Guys can you please help me with The Question #15 A). and B). of The Factoring for me, please? :)

The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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A complete graph is one in which there is an edge connecting every vertex to every other vertex. In order to determine for what values of n a complete graph with n vertices has an Euler circuit and a Hamiltonian circuit, let's discuss the definitions and requirements of each type of circuit.

1. Euler Circuit: An Euler circuit is a path that traverses each edge of a graph exactly once and returns to its starting vertex. For a graph to have an Euler circuit, all vertices must have an even degree (number of edges connected to the vertex).

2. Hamiltonian Circuit: A Hamiltonian circuit is a path that visits every vertex in a graph exactly once and returns to its starting vertex. A complete graph always has a Hamiltonian circuit, regardless of the number of vertices.

Now, let's determine for what values of n a complete graph has an Euler circuit:

In a complete graph with n vertices, each vertex is connected to every other vertex, which means the degree of each vertex is (n-1). For a complete graph to have an Euler circuit, all vertices must have an even degree. This implies that (n-1) must be even, so n must be odd.

So, for a complete graph with n vertices to have an Euler circuit, n must be an odd number.

In summary:
- A complete graph with n vertices always has a Hamiltonian circuit.
- A complete graph with n vertices has an Euler circuit if n is an odd number.

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The constant of proportionality from the proportional relationship is 3/2

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.

To determine the constant of proportionality, we need to use the proportional relationship given.

y = kx

k = constant of proportionality

3/8 = k(1/4)

Solve for k

k = [(3/8) / (1/4)]

k = 3/2

k = 1.5

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Answer:

y = 17(7) + 6

Step-by-step explanation:

Given that:

Amount owed = $125

Payment per week = $7

Number of whole weeks to pay :

$125 / $7 = 17.85 = 17 whole weeks

$125 - (17 * 7) = $125 - $119 = $6

Using slope intercept notation :

y = mx + c

Where m = slope ; c = intercept. ;

m = 17,; x = $7, c = $6

y = 17(7) + 6

The best way to remedy Ask customers throughout the day on both weekdays and weekends.

The cause of the bias in the survey is likely sampling bias. This means that the sample of 110 customers may not be representative of the entire population of food court shoppers. The bias can arise if the sample is not selected randomly or if certain groups of shoppers are overrepresented or underrepresented in the sample.

To remedy the sampling bias, the best way would be to  Ask customers throughout the day on both weekdays and weekends.

By surveying customers at different times, including both weekdays and weekends, a more diverse and representative sample can be obtained. This will help to capture the preferences of a wider range of food court shoppers and reduce the bias introduced by sampling only weekday mornings.

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The manager of a shopping mall wishes to expand the number of shops available in the food court. He has a market researcher survey the first 110 customers who come into the food court during weekday mamings in distin what types of food the shoppers would like to see added to the food court,

Which of the following is the best way to remedy this problem?

OA cisne the sample size so that more people respond to the question OB Ask customers throughout the day on both weekdays and hands

OC Reward the question so that it is balanced

Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.

A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test  we can find the mean difference between pairs of measurements is zero or not. So  paired t-test is used, when data is in the form of matched pairs

Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

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The best response for a person handling biohazards with an open wound on their hands is to not  work with biohazards until the cut is healed or cleared by a healthcare professional to work with the use of waterproof bandages and double gloves.

Biohazards are extremely dangerous because they can get into the human body and cause a lot of damage.

This is why a person with an open would or existing cut should not handle a biohazard until they are cleared to to so by a trained healthcare professional.

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Answer:

Coefficients= 4, 3

No constants

Only variables x and y

Step-by-step explanation:

Constants could also be found after solving for the variables

Answer:

5

Step-by-step explanation:

The degree of a polynomial simply means what the highest power of an variable is. In this case we see that y⁵ < y³ < y², so 5 would be our highest exponent and answer.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{5}}}}}\)

Step-by-step explanation:

In the polynomial with one variable , highest power ( exponent ) is the degree of the polynomial.

In polynomial \( \sf{4 {y}^{3} + 3 {y}^{2} - {y}^{5} }\)

The power of 4y in the first term = 3

The power of 3y in the second term = 2

The power of y in the third term = 5

Since, the highest power is 5 , the degree of the polynomial is 5 .

Hope I helped!

Best regards!!

