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3 years ago

X^2 +x-6=0 How to solve this ?

Mathematics

1 answer:

Svetach [21]3 years ago

6 0

Answer:

x = 2, x = -3

Step-by-step explanation:

We are given the following quadratic equation and we are to solve it for x:

$x ^ 2 + x - 6 = 0$

We need to find such factors of -6 that when added give a result of 1 and when multiplied, give a product of -6.

$x ^ 2 + x - 6 = 0$

$x ^ 2 - 2x + 3x - 6 = 0$

$x ( x - 2 ) + 3 ( x - 2 ) = 0$

$(x-2) = 0, (x+3)=0$

x = 2, x = -3

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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

A shipping company is loading cube shaped crates into a larger cube shaped container the smaller cubes have side lengths 21/2 fe

zheka24 [161]

Answer:

64 crates

Step-by-step explanation:

Smaller Cube Side Length = 2 1/2 feet, or, 2.5 feet

Larger Container (Cube) Side Length = 10 feet

We find volume of larger container and find volume of small crates. We divide the large volume by volume of each crate. This will give us number of crates we can fit.

Volume of Cube = x^3

Where x is the side length of the cube

Now,

Small Crate Volume = (2.5)^3 = 15.625 cubic feet

Large Container Volume = 10^3 = 1000 cubic feet

Number of crates that would fit = 1000/15.625 = 64

So, 64 crates will fit in the largest shipping container

7 0

3 years ago

Please answer for branliest

Lostsunrise [7]

Answer:

50%

Step-by-step explanation:

There are 2 cards greater than 5 , that is 6 and 7 , then

P( greater than 5 ) = $\frac{2}{4}$ = $\frac{1}{2}$ = 50%

4 0

3 years ago

A linear function has a slope of Negative StartFraction 7 Over 9 EndFraction and a y-intercept of 3. How does this function comp

dem82 [27]

It has the same slope and the same y-intercept, that is, option a is the right choice.

A linear function in the slope-intercept is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept.

We are given two linear functions and are asked to compare them.

First linear function:

Slope (m) = -7/9.

y-intercept (b) = 3.

Therefore, the linear function is: y = (-7/9)x + 3.

Second linear function:

Function given: y + 11 = (-7/9)(x - 18)

or, y + 11 = (-7/9)x + (-7/9)(-18)

or, y = (-7/9)x + 14 - 11 = (-7/9)x + 3.

Therefore, slope (m) = (-7/9)

y-intercept (b) = 3.

Therefore, we can say that it has the same slope and the same y-intercept, that is, option a is the right choice.

Learn more about linear functions at

brainly.com/question/15602982

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7 0

2 years ago

Sam Seller pays a local club $40 a month. Each week he has dinner for a flat fee of $20.00. Sam takes a cab, which charges him $

zhenek [66]

It cost sam $72.75. Thats all that costed him

8 0

3 years ago