On a loan of $4,500 for 2 1/2 years at 4% per year, how much do you wind up paying to pay off the loan?

Consider a uniform distribution created by a random number generator. The distribution looks like a square with a length of 1 an

vekshin1

The rigorous way to do this would be to compute a few integrals, but less work is usually better. Each of these probabilities correspond to the areas of rectangles. Each rectangle will have a height of 1, and the probability of interest will tell you everything you need to know about their lengths.

$\mathbb P(0\le X\le0.4)\implies \text{length}=0.4\implies\mathbb P(0\le X\le0.4)=0.4\times1=0.4$

$\mathbb P(0.4\le X\le1)\implies \text{length}=0.6\implies\mathbb P(0\le X\le0.4)=0.6$

Alternatively, you can use the fact that $\mathbb P(0.4\le X\le 1)=1-\mathbb P(0\le X\le 0.4)$ to get the same result.

$\mathbb P(X>0.6)=\mathbb P(0.60.6)=0.4$

$\mathbb P(X\le0.6)\implies \text{length}=0.6\implies\mathbb P(X\le0.6)=0.6$

$\mathbb P(0.23\le X\le0.76)\implies \text{length}=0.76-0.23=0.53\implies\mathbb P(0.23\le X\le0.76)=0.53$

3 0

3 years ago

What is the domain and range of the graph below in interval notation? If union is needed, use Capital U. If infinity is needed u

elena55 [62]

Answer:

DOMAIN: $(-\infty,1]\cup(2,\infty)$

RANGE: $(-\infty,\infty)$

Step-by-step explanation:

The domain of a graph is the span of x-values covered by the graph, while the range of a graph is the span of y-values covered by the graph.

DOMAIN:

From the graph, we can see that the x-values covers everything to the left of x=1. Then we stop and then continue beginning at x=2 all the way until positive infinity.

However, note that at x=1, the dot is a closed circle while at x=2, the dot is an open circle. Thus, we will include x=1 into our domain but not include x=2 into our domain.

So, our domain is all values greater than or less than 1, and all values greater than 2.

In interval notation, this is:

$(-\infty,1]\cup(2,\infty)$

We use brackets with the 1 because we include it in our domain and we use parentheses with the 2 since we do not.

RANGE:

Looking at the graph, it seems that all y-values are covered. The part of the graph on the left covers all y-values less than or equal to 3, while the part of the graph on the right covers all y-values greater than -1. Thus, all y-values are covered.

Our range is all real numbers.

In interval notation, this is:

$(-\infty,\infty)$

5 0

3 years ago

The radius of a well is 1.4m and its depth 35 m is half-filled with water. find the volume of water inside the drum.

Rzqust [24]

Answer:

≈ 108 m³

Step-by-step explanation:

You're searching for the volume of a cylinder. The formula needed to find it is V=πr²h.

In this case, the radius r is 1.4m and the height h is 35/2=17.5m, as it is only half filled.

Now when inserting values, you get: V=π*1.4²*17.5 which is 107.757 m³

8 0

3 years ago

Read 2 more answers

Thirty subtracted from four times a number is greater than the opposite of 10

Arada [10]

30-4x>-10

Hope I helped

5 0

4 years ago

-3x+18=7x what could you do to isolate the variable term to one side of the equation

Alexxandr [17]

Answer:

7x=−x+24 7 x = − x + 24

Step-by-step explanation:

The equations we solved in the last section simplified nicely so that we could use the. Our strategy will involve choosing one side of the equation to be the variable side, and step by step, to isolate the variable terms on one side of the equation

7 0

3 years ago

Read 2 more answers