Answer:  3x+2y=16 x+5y=14

Step-by-step explanation:

Step-by-step explanation:

1. From equation2, x =14-5y

Put into equation1, 3(14-5y) +2y

Now, 42-15y + 2y =16

-13y = 16-42

-13y = -26

y = 2

Now substitute into equation2

x + 5(2) = 14

x = 14 - 10

x =4

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = \(2 \times width\)

Base area = lb

= \(2x^2\)

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

\(h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}\)

Now, cost is

\(= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}\)

now we have to minimize C(x)

So, we need to compute the C'(x)

\(= 52x - \frac{648}{x^2}\)

C"(x)  \(= 52x - \frac{1,296}{x^3}\)

now for the critical points, we will solve the equation C'(x) = 0

\(= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}\)

\(C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0\)

So, x is a point of minima that is

= \((\frac{648}{52} )^\frac{1}{3}\)

Now, Base material cost is

\(= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}\)

= 139.75

Side material cost is

\(= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3} }\)

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

The cost of the side material is $279.50, the cost of the base material is $139.75 and the total cost is $419.25 and this can be determined by using the arithmetic operations.

Given :

Let the width of the rectangular storage container be 'x' then according to the given data the length is '2x' and let the height of the container be 'h'.

The base area of the rectangular storage container is given by:

Base Area = \(2x^2\)   ----- (1)

The side area of the rectangular storage container is given by:

Side Area = 2(2x)h + 2xh

                 = 6xh    ---- (2)

Now, the volume of the rectangular storage container is given by:

Volume = lbh

Put the values of known terms in the above equation.

24 = \(2x^2h\)

\(h = \dfrac{12}{x^2}\)

Now, the cost is given by:

\(\rm C(x)=13(2x^2)+9(6xh)\)

\(\rm C(x)= 26x^2 + \dfrac{648}{x}\)

Now, to minimize C(x) differentiate the C(x) with respect to x.

\(\rm C'(x)=52x -\dfrac{648}{x^2}\)   ---- (3)

Now, equate the above equation to zero.

\(0 = 52x =\dfrac{648}{x^2}\)

\(x = \sqrt[3]{\dfrac{648}{52}}\)

Now, differentiate equation (3) with respect to x.

\(\rm C"(x) = 52+\dfrac{1296}{x^3}\)

Now, put the value of x in the above equation.

\(\rm C"(x) = 52+\dfrac{1296}{\dfrac{648}{52}}\)

\(\rm C"(x) = 52+104\)

\(\rm C"(x) = 156 > 0\)

Therefore, 'x' is the point of minima.

Now, the cost of the base material is:

\(= 13\times 2 \times (\dfrac{648}{52})^\frac{2}{3}\)

= $139.75

Now, the cost of the side material is:

\(=\dfrac{648}{\sqrt[3]{\dfrac{648}{52}} }\)

= $279.50

Therefore, the total cost is given by:

= 139.75 + 279.50

= $419.25

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Answer:

k=5

Step-by-step explanation:

for every one unit on the x, the y goes up five. So, the ratio is 5:1 or five.

Answer:

0+10

Step-by-step explanation:

yes

Answer:

156

Step-by-step explanation:

Answer:

the answer is c.

Step-by-step explanation:

Answer:

1.57 cubic centimeters

Step-by-step explanation:

V= πr²h

π = 3.14

r = 0.5

h = 2

V = 3.14(0.5)²(2)

V = 3.14(0.25)(2)

V = (0.785)(2)

V = 1.57 cubic cm

volume of the pyramid is approximately 52.3 cubic inches.

What is volume of a pyramid ?

The formula for the volume of a pyramid is given by:

V = (1/3) * B * h. Where B is the area of the base and h is the height of the pyramid.

we know that each side of the square base has a length of:

\(\sqrt{(14.1)} = 3.75\ in\)

The volume of the pyramid can now be calculated as:

\(V = (1/3) * (3.75 \ in)^2 * 11.1 \ in\)

≈ 52.3 in^3

Therefore, the volume of the pyramid is approximately 52.3 cubic inches.

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The correct answer is D. $2.75 / $3.24

To determine how much you should expect to pay for gas in Philadelphia versus Cleveland, we need to compare the transportation expenses in both cities. Based on the given data, the transportation expenses are as follows:

Philadelphia: $117

Cleveland: $106

To calculate the expected gas prices, we need to consider the transportation expenses relative to the national average. The formula to find the expected gas price is:

Expected Gas Price = National Average * (Transportation Expense / National Average)

National Average for gas = $2.59

For Philadelphia:

Expected Gas Price in Philadelphia = $2.59 * ($117 / 92) ≈ $3.30

For Cleveland:

Expected Gas Price in Cleveland = $2.59 * ($106 / 78) ≈ $3.51

Comparing the expected gas prices, we find that:

A. $3.03 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

B. $1.95 / $2.59: This option does not match the expected gas prices in Philadelphia and Cleveland.

C. $2.34 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

D. $2.75 / $3.24: This option matches the expected gas prices in Philadelphia and Cleveland.

Therefore, the correct answer is:

D. $2.75 / $3.24

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The number of favorable outcomes for events A and B would be: (1,2,3,4)

The sample space that is used to determine the probability of A given B is  (2, 4.6)

The probability for event A and B occurring would be: 1/6

The probability of event A given event B will be 2/3

The sample space refers to the collection of all the outcomes that can be expected from a set of randome experiments. Probability refers to the number of favorable outcomes divided by the number of tottal outcocmes.

