Which expression shows the amount of tax on a T-shirt that costs x dollars, if tax is 7%?

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

The gas mileage for a certain vehicle can be approximated by m=−0.05x2+3.5x−49, where x is the speed of the vehicle in mph. Dete

Whitepunk [10]

Answer:

Step-by-step explanation:

Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;

m = −0.05x²+3.5x−49

when m= 9

9 = −0.05x²+3.5x−49

−0.05x²+3.5x−49 = 9

0.05x²-3.5x+49 = -9

Multiplying through by 100

5x²+350x−4900 = 900

Dividing through by 5;

x²+70x−980 = 180

x²+70x−980 - 180 = 0

x²+70x−1160 = 0

Using the general formula to get x;

a = 1, b = 70, c = -1160

x = -70±√70²-4(1)(-1160)/2

x = -70±√4900+4640)/2

x = -70±(√4900+4640)/2

x = -70±√9540/2

x = -70±97.7/2

x = -70+97.7/2

x = 27.7/2

x = 13.85mph

x ≈ 14 mph

Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph

4 0

2 years ago

In right triangle ABC, angle A and angle B are complementary angles. The value of cos A is 9/41. What is the value of sin B?

Margaret [11]

SinB = 9/41

I explained my reasoning down below

5 0

2 years ago

If 2A:3B=5:6 and 3B:2C=36:15 then find A:C

Aleonysh [2.5K]

Answer:

A: C = 2: 1

Step-by-step explanation:

Please see the attached pictures for the full solution.

Further explanantion (2nd image):

The reason why the ratio of A: C is equal to the ratio if 2A: 2C is that the number of parts of A and C is equal, which is 2 parts. If I were to divide both 2A and 2C by 2 to find the ratio of A: C, I would obtain 15: 15/2. However, ratios are expressed as whole numbers and thus, we would multiply the whole ratio by 2 again and the answer would still be 30: 15. This ratio is not in the simplest form since both can be divided by 15. Thus, dividing both sides of the ratio by 15 will leave us with the final answer of

A: C= 2: 1.

☆ An alternative method is to simplify the ratio 3B: 2C at the beginning.

3B: 2C

= 36: 15

= 12: 5

Multiply the first ratio by 2 so 3B has 12 parts in both ratios:

2A: 3B

= 10: 12

Combining the 2 ratios together,

2A: 3B: 2C

= 10: 6: 5

2A: 2C

= 10: 5

= 2: 1

A: C= 2: 1

6 0

2 years ago

A middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two students from the club will be selected at r

laila [671]

Answer:

Probability that Adam and Ella will be selected:

$\displaystyle \frac{1}{10}=0.1$

Step-by-step explanation:

Probabilities

The probability of a random event E to occur is a real number between 0 and 1, both inclusive, where 0 indicates an impossible event and 1 a sure event. There are many techniques to compute probabilities depending on the particular situation and distribution.

This question will be solved by simple calculations and logic, given its simplicity. We know the middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two of them are going to be selected at random to participate in the county chess tournament. We can calculate the number of different ways it can be done without any restriction. It's called the sample space.

The sample space of this event is the combination of 5 members regardless of their position. If {a,b,c,d,e} are the five members, then the possible combinations are {ab,ac,ad,ae,bc,bd,be,cd,ce,de}. Notice that there are only 10 possibilities because the combination ab is the same as ba since it's the same team for the tournament.

We can see there is only one combination of two specific letters out of 10. If a=Adam and e=Ella, only one combination is ae, the other 9 don't include both members, so the probability is

$\displaystyle P(ae)=\frac{1}{10}=0.1$

3 0

2 years ago