What's the area of a trapezoid

To find the number of bicycles that must be manufactured to minimize the cost, we need to determine the value of x that corresponds to the minimum point of the cost function C(x).

We can find this by taking the derivative of C(x) with respect to x and setting it equal to zero. Let's differentiate C(x):

C'(x) = 6x - 1500

Now we set C'(x) = 0 and solve for x:

6x - 1500 = 0

6x = 1500

x = 250

Therefore, the number of bicycles that must be manufactured to minimize the cost is 250 bicycles.

Learn more about derivative here: brainly.com/question/32263525

#SPJ11

Answer:

5 5/6

Step-by-step explanation:

Convert to improper numbers

2 1/3 = 7/3

2 1/2 = 5/2

7/3 * 5/2 = 35/6

35/6 as a mixed fraction is 5 5/6

Answer:

5 \(\frac{5}{6}\)

Step-by-step explanation:

2 1/3 * 2 1/2 = 7/3 * 5/2 (converting into improper fraction)

= 7*5 / 3*2

= 35 / 6

= 5 \(\frac{5}{6}\)      (35/6 as mixed fraction)

In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:  

In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.

Based on the given quantities' scale, we know that x, y, and z have a relationship where:

z = x/y

Then, the mathematical combinations that might be meaningful are:

- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

Learn more about Mathematical Combinations here: brainly.com/question/23327429

#SPJ11

Answer:

Step-by-step explanation:

The eigenvector for λ1 is (x1 x2) = ((√3 - 1)x2 x2), where x2 is a free parameter.

To compute \(e^A^t\) for the given coefficient matrices, we need to diagonalize the matrices and find the eigenvalues and eigenvectors.

Once we have the eigenvalues and eigenvectors, we can compute \(e^A^t\) using the formula \(e^At = P * diag(e^λt) * P^(-1)\), where P is the matrix of eigenvectors and diag(e^λt) is a diagonal matrix with the eigenvalues exponentiated by t.

Let's start with the first system:

X' = (4 3 -4 -4)X

To find the eigenvalues and eigenvectors, we solve the equation (A - λI)X = 0, where A is the coefficient matrix, λ is the eigenvalue, I is the identity matrix, and X is the eigenvector.

For the matrix A = (4 3 -4 -4), we have:

(A - λI)X = 0

(4 3 -4 -4 - λ)(x1 x2) = 0

Expanding the determinant, we get:

(4-λ)(-4-λ) - (3)(-4) = 0

λ^2 - 4λ + 4 - 12 = 0

λ^2 - 4λ - 8 = 0

Solving this quadratic equation, we find the eigenvalues:

λ1 = 2 + 2√3 ≈ 5.464

λ2 = 2 - 2√3 ≈ 0.536

Now, for each eigenvalue, we need to find the corresponding eigenvector by solving (A - λI)X = 0.

For λ1 = 2 + 2√3, we have:

(2 3 -4 -4 - (2 + 2√3))(x1 x2) = 0

(-2 - 2√3 3 -4)(x1 x2) = 0

Solving this system of equations, we find the eigenvector:

x1 = (√3 - 1)x2

Similarly, for λ2 = 2 - 2√3, we find the eigenvector:

x1 = (-√3 - 1)x2

Now that we have the eigenvalues and eigenvectors, we can compute \(e^A^t\) using the formula mentioned earlier. However, since the specific values of A are not provided, I cannot proceed with the computation.

Learn more about Coefficient matrices

brainly.com/question/31736748

#SPJ11

If given the continuous random variables, X and Y, the mean of X + Y would be B. a + c

To obtain the mean of two variables, we have to take the sum of their means. This is slightly different from simplet numbers where we add all the numbers and divide by the totality of them all.

For random variables as indicated in the question above, given mean of X as a and the mean of Y as c, the mean of X + Y can be obtained by summing the two means. So, option B is correct.

Learn more about continuous random variables here:

https://brainly.com/question/27761372

#SPJ1

The inequality used to determine v, the minimum number of visits Taylor needs to earn her first free movie ticket is 75 + 6.5v ≥ 100.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given,

Points for signing up = 75 points

Points for each visit to the movie theater = 6.5 points

Let v be the minimum number of visits Taylor needs to earn her first free movie ticket.

Points earned for v visits = 6.5v

She needs at least 100 points for a free movie ticket.

75 + 6.5v will be the points she earn for a free movie ticket.

This expression must be greater than 100, which is the required points for a free movie.

75 + 6.5v ≥ 100

Hence the inequality representing the situation is 75 + 6.5v ≥ 100.

Learn more about Inequalities here :

https://brainly.com/question/19516092

#SPJ1

Answer:

i think it would weigh 330 pounds because in each brick it weighs 55  pounds

Step-by-step explanation:

The total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.

A complex number is the combination of real and imaginary number. It can be written as,

\(a+bi\)

Here, (a) is a real number and (b) is an imaginary number.

Melissa and Tomas are playing a game with complex numbers.  Melissa has a score of 5 – 4i and Tomas has a score of 3 2i. The sum of their score is,

\(S=5 -4i +(3+2i)\\S=5+3-4i+2i\\S=8-2i\)

Hence, the total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.

