Answer:
[tex]\boxed{\ P(B)=0.3 \ }[/tex]
Step-by-step explanation:
Hi,
We know that
P(A or B)=P(A)+P(B)-P(A and B)
so P(B)= P(A or B) - P(A) + P(A and B)
so
P(B) = 0.5 - 0.4 + 0.2 = 0.3
thanks
A random sample pulled 43 catfish from a large lake. They were marked and released. A second sample pulled out 88 catfish. Seventeen had been marked. Calculate the estimated population
Answer: 114
Step-by-step explanation: You have 43 new catfish then you catch 88 but 17 of them have already been marked so you do not want to count those in the estimated population again because they have already been counted so you take 88 minus 17 and you get 71 new fish. So then you add the first new sample of fish 43 and then you add the second new sample of fish 71 and then you get 114
In football seasons, a team gets 3 points for a win, 1 point for a draw and 0 points for a
loss. In a particular season, a team played 34 games and lost 6 games. If the team had a
total of 70 points at the end of the season, what is the difference between games won and lost
Answer:
The difference between the games won and lost = 21 - 6 =15
Step-by-step explanation:
According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.
A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.
The team played a total of 34 games.
Total games played = 34
Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,
34 - 6 = 28 games was won or draw
Let
the number of games won = x
the number of game drew = y
3x + y = 70.............(i)
x + y = 28................(ii)
x = 28 - y
insert the value of x in equation(i)
3(28 - y) + y = 70
84 - 3y + y = 70
84 - 70 = 3y -y
14 = 2y
divide both sides by 2
y = 14/2
y = 7
insert the value of y in equation(ii)
x + y = 28
x = 28 - 7
x = 21
The team won 21 games , drew 7 games and lost 6 games.
The difference between the games won and lost = 21 - 6 =15
Find the population mean or sample mean as indicated.
Sample 17, 13, 5, 12, 13
Answer:
13
Step-by-step explanation:
I think
What is the slope of the line?
Write an equation of a line that is parallel to the line 3y=-x+6 and passes through the point (6,2).
Answer:
y = x+2
y =-x+2 shows 0
We want to show 1 both sides
2y = x+2 shows 2
y = x+2 shows 0 as explained below.
Step-by-step explanation:
3y−x=6
Solve for y.
y=2+x3
Rewrite in slope-intercept form.
y=13x+2.
Use the slope-intercept form to find the slope and y-intercept.
Slope: 13 y-intercept: 2
Any line can be graphed using two points. Select two
x values, and plug them into the equation to find the corresponding y values.
xy 02, 33
Graph the line using the slope and the y-intercept, or the points.
Slope:
13y-intercept: 2x y (0,2) (3,3)
A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will not be sold if there are actually three dead batteries in the package
Answer:
There is a probability of 76% of not selling the package if there are actually three dead batteries in the package.
Step-by-step explanation:
With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:
n=4 (the amount of batteries picked for the sample).p=3/10=0.3 (the proportion of dead batteries).k≥1 (the amount of dead batteries in the sample needed to not sell the package).The probability of having k dead batteries in the sample is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]
Then, the probability of having one or more dead batteries in the sample (k≥1) is:
[tex]P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{4}{0} p^{0}q^{4}=1*1*0.7^4=0.2401\\\\\\P(x\geq1)=1-0.2401=0.7599\approx0.76[/tex]
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 49 cubic feet. What dimensions yield the minimum surface area? Round to the nearest tenth.
Answer:
b = 4.6 ft
h = 2.3 ft
Step-by-step explanation:
The volume of the tank is given by:
[tex]b^2*h=49[/tex]
Where 'b' is the length of the each side of the square base, and 'h' is the height of the tank.
The surface area can be written as:
[tex]A=b^2+4bh\\A=b^2+4b*({\frac{49}{b^2}})\\A=b^2+\frac{196}{b}[/tex]
The value of b for which the derivate of the expression above is zero is the value that yields the minimum surface area:
[tex]\frac{dA}{db} =0=2b-\frac{196}{b^2}\\2b^3=196\\b=4.61\ ft[/tex]
The value of h is then:
[tex]h=\frac{49}{4.61^2}\\h=2.31\ ft[/tex]
Rounded to the nearest tenth, the dimensions are b = 4.6 ft and h = 2.3 ft.
From the top of the cliff 8m high,two boats are seen in the direction due west.find the distance between the boats if the angles of depression from the top of the cliff are 45° and 30°.Find also the actual distance of the farther boat from the top of the cliff.
Answer:
Distance between 2 boats= 5.86m (3 s.f.)
Actual distance from farther boat from top of cliff= 16m
Step-by-step explanation:
Please see the attached pictures for full solution.
Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Find the quantity Q(t) of salt in the tank at time t > 0.
