If you laid 9 bolts end to end, that measure 7/8 inch how long would the row of bolts be?

An optimization problem seeks to maximize or minimize an objective function, involving endogenous and exogenous variables and is widely used in various fields. Linear optimization uses linear equations and can often be solved with gradient-based techniques in software like MS Excel.

The goal of an optimization problem is to find the maximum or minimum value of a specific function, which is known as the objective function. This function typically represents a scenario such as profit maximization or cost minimization in different fields such as business, economics, and engineering. In an optimization model, there are typically three components: the goal (e.g., maximize profits), the endogenous variables (e.g., the amount of goods produced or the number of hours worked), and the exogenous variables (e.g., price of the goods, wage rates). Linear optimization problems, in particular, represent the objective function and constraints as linear equations and are solved using various mathematical techniques.

Most optimization techniques, such as those used in MS Excel, are gradient-based and offer a systematic approach for finding the optimal solution that either maximizes or minimizes the objective function while satisfying a set of constraints. Whether the objective is to maximize utility or minimize costs, similar approaches can be applied, and sometimes the objective function can be stated in the minimization form in any linear optimization problem by using a transformation.

In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Here, given relation between enrollment year and total number of enrollment

y = 0.051x + 0.470 ..............(i)

y = -0.041x + 1.850 ................(ii)

On comapring eq. (i) and eq. (ii), we get

0.051x + 0.470 = -0.041x + 1.850

0.051x + 0.041x = 1.850 - 0.470

0.092x = 1.380

x = 1.380 / 0.092

x = 15

put the value of x in equation (i), we get

y = 1235

Thus, In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.

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Solution:

we are given that

Zach has 53 flowers to plant.

He wants to plant them in groups of 10s and 1s.

zach can plant 10 flowers in each flower box.

Zach only wants to plant a group of ten flowers in each box.

We have been asked to find  Is there any way that zach could plant all 53 flowers using boxes only?

since zach can plant 10 flowers in each flower box. so in 5 boxes he can plant

50 flowers.

Now we have 3 left. These 3 can be planted in pot.

But he wants to use boxes only with 10 flowers in each box.

So its not possible to plant all 53 flowers using boxes only.

Answer:

2.28%

Step-by-step explanation:

Let X be the  number of books borrowed from a library each week

Given that X is normal with mean = 190 and std dev = 30

Thus Z score would be

Z=[tex]\frac{x-190}{30}[/tex]

Required probability or chance = P(X>250)

=P([tex]z>\frac{250-190}{30}[/tex]

=P(Z>2)

=0.5-0.4772

=0.0228

=2.28%

Answer:

2.5 for plato

Step-by-step explanation:

#platolivesmatter

Answer:

  2 7/27 hours, about 2 hours 15 minutes, 33 seconds

Step-by-step explanation:

You want to know how long it takes for Rich and Michelle to meet if they start 305 miles apart and are driving toward each other. Rich is driving 70 mph, and Michelle is driving 65 mph.

The speed at which they are moving toward each other is ...

  70 mph + 65 mph = 135 mph

That means they will reduce their separation distance to zero after ...

  time = distance / speed

  time = (305 mi)/(135 mi/h) = 2 7/27 h

It will take 2 7/27 hours, about 2.26 hours, for Rich and Michelle to meet.

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Answer:

Part A

"If you share 7 apples equally with 3 people, then there are  

2  1/ 3  ..."

First, complete the sentence. Then, briefly explain what the whole number 2, the denominator 3, and the numerator 1 mean in this problem.

Step-by-step explanation:

here is the full question just say answer by commenting

Answer:

(a) $1428

(b) $228

(c) 11 months

Step-by-step explanation:

(a) Total installment price = 119 × 12 = $ 1428

(b) The carrying charges = amount paid - cash price

                                   = 1428 - 1200 = $ 228

(c) No. of needed to save the money = 1200 ÷ 119 = 10.08 ≈ 11 months

Answer:    A=1428.00

                 B=228.00

                 C=11

You have the main rule: no vowel is isolated between two consonants.

The word FIXTURE consists of 4 consonants and 3 vowels.

There are such possible cases:

1. Formed word begins with three vowels and ends with 4 consonants.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

2.  Formed word begins with two vowels and ends with one vowel (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

3. Formed word begins with one vowel and ends with two vowels (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

4. Formed word begins with with 4 consonants and ends with 3 vowels.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

5. In total 144+144+144+144=576 different words.

To solve the inequality and graph its solution, solve the two separate inequalities: 2t + 1 > 9 and -18 > 5t - 3. The solution is t > 4 or t < -3.6. Graph the solution by plotting the points 4 and -3.6 on a number line, and shading the area to the right of 4 and the left of -3.6.

To solve the inequality and graph its solution, we need to solve the two separate inequalities:

1) 2t + 1 > 9

2) -18 > 5t - 3

For the first inequality, we can subtract 1 from both sides and divide by 2 to obtain t > 4.

For the second inequality, we can add 3 to both sides and divide by 5 to obtain t < -3.6.

Thus, the solution to the original inequality is t > 4 or t < -3.6.

To graph the solution, we would plot the points 4 and -3.6 on a number line, and shade the area to the right of 4 and the left of -3.6.

To solve the inequalities 2t + 1 > 9 and –18 > 5t – 3, we must solve each separately, and since it's an 'or' inequality, we combine the solution sets. The solutions are t > 4 and t < -3. Graphically, these solutions represent non-overlapping shaded regions on a number line.

To solve the inequality 2t + 1 > 9 or –18 > 5t – 3, we need to consider them separately as each inequality represents a different solution set.

For the first inequality:

For the second inequality:

We interpret these results as two separate conditions:

Since the original statement uses 'or', the solution set includes all the values that satisfy either inequality. Therefore, graphically, we would show these on a number line with a shaded region to the right of 4 and another shaded region to the left of -3. The areas do not overlap because there are no t values that can simultaneously be greater than 4 and less than -3.