[(51 + 3) − 32] ÷ 9 ⋅ 2.

a student either knows the answer or guesses. Let 3434 be the probability that he knows the answer and 1414 be the probability t

Arlecino [84]

Answer: $\dfrac{12}{13}$

Step-by-step explanation:

Let A = he known the answer then A' = he guess the answer.

B = he answered it correctly

As per given , we have

$P(A)=\dfrac{3}{4}\ \ ,\ \ P(A')=\dfrac{1}{4}$

$P(B|A)=1$

$P(B|A')=\dfrac{1}{4}$

By Bayes theorem , we have

$P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A')P(A')}\\\\ P(A|B)=\dfrac{1\times\dfrac{3}{4}}{1\times\dfrac{3}{4}+\dfrac{1}{4}\times\dfrac{1}{4}}\\\\= \dfrac{12}{13}$

The probability that the student knows the answer given that he answered it correctly is $\dfrac{12}{13}$ .

6 0

3 years ago

What is 145 divided by 6

Annette [7]

21.4666 hope this helps! ❤️

7 0

3 years ago

Read 2 more answers

Your parents decide they would like to install a rectangular swimming pool in the backyard. There is a 15-foot by 20-foot rectan

Lilit [14]

Answer:

perimeter: 46 ft
area: 126 ft²

Step-by-step explanation:

Since the 3 ft edge is on both sides of the pool, each dimension of the pool is 6 ft shorter than the corresponding dimension of the space. The pool will be 15 ft -6 ft = 9 ft in one direction and 20 ft -6 ft = 14 ft in the other direction.

The perimeter of the pool is the sum of its side lengths:

P = 9 ft + 14 ft + 9 ft + 14 ft = 2(9 ft +14 ft) = 2(23 ft)

P = 46 ft

__

The area of the pool is the product of its length and width:

A = (14 ft)(9 ft) = 126 ft²

The perimeter and area are 46 ft and 126 ft², respectively.

5 0

3 years ago

Topic: The Quadratic Formula

Finger [1]

Answer:

Step-by-step explanation:

The quadratic formula for a equation of form

ax²+bx + c = 0 is

$x= \frac{-b +- \sqrt{b^2-4ac} }{2a}$

For the first equation,

x²+3x-4=0,

we can match that up with the form

ax²+bx + c = 0

to get that

ax² = x²

divide both sides by x²

a=1

3x = bx

divide both sides by x

3 = b

-4 = c

. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.

Plugging our values into the equation, we get

$x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1$

as our possible solutions

Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.

Next, we have

x²+3x+4=0

Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus

$x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\$

Because √-7 is not a real number, this has no real solutions. However,

(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions

Finally, for

4x² + 1= 4x,

we can start by subtracting 4x from both sides to maintain the desired form, resulting in

4x²-4x+1=0

Then, a=4, b=-4, and c=1, making our equation

$x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2$

Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution

7 0

3 years ago

The graph of a linear function passes through the points (2, 4) and (8, 10).

Keith_Richards [23]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ 4}})\quad 
% (c,d)
&({{ 8}}\quad ,&{{ 10}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-4}{8-2}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\qquad 
\begin{array}{llll}
\textit{plug in the values for }
\begin{cases}
y_1=4\\
x_1=2\\
m=\boxed{?}
\end{cases}\\
\textit{and solve for "y"}
\end{array}$

8 0

3 years ago