MATHEMATICS COLLEGE

The Foot Locker is having a 60% off sale on shorts. John paid $18 for a pair of shorts. What was the original price of the shorts?

Answers

Answer 1

Answer:

Answer:

$30 is the price of the original pair of sneakers.

Step-by-step explanation:

You wanna cross multiply so you put :

18. 60

_ = _

x. 100

You multiply 18 the cost of the sneakers by 100 and then divide the product (1800) by 60 and you get $30.

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Answer 2

Answer:

Final answer:

The issue pertains to the math topic of discovering a specific percentage of a total. In this case, the $18 John paid for the shorts upon a 60% off sale represents 40% of the original price. Solving the proportion shows us that the original price of the shorts was $45.

Explanation:

The problem is related to the concept of percentages in mathematics, which involves finding a certain percentage of a total value. Here, we know that John paid $18 for the shorts, which represents 40% of the original price because the shorts are on a 60% off sale (100% - 60% = 40%).

To find the original price, we set up a proportion and solve for the original price (symbolized here as x):

40/100 = 18/x

A cross multiplication gives us: 40*x = 1800

To solve for x, we divide both sides by 40: x = 1800/40 = $45

So, the original price of the shorts was $45 before the sale.

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Jonah read 5 1/2 chapters in his book in 90 minutes how long did it take him to read one chapter

Answers

Answer:

around 16 minutes. you partition an hour and a half (all out) by what number of sections he read (5.5

Step-by-step explanation:

Liam uses checks and a debit card, but does not always write all the transactions in his checkbook register. He has lost track of his checkbook balance. Liam looks up the “available balance” using online banking, and writes it on the next line as his new checkbook balance available to spend. What is wrong with Liam’s method?a.
Liam’s method fails to consider whether he has written any outstanding checks.
b.
The reconciliation worksheet will not work properly using Liam’s adjusted checkbook balance.
c.
Liam could have unexpected non-sufficient funds fees due on any checks that have not yet cleared the bank.
d.
All of the above.

Please select the best answer from the choices provided

A
B
C
D

Answers

All of the above is wrong with Liam’s method and is therefore denoted as option D.

What is a Checkbook?

This is defined as a book containing blank checks to be drawn on a bank. The available and checkbook balance may vary especially if not all checks haven't been drawn.

The problem with Liam’s method therefore include the following:

Liam’s method fails to consider whether he has written any outstandingchecks.

The reconciliation worksheet will not work properly using Liam’s adjusted checkbook balance.

Liam could have unexpected non-sufficient funds fees due on any checks that have not yet cleared the bank.

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All of the above is the answer

2. Customers who purchase a certain model of car can order an engine in any of three sizes. Of all cars of this type sold, 45% have a small engine, 35% have a medium-sized engine, and 20% have a large engine. Of cars with the small engine, 10% fail an emission test within two years of purchase, while 12% of those with the medium size and 15% of those with the large engine fail. If a randomly chosen car of this model fails an emission test within two years, what is the probability it is a car with a small engine

Answers

Answer: 0.1397 ; 0.385

Step-by-step explanation:

Given the following :

Small engine population = 45% ; 10% fail

Medium engine population = 35% ; 12% fail

Large engine population = 20% ; 15% fail

Probability that a randomly chosen car fails emission test :

P(failure) = Σ(population % * failure %)

P(failure) = (45%*10%) + (35%*12%) + (20%*15%)

P(failure) = 0.045 + 0.042 + 0.03 = 0.117

B) what is the probability it is a car with a small engine

P = small engine cars with emission failure / total emission failure

= (0.45 × 0.1) / 0.117 = 0.045 / 0.117 = 0.3846

= 0.385

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (x2 + y2)y' = y2 1. A unique solution exists in the region y ≥ x.
2. A unique solution exists in the entire xy-plane.
3. A unique solution exists in the region y ≤ x.
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
5. A unique solution exists in the region x2 + y2 < 1.

Answers

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

The correct option is 4.

The given differential equation is:

(x² + y²)y' = y²

The equation can be rewritten as:

$x^2 + y^2 (dy)/(dx) = y^2$

We need to determine a region of the xy-plane for which the differential equation would have a unique solution whose graph passes through a point (x₀, y₀) in the region.

To determine the region, we can use the existence and uniqueness theorem for first-order differential equations.

According to the theorem, a unique solution exists in a region if the differential equation is continuous and satisfies the Lipschitz condition in that region.

To check if the differential equation satisfies the Lipschitz condition, we can take the partial derivative of the equation with respect to y:

dy/dx = y / (x² + y²)

The partial derivative is continuous and bounded in the entire xy-plane except at the origin (x=0, y=0).

Therefore, the differential equation satisfies the Lipschitz condition in the entire xy-plane except at the origin.

Since the differential equation is continuous in the entire xy-plane, a unique solution exists in any region that does not contain the origin. Therefore, the correct answer is:

A unique solution exists in the region consisting of all points in the xy-plane except the origin.

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Final answer:

The differential equation will have a unique solution in the entire xy-plane except at the origin, as both the function and its partial derivatives are continuous and well-defined everywhere except at that point.

Explanation:

To determine a region of the xy-plane where the differential equation (x2 + y2)y' = y2 has a unique solution passing through a point (x0, y0), we need to consider where the function and its derivative are continuous and well-defined. According to the existence and uniqueness theorem for differential equations, a necessary condition for a unique solution to exist is that the functions of x and y in the equation, as well as their partial derivatives with respect to y, should be continuous in the region around the point (x0, y0).

We note that both the function (x2 + y2)y' and its partial derivative with respect to y, which is 2y, are continuous and well-defined everywhere except at the origin where x = 0 and y = 0. Therefore, a unique solution exists in the region consisting of all points in the xy-plane except the origin.

From the given options, the correct answer is:

4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.

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Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = e^x^2 ln 4x^3

Answers

$(d(lnx))/(dx)=(1)/(x)$

Answer:

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

Step-by-step explanation:

We are given that a function

$y=e^(x^2)ln(4x^3)$

We have to differentiate w.r.t x

$(dy)/(dx)=e^(x^2)* 2xln(4x^3)+e^(x^2)* (1)/(4x^3)* 12x^2$

By using formula

$(d(lnx))/(dx)=(1)/(x)$

$(d(e^x))/(dx)=e^x$

$(dy)/(dx)=e^(x^2)(2xln(4x^3)+(3)/(x))$

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

Hence, the derivative of function

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

Determine the equivalent system for the given system of equations.4x − 5y = 2
3x − y = 8

4x − 5y = 2
13x − 8y = 4
4x − 5y = 2
10x + 3y = 15
4x − 5y = 2
13x − 8y = 26
4x − 5y = 2
7x + 6y = 10