1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ozzi
3 years ago
13

Which expression is equivalent to

Mathematics
1 answer:
mario62 [17]3 years ago
7 0

Answer:

a

Step-by-step explanation:

You might be interested in
The probability that a lab specimen contains high levels of contamination is 0.10. Five samples are checked, and the samples are
raketka [301]

Answer:

(a) 0.59049 (b) 0.32805 (c) 0.40951

Step-by-step explanation:

Let's define

A_{i}: the lab specimen number i contains high levels of contamination for i = 1, 2, 3, 4, 5, so,

P(A_{i})=0.1 for i = 1, 2, 3, 4, 5

The complement for A_{i} is given by

A_{i}^{$c$}: the lab specimen number i does not contains high levels of contamination for i = 1, 2, 3, 4, 5, so

P(A_{i}^{$c$})=0.9 for i = 1, 2, 3, 4, 5

(a) The probability that none contain high levels of contamination is given by

P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})=(0.9)^{5}=0.59049 because we have independent events.

(b) The probability that exactly one contains high levels of contamination is given by

P(A_{1}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}∩A_{4}^{$c$}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5})=5×(0.1)×(0.9)^{4}=0.32805

because we have independent events.

(c) The probability that at least one contains high levels of contamination is

P(A_{1}∪A_{2}∪A_{3}∪A_{4}∪A_{5})=1-P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})=1-0.59049=0.40951

6 0
3 years ago
Evaluate the iterated integral 2 0 2 x sin(y2) dy dx. SOLUTION If we try to evaluate the integral as it stands, we are faced wit
nignag [31]

Answer:

Step-by-step explanation:

Given that:

\int^2_0 \int^2_x \ sin (y^2) \ dy dx \\ \\ \text{Using backward equation; we have:} \\ \\  \int^2_0\int^2_0 sin(y^2) \ dy \ dx = \int \int_o \ sin(y^2) \ dA \\ \\  where; \\ \\  D= \Big\{ (x,y) | }0 \le x \le 2, x \le y \le 2 \Big\}

\text{Sketching this region; the alternative description of D is:} \\ D= \Big\{ (x,y) | }0 \le y \le 2, 0 \le x \le y \Big\}

\text{Now, above equation gives room for double integral  in  reverse order;}

\int^2_0 \int^2_0 \ sin (y^2) dy dx = \int \int _o \ sin (y^2) \ dA  \\ \\ = \int^2_o \int^y_o \ sin (y^2) \ dx \ dy \\ \\ = \int^2_o \Big [x sin (y^2) \Big] ^{x=y}_{x=o} \ dy  \\ \\=  \int^2_0 ( y -0) \ sin (y^2) \ dy  \\ \\ = \int^2_0 y \ sin (y^2) \ dy  \\ \\  y^2 = U \\ \\  2y \ dy = du  \\ \\ = \dfrac{1}{2} \int ^2 _ 0 \ sin (U) \ du  \\ \\ = - \dfrac{1}{2} \Big [cos  \ U \Big]^2_o \\ \\ =  - \dfrac{1}{2} \Big [cos  \ (y^2)  \Big]^2_o  \\ \\ =  - \dfrac{1}{2} cos  (4) + \dfrac{1}{2} cos (0) \\ \\

=  - \dfrac{1}{2} cos  (4) + \dfrac{1}{2} (1) \\ \\  = \dfrac{1}{2}\Big [1- cos (4) \Big] \\ \\  = \mathbf{0.82682}

5 0
3 years ago
If you throw a ball at a rectangular board that is 4 ft. by 5 ft. with a smaller 2 ft. by 2 ft. square painted in the center of
bekas [8.4K]

Answer:

Step-by-step explanation:

Probability=(2*2)/(4*5)=1/5=20 %

8 0
3 years ago
(05.02 LC)What is the area, in square inches, of the figure shown here? A parallelogram with a height of 4inches is shown. The h
antoniya [11.8K]

Answer:

36 in²

Step-by-step explanation:

The figure that is been described is a Parallelogram.

The area of a Parallelogram is = Base × Height

From the question, the Height of the Parallelogram = 4 inches

The Base of the Parallelogram is calculated as the Length or base of the rectangle + base of the triangle

= 5 inches + 4 inches

= 9 inches

Area of the Parallelogram = 9 inches × 4 inches

= 36 square inches or 36 in²

6 0
3 years ago
If x = -6, which inequality is true?
lakkis [162]

Answer:

D

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Classify each polygon by the number of sides. Tell whether it's convex or concave.<br>​
    8·1 answer
  • If a 40 foot telephone pole casts a 34 foot shadow at the same time that a nearby tree casts a 28 foot shadow, how tall is the t
    8·1 answer
  • Explain how to find 4x80
    14·2 answers
  • The money in michelle's bank account increased from $250 to $500. what was her percent of increase?
    10·2 answers
  • An artist is painting a parallelogram with a base of 45 cm and a height of 34 cm. One tube of paint will cover 400 cm.
    12·1 answer
  • Answer please ASAP now
    12·1 answer
  • -y=-6x-3<br> write in the slope-intercept form please!: y=mx+b<br> please show work too!
    13·1 answer
  • Subtract 4x + 2y - 16z from ( -12x + 2y - 4z ).
    5·1 answer
  • 3. Find how many numbers between 232 and 252.​
    11·1 answer
  • Express the formula in terms of the height, Use that formula to find the height when the volume is and the radius is
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!