Learn more about the complex number here;

https://brainly.com/question/2218826

Answer:

8-2i

Step-by-step explanation:

c

Answer:

2.2 to correctly combine me with yours we stick

In a bag, there are 2 yellow marbles and 8 brown marbles. Nancy takes out two marbles without replacing them. The question asks for the probability that both marbles will be yellow.

To find the probability, we need to consider the total number of possible outcomes and the number of favourable outcomes. In this case, since Nancy takes out two marbles without replacement, the total number of possible outcomes is the number of ways to choose 2 marbles out of 10 (2 yellow + 8 brown). This can be calculated using the combination formula: C(10, 2) = 10! / (2! * (10-2)!) = 45. The number of favorable outcomes is the number of ways to choose 2 yellow marbles out of the 2 available, which is 1. Therefore, the probability of drawing two yellow marbles is 1/45.

To learn more about probability click here: brainly.com/question/31828911

#SPJ11

The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

To know more about parameters refer here:

https://brainly.com/question/29911057#

#SPJ11

Let x be the number of pepperoni pizzas you must order and y be the number of cheese pizzas.

Then, we have the following system:

I) x + y = 34

II) 4x + 3y = 120

First, we multiply equation I by 3:

I) 3x + 3y = 102

II) 4x + 3y = 120

Now, we subtract equation I from equation II:

(4x - 3x) + (3y - 3y) = 120 - 102

x = 18

Then, y = 34 - 18 = 16

You must order 18 persona-size pepperoni pizzas and 16 personal-size cheese pizzas.

Answer:

0, 3 , 8

Step-by-step explanation:

substitute n = 1, 2, 3 into the pattern rule

T₁ = 1² - 1 = 1 - 1 = 0

T₂ = 2² - 1 = 4 - 1 = 3

T₃ = 3² - 1 = 9 - 1 = 8

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

To know more about sequence visit:

https://brainly.com/question/21961097

#SPJ1

Answer:

Final Answer: There are 100 wizards in the magic club

Step-by-step explanation:

Since this question is asking for how many wizards are in magic club, we can represent wizards with the variable "w"

w = wizards

Next, we know that there are 120 goblins and that there are 20% more goblins than wizards in magic club.

120 = w + 20%w

120 = w + 0.2w

(percentages are just the percent/100)

120 = 1.2w

1200 = 12w

100 = w

Answer:

3^2 is not 6, it is 9 so that would have made your final answer wrong. It was supposed to be 90 not 60

The clearinghouse and research middle on servant management is now called c. The Greenleaf Center for Servant Leadership.

The middle turned into named after Robert K. Greenleaf, who first brought the idea of servant leadership in his essay "The Servant as Leader" published in 1970. The Greenleaf Center for Servant Leadership serves as a worldwide useful resource for promoting the knowledge and exercise of servant leadership.

It conducts studies, provides educational applications, and gives a platform for individuals and businesses to study and interact with servant management ideas. The middle's recognition is on nurturing moral and compassionate management that prioritizes the nicely-being and growth of individuals and the groups they serve. Through its initiatives, the Greenleaf Center pursuits to inspire and empower leaders to create a superb and impactful exchange by embracing the servant management philosophy.

To know more about servant leadership,

https://brainly.com/question/32614924

#SPJ4

The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership.

The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership. It is a nonprofit organization that was founded in 1964 by Robert K. Greenleaf. The center is dedicated to promoting the principles of servant leadership, which emphasizes serving others and putting their needs first.

The Greenleaf Center conducts research, provides resources and training, and serves as a hub for individuals and organizations interested in servant leadership.

About clearinghouse and research center here:

https://brainly.com/question/30246172

#SPJ11

Step-by-step explanation:

she painted half of the still to be painted area.

after the first weekend there were 800 of 1600 ft² painted, and therefore 1600 - 800 = 800 ft² left to be painted.

on the second weekend she then painted half of that :

800 / 2.

that means she painted 800/2 = 400 ft², and that left 800 - 400 = 400 ft² to be painted on the following weekends.

if we look in detail, we find the starting 800 ft² of the second weekend are already the result of the first weekend.

800 = 1600 / 2

so,

800 / 2 = 1600 / 2 / 2 = 1600 / 2² = 1600 / 4.

and the same principle goes on weekend after weekend.

therefore, the expression for the nth weekend could be

1600 × (1/2)^n ft²

that means, she painted

on the 1st weekend : 1600 × 1/2 = 800 ft²

on the 2nd weekend : 1600 × 1/4 = 400 ft²

on the 3rd weekend : 1600 × 1/8 = 200 ft²

on the 4th weekend : 1600 × 1/16 = 100 ft²

...

that also means : she will never be finished, as she always paints only half of what is still left open, and that leaves always some part open. it will be tinier and tinier over time, but never 0.

Answer:

i think is C

I'm not sure about it

Answer:

It should take about 4.75 min.

