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3 years ago

Jennifer spent $75 on each visit to the grocery store. Write an equation to represent the amount she

Mathematics

1 answer:

nekit [7.7K]3 years ago

8 0

A 1 visit = 75 x 1 = 75 $ ; 2 visits = 75 x 2 = 150 $ ...

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How many equivalence relations are there on the set 1, 2, 3]?

Alex787 [66]

Answer:

We need to find how many number of equivalence relations are on the set {1,2,3}

A relation is an equivalence relation if it is reflexive, transitive and symmetric.

equivalence relation R on {1,2,3}

1.For reflexive, it must contain (1,1),(2,2),(3,3)

2.For transitive, it must satisfy: if (x,y)∈R then (y,x)∈R

3. For symmetric, it must satisfy: if (x,y)∈R,(y,z)∈R then (x,z)∈R

Since (1,1),(2,2),(3,3) must be there is R, (1,2),(2,1),(2,3),(3,2),(1,3),(3,1). By symmetry,

we just need to count the number of ways in which we can use the pairs (1,2),(2,3),(1,3) to construct equivalence relations.

This is because if (1,2) is in the relation then (2,1) must be there in the relation.

the relation will be an equivalence relation if we use none of these pairs (1,2),(2,3),(1,3) . There is only one such relation: {(1,1),(2,2),(3,3)}

we can have three possible equivalence relations:

{(1,1),(2,2),(3,3),(1,2),(2,1)}

{(1,1),(2,2),(3,3),(1,3),(3,1)}

{(1,1),(2,2),(3,3),(2,3),(3,2)}

6 0

4 years ago

If f(x)=ln(sin(2x)), f''(π/4) is equal to

Licemer1 [7]

Use the chain rule to compute the second derivative:

$f(x)=\ln(\sin(2x))$

The first derivative is

$f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}$

$f'(x)=2\cot(2x)$

Then the second derivative is

$f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'$

$f''(x)=-4\csc^2(2x)$

Then plug in π/4 for <em>x</em> :

$f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4$

4 0

4 years ago

CHALLENGE PROBLEM Danny's Department Store advertises savings of

Oksanka [162]

Discount are used to reduce the costs of items

The percent paid to determine the advertisement is incorrect

<h3>How to determine the correct percentage</h3>

The initial prices are given as: $44.00 to $152.00

And the discount is: 45% to 51%

At a discount of 45%, the price of the items would be:

$Price = \$44.00 * (1 - 45\%)$

$Price = \$24.2$

$Price_2 = \$152.00 * (1 - 45\%)$

$Price_2 = \$83.6$

At a discount of 51%, the price of the items would be:

$Price = \$44.00 * (1 - 51\%)$

$Price = \$21.56$

$Price_2 = \$152.00 * (1 - 51\%)$

$Price_2 = \$74.48$

The calculates prices show that the percent paid to determine the advertisement is incorrect