Determing wheter two ratios form a proportion

The length of the cable is the number of units on it.

The cable is 35.26 feet long

The function is given as:

[tex]h(x) = 15\cos(x/15)[/tex]

For all the lengths, we have the following differential equation

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (\frac{dy}{dx})^2} \, dx[/tex]

So, we have:

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (15 * \frac{1}{15} * \tanh^2(\frac{x}{15}))} \, dx[/tex]

Evaluate

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + \tanh^2(\frac{x}{15})} \, dx[/tex]

This gives

[tex]Length = \int\limits^{15}_{-15} {\sqrt{cosh^2(\frac{x}{15})} \, dx[/tex]

Evaluate the exponents

[tex]Length = \int\limits^{15}_{-15} {cosh(\frac{x}{15}) \, dx[/tex]

The above function is an even function.

So, we have:

[tex]Length = 2\int\limits^{15}_{0} {cosh(\frac{x}{15}) \, dx[/tex]

Integrate

[tex]Length = 2 * [\frac{sinh(\frac{x}{15})}{1/15}]|\limits^{15}_{0}[/tex]

Simplify

[tex]Length = 30 * [\sinh(\frac{x}{15})]|\limits^{15}_{0}[/tex]

Expand

[tex]Length = 30 * [\sinh(\frac{15}{15}) - \sinh(\frac{0}{15})][/tex]

Solve

[tex]Length = 35.26[/tex]

Hence, the length of the cable is 35.26 feet

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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

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.

Answer:

A if you look close at the story you will learn alot! hope this helps!

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

The price of the gas is $3.96.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Gas prices in Cook-County are at $3.30 per gallon.

If a market scientist predicts a 20% increase in the price of gas in the coming month,

that means,

100 + 20% = 120% increase = 1.2 in decimals.

The price of gas,

= 3.30 + 3.30 x 1.2

= 3.96

Therefore, the new price is $3.96.

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#SPJ2

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.

Try this option:

[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]

answer: B

B)    3 cm

Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]

Vcone =

1

3

πr2h

36π =

1

3

π(6)2h

36π = 12πh

h = 3

Thus, the height is 3 cm.

Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.

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.

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

The description relates to an isosceles right triangle.

An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.

In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.

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Answer:

√3

Step-by-step explanation:

got 100%