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3 years ago

Is (2,3) a solution to the system of inequalities 4x+3y<20 10x+y>10

Mathematics

2 answers:

stiks02 [169]3 years ago

7 0

Yes it is a solution because if you take the equation and plug the point in for the x and y :

4 (2) + 3 (3) < 20
8 + 9 < 20
17 < 20
which is true

10 (2) + (3) > 10
20 + 3> 10
23>10
which is also true

defon3 years ago

3 0

Hope this helps..... :)

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7.109) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken

Rina8888 [55]

Answer:

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The leading brand of dishwasher detergent has a 30% market share.

This means that $p = 0.3$

A sample of 25 dishwasher detergent customers was taken.

This means that $n = 25$

a. What is the probability that 10 or fewer customers choose the leading brand?

This is:

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{25,0}.(0.3)^{0}.(0.7)^{25} = 0.0001$

$P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014$

$P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074$

$P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243$

$P(X = 4) = C_{25,4}.(0.3)^{4}.(0.7)^{21} = 0.0572$

$P(X = 5) = C_{25,5}.(0.3)^{5}.(0.7)^{20} = 0.1030$

$P(X = 6) = C_{25,6}.(0.3)^{6}.(0.7)^{19} = 0.1472$

$P(X = 7) = C_{25,7}.(0.3)^{7}.(0.7)^{18} = 0.1712$

$P(X = 8) = C_{25,8}.(0.3)^{8}.(0.7)^{17} = 0.1651$

$P(X = 9) = C_{25,9}.(0.3)^{9}.(0.7)^{16} = 0.1336$

$P(X = 10) = C_{25,10}.(0.3)^{10}.(0.7)^{15} = 0.0916$

Then

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0001 + 0.0014 + 0.0074 + 0.0243 + 0.0572 + 0.1030 + 0.1472 + 0.1712 + 0.1651 + 0.1336 + 0.0916 = 0.9021$

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

3 0

3 years ago

Write an equation of a line containing the point (-2, 1) and is perpendicular to y= -1/4x-4

frosja888 [35]

the answer should be -4

hope this is correct for you and this helped

6 0

3 years ago

the frequency table shows the number of books some students read last summer. Based on the data in the table, which statement is

Whitepunk [10]

Answer:

A.) nine more girls read 6 or more than boys who read 6 or more books

Step-by-step explanation:

Let's examine the statements ...

a) 24 is 9 more than 15 . . . TRUE

b) 41 is 6 more than 36 . . . false

c) 32 is twice as many as 15 . . . false

d) 24 is twice as many as 48 . . . false

3 0

3 years ago

If u-ai + bj and v-ci + dj are vectors, then which of the following statements is not true?

alukav5142 [94]

Answer:

Option C

Step-by-step explanation:

Given that u-ai + bj and v-ci + dj are vectors

We have dot product

$u.v = (ai+bj).(ci+dj)$ hence inner product of u and v. So option a is true

The dot product of u and v is a scalar is true because dot product is always a scalar

The dot product of u and v is a vector. is false because dot product is only a scalar and has no direction and hence cannot be a vector

The dot product of u and v is given by the expression ac+bd

True because we multiply corresponding i components and j components and add.

So only C is not true.

7 0

3 years ago

In the first year of a 10,000 investment the interest rate was 6%. All earned interest remained invested for the second year, an

Aleks04 [339]

Answer:

13.4%

Step-by-step explanation:

First year:

$10,000*6% = $600

New balance = $10,600

Second Year:

$10,600*7% = $742

$10,600+ $742 = $11,342

Total Return:

Final Balance - Initial balance

$11,342 - $10,000 = $1,342

$10,000*x ÷ $1,342

x = $1,342/$10,000

x = 0.1342

0.134 = 13.4%

7 0

3 years ago