((7 x 6) x 4) + (6 x 4) x 2) = 216

the fourth one, ((8 x 4) x 4) + ((4 x 3) x 2) = 152

Step-by-step explanation:

Answer:

Step-by-step explanation:

x -  9 = 17

x = 26

the answer is D

The gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

To find the gradient of the function \(\( f(x, y) = e^{3x} \sin(4y) \)\) at the point \(\((-1, -3)\)\), we need to compute the partial derivatives with respect to \(\(x\) and \(y\)\) and evaluate them at that point.

The gradient of a function is given by:

\(\[\nabla f(x, y) = \left(\frac{{\partial f}}{{\partial x}}, \frac{{\partial f}}{{\partial y}}\right)\]\)

Let's calculate the partial derivatives:

\(\[\frac{{\partial f}}{{\partial x}} = \frac{{\partial}}{{\partial x}}\left(e^{3x} \sin(4y)\right) = 3e^{3x} \sin(4y)\]\)

\(\[\frac{{\partial f}}{{\partial y}} = \frac{{\partial}}{{\partial y}}\left(e^{3x} \sin(4y)\right) = 4e^{3x} \cos(4y)\]\)

Now, we can evaluate these derivatives at the point \(\((-1, -3)\):\)

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{3(-1)} \sin(4(-3)) = 3e^{-3} \sin(-12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{3(-1)} \cos(4(-3)) = 4e^{-3} \cos(-12)\]\)

Simplifying further:

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{-3} \sin(-12) = -3e^{-3} \sin(12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{-3} \cos(-12) = 4e^{-3} \cos(12)\]\)

Therefore, the gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

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There are three odd numbers on a standard number cube and one of them is three, so the probability of rolling a 3 or an odd number is 4/6 or 2/3.

The probability of an event happening is defined as the ratio of the number of ways the event can happen to the total number of outcomes. Suppose we roll a standard number cube, which has six faces, numbered 1 through 6. To find the probability of rolling a 3 or an odd number, we need to count the total number of ways we can roll a 3 or an odd number, and then divide that by the total number of possible outcomes. There are three odd numbers on a standard number cube: 1, 3, and 5. There is only one way to roll a 3. Therefore, the total number of ways we can roll a 3 or an odd number is: 3 (the number 3) + 3 (the odd numbers 1, 3, and 5, minus the 3 that we've already counted) = 6. So the probability of rolling a 3 or an odd number is:6 (the total number of ways we can roll a 3 or an odd number) ÷ 6 (the total number of possible outcomes) = 1/1

= 2/3.

Therefore, the probability of rolling a 3 or an odd number is 2/3.

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Answer:

5+4x=25

Step-by-step explanation:

Answer:

5+4x=25

Step-by-step explanation:

Ginny should reorder when the inventory level reaches 116.515 pounds to maintain a 95% service level

To calculate the reorder point, we need to consider two factors: the lead time (time between ordering and receiving the delivery) and the safety stock (the extra amount of flour kept in case of unexpected demand or delay in delivery).

Using the formula: Reorder point = (Average daily usage x Lead time) + Safety stock, we can calculate the reorder point.

Here, the average daily flour consumption is 35 pounds with a standard deviation of 7 pounds, and the average delivery time from the supplier is 3 days with a standard deviation of 0.5 days. She decides to order 72 pounds at a time.

The lead time is 3 days, and the safety stock can be calculated using the service level and standard deviation of demand during lead time. Assuming a 95% service level, we can use the z-score of 1.645 (from the standard normal distribution table) to calculate the safety stock.

Safety stock = (z-score x Standard deviation of demand during lead time) = (1.645 x 7) = 11.515 pounds

Now, we can calculate the reorder point:

Reorder point = (Average daily usage x Lead time) + Safety stock = (35 x 3) + 11.515 = 116.515 pounds

Therefore, Ginny should reorder when the inventory level reaches 116.515 pounds to maintain a 95% service level. This ensures that she has enough flour to cover her daily usage and also account for any unexpected demand or delivery delays.

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The episode with commercials consists of 60 minutes, and without those, it consists of 41.5minutes; therefore, 60-41.5=18.5 minutes are only commercials when the episode airs.

Divide those 18.5minutes into intervals of 0.5 minutes by calculating

Therefore, the equation is

Solving for c,

Then, the episode included 37 1/2-minute commercials.