Answer:
The quantity of salt at time t is [tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex], where t is measured in minutes.
Step-by-step explanation:
The law of mass conservation for control volume indicates that:
[tex]\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}[/tex]
Where mass flow is the product of salt concentration and water volume flow.
The model of the tank according to the statement is:
[tex](0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}[/tex]
Where:
[tex]c[/tex] - The salt concentration in the tank, as well at the exit of the tank, measured in [tex]\frac{pd}{gal}[/tex].
[tex]\frac{dc}{dt}[/tex] - Concentration rate of change in the tank, measured in [tex]\frac{pd}{min}[/tex].
[tex]V[/tex] - Volume of the tank, measured in gallons.
The following first-order linear non-homogeneous differential equation is found:
[tex]V \cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]60\cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]\frac{dc}{dt} + \frac{1}{10}\cdot c = 3[/tex]
This equation is solved as follows:
[tex]e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }[/tex]
[tex]\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C[/tex]
[tex]c = 30 + C\cdot e^{-\frac{t}{10} }[/tex]
The initial concentration in the tank is:
[tex]c_{o} = \frac{10\,pd}{60\,gal}[/tex]
[tex]c_{o} = 0.167\,\frac{pd}{gal}[/tex]
Now, the integration constant is:
[tex]0.167 = 30 + C[/tex]
[tex]C = -29.833[/tex]
The solution of the differential equation is:
[tex]c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }[/tex]
Now, the quantity of salt at time t is:
[tex]m_{salt} = V_{tank}\cdot c(t)[/tex]
[tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex]
Where t is measured in minutes.
Which table represents a function?
Write a simplified expression for the area of the rectangle below
Answer:
12x+40
Step-by-step explanation:
A=l*w
A=20(3/5x+2)
A=4*3x+20*2
A=12x+40
Answer:
[tex] = 12x + 40[/tex]
Step-by-step explanation:
[tex]area = l \times b \\ = 20 \times (\frac{3}{5} x + 2) \\ = \frac{60x}{5} + 40 \\ = 12x + 40[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
128 less than a number is 452
Answer:
580
Step-by-step explanation:
"128 less than a number is 452" is represented by:
n - 128 = 452
Solve for 'n':
n - 128 + 128 = 452 + 128 (Addition Property of Equality)
n = 580
2. Calculate the midpoint of the given
segment
|(-2, -3)
(0.1)
(2, 3)
Answer:0,1
Step-by-step explanation:
It’s on edge
what is tge surface area of tge dquare pyramid GELP IM TIMED AND ABOUT TO RUN OUT OF TIME
Answer:
Step-by-step explanation:
Damian reads 21 pages in 1 hour. How many pages can he read in 3 hours? StartFraction 21 pages Over 1 hour EndFraction = StartFraction question mark pages Over 3 hours EndFraction To go from 1 hour to 3 hours, you _______ . Damian can read _________ pages in 3 hours.
Answer: (Multiply by 3)
63 pages in 3 hours
Step-by-step explanation:
Answer:
To go from 1 hour to 3 hours, you
✔ multiply by 3
.
Damian can read
✔ 63
pages in 3 hours.
Step-by-step explanation:
Which of the following sets would have a graph with an open circle on 5 and a ray pointing right on the number line?
The open circle means we do not include the endpoint, hence the use of a greater than symbol. If we were to include the endpoint, then we'd have greater than or equal to. We can rule out choice B due to this reasoning.
The ray pointing to the right indicates we are talking about x values larger than 5, so we can rule out choice A and conclude the answer is C.
Side note: The notation [tex]x \in \mathbb{R}[/tex] is saying "x is a real number"
What is the range of the relation {(2, 4), (3, 4), (4,7), (5,7), (6,5)}?
Answer:
The range is {4,5,7}
Step-by-step explanation:
The range of a relation is the output values The values are 4,7,5 we normally put them in order from smallest to largest
The range is {4,5,7}
Which statement about the two-way frequency table is true?
Answer:
Which statements?
Step-by-step explanation:
Can you write the statements please?
Angle-Angle-Side (AAS) is not a congruency of triangles theorem.
Answer:
False
Step-by-step explanation:
AAS is one of the POSTULATE to prove triangles' congruency.
Answer:n
Step-by-step explanation:
pls help, you will get branliest !!
Answer:
4.......................
simplify (51/3)^3
i will give brainlist
Answer: D. 5
Step-by-step explanation:
Typically when you have exponents in a form like this, you would multiply 1/3 with 3 to get 1/3 * 3/1. The threes cancel out and you're left with an exponent of 1. And 5 to the 1 power is 5.
