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padilas [110]
3 years ago
5

Verify that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus by showing that it is a pa

rallelogram with perpendicular diagonals.

Mathematics
1 answer:
NARA [144]3 years ago
4 0
I graphed the given points and used Pythagorean theorem to get the value of each side of the rhombus.

Each side of the rhombus served as the hypotenuse of the imaginary right triangle formed in the graph. The diagonals formed are mutually bisecting and have cut each diagonal in equal parts.

Pls. see attached graph.


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Suppose X has an exponential distribution with mean equal to 23. Determine the following:
e-lub [12.9K]

Answer:

a) P(X > 10) = 0.6473

b) P(X > 20) = 0.4190

c) P(X < 30) = 0.7288

d) x = 68.87

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

In which \mu = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

Mean equal to 23.

This means that m = 23, \mu = \frac{1}{23} = 0.0435

(a) P(X >10)

P(X > 10) = e^{-0.0435*10} = 0.6473

So

P(X > 10) = 0.6473

(b) P(X >20)

P(X > 20) = e^{-0.0435*20} = 0.4190

So

P(X > 20) = 0.4190

(c) P(X <30)

P(X \leq 30) = 1 - e^{-0.0435*30} = 0.7288

So

P(X < 30) = 0.7288

(d) Find the value of x such that P(X > x) = 0.05

So

P(X > x) = e^{-\mu x}

0.05 = e^{-0.0435x}

\ln{e^{-0.0435x}} = \ln{0.05}

-0.0435x = \ln{0.05}

x = -\frac{\ln{0.05}}{0.0435}

x = 68.87

5 0
3 years ago
4. If your company purchases an annuity that will pay $50,000/year for 10 years at a 11% discount rate, what is the value of the
julsineya [31]

Answer:

The value of the annuity is $326,852.3766.

Step-by-step explanation:

Here is the required formula to find the present value of annuity:

We can find the present value of annuity:

PV = P + P (\frac{1-(1+r)^{-(n-1)} }{r})

Here:

            P = $50,000

            n = represents the number of number of periods

            r = 0.11

PV = 50,000 + 50,5000 (\frac{1-(1+0.11)^{-(10-1)} }{0.11})

PV = $326,852.3766

The value of the annuity is $326,852.3766 i.e. PV = $326,852.3766.

Keywords: discount rate,  present value of annuity

Learn more about present value of annuity from brainly.com/question/13218793

#learnwithBrainly

4 0
3 years ago
The class​ ________ is the​ breadth, or​ range, of numbers we plan to put into each class of a frequency distribution using grou
NikAS [45]

Answer:

Width

Step-by-step explanation:

When we have quantitative data it is grouped in classes. There are three ways in which the data can be grouped they are:

Single value grouping where each class has one distinct value.

In Cutpoint grouping is used when the observations have decimal points

In Limit grouping a classes are set based on a specified range of values. Here limit grouping is being done and the range of each class is called width.

4 0
3 years ago
-1/2 + ( 3/4 x 4/9)= <br><br><br><br>​
Bogdan [553]

Answer:

Too tired to explain, here's some digital steps by Symbolab:

6 0
3 years ago
If y varies inversely as x and if y = 5 when x = 4, find x when y =40​
luda_lava [24]

Answer:

x=35

Step-by-step explanation:

cross multiply

5/4 40/x

40*4/5

=160/5

x=35

6 0
3 years ago
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