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2 years ago

A parallelogram with sides of 6 and 10 has an area of 30. Find the measure of the small angle of the parallelogram.

1 answer:

4 0

A = 2 * (0.5ab) + b (10 - a) = ab + 10b - ab = 10b

10b = 30√2; b = 3√2

sin α = 3√2 / 6; α = 45 degrees

Small angle: 45°; Large angle: 135°

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The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in t

ziro4ka [17]

The total tickets to be purchased to guarantee the win = 504 tickets

Step-by-step explanation:

Step 1 :

Number of entries in the trifecta race = 9

The win is to select the first finisher, second finisher and third finisher in their proper order.

We need to find the number of tickets to be purchased to guarantee the win

Step 2 :

Number of ways to select the first finisher = 9

Number of ways to select the second finisher = 8 [the first is selected and fixed. So the number of available finishes is reduced by 1]

Number of ways to select the third finisher = 7

Hence the total tickets to be purchased to guarantee the win = 9 × 8 × 7 = 504

Step 3 :

Answer :

The total tickets to be purchased to guarantee the win = 504 tickets

3 0

2 years ago

At a local baseball game there are 3 hot dog vendors. collectively the vendors sold 1,700 hot dogs. if vendor a sold 456, vendor

Vera_Pavlovna [14]

The answer is C.

Vendor A= 456/1700, which is .268 or 27%
Vendor B= 607/1700, which is .357 or 36%
Vendor C= 637/1700, which is .374 or 37%

For a total of 100%

8 0

2 years ago

Read 2 more answers

Agent Hunt transferred classified files from the CIA mainframe onto his flash drive. The drive had some files on it before the t

topjm [15]

Answer: The drive was 24.32% full when the transfer began.

Step-by-step explanation:

Given: The rate of transferring file = 4.44 megabytes per second.

After 32 seconds, the amount of data on the drive = 384 megabytes

The amount of transferred data = $32\times4.4=140.8$ megabytes

Therefore, the amount of data in the drive at the beginning is given by :-

$\text{Beginning amount=Amount after 32 seconds -Amount transferred}\\\\\Rightarrrow\ \text{Beginning amount=}384-140.8=243.2$

The drive had a maximum capacity of 1000 megabytes.

$\frac{243.2}{1000}\times100=24.32\%$

Hence, the drive was 24.32% full when the transfer began.

4 0

1 year ago

Read 2 more answers

Mrs.Steﬀen’s third grade class has 30 students in it. The students are divided into three groups(numbered 1, 2,and 3),each havin

qaws [65]

Answer:

a. $\\ 10! = 3628800$ ;

b. $\\ 10!*10!*10! = 47784725839872000000 = 4.7784725839872*10^{19}$

Step-by-step explanation:

We need here to apply the Multiplication Principle or the Fundamental Principle of Counting for each answer. Answer b needs an extra reasoning for being completed.

The Multiplication Principle states that if there are n ways of doing something and m ways of doing another thing, then there are n x m ways of doing both (Rule of product (2020), in Wikipedia).

<h3>In how many ways can ten students line up? </h3>

There are ten students. When one is selected, there is no other way to select it again. So, no repetition is allowed.

Then, in the beginning, there are 10 possibilities for 10 students; when one is selected, there are nine possibilities left. When another is selected, eight possibilities are left to form the file, and so on.

Thus, we need to multiply the possibilities after each selection: that is why the Multiplication Principle is important here.

This could be expressed mathematically using n!:

$\\ n! = n * (n-1)! * (n-2)! *...* 2*1.$

For instance, $\\ 5! = 5 * (5-1)! * (5-2)! *...*2*1 = 5 * 4 * 3 * 2 * 1 = 120.$

So, for the case in question, the ten students can line up in:

$\\ 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800$ ways to line up in a single file.

<h3>Second Question</h3>

For this question, we need to consider the former reasoning with extra consideration in mind.

The members of Group 1 can occupy only the following places in forming the file:

$\\ G1 = \{ 1, 4, 7, 10, 13, 16, 19, 22, 25, 28\}^{th}$ places.

The members of Group 2 only:

$\\ G2 = \{ 2, 5, 8, 11, 14, 17, 20, 23, 26, 29\}^{th}$ places.

And the members of Group 3, the following only ones:

$\\ G3 = \{ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30\}^{th}$ places.

Well, having into account these possible places for each member of G1, G2 and G3, there are: 10! ways for lining up members of G1; 10! ways for lining up members of G2 and, also, 10! ways for lining up members of G3.

After using the Multiplication Principle, we have, thus:

$\\ 10! * 10! * 10! = 47784725839872000000 = 4.7784725839872 *10^{19}$ ways the students can line up to come in from recess.

3 0

1 year ago

How do I determine the 50th term for the sequence -5, -1, 3, 7, 11

Aneli [31]

The sequence is going up by 4 so u have to multiply each term by four and the -5 is it’s 0th term as well it’s beginning so you have to input that in the equation as well
4(50) - 5 = 200 - 5 = 195
I’m not very good at explaining so I hope u get it

3 0

2 years ago