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enot [183]
3 years ago
7

Answer for both and explain B 20+ points

Mathematics
1 answer:
Alexxx [7]3 years ago
6 0

Answer:

<u>Given function:</u>

  • g(x) = x² - 6x + c

a)

  • c = 2

<u>Th x-intercept found when g(x) = 0</u>

  • x² - 6x + 2 = 0

<u>Solve the equation to find the values of x:</u>

  • x² - 6x + 2 = 0
  • x² - 6x + 9 = 7
  • (x - 3)² = 7
  • x - 3 = ±√7
  • x = 3 ± √7

The x-intercepts are (3 + √7, 0) and (3 - √7, 0)

b)

  • c = 10

<u>Solve as above:</u>

  • x² - 6x + 10 = 0
  • x² - 6x + 9 + 1 = 0
  • (x - 3)² = -1

The left side is a square of a number which is always positive, the right side is negative.

It means there is no solution, so no-x-intercepts.

The graph of the function lies above the x-axis.

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The lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 h
DaniilM [7]

Answer:

Probability that a battery will last more than 19 hours is 0.0668.

Step-by-step explanation:

We are given that the lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 hours.

<em>Let X = lifetime of a battery in a certain application</em>

So, X ~ N(\mu=16,\sigma^{2} =2^{2})

The z-score probability distribution for normal distribution is given by;

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

where, \mu = mean lifetime = 16 hours

            \sigma = standard deviation = 2 hours

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, the probability that a battery will last more than 19 hours is given by = P(X > 19 hours)

  P(X > 19) = P( \frac{  X -\mu}{\sigma} > \frac{19-16}{2} ) = P(Z > 1.50) = 1 - P(Z \leq 1.50)

                                              = 1 - 0.9332 = 0.0668

<em>Now, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.</em>

Hence, the probability that a battery will last more than 19 hours is 0.0668.

5 0
3 years ago
A study of six hundred adults found that the number of hours they spend on social networking sites each week is normally distrib
babymother [125]
The answer is C. 0.313
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3 years ago
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Primitive function for:<br><br> 1. f(x)=4e2x+e−x, sådan att F(0)=2
Free_Kalibri [48]

The primitive function for f(x) = 4e^{2x} + e^{-x} is given by it's indefinite integral.

To calculate it, recall:

\frac{d}{dx}e^{ax}=ae^{ax}

\int c f(x)dx = c\int f(x)dx

Let's begin

\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1}  + c\\

F(x) = 2e^{2x}-e^{-x} +c

To find the costant, we just need to use the fact that F(0)=2

F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3

Therefore,

\boxed{F(x) = 2e^{2x} - e^{-x} -3 }

6 0
3 years ago
What are all the solutions of x2 + 3x – 4 = 0?
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X^2 +3x-4=0
(X+4)(x-1)=0 so x = -4 and x=1 are solutions
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A recipe requires 1/2 cup of milk and 1/3 cup of water. How much more milk is required for the recipe water?
Lapatulllka [165]

1/2-1/3

(1/2)x3-(1/3)x2

3/6-2/6

1/6

7 0
3 years ago
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