To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:

m = (y2 - y1) / (x2 - x1)

For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:

m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))

Simplifying this expression, we get:

m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)

This simplifies to:

m = -20 / -3

Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.

Answer:

Kim's paper airplane flew farther then 4 feet 7 times.

Step-by-step explanation:

Answer:

7 times

Step-by-step explanation:

Answer:

1   1/4

Step-by-step explanation:

Just divide them, 3/4 divided by 3/5, then switch the fraction and sign.

Answer:

15/12

Step-by-step explanation:

3/4 divided by 3/5

That would become 3/4 times 5/3 because you take the reciprocal

3 x 5 = 15

4 x 3 = 12

So, 15/12 or 1.25

Answer:

The answer is

Step-by-step explanation:

To find the length of the shorter piece we must first find the total parts

That's

2 + 5 = 7

Looking at the ratio above we can see that 2 is the smaller part which makes it the shorter piece

Now divide 2 by the total parts and multiply by 120

That's

\( \frac{2}{7} \times 120 \\ = \frac{240}{7} \\ = 34.285714\)

We have the final answer as

Hope this helps you

Answer:

3x²

Step-by-step explanation:

x is to the left, and 3x is below.

x × 3x = 3x²

The number of bags of candy that could one from trick-or-treating for one hour at the same average pace is 2/3.

The rate of work always depends on the time and work provided.

Rate of work=1/Time taken

Total work done= No. of days* efficiency.

Time taken=1/rate of work

Work done= Time taken*rate of work

If a piece of work is done in x number of days, then the work done in one day is 1/x

Three friends were able to fill six bags of candy wall trick-or-treating for three hours, then

3friends⇒6 bags⇒3 hours

Now, we have to find how many bags of candy could one from trick-or-treating for one hour at the same average pace then,

1 friend⇒?⇒1 hour

then,

=6*(1/3)*(1/3)

=2/3

Therefore, the number of bags of candy that could one from trick-or-treating for one hour at the same average pace is 2/3.

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The shortest lifespan will last less than 2.5 years.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

First, we must utilize the conventional normal table to determine the value for z if 10% of the region (probability) to its left will be present. We can observe that about z = -1.282.

Now, we have to find the value of x, that corresponds to the value of z.

Since,

(x - μ) / σ = z

(x - 3.1) / 0.5 = -1.282

                 x = 2.459

Hence, the shortest lifespan will last less than 2.5 years.

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Answer:

math math math ;D

Step-by-step explanation:

afdgdfgdagf

Answer: 1

Step-by-step explanation:

16 * 1/2 = 8

7x + 1 = 8

7x = 7

x = 1

Answer:

x = 1

Step-by-step explanation:

\(\frac { 7 x + 1 } { 16 } = \frac { 1 } { 2 }\\7x+1=\frac{16}{2} \\7x+1=8 \\7x=8-1 \\7x = 7\\x = \frac{7}{7} \\\bigstar \; \boxed{x = 1}\)

Hope it helps ⚜

The error in the measurement is 3.5%.

Percentage error is a measurement of the discrepancy between an observed (measured) and a true (expected, accepted, known etc.) value. Mathematically, we can write -

\($\delta = \left| \frac{v_A - v_E}{v_E} \right| \cdot 100\%\)

Given is that James tries to cut a wooden board 20 inches long. The wooden board ends up being 20.7 inches long.

We can write the percentage error as -

p% = |20.7 - 20|/20 x 100

p% = 0.7 x 5

p% = 3.5%

Therefore, the error in the measurement is 3.5%.

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If Maria and Cindy both arrived early for work, Cindy arriving 23(1/2) minutes earlier than maria, and the total number of minutes that they were early by, was 38 minutes, then Maria arrived ahead of stipulated time by 14.5 minutes, while Cindy arrived earlier by 38 minutes, determined by solving a linear equation.

As per the question statement, Maria and Cindy both arrived early for work, Cindy arriving 23(1/2) minutes earlier than maria, and the total number of minutes that they were early by, was 38 minutes.

We are required to calculate the individual minutes by which, each of Maria and Cindy arrived earlier by.

To solve this question, let us assume that Maria arrived early by "x" minutes, and already given that Cindy arrived 23(1/2) minutes earlier than maria.

Since the total number of minutes that they were early by, was 38 minutes, we can form a linear equation, based on our assumption and the condition provided in the question statement, which goes as,

[{x + 23(1/2)} = 38]

Or, [(x + 23.5) = 38]

Or, [(x +23.5) = 38]

Or, [x = (38 - 23.5)]

Or, [x = 14.5]

That is, Maria arrived ahead of stipulated time by 14.5 minutes.

