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Elden [556K]
3 years ago
15

A bicycle cost $ 129.50. You pay $7.77 in sales tax. What is the tax rate?

Mathematics
1 answer:
viva [34]3 years ago
6 0
7.77/129.5 = 0.06
Therefore the tax rate is 6%
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An urn contains 2 red marbles and 3 blue marbles. 1. One person takes two marbles at random from the urn and does not replace th
Ghella [55]

Answer:

A) The best way to picture this problem is with a probability tree, with two steps.

The first branch, the person can choose red or blue, being 2 out of five (2/5) the chances of picking a red marble and 3 out of 5 of picking a blue one.

The probabilities of the second pick depends on the first pick, because it only can choose of what it is left in the urn.

If the first pick was red marble, the probabilities of picking a red marble are 1 out of 4 (what is left of red marble out of the total marble left int the urn) and 3 out of 4 for the blue marble.

If the first pick was the blue marble, there is 2/4 of chances of picking red and 2/4 of picking blue.

B) So a person can have a red marble and a blue marble in two ways:

1) Picking the red first and the blue last

2) Picking the blue first and the red last

C) P(R&B) = 3/5 = 60%

Step-by-step explanation:

C) P(R&B) = P(RB) + P(BR) = (2/5)*(3/4) + (3/5)*(2/4) = 3/10 + 3/10 = 3/5

3 0
3 years ago
Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”
Leviafan [203]

Answer:

The equation determine a relation between x and y

x = ± \sqrt{1-(y-2)^{2}}

y = ± \sqrt{1-x^{2}}+2

The domain is 1 ≤ y ≤ 3

The domain is -1 ≤ x ≤ 1

The graphs of these two function are half circle with center (0 , 2)

All of the points on the circle that have distance 1 from point (0 , 2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation x² + (y - 2)² and the relation "(x , y) R (0, 2)", where

 R is read as "has distance 1 of"

- This relation can also be read as “the point (x, y) is on the circle

 of radius 1 with center (0, 2)”

- “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”

* <em>Lets solve the problem</em>

- The equation of a circle of center (h , k) and radius r is

  (x - h)² + (y - k)² = r²

∵ The center of the circle is (0 , 2)

∴ h = 0 and k = 2

∵ The radius is 1

∴ r = 1

∴ The equation is ⇒  (x - 0)² + (y - 2)² = 1²

∴ The equation is ⇒ x² + (y - 2)² = 1

∵ A circle represents the graph of a relation

∴ The equation determine a relation between x and y

* Lets prove that x=g(y)

- To do that find x in terms of y by separate x in side and all other

  in the other side

∵ x² + (y - 2)² = 1

- Subtract (y - 2)² from both sides

∴ x² = 1 - (y - 2)²

- Take square root for both sides

∴ x = ± \sqrt{1-(y-2)^{2}}

∴ x = g(y)

* Lets prove that y=h(x)

- To do that find y in terms of x by separate y in side and all other

  in the other side

∵ x² + (y - 2)² = 1

- Subtract x² from both sides

∴ (y - 2)² = 1 - x²

- Take square root for both sides

∴ y - 2 = ± \sqrt{1-x^{2}}

- Add 2 for both sides

∴ y = ± \sqrt{1-x^{2}}+2

∴ y = h(x)

- In the function x = ± \sqrt{1-(y-2)^{2}}

∵ \sqrt{1-(y-2)^{2}} ≥ 0

∴ 1 - (y - 2)² ≥ 0

- Add (y - 2)² to both sides

∴ 1 ≥ (y - 2)²

- Take √ for both sides

∴ 1 ≥ y - 2 ≥ -1

- Add 2 for both sides

∴ 3 ≥ y ≥ 1

∴ The domain is 1 ≤ y ≤ 3

- In the function y = ± \sqrt{1-x^{2}}+2

∵ \sqrt{1-x^{2}} ≥ 0

∴ 1 - x² ≥ 0

- Add x² for both sides

∴ 1 ≥ x²

- Take √ for both sides

∴ 1 ≥ x ≥ -1

∴ The domain is -1 ≤ x ≤ 1

* The graphs of these two function are half circle with center (0 , 2)

* All of the points on the circle that have distance 1 from point (0 , 2)

8 0
3 years ago
Describe the end behavior of the following function: F(x)=2x^4+x^3
Anika [276]

Answer:

Rises to the left and rises to the right.

Step-by-step explanation:

Since, the given function is f(x)=2x^{4}+x^{3}, and the end behavior of the given function is determined as:

Consider the given function f(x)=2x^{4}+x^{3}, identify the degree of the function:

The degree of the function is : 4 which is even

And then identify the leading coefficient of the given function that is +2 which is positive in nature.

Hence, the function is positive and even in nature, therefore, the end behavior of the function will be rising to the left and rising to the right.

3 0
2 years ago
How do i find the average speed for his question: "A bicycle racer rides from a starting marker at 10m/s. She then rides back al
padilas [110]

To find the average speed for the whole race, you just have to add the speed from a starting marker and the speed from the turnaround marker going back and divide it by 2 since there are only two speeds involved.

10 m/s + 16m/s = 26 m/s / 2 = 13 m/s

Therefore, the average speed for the whole race is 13 m/s.

7 0
3 years ago
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The one that makes the most sense is C
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