Step-by-step explanation:

Hope this helps and could you mark me as the brainliest

The probability of grabbing one blue pen from the given box of 12 pens.

As given in the question,

Total number of given red pens in a box = 4

Total number of given blue pens in a box = 3

Total number of given black pens in a box = 5

Total number of pens in a given box = 4+ 3+ 5

                                                            = 12

Total number of grabbing one pen from the box = ¹²C₁

Total number of grabbing one blue pen out all the pens in the box

= ⁴C₀ × ³C₁ × ⁵C₀

Probability of selecting one blue pen from the box

= (Total number of favourable outcomes )/ ( total number of outcomes)

= (  ⁴C₀ × ³C₁ × ⁵C₀ ) / ( ¹²C₁ )

= ( 1 × 3 × 1 ) / 12

= 3/12

= 1 / 4

Therefore, the probability of grabbing one blue pen from the box of 4 red, 3blue and 5 black pens is equal to ( 1/4 ).

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer:

10.2°

Step-by-step explanation:

I'm not sure if my answer is correct and I'm not too good at explaining but I'll try.

The height of the triangle would be 199 ft and it's length would be 1104 ft. Since were looking for the angle of depression, the angle would obviously be outside of our triangle (as shown in the picture). The height and length wouldn't change at all so we can just label the imaginary lines with their corresponding measurements.

The angle that we're looking for is marked in the picture. Since we are given the opposite and the adjacent side, we can use the inverse of tan to figure out our angle, which is 10.2°.

You can also use the "Z" rule and our angle would be where it's shown in the third picture. Nothing would change because our opposite side would still be 199 ft and our adjacent side would still be 1104 ft.

The given statement is FALSE. The determinant of the sum of two matrices does not equal the sum of the determinants of the matrices.

In fact, the determinant of the sum of two matrices is generally not even equal to the sum of the determinants of the matrices.
This property does not hold true for determinants. In general, the determinant of the sum of two matrices A and B

(det(A+B)) is not equal to the sum of their individual determinants (det(A) + det(B)).

learn more about determinants:https://brainly.com/question/16981628

#SPJ11

Answer:

49 ft

Step-by-step explanation:

h=−16(t−14)^2+49

The path of the marshmallow is an inverted parabola. It has symmetry with respect to its vertical axis.

We take the derivative of the height function.

dh/dt = -32(t - 14)

dh/dt = -32t + 448

We set the derivative equal to zero ti find the value of t corresponding to a maximum value of h.

-32t + 448 = 0

-32t = -448

t = 14

Maximum height occurs at t = 14 seconds.

h=−16(t−14)^2+49

t = 14

h=−16(14−14)^2+49

h = 49

Maximum height is 49 feet.

Answer:

$47

Step-by-step explanation:

To solve this problem, we need to use the Laplace transform and the recursive relation (7) as follows:

(a) We know that T(1/2) = r2. Using the recursive relation (7), we can express T(s) in terms of T(s-1/2) as:

T(s) = sT(s-1/2)

Substituting s = 1 in the above equation, we get:
T(1) = 1 * T(1/2)
T(1) = T(1/2) = r2

Now, taking the Laplace transform of both sides of the recursive relation (7), we get:
L{tT(s)} = L{xT(s-1/2)}

Using the property of Laplace transform that L{t^n} = n!/s^(n+1), we can rewrite the left-hand side as:
L{tT(s)} = -d/ds L{T(s)}

Similarly, using the property of Laplace transform that L{x^n} = n!/s^(n+1), we can rewrite the right-hand side as:
L{xT(s-1/2)} = -d/ds L{T(s-1/2)}

Substituting these expressions in the Laplace transform equation, we get:
-d/ds L{T(s)} = -d/ds L{T(s-1/2)}

Simplifying the above equation, we get:
L{T(s)} = L{T(s-1/2)}

Now, using the initial condition T(1/2) = r2, we can rewrite the above equation as:
L{T(s)} = L{T(s-1/2)} = r2/s

Taking the Laplace transform of t-1/2, we get:
L{t-1/2} = 1/s^(3/2)

Multiplying this expression by L{T(s)} = r2/s, we get:
L{t-1/2} L{T(s)} = r2/s^(5/2)

The answer to part (a) is L{t-1/2} = r2/s^(5/2).

(b) To determine L{x7/2}, we can use the fact that L{x^n} = n!/s^(n+1). Thus, we have:
L{x7/2} = (7/2)!/s^(7/2+1)

Simplifying the above expression, we get:
L{x7/2} = 7!/2^7 s^(1/2)

Now, multiplying this expression by L{T(s)} = r2/s, we get:
L{x7/2} L{T(s)} = 7!/2^7 r2 s^(-3/2)

The answer to part (b) is L{x7/2} = 7!/2^7 r2 s^(-3/2).

To learn more about Laplace transform visit:

brainly.com/question/31041670

#SPJ11

Answer:

x = about 2.7

Step-by-step explanation:

We can use proportions to find x.

For side 1, we have 6:2 = 3.

For side 2, we have 8:x=3 ... 8:3 = x ... x=2.6....7

x = about 2.7