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3 years ago

Can anyone help me with my homework

Mathematics

1 answer:

Ivahew [28]3 years ago

3 0

Answer:

1) NO

2) YES

3) YES

4) YES

Step-by-step explanation:

A function is a relation that maps elements from a set (the domain, the set of the inputs) into elements from another set (the range, the set of the outputs).

The condition for a function is that each element in the domain can be mapped into only one element in the range.

(Or each input can be mapped into only one output).

Now let's apply this theory to the exercises here.

In all the cases we have relations, so we need to check if one (or more) of the inputs is mapped into more than one output.

Also remember that in the point notation (x, y) the first value is the input and the second is the output.

Here we can see the points (-1, 5) and (-1, 2)

So the input -1 is mapped into two different outputs, 5 and 2.

This means that this is not a function.

In this case, we can see that all the inputs are different (1, -2, 3, 5), so this is a function.

Again, here we can see that each input is being mapped into only one output, then this is a function.

In a graph, the horizontal position represents the input value and the vertical position represents the output value.

One way to tell if a graph belongs to a function or not, is to see if there is a vertical line such that more than one point intersects that line. If that happens, then we have two points with the same input value but different output value and the relation is not a function.

In this case, we can see that this does not happen, and then we can conclude that the graph represents a function.

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Lucas bought a used car for x dollars. one year later the value of the car was 0.80 x. which expression is another way to descri

Mariana [72]

Knowing that a year later, the car is only worth 0.80 x, you can simplify that by stating that one year after purchase, the car is only worth 80% of its original purchase price.
Another way of stating that is that the car lost 20% of its value of the course of one year.

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3 years ago

A town has accumulated 4 inches of snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated

zimovet [89]

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Answer:

2 hours

Step-by-step explanation:

The initial difference in depth is 10-4 = 6 inches. The difference in snowfall rates is 6-3 = 3 inches per hour.

At that rate, the difference in depth will be made up in ...

(6 in)/(3 in/h) = 2 h

In 2 hours the snowfall in the two towns will be equal.

_____

You could write equations for depth, then equate them.

d1 = 4 +6h

d2 = 10 +3h

d1 = d2 . . . . . . . . . . for some value of h the depths will be equal

4 +6h = 10 +3h

h(6 -3) = 10 -4 . . . . . subtract 3h+4 from both sides

h = 6/3 = 2

Snowfall will be equal in 2 hours.

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3 years ago

Camila sets up a passcode on her tablet, which allows only nine-digit codes. A spy sneaks a look at Camila's tablet and sees her

laila [671]

Answer:

$\frac{1}{10^9}$ probability the spy is able to unlock the tablet on his first try.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

1 correct password, so $D = 1$

Total outcomes:

Nine-digit codes.

For each digit, there are 10 possible outcomes. So

$T = 10^9$

What is the probability the spy is able to unlock the tablet on his first try?

$p = \frac{D}{T} = \frac{1}{10^9}$

$\frac{1}{10^9}$ probability the spy is able to unlock the tablet on his first try.

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3 years ago

Jayden bought a new computer with 2.56 x 10" bytes of hard drive space. He also signed up for a

Mice21 [21]

Answer:

2.56x10=25.6

Step-by-step explanation:

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3 years ago

What are the limits of integration if the summation the limit as n goes to infinity of the summation from k equals 1 to n of the

Fofino [41]

Answer:

$\int_{2}^{9}x^2 dx$ so the limits are 2 and 9

Step-by-step explanation:

We want to express $\lim_{n\rightarrow \infty} \sum_{k=1}^n\frac{7}{n}(2+\frac{7k}{n})^2$ as a integral. To do this, we have to identify $\sum_{k=1}^n\frac{7}{n}(2+\frac{7k}{n})^2$ as a Riemann Sum that approximates the integral. (taking the limit makes the approximation equal to the value of the integral)

In general, to find a Riemann sum that approximates the integral of a function f over an interval [a,b] we can the interval in n subintervals of equal length and approximate the area (integral) with rectangles in each subinterval and them sum the areas. This is equal to

$\sum_{k=1}^n f(y_k) \frac{b-a}{n}$ , where $y_k\in[a+(k-1)\frac{b-a}{n},a+k\frac{b-a}{n}]$ is a selected point of the subinterval.

In particular, if we select the ending point of each subinterval as the $y_k$ , the Riemann sum is:

$\sum_{k=1}^n f(a+k\frac{b-a}{n}) \frac{b-a}{n}$ .

Now, let's identify this in $\sum_{k=1}^n\frac{1}{7n}(2+\frac{7k}{n})^2$ .

The integrand is x² so this is our function f. When k=n, the summand should be $\frac{b-a}{n}f(b)=\frac{b-a}{n}b^2$ because the last selected point is b. The last summand is $\frac{7}{n}(9)^2$ thus b=9 and b-a=7, then 9-a=7 which implies that a=2.

To verify our answer, note that if we substitute a=2, b=9 and f(x)=x² in the general Riemann Sum, we obtain the sum inside the limit as required.

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3 years ago