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2 years ago

Which are the roots of the quadratic function f(q) = q2 – 125? Select two options.

Mathematics

2 answers:

julsineya [31]2 years ago

8 0

Answer:

What are the options?

Step-by-step explanation:

Assoli18 [71]2 years ago

3 0

Answer:

±11.18

Step-by-step explanation:

the function is:

$f(q)=q^2-125$

and to find the roots we need to find which values of $q$ makes the function result in zero:

$q^2-125=0$

solving for $q$ :

$q^2=125\\q=\sqrt{125}$

A square root has two solutions, one positive and one negative, so the solutions are:

$q=$ ± $\sqrt{125}$ ≈ ±11.18

the roots of the quadratic equation are +11.18 and -11.18

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Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in

ASHA 777 [7]

Answer:

a) There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c) The expected number of Chrome users is 4.074.

d) The variance for the number of Chrome users is 3.2441.

The standard deviation for the number of Chrome users is 1.8011.

Step-by-step explanation:

For each Internet browser user, there are only two possible outcomes. Either they use Chrome, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

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 combinatios 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.

In this problem we have that:

Google Chrome has a 20.37% share of the browser market. This means that $p = 0.2037$

20 Internet users are sampled, so $n = 20$ .

a.Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is P(X = 8).

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

$P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243$

There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b.Compute the probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

Either there are less than 3 Chrome users, or there are three or more. The sum of the probabilities of these events is decimal 1. So:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{20,0}.(0.2037)^{0}.(0.7963)^{20} = 0.0105$

$P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538$

$P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.1950$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1950 = 0.8050$

There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c.For the sample of 20 Internet browser users, compute the expected number of Chrome users

We have that, for a binomial experiment:

$E(X) = np$

$E(X) = 20*0.2037 = 4.074$

The expected number of Chrome users is 4.074.

d.For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

We have that, for a binomial experiment, the variance is

$Var(X) = np(1-p)$

$Var(X) = 20*0.2037*(0.7963) = 3.2441$

The variance for the number of Chrome users is 3.2441.

The standard deviation is the square root of the variance. So

$\sqrt{Var(X)} = \sqrt{3.2441} = 1.8011$

The standard deviation for the number of Chrome users is 1.8011.

6 0

2 years ago

Simplify i³⁸. [i=√(-1)]

Tju [1.3M]

For the answer to the question above, the answer is simple, and it is -1 (because even powers of an imaginary number or i will always give a -1).I hope my answer helped you with your problem. Have a nice day!

5 0

2 years ago

Read 2 more answers

Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?

Alexandra [31]

Answer:

On a coordinate plane, an exponential function increases in

quadrant 3 into quadrant 4 and approaches y = 0. It goes through

(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25) ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The function $f(x)=\frac{1}{4}(8)^{x}$ is reflected across the

y-axis and then across the x- axis

- Lets revise the reflection of a function across the axes

- If the function f(x) reflected across the x-axis, then the new function

h(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new function

g(x) = f(-x)

∵ $f(x)=\frac{1}{4}(8)^{x}$ is reflected across the y-axis

- Change the sign of x

∴ Its image is g(x) where $g(x)=\frac{1}{4}(8)^{-x}$

∵ $g(x)=\frac{1}{4}(8)^{-x}$ is reflected across the x-axis

- Change the sign of y

∴ Its image is h(x) where $h(x)=-\frac{1}{4}(8)^{-x}$

∴ h(x) is the image of f(x) after reflected across the y-axis then

reflected across the x-axis

* Look to the attached graph for more understand

- f(x) represented by red

- g(x) represented by blue

- h(x) represented by green

* From the graph

- The green graph is in the 3rd and 4th quadrants

- Approaches y = 0 (x-axis)

- point (-1 , -2) lies on it

- It cross the y-axis at point (0 , -0.25)

∴ The answer is the last one

On a coordinate plane, an exponential function increases in

quadrant 3 into quadrant 4 and approaches y = 0. It goes through

(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25)

8 0

2 years ago

Read 2 more answers

I need help please

Sidana [21]

7 1/2
you go to both sides of the graph and count in till u get to the middle

7 0

1 year ago

Read 2 more answers

Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation 5.9cm . What percent of t

xz_007 [3.2K]

Answer:

8.7% of the residuals are greater than 8 cm.

Step-by-step explanation:

We are given that the distribution of residuals is approximately normal with mean 0 cm and standard deviation 5.9 cm.

Let X = distribution of residuals

So, X ~ N( $\mu=0,\sigma^{2} = 5.9^{2}$ )

The z score probability distribution is given by ;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean residual = 0 cm

$\sigma$ = standard deviation = 5.9 cm

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, percent of the residuals that are greater than 8 cm is given by = P(X > 8 cm)

P(X > 8 cm) = P( $\frac{X-\mu}{\sigma}$ > $\frac{8-0}{5.9}$ ) = P(Z > 1.36) = 1 - P(Z $\leq$ 1.36)

= 1 - 0.9131 = 0.0869 or 8.7%

The above probability is calculated using z table by looking at value of x = 1.36 in the z table which have an area of 0.9131.

Therefore, 8.7% of the residuals are greater than 8 cm.

8 0

1 year ago