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Answer:

????

Step-by-step explanation:

We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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Answer:

1. 480
2. 30
3. 5
4. 480%

Step-by-step explanation:

1.
25% = 120
100% = 120 x 4 = 480
2.
100% = 120
25% = 120 : 4 = 25
3.
120 = 100%
6 = 6/120 x 100 = 5%
4.
25 = 100%
120 = 120/25 x 100 = 480%

The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

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Answer:

I got 387.5

Step-by-step explanation:

I divided the ounces by how many ounce there is per gram,,, but i might be wrong.

Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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a. The value of c is 1/2.

b. The cumulative distribution function of x is \(F(x) = 0 for x < -1, F(x) = (1/2) + (1/2)x - (1/2)x^3 for -1 ≤ x ≤ 1, and F(x) = 1 for x > 1.\)

c. E(X) = 0. d. Var(X) = 1/3.

a. To find the value of c, we need to use the fact that the total area under the density function must be equal to 1:

Integral from -1 to 1 of f(x) dx = 1

Using the given formula for f(x), we get:

Integral from -1 to 1 of c\((1 - x^2)^-1\) dx = 1

Taking the integral of \((1 - x^2)^-1\) with respect to x, we get:

\(-ln|1 - x^2|\) from -1 to 1

Substituting the limits and equating to 1, we get:

-ln(1 - 1) + ln(1 - (-1)) = 1

ln(2) = 1

Therefore, c = 1/ln(2).

b. The cumulative distribution function (CDF) of x is given by:

F(x) = Integral from -∞ to x of f(t) dt

For x < -1, F(x) = 0 since the density function is 0 in this region.

For -1 ≤ x < 1, we have:

F(x) = Integral from -1 to x of \(c(1 - t^2)^-1 dt\)

Using substitution u = \(1 - t^2, du/dt = -2t\), we can rewrite this as:

F(x) = Integral from 0 to \(1-x^2 of c u^-1 (du/(-2t))\)

= (-1/2) c ln|u| from \(0 to 1-x^2\)

= (-1/2) c ln\((1/(1-x^2))\)

= (1/2) ln(1/\((1-x^2))\)

For x ≥ 1, F(x) = 1 since the density function is 0 in this region.

c. To find E(X), we need to take the expected value of X:

E(X) = Integral from -∞ to ∞ of x f(x) dx

For x < -1 or x > 1, f(x) is 0, so we can ignore those regions.

For -1 ≤ x ≤ 1, we have:

E(X) = Integral from -\(1 to 1 of x c(1 - x^2)^-1 dx\)

Using substitution u = 1 - x^2, du/dx = -2x, we can rewrite this as:

E(X) = Integral from 0 to 1 of \((1 - u) c u^-1 (-du/(2x))\)

= (-c/2) Integral from 0 to 1 of\((1 - u) u^-1 du\)

= (-c/2) ln(u) from 0 to 1

= (-c/2) ln(1/1)

= 0

Therefore, E(X) = 0.

d. To find Var(X), we first need to find \(E(X^2):\)

E(X^2) = Integral from -∞ to ∞ of\(x^2 f(x) dx\)

For x < -1 or x > 1, f(x) is 0, so we can ignore those regions.

For -1 ≤ x ≤ 1, we have:

E\((X^2)\)= Integral from -\(1 to 1 of x^2 c(1 - x^2)^-1 dx\)

Using substitution u = \(1 - x^2, du/dx = -2x\), we can rewrite this as:

E\((X^2)\) = Integral from 0 to \(1 of (1 - u) c u^-1 (-du/(2x))\)

= (-c/2) Integral

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Answer:

The equation of the line that passes through points is m = 6/4

Step-by-step explanation: sorry if this is wrong

Answer:

x=2

Step-by-step explanation:

4x-6=6-2x

(add 2x and 6 to both sides)

6x=12

(divide by six)

x=2

Double Check:

4(2)-6=2

6-2(2)=2

4(2)-6=6-2(2)

Answer:

x=2

Step-by-step explanation:

4x-6=6-2x

move the variables to right and constants to the left

4x+2x=6+6

combine like terms

6x=12

isolate x by dividing by 6 on both sides to find it's value

x=2

i hope this helps :)