Answer:
[tex]P(A U B ) = \frac{13}{25}[/tex]
Step-by-step explanation:
STEP:-1
Given that events A and B are independent then
P(A ∩B ) = P(A) P(B)
Given that P(A) = 2/5 and P(B) = 1/5
STEP:- 2
P(A ∩B ) = P(A) P(B)
[tex]P(A U B) = P(A) +P(B) - P(A n B )[/tex]
[tex]P(A U B ) = P(A) +P(B) - P(A) P(B)[/tex]
Step(iii):-
[tex]P(A U B ) = \frac{2}{5} +\frac{1}{5} - \frac{2}{5} X \frac{1}{5}[/tex]
[tex]P(A U B ) = \frac{3}{5} - \frac{2}{5} X \frac{1}{5}[/tex]
[tex]P(A U B ) = \frac{3}{5} - \frac{2}{25}[/tex]
[tex]P(A U B ) = \frac{15-2}{25} = \frac{13}{25}[/tex]
What is the equation of the line that passes through the point (-8, 3) and has a
slope of -1?
Answer:
y=-x-5
Step-by-step explanation:
y-3=-1(x-(-8))
y-3=-1(x+8)
y-3=-1x-8
y=-1x-8+3
y=-1x-5
Classify the decimal expansion of each fraction as a terminating decimal or a repeating decimal. Drag and drop the fractions into the boxes to correctly complete the table. Terminating Decimal Repeating Decimal 56/72 21/22 11/121 60/120
Answer: 56/72 = 0.777777777778 -> repeating decimal
21/22 =0.954545454545 -> repeating decimal
11/121 = 0.0909090909091 -> repeating decimal
60/120 = 0.5 -> terminating decimal
Step-by-step explanation:
True or False?
k = is a solution to the inequality 12k + 2 < 12. I really need to pass this test please help
Answer: k = 0 is a solution
Step-by-step explanation:
2 < 12
0 + 2 < 12
12(0) + 2 < 12, substitute 0 for k
12k + 2 < 12
A line has the equation y = 1/2x + 3. Convert this equation to standard form and write another equation that will have the same graph.
Equation of a line in standard form is Ax + By = C
A is a pos. integer and B + C are integers
1) multiply all terms in the equation by 2
2y = x - 6
2) subtract 2y from both sides
2y - 2y (cancelled out) = x - 2y - 6
x - 2y - 6 = 0
3) add 6 to both sides
x-2y = 0 +6 (-6 and +6 cancel out)
therefore,
x - 2y = 6
is the equation in standard form
The formula v=√ 2gh gives the velocity v, in feet per second, of an object when it falls h feet accelerated by gravity g, in feet per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 48 feet per second.
Hi there!
[tex]\large\boxed{36 \text{ feet}}[/tex]
v = √2gh
Plug in the given velocity and acceleration due to gravity:
48 = √2(32)h
Square both sides:
2304 = 2(32)h
Simplify:
2304 = 64h
Divide both sides by 64:
h = 36 feet.
Concerns about the climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g. from renewable sources) and petrodiesel (from fossil fuel). Random samples of 34 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?
Answer:
a) 99% of the sample means will fall between 0.933 and 0.941.
b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?
Samples of 34 means that [tex]n = 34[/tex]
We have that [tex]\mu = 0.937, \sigma = 0.009[/tex]
By the Central Limit Theorem, [tex]s = \frac{0.009}{\sqrt{34}} = 0.0015[/tex]
Within what interval will 99% of the sample means fail?
Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.
0.5th percentile:
X when Z has a pvalue of 0.005. So X when Z = -2.575.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.575 = \frac{X - 0.937}{0.0015}[/tex]
[tex]X - 0.937 = -2.575*0.0015[/tex]
[tex]X = 0.933[/tex]
99.5th percentile:
X when Z has a pvalue of 0.995. So X when Z = 2.575.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.575 = \frac{X - 0.937}{0.0015}[/tex]
[tex]X - 0.937 = 2.575*0.0015[/tex]
[tex]X = 0.941[/tex]
99% of the sample means will fall between 0.933 and 0.941.
(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?
By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.
Find the roots/zeroes of the following polynomial
x^2−19=6
Answer:
x=5 and x=-5
Step-by-step explanation:
1. first you would subtract 6 from both sides to set the equation = to zero.
2. The equation would then be x^2-25=0.
3. that is a difference of two squares polynomial. So when you factor it, it is (x+5)(x-5)=0
4. by the zero product property, the roots are 5 and -5.
Can someone please help?
Answer:
3) 35.98
4) 63.98
Step-by-step explanation:
3) [(7+7)×3.14÷2]+14=35.98
4) (7+7)×3.14+14×3=63.98
Identify domain & Range please!
9c + 1 =10 .............................................................................
Answer:
C = 1
Step-by-step explanation:
9C + 1 = 10 ---> 9C + 1 -1 = 10 - 1 (minus 1 for both side, equation still satisfied),
--> 9C = 9 --> C = 1 (Divided both side by 9)
If it is helpful, please give me Brainliest.
A sink can hold 10 gallons of water.How many quarts of water can the sink hold?