From the data given, the probability of getting an even number and a number less than 5 will be 5/6 amd this is in the same ratio as 2/3. The probability of event A and B occurring will be 1/6.

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Given information: Two points A (0, 0) and B(0, L) on the by-plane for some positive distance L. Electric field E (2L, 4L) has to be found for the following conditions: (a) Point charges +Q and −Q are put at A and B, respectively.

Coulomb's law is given as'

= \(1/4πε₀ Q₁Q₂/r²\)

where ε₀ is the permittivity of free space.

Electric field E

= F/Q₁ = 1/4πε₀ Q₂/r²

On substituting values in the above expression for part (a), we get,Let +Q = 2Q (as −Q = Q)

The distance between A and P is

\(r1 = √((2L)²+(4L)²) = 2L√5\)

The distance between B and P is

\(r2 = √(2L)²+(4L - L)² = 3L√2\)

The electric field due to −Q at P is

\(:E2 = 1/4πε₀ (-Q)/(3L√2)² = -Q/18πε₀L²\)

The electric field E

\(= E1 + E2 = Q/20πε₀L² - Q/18πε₀L² = -Q/180πε₀L²\)

For part (b), we use Gauss's law to calculate the electric field for an infinite line charge. Gauss's law is given by:

\(∮E.ds = Q/ε₀\)

The electric field Eat distance r from the line charge of density ρ is given Bye

= ρ/2πε₀rLet +ρ L = 2ρ L (as −ρ L = ρ L)

Charge Q₁ = length of line charge at A = Charge Q₂ = length of line charge at B = L

The distance between A and P is r1 = 2LThe distance between B and P is r2 = L

The electric field due to +ρ L at P is:

\(E1 = (2ρ L)/(2πε₀2L) = ρ L/πε₀\)

The electric field due to −ρ L at P is:

\(E2 = (-ρ L)/(2πε₀L) = -ρ L/2πε₀\)

The electric field

\(E = E1 + E2 = ρ L/πε₀ - ρ L/2πε₀ = ρ L/2πε₀\)

The required electric field at

\(E(2L, 4L) is -Q/180πε₀L²\)

for part (a) and ρ L/2πε₀ for part (b).

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Answer: B

Step-by-step explanation: The function C(x) = s(j(x)) shows you how to solve it.

First in the parenthesis j(x) so you have to substitute since they told you

j(x) = x-5

Next s(x-5) and s(x-5) = 0.75(x-5) through substitution  

Answer: -3/x^2

Step-by-step explanation:

Hope this helps

Answer:

-3/x^2

Step-by-step explanation:

To determine which point maximizes the objective function, we need to evaluate the objective function at each of the given points and then compare the results. The point that produces the highest value for z will be the solution.

a. (1, 1)

z = 3(1) + 5(1) = 8

b. (2, 7)

z = 3(2) + 5(7) = 41

c. (5, 10)

z = 3(5) + 5(10) = 55

d. (6, 3)

z = 3(6) + 5(3) = 33

Therefore, the point that maximizes the objective function is (5, 10) with a value of z = 55.

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Answer:

a

Step-by-step explanation:

Answer: 12/36 and simplified would be 1/3

Step-by-step explanation:

12 - hard boiled eggs

——

36 - scrambled

Divide them by 12 and you get a simplified fraction

Answer:

58 weeks

Step-by-step explanation:

Water tank A = 522 - 4x

Water tank B = 696 - 7x

Where,

x = number of weeks

Equate both equations

522 - 4x = 696 - 7x

Collect like terms

522 - 696 = -7x + 4x

-174 = -3x

Divide both sides by - 3

x = -174/-3

x = 58 weeks

The amount of water in the two tanks will be the same in 58

weeks

Answer:

I put the equation into desmos online graphing calculator

Answer:

Step-by-step explanation:

(0,3/4)  (1,3/4)

Answer:

Step-by-step explanation:

30*20%= 6 so $6.00 tip

Total with tip is $36.00

Answer:

36

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Answer:

let

diagonal 1=6cm

diagonal 2=10cm

Area of rhombus=½*diagonal 1*diagonal 2=½*6*10

=30cm²

Answer:

Area of rhombus is 30cm².

Step-by-step explanation:

A rhombus having diagonals 6cm and 10cm . Find the area of rhombus.

Solution :-

Let us assume that

Finding the area of rhombus

Using Formula :-

Area of rhombus = ½ × \(diagonal_1\)×\(diagonal_2\)

Substitute the values of both diagonals.

Area of rhombus = ½ × 6cm × 10cm

Multiply the numbers

Area of rhombus = ½ × 60cm²

Divide we get ,

Area of rhombus = 30 cm