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Morgarella [4.7K]

3 years ago

9

Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each wit

h probability of success (correct) given by p= 0.2. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.

1 answer:

Nezavi [6.7K]3 years ago

7 0

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of guesses made for the sat questions.

Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2

Probability of failure, q = 1 - p = 1 - 0.2 = 0.8

the probability that the number x of correct answers is fewer than 4 is expressed as

P(x < 4)

From the binomial distribution calculator,

P(x < 4) = 0.97

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asambeis [7]

The solution is indeed accurate.

4 0

3 years ago

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A geometric sequence has first term 1/9 and common ratio 3. Which is the first term of the sequence which exceeds 1000?

Svetach [21]

$a_{n}= \frac{1}{9} (3)^{n-1}$
(We know this from a=1/9 and r=3)
Simplifying this, we get:
$\frac{1}{9} (3)^{-1} (3)^n$

Since we're finding the first term that exceeds 1000, let's set it equal to 1000.

$\frac{1}{27}(3)^n=1000$
Multiplying both sides by 27
$3^n=27000$

$log_{3}27000=n$

n≈9.2

We have to round n up, since if n=9, the value would be <1000.
Therefore n=10. Substituting n=10,
$\frac{1}{27}3^{10}$
=2187

Therefore the first term that exceeds 1000 is 2187, and it is the 10th term

3 0

2 years ago

What is the product in simplest form x^2+9x+18/x+2 times x^2-3x-10/x^2+2x-24

german

$\dfrac{x^2+9x+18}{x+2}\cdot\dfrac{x^2-3x-10}{x^2+2x-24}=\dfrac{x^2+6x+3x+18}{x+2}\cdot\dfrac{x^2-5x+2x-10}{x^2+6x-4x-24}\\\\=\dfrac{x(x+6)+3(x+6)}{x+2}\cdot\dfrac{x(x-5)+2(x-5)}{x(x+6)-4(x+6)}$

$=\dfrac{(x+6)(x+3)}{x+2}\cdot\dfrac{(x-5)(x+2)}{(x+6)(x-4)}=\dfrac{(x+3)(x-5)}{x-4}\\\\=\dfrac{x^2-5x+3x-15}{x-4}=\dfrac{x^2-2x-15}{x-4}$

5 0

2 years ago

Read 2 more answers

A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the

pochemuha

Answer:

The quadratic function whose graph contains these points is $y=-x^{2}-2x-2$

Step-by-step explanation:

We know that a quadratic function is a function of the form $y=ax^{2}+bx+c$ . The first step is use the 3 points given to write 3 equations to find the values of the constants <em>a</em>,<em>b</em>, and <em>c</em>.

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

$-2=a*0^{2}+b*0+c\\c=-2$

$-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17$

$-17=a*3^{2}+b*3+c\\ c=-9a-3b-17$

We can solve these system of equations by substitution

Substitute $c=-9a-3b-17$

$-9a-3b-17=25a+5b-17\\-9a-3b-17=-2$

Isolate a for the first equation

$-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}$

Substitute $a=\frac{b}{2}$ into the second equation

$-9\left(-\frac{b}{2}\right)-3b-17=-2$

Find the value of b

$-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2$

Find the value of a

$a=\frac{b}{2}\\ a=-1$

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

$y=-x^{2}-2x-2$

As you can corroborate with the graph of this function.

8 0

3 years ago

Round to the nearest thousand 5.2182

steposvetlana [31]

Answer:

5.218

Step-by-step explanation:

5 or more, you add one. Four or less, you change it to zero.

6 0

3 years ago