What is the range of g(x)=-1/2|x-6|+1
Answer:
The answer is A: ( - ∞, 1 )
Step-by-step explanation:
Ann pays $300 for membership to a local gym. She is allowed to bring one guest on any visit. John pays Ann $5 to go to the gym with her occasionally. Describe what the expression 300 - 5t could represent. Then evaluate the expression for T equals five 10 15 and 20
Answer:
f
Step-by-step explanation:
uppose the correlation between two variables, math attitude (x) and math achievement (y) was found to be .78. Based on this statistic, we know that the proportion of the variability seen in math achievement that can be predicted by math attitude is:
Answer:
The proportion of the variability seen in math achievement that can be predicted by math attitude is 0.78, the same value as the correlation coefficient.
Step-by-step explanation:
The correlation coefficient r between this two variables is found to be 0.78.
This coefficient can be calculated as:
[tex]r=\dfrac{SSY'}{SSY}[/tex]
where SSY' is the sum of the squares deviation from the mean for the predicted value and SSY is the sum of the squares deviation from the mean for the criterion variable.
Then, the value of the coefficient r is giving the proportion of the variability seen in the criterion value Y that can be explained by the predictor variable X.
Answer:
r=SSY'/SSY
Step-by-step explanation:
en una division el 42 es el cociente el divisor 12 y el dividendo 513 ¿Cual es el resto?
Answer:
El resto es 9.
Step-by-step explanation:
En una división el cociente es el resultado que se obtiene, el divisor es el número por el que se divide otro número, el dividendo es el número que va a dividirse entre otro y el resto es lo que queda cuando un número no puede dividirse exactamente entre otro. De acuerdo a esto, la división planteada se encuentra en la imagen adjunta donde al resolverla se encuentra que el número que queda es 9 y este es el resto.
Flip a fair two sided coin 4 times. Find the probability the first or last flip is a tail.
Answer:
1/4
Step-by-step explanation:
Flip a fair two sided coin 4 times, the probability the first or last flip is a tail is
P = (1/2) x 1 x 1 x (1/2) = 1/4
(The probability of getting tail in first flip = 1/2, in the 2nd and 3rd flip, tail and head are both accepted, the probability of getting tail in last flip = 1/2)
Hope this helps!
What is the value of x?
A-17
B-26
C-39
D-41
Answer: 41
Step-by-step explanation:
a^2 + b^2 = c^2
40^2 + 9^2 = c^2
c = √1681 = 41
Answer:
D: 41
Step-by-step explanation:
Using Pythagorean Theorem
c² = a² + b²
Where c is hypotenuse, x
a is the base, 9
b is the perpendicular, 40
Putting in the formula
x² = (40)²+(9)²
x² = 1600 + 81
x² = 1681
Taking square root on both sides
x = 41
Prove the Triangle Proportinality Theorem
Answer:
Step-by-step explanation:
Given: DE║BC
To prove: [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex]
Statements Reasons
1). DE║BC 1). Given
2). ∠1 ≅ ∠4, ∠3 ≅ ∠4 2). Corresponding angles theorem
3). ΔADE ~ ΔABC 3). AA Similarity theorem
4). [tex]\frac{\text{AB}}{\text{AD}}=\frac{\text{AC}}{\text{AE}}[/tex] 4). Corresponding sides are proportional
5). [tex]\frac{\text{AD+DB}}{\text{AD}}=\frac{\text{AE+EC}}{AE}[/tex] 5). Segment addition postulate
6). [tex]1+\frac{\text{DB}}{\text{AD}}=1+\frac{\text{EC}}{\text{AE}}[/tex] 6). [tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]
7). [tex]\frac{\text{DB}}{\text{AD}}=\frac{\text{EC}}{\text{AE}}[/tex] 7). Subtract 1 from both sides
8). [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex] 8). Take the reciprocal of both sides
I need help solving this problem. It tells me that I could use any method provided above but I don't really get it. Could someone help?
The Problem:
You have to be careful when using a ladder. If you place the ladder too close to the wall, it could tip over. If you place the ladder too far from the wall, it could slide down. To prevent this, safety experts recommend the 4-to-1 Rule: for every 4 feet you want to go up the wall, place the base of the ladder one foot away from the wall.
The longest ladder available at many hardware stores is 40 feet. What is the highest you could reach with this ladder?
The problem gives me three methods to pick from to solve the problem. Each method had a clue underneath.
Hints:
Method 1: Know that the height must be 4x the base. Also know that hypotenuse is the longest side, so height must be shorter than 40 (and base must be shorter than 10 feet).
Method 2: Base^2+Height^2=40^2
Height= 4 • base
Method 3:
Base^2+Height^2=40^2
Base= 0.25 • height
The answers this problem asks for is:
The base, height and length.
Answer:
The highest you could reach with this ladder is 30 feet or 9.14 meters.
Which type of symmetry?
Answer:
both rotational and reflectional
Answer: both rotational and reflectional
Step-by-step explanation: a p e x