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Otrada [13]
3 years ago
5

There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. How many of these sets contain any 2

numbers? PLS HELP I'M REALLY STUCK AND DON'T JUST STEAL THE POINTS PLEASE
Mathematics
2 answers:
Studentka2010 [4]3 years ago
5 0

Answer:

45 different sets

Step-by-step explanation:

There are 10 numbers in {0,1,2,3,4,5,6,7,8,9}.

We are looking for a combination since order doesn't mater

There are 10 options for the first number

We have chosen 1

Now there are 9 numbers

10*9

But since order doesn't matter, we divide by 2

The set {1,2} is the same as the set {2,1}

90/2 = 45

Leokris [45]3 years ago
4 0

Answer:

90

Step-by-step explanation:

it is 90 because in the first slot there can be any 10 numbers and in the second slot the set can contain any of the remaining 9 numbers and then we can multiply these two numbers together to find the total amount of sets.

hope this helps :)

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PLS ANSWER
djyliett [7]

Answer: reflection

Step-by-step explanation:

A reflection is like a mirror in the middle you can see they are the same in the line down the middle so <em>reflection </em>

8 0
3 years ago
Find an m &gt; 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.
Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

x^4-(3m+2)x^2+m^2=0

x^4+0x^3-(3m+2)x^2+0x+m^2=0

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}

=\frac{0}{1}=0

\implies a=0----(1)

(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}

=\frac{-3m-2}{1}

3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2

-10b^2=-3m-2

\implies b^2=\frac{3m+2}{10}-----(2)

(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2

9b^4=m^2

9(\frac{3m+2}{10})^2=m^2

9(\frac{9m^2+4+12m}{100})=m^2

81m^2+36+108m=100m^2

-19m^2+108m+36=0

19m^2-108m-36=0

19m^2-114m+6m-36=0

19m(m-6)+6(m-6)=0

(19m+6)(m-6)=0

\implies m=-\frac{6}{19}\text{ or }m=6

But m > 0,

Hence, the value of m is 6.

4 0
3 years ago
What is the slope of a line that contains the points (1 -2) and (4, -3).
Naddika [18.5K]

Answer:

-\frac{1}{3}

Step-by-step explanation:

Use the definition of slope:

m=\frac{y_2-y_1}{x_2-x_1}\\

Replace the values in the equation and solve:

m=\frac{-3-(-2)}{4-1} \\m=\frac{-1}{3}\\m=-\frac{1}{3}

4 0
2 years ago
What is the equation? Pls show your work.
Semmy [17]

Answer:

y=2x-2

Step-by-step explanation:

y=mx+b is point slope form.

let m= the slope

b=y intercept

the y intercept is -2

y=mx-2

then after finding the slope (2) put that in

y=2x-2

4 0
3 years ago
In the past, the population proportion of consumers preferring orange juice with no pulp was equation. To test if this populatio
geniusboy [140]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

P = 0.45

For the alternative hypothesis,

P ≠ 0.45

b) For the decision rule, we would reject H0 if 0.1 > p value and accepth H0 if 0.1 < p value

Considering the population proportion, probability of success, p = 0.45

q = probability of failure = 1 - p

q = 1 - 0.45 = 0.55

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 52

n = number of samples = 120

p = 52/120 = 0.43

c) We would determine the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.43 - 0.45)/√(0.45 × 0.55)/120 = - 0.44

Recall, population proportion, P = 0.45

The difference between sample proportion and population proportion(P - p) is 0.45 - 0.43 = 0.02

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.45 - 0.02 = 0.43

the p for the right tail is 0.45 + 0.02 = 0.47

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.3336

We would double this area to include the area in the right tail of z = 0.44 Thus

p = 0.3336 × 2 = 0.67

d) Since alpha, 0.1 < than the p value, 0.67, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the​ null hypothesis

4 0
3 years ago
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