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3 years ago

Which graph shows a set of ordered pairs that represent a function?Need help

Mathematics

2 answers:

Sveta_85 [38]3 years ago

8 0

Answer:

The third graph, the top right graph

Step-by-step explanation:

A function when determined graphically is a graph that passes the straight line test, which means if there is any two points on the graph which you can plot a vertical straight line going through both of them it is not a function. If 1 x value is equal to 2 y values, it is not a function.

Rus_ich [418]3 years ago

4 0

The third graph because I just take it

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How many different 10-letter permutations can be formed from 8 identical H's and two identical T's?

melamori03 [73]

Answer:

<h3>45 different permutations</h3>

Step-by-step explanation:

Given 10 letters with 8 identical H's and two identical T's, the number of different permutations will be expressed as;

$= \dfrac{10!}{8!2!}$

$= \dfrac{10*9*8!}{8!*2!}\\ \\= \dfrac{10*9}{2*1}\\ \\= \dfrac{90}{2}\\ \\= 45$

<em>Hence the number of different 10-letter permutations that can be formed from 8 identical H's and two identical T's is 45</em>

4 0

3 years ago

Find the area of the region that lies inside the first curve and outside the second curve.

marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = $\dfrac{1}{2}$

$\theta = -\dfrac{\pi}{3}, \ \ \dfrac{\pi}{3}$

Now, the area of the region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \ \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ 5^2 d \theta$

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \ \theta d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ d \theta$

$A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} \dfrac{cos \ 2 \theta +1}{2} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}$

$A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} {cos \ 2 \theta +1} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}} \ \ - \dfrac{25}{2} \begin {bmatrix} \dfrac{2 \pi}{3} \end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3}) \end {bmatrix} - \dfrac{25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} + \dfrac{\pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}$

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx

7 0

3 years ago

Jonathan worked at McDonalds 20 hours a week and earned $195. Use the equation 20h = 195 to find Jonathan's hourly wage. *

svlad2 [7]

Answer: 9.75

Explanation:

To find your answer, you need to divide 195 by 20, which is 9.75

7 0

3 years ago

Christian sold tickets to the game . Good seats were $5 each and poor seats cost $2 each. 210 people attended and paid $660. How

Sholpan [36]

People who purchased good seats will be labeled as a
people who purchased poor seats will be labeled as b
therefore...
5a + 2b = 660
a + b = 210
Now, all that has to be done is for the system to be solved.
-2(a+b=210)

5a + 2b = 660
-2a - 2a = -420

3a=240
a= 80
*3 people purchased good seats.

Now we can plug that number in

5(80) + 2b = 660
400 + 2b = 660
2b = 260
b = 130
*130 people purchased poor seats

5 0

3 years ago

Is {3,…} a defined set

Reptile [31]

Answer:

I am odd number my digits add up to 7 i am bigger than 50 and smaller 100

6 0

3 years ago

Which graph shows a set of ordered pairs that represent a function?Need help​

Which graph shows a set of ordered pairs that represent a function?Need help