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3 years ago

The measure of angle 1 is 27 degrees. Complement: Supplement:

Mathematics

1 answer:

Paladinen [302]3 years ago

3 0

Answer:

Complement: 63°

Supplement: 153°

Step-by-step explanation:

NOTE: Supplementary angles are two angles that have a sum of 180°. Complementary angles are two angles that have a sum of 90°.

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A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 10 of merlot, and 12 of cabe

e-lub [12.9K]

Answer:

Step-by-step explanation:

From the given information:

The total number of wine = 9 + 10 + 12 = 31

(1)

The number of distinct sequences used for serving any five wines can be estimated by using the permutation of the number of total wines with the number of wines served.

i.e

= $^{31}P_5$

$=\dfrac{31!}{(31-5)!}$

$=\dfrac{31!}{(26)!}$

$=\dfrac{31\times 30\times 29\times 28\times 27\times 26!}{(26)!}$

= 20389320

(2)

If the first two wines served = zinfandel and the last three is either merlot or cabernet;

Then, the no of ways we can achieve this is:

= $^9P_2\times ^{22}P_3$

$= \dfrac{9!}{(9-2)!}\times \dfrac{22!}{(22-3)!}$

$= \dfrac{9!}{(7)!}\times \dfrac{22!}{(19)!}$

$= \dfrac{9*8*7!}{(7)!}\times \dfrac{22*21*20*19!}{(19)!}$

= 665280

(3)

The probability that no zinfandel is served is computed as follows:

Total wines (with zinfandel exclusion) = 31 - 9 = 22

Now;

the required probability is:

$= \dfrac{^{22}P_5 }{^{31}P_5}$

$= \dfrac{\dfrac{22!}{(22-5)!} } {\dfrac{31!}{(31-5)!} }$

$= \dfrac{\dfrac{22!}{17!} } {\dfrac{31!}{(26)! }}$

$= \dfrac{(\dfrac{22*21*20*19*18*17!}{17!})} {(\dfrac{31*30*29*28*27*26!}{(26)! })}$

= 0.1549

≅ 0.155

4 0

3 years ago

Help me to find the answers to the question

Nataly [62]

The difference in the rate of change (RTC) would be 0.2.
The graph has a Slope of 0.4 and the table has a Slope of 0.2
Then you must subtract to find the difference
0.4 - 0.2 = 0.2

Hope this helped!

5 0

3 years ago

Read 2 more answers

The function g is a transformation of f. If g has a y-intercept at 4, which of the following functions could represent g?

guajiro [1.7K]

Answer:

g(x) = f(x) - 2

g(x) = f(x + 2)

Step-by-step explanation:

y-intercept of a function:

The y-intercept of a function is the value of y when x = 0.

Function f:

Graph given in this question

When $x = 0, y = 6$ , so the y-intercept is 6.

Additionally, when $x = -2, y = 4$

If g has a y-intercept at 4, which of the following functions could represent g?

Either we subtract 2 from f, that is:

$g(x) = f(x) - 2$

Or we can also add 2 on the domain, that is, moving 2 units to the right, so:

$g(x) = f(x+2)$

So the first two options are correct.

8 0

3 years ago

Tom's and Tim's ages add up to 21 years. In 3 years, Tom will be twice Tim’s age. How old are they now? A. Tom is 15, and Tim is

Ierofanga [76]

Answer:

A. Tom is 15, and Tim is 6.

Step-by-step explanation:

Method A: Use the choices to find the answer

Since you are given choices, you can try each choice until you see that one of the choices works.

Try choice A.

Ages now: 15 + 6 = 21 (This checks out.)

Ages in 3 years: Tom 15 + 3; Tim 6 + 3

(15 + 3)/(6 + 3) = 18/9 = 2 (This also checks out.)

The first choice works, so the answer is A.

Method B: Write an equation to solve the problem

Let Tom's age now = t.

Their ages add to 21, so Tim's age now is 21 - t.

In 3 years, Tom's age will be t + 3, and Tim's age will be 24 - t.

In 3 years, Tom's age will be twice Tim's age:

t + 3 = 2(24 - t)

t + 3 = 48 - 2t

3t = 45

t = 15

Tom's age is 15.

Tim's age is 21 - 15 = 6.

Tim's age is 6.

6 0

4 years ago

15. Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

ycow [4]

Answer:

y = -2(x -1)^2 -2

Step-by-step explanation:

My "work" consists of providing a table of values to a calculator and asking it for a quadratic model. The result is ...

y = -2(x -1)^2 -2

If you like to do these "by hand", you can write the model, then solve for its parameters using the given points.

We observe that the first and third points have the same y-coordinate. Then the vertex of the quadratic will be halfway between the corresponding x-values, at ...

h = (-2 +4)/2 = 1

So, one of the parameters of the model is found already. Using the second point and one other, we can find the remaining parameters for our model:

y = a(x -1)^2 +k

for (4, -20) ...

-20 = a(4 -1)^2 +k = 9a +k

for (0, -4) ...

-4 = a(0 -1)^2 +k = a + k

Subtracting the second equation from the first, we get

-16 = 8a

-2 = a . . . . . divide by 8

Substituting this value of a into the second equation, we have ...

-4 = -2 +k

-2 = k . . . . . . add 2

So, our model is ...

y = -2(x -1)^2 -2

3 0

3 years ago