Answer:
The sink can hold 40 quarts of water
Step-by-step explanation:
1 gal = 10 qt
10 gal = 40 qt
Answer:
40
Step-by-step explanation:
There are 4 quarts in a gallon
4 quarts per gallon x 10 gallons = 40 quarts total
Which expressions describe the area of the shaded region? Select all that apply. A rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles. An area that includes 9 smaller rectangles and is the intersection of 3 of the 12 columns and 3 of the 6 rows is shaded. A. 3 12 × 3 6 B. 3 10 × 1 2 C. 1 4 × 1 2 D. 1 4 × 1 3 E. 4 12 × 3 6 7 / 8 4 of 8 Answered
Answer: (B) I hope that helps you
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
Answer:
0.6826894809 (highest precision)
Step-by-step explanation: (Can I get brainliest? Thanks)
1. Normal distribution: Z ~ (0,1^2)
2. Z distribution formula:
[tex]Z=\frac{x-mu}{std}[/tex]
mu = mean
std = standard deviation
3. Use normalcdf function on a graphing calculator (Or it is impossible to do by hand)
P(400≤Z≤350) = normalcdf (lower bound, upper bound, mu, std)
P(400≤Z≤350) = normalcdf (350, 400, 400, 50)
P(400≤Z≤350) ≈ 0.68 ≈ 68%
Someone please help me it’s so hard
Answer:
m=2
b=1
Equation is y=2x+1
Help fast plz 100 points!
Answer: A
Step by step: The explain is in my photo.
Answer:
A
Step-by-step explanation:
6 (1/3x-2) please help me
Answer:
The answer will be 2x-12
Step-by-step explanation:
Hope this Helped
Answer:
2x-12
Step-by-step explanation:
Hey There!
To solve this problem we need to use distributive property
We have to distribute 6 to whats inside of the parenthesis (1/3x and -2)
6(1/3x)=2x
6x-2=-12
so the answer is
2x-12
hope this helps :)
Alina's softball coach writes the team's number of games played and number of wins on a board in the locker room as shown, but the number of wins was accidentally erased. The coach knows that the ratio of wins to games played so far this season is equal to 0.8. How many wins does the team have?
A: 3 wins
B: 8 wins
C: 10
D: 12
Answer:
A
Step-by-step explanation:
3x + y = 4
8x + 2y = 10
Answer:
I take it that we solve for x and y, so we have
3x + y = 4, so we have y = 4 - 3x
and plug that in to
8x + 2y = 10
8x - 6x + 8 = 10
so
2x = 2
x = 1
y = 4 - 3
y = 1
What is the revenue of the company when it
spends $15 million on advertising? Show work
Answer:
$32 million
Step-by-step explanation:
I'm assuming the data set is in millions of dollars. Using some quick logic, the formula is revenue = (advertising)(2) + 2
R = 15(2) + 2R = 30 + 2R = 32 ($32 million?)Find the Area of the Shaded Region.
Round to the nearest tenth if necessary.
18 m
25 m
5 m
50 m
9514 1404 393
Answer:
610 m²
Step-by-step explanation:
If we extend the horizontal line across the right-hand portion of the figure, then the figure is divided into two rectangles:
bottom: 5 m × 50 m = 250 m²
top: 18 m × 20 m = 360 m²
The sum of these areas is the shaded area:
shaded area = 250 m² +360 m² = 610 m²
A pool can be filled by one pipe in 6 hours and by a second in 12 hours . How long will it take using both pipes to fill the pool?
Answer:
18
Step-by-step explanation:
During her morning run Olivia’s heart beats 330 times in 3 minutes. Enter the number of beats Olivia’s heart would have in 4 minutes at this rate.
Answer:
440 beats
Step-by-step explanation:
330/3 = 110 beats per minute
110 * 4 = 440
Answer:
440
Step-by-step explanation:
if you divide 330 by 3 that would be 110 in 1 minute so multiply that by 4 and you get 440
the simple interest formula is I=Prt. what is the t stands for?
Answer:
t = time, usually in years
Step-by-step explanation:
t = time, usually in years
Answer:
T is the time
There are 24 hours in one day.
Write the expression that
gives the number of hours in de
days.
YA BOI NEEDS THEM POINTS I HOPE YOU UNDERSTAND BRAINLIEST WOULD BE APPRECIATED!?{!?!?!?!?!
Which fraction is not greater than 2/5
Answer:
1/5
Step-by-step explanation:
Because it is 0.2 and 2/5 equal 0.4
The graph Shows the amount of money earned by an employee based on the time he spent working Which list shows the dependent quantities in the graph ( I'll show a picture)
Answer:
d
Step-by-step explanation:
d
Solve for x.
x^2+2=102
PLEASE HELP ASAP PLEASE
Answer:
Yo
So, if ya wanna solve this question and of course questions alike, ya gotta pay attention to the graph. mean All of these parabolic chart have the domain of R
Step-by-step explanation:
So there ya go
D=R
and now bout the range ya gotta find the vertex, which is:
[tex] x = \frac{ - b}{2a} \: \: y = \frac{Δ}{4a} [/tex]
now pay attention
X=2/–2=–1
y=–(–1)²–2(–1)+3=4
Now the highest point of your parabolic chart is 4 and the lowest point is endless which is (–♾,4]
Well, finally your answer is D
Is the slope for the line below positive or negative
Answer:
negative
Step-by-step explanation:
positive -> as x increases, y increases
negative -> as x increases, y decreases
In a lottery game, a machine has 48 balls marked with numbers from 1-48 and six of them are taken out at random. A player picks six of these numbers, trying to match the six balls that come out of the machine in any order. If exactly 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize? Give answer as a fraction or decimal rounded to 4 significant digits in either standard or scientific notation. Hint: there is more than one way to win, take into consideration all the ways to pick the 4 winning numbers and the 2 losing numbers.
Answer:
7.5
Step-by-step explanation:
5.6+45,693u+ 2a+ = 7.5