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3 years ago

F(x) = x ^ 2 - 8x + 7

1 answer:

5 0

Answer:
They have the same x-value
f(x) has the greater minimum
Step-by-step explanation:
To find the vertex of a second degree equation, in this case the minimum value, we can use the following equation:
x = -b / 2a
Remember that a second degree equation has the following form:
ax^2 + bx + c
so a = 1, b = -8 and c = 7. Now you have to substitute in the previous equation
x = - (-8) / 2(1)
x = 8 / 2
x = 4
This means that the two functions have the same x-value.
The y value of f(x) would be
f(4) = (4)^2 - 8(4) + 7
f(4) = 16 - 32 + 7
f(4) = -9
So the vertex, or minimun value of f(x) would be at the point (4, -9).
The vertex, or minimun value of g(x) is at the point (4, -4).
So f(x) has a minimum value of -9 and g(x) a minimum value of -4.

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What is zero to the power of 5? ill give 35 points to the first person to answer.

yan [13]

Now,

0^5

= 0

It is a right answer...

Thank you ♥♥

5 0

2 years ago

Read 2 more answers

Let the number of chocolate chips in a certain type of cookie have a Poisson distribution. We want the probability that a cookie

ludmilkaskok [199]

Answer:

$\lambda \geq 6.63835$

Step-by-step explanation:

The Poisson Distribution is "a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event".

Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that $X \sim Poisson(\lambda)$

The probability mass function for the random variable is given by:

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda$

On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

$P(X\geq 2)=1-P(X$

Using the pmf we can find the individual probabilities like this:

$P(X=0)=\frac{e^{-\lambda} \lambda^0}{0!}=e^{-\lambda}$

$P(X=1)=\frac{e^{-\lambda} \lambda^1}{1!}=\lambda e^{-\lambda}$

And replacing we have this:

$P(X\geq 2)=1-[P(X=0)+P(X=1)]=1-[e^{-\lambda} +\lambda e^{-\lambda}[]$

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)$

And we want this probability that at least of 99%, so we can set upt the following inequality:

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)\geq 0.99$

And now we can solve for $\lambda$

$0.01 \geq e^{-\lambda}(1+\lambda)$

Applying natural log on both sides we have:

$ln(0.01) \geq ln(e^{-\lambda}+ln(1+\lambda)$

$ln(0.01) \geq -\lambda+ln(1+\lambda)$

$\lambda-ln(1+\lambda)+ln(0.01) \geq 0$

Thats a no linear equation but if we use a numerical method like the Newthon raphson Method or the Jacobi method we find a good point of estimate for the solution.

Using the Newthon Raphson method, we apply this formula:

$x_{n+1}=x_n -\frac{f(x_n)}{f'(x_n)}$

Where :

$f(x_n)=\lambda -ln(1+\lambda)+ln(0.01)$

$f'(x_n)=1-\frac{1}{1+\lambda}$

Iterating as shown on the figure attached we find a final solution given by:

$\lambda \geq 6.63835$

4 0

3 years ago

Kallie is selling lemonade and ice pops to raise money for a trip to the local water park. A cup of lemonade costs $0.75, and

qaws [65]

Answer:

1.25x+0.75y>25

x+y>20

Explanation:

Selling 20 cups of lemonade and 15 ice pops will raise enough money to go to the water park.

0.75x+1.25y≥25

8 0

3 years ago

Solve V=1/3bh for h. (1/3 is a fraction, idk if that matters.)

Vadim26 [7]

Answer:

3V/b = h

Step-by-step explanation:

Step 1: Write equation

V = 1/3bh

Step 2: Multiply both sides by 3

3V = bh

Step 3: Divide both sides by b

3V/b = h

8 0

3 years ago

Need help!

siniylev [52]

Correct Inputs :-

In ΔABC right angled at A, D and E are points on BC, C such that BD = CD and AD ⊥ BC

$\underline{\underline{\large\bf{Solution:-}}}\\$

$\longrightarrow$ Let us know about definition of altitude first. The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.

$\leadsto$ Median is the line segment from a vertex to the midpoint of the opposite side.

Let us Check all options one by one

CD is line segment which starts from vertex C but don't falls on opposite side AB thus it is not an altitude.❌

BA is line segment which starts from vertex B and falls perpendicularly on opposite sides AC and is thus an altitude.✔️

AD is line segment which starts from vertex A and falls perpendicularly on opposite side BC and is thus an altitude.✔️

AE is a line segment which starts from vertex A but doesn't falls perpendicularly on opposite side BC and is thus not an altitude.❌

AD falls on BC with D as mid point because BD = CD and is thus a median. ✔️

8 0

2 years ago