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3 years ago

14

A box contains three pen, two markers and a highlighter. Tara selects one item at random and does not return it to the box. She

then selects item at random. What is the probability the Tara selects 1 pen and 1 marker?

1 answer:

kakasveta [241]3 years ago

3 0

Two out of six probability

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f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans

Kruka [31]

Answer:

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

Step-by-step explanation:

We want to find the Riemann sum for $\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx$ with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$

where $\Delta{x}=\frac{b-a}{n}$ .

Step 1: Find $\Delta{x}$

We have that $a=0, b=\frac{3\pi }{4}, n=6$

Therefore, $\Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}$

Step 2: Divide the interval $\left[0,\frac{3 \pi}{4}\right]$ into n = 6 sub-intervals of length $\Delta{x}=\frac{\pi}{8}$

$a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b$

Step 3: Evaluate the function at the left endpoints

$f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3$

$f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386$

$f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964$

$f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527$

$f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0$

$f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527$

Step 4: Apply the Left Riemann Sum formula

$\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315$

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

5 0

3 years ago

I really need help please! Number 5!! (Factoring)<br><br> Please show how you got it.

Citrus2011 [14]

Answer:

(4×-3)(2x-1)

Step-by-step explanation:

8x²-10x+3

8x²-4x-6x+3

4x(2x-1)-3(2x-1)

(4×-3)(2x-1)

7 0

3 years ago

solong [7]

Answer:

Step-by-step explanation:

i dont know the answrrrr

3 0

3 years ago

The cost of 2 markers and 5 pencils is $3.25. The cost of 4 markers and 6 pencils is $5.50.

mihalych1998 [28]

Answer: markers are a dollar each and pencils are twenty five cents each

Step-by-step explanation:

2x1 = 2

5x.25 = 1.25

2+1.25= 3.25

4x1 = 4

6x.25= 1.50

4+1.30 = 5.50

Hope this helps and if you need me to explain it better feel free to ask!

5 0

3 years ago

Simplify each expression by combining like terms. 7x - 4x + 28

Pepsi [2]

3x + 28

We can combine 7x and -4x because they are like terms. 7x -4x is equal to 3x. Now we rewrite the expression as 3x + 28.

7 0

2 years ago