How many combinations of three books can be selected from 40 books?

What is the measure of angle c in degrees? * 150 30 90 60

Dmitry [639]

Answer:

Option (2)

Step-by-step explanation:

Measure of angle formed by two tangents from a point outside the circleis half the difference of the measures of the intercepted arcs.

From the figure attached,

m∠C = $\frac{1}{2}[m(\text{major arc AB})-m(\text{minor arc AB)}]$

= $\frac{1}{2}[(360-m\widehat{AB})-m(\widehat{AB})]$

= $\frac{1}{2}[360-2m(\widehat{AB})]$

= $180-m\widehat{AB}$

= 180 - 150

= 30°

Therefore, measure of angle C will be 30°.

Option (2) is the answer.

4 0

3 years ago

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

Factor 20x2 + 25x – 12x – 15 by grouping. 1. Group terms with common factors. 2. Factor the GCF from each group. 3. Write the po

RUDIKE [14]

Step 1:

 (((22•5x2) + 25x) - 12x) - 15)))


The first term is, 20x2 its coefficient is 20 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is -15


step 2 above, -12 and 25
 20x2 - 12x + 25x - 15

Step-4 : Add up the first 2 terms, pulling out like factors :
 4x • (5x-3)
 Add up the last 2 terms, pulling out common factors :
 5 • (5x-3)
Step-5 : Add up the four terms of step 4 :
 (4x+5) • (5x-3)
 Which is the desired factorizationFinal result : (5x - 3) • (4x + 5)

5 0

3 years ago

Read 2 more answers

Help! Will give brainly! Explain why the value x=4 is not a solution to the inequality 2x>10

melamori03 [73]

Answer

8 is not greater than 10

Step-by-step explanation:

2x>10

2(4)>10

8<10

x=4 can not be the solution to this equation because 8 is less than 10

*just as a side note think of the > sign as an alligator, the mouth always is open towards the larger number

7 0

3 years ago

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Consider the formula for the slope between two coordinates

krek1111 [17]

The following equations is equivalent to the slope formula is A) y₂= m(x₂-x₁) + y₁.

<h3>What is slope?</h3>

The angle of inclination of a line with respect to the horizontal is quantified. In analytical geometry, a line, ray, or line segment's slope is the proportion of the vertical to the horizontal distance between any two points ("slope equals rise over run").

<h3>What is equation?</h3>

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. We discover that the variable x has a value of 7 after solving this equation.

Given that,

Take a look at the formula below for the slope between two coordinate locations, m.

m = $\frac{y_{2}- y_{1} }{x_{2}-x_{1} }$

Here, slope is

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Where m is the slope and y₁ and y₂ and x₁ and x₂ are coordinates of the axis.

The first step is to multiply x₂-x₁ on both sides in order to acquire y₂ on its own.

so you must add y₁ to both sides in order to get y₂ alone.

m(x₂-x₁) +y₁ = y₂.

Therefore, the following equations is equivalent to the slope formula is A) y₂ = m(x₂-x₁) + y₁.

To know more about the slope, visit:

brainly.com/question/16508963

#SPJ9

5 0

1 year ago