Answer:
B
Step-by-step explanation:
P(AUB)=P(A)+P(B)-P(A∩B)
191/400=7/20+P(B)-49/400
P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4
The value of P(B) is 1/4.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = p/q
Given data as :
P(A) = 7/20,
P(A∪B) = 191/400,
P(A∩B) = 49/400 ,
P(AUB) = P(A) + P(B) - P(A∩B)
Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,
191/400 = 7/20 + P(B) - 49/400
Rearrange the terms in the equation,
P(B) = 191/400 + 49/400 - 7/20
P(B) = 240/400 - 7/20
P(B) = 12/20 - 7/20
P(B) = 5/20
P(B) = 1/4
Hence, the value of P(B) is 1/4.
Learn more about probability here :
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any equations that equal three?
x = 4 7 9 I dont mind for a step by step
Answer:
[tex]\boxed{\sf x = 9}[/tex]
Step-by-step explanation:
According to chord-chord theorem:
=> [tex]x* 2 = 3 * 6[/tex]
=> [tex]2x = 18[/tex]
Dividing both sides by 2
=> x = 18/2
=> x = 9
X cubed = 343^-1 find the positive value of x
9514 1404 393
Answer:
x = 1/7
Step-by-step explanation:
x³ = 1/343
x = 1/∛343 = 1/7
The positive value of x is 1/7.
_____
Additional comment
A square root (or any even-index root) will have both positive and negative real values. A cube root (or any odd-index root) will have only one real value, whose sign will match the sign of the value being rooted.
343^(-1/3) is the cube root of a positive number, so it will be a positive real number.
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.
(a)
[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]
[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]
[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]
(b)
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]
Which is the correct label of the line? (1 point)
a
AC
O
CD
D
Ο OllA
Answer:
The correct label of the line is CD
Suppose a newspaper wants to conduct a survey on heating oil consumption in Iowa. For the survey, the newspaper randomly picks 26 households. What is the sample distribution of the sample sum
Answer:
noent einda pergnta poudsesrmaesspeeciicofl
Step-by-step explanation:
can any one give me answer plz?
Answer:
D
Step-by-step explanation:
since
cos(2x) = 1 - 2×sin²(x)
and for x near 0, sin(x) is very similar to x.
on tuesday, david picked a apples each hour for 5 hours, and elanor picked b apples each hour for 8 hours. which of the following represents the total number of apples picked by david and elanor on tuesday? a) 13ab b) 40ab c) 5a + 8b d) 8a + 5b
Answer:
c) 5a + 8bStep-by-step explanation:
[tex]a \: apples = 1 \: hours\\x \: apples = 5 \: hours\\x = 5a\\Total \:no \:of \:apples \:picked\\\:by \:david \:= 5a\\\\\\b \:apples = 1 \:hour\\x \:apples = 8 hours\\x = 8b\\Total \:no \:of \:apples \:picked\\ \:by \:elanor = 8b\\\\Total \:no \:of \:Apples =5a+8b[/tex]
Which represents the inverse of the function f(x) = 4x?
h(x) = x+ 4
H(x) =x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
h(x)=1/4x
Step-by-step explanation:
function×inverse=-1
4x=-1
Answer:
h(x) = 1/4x
Step-by-step explanation:
y = 4x
x = 4y
1/4 x = y
Change the following fractions to 24ths.
3/4= ??
5/6= ??
18/24, 20/24
Step-by-step explanation:
3/4=?/24
5/6=?/24
3X6=18
4X6=24
5X4=20
6X4=24
Answer:
7/8 = 21/24
5/6 = 20/24
3/4 = 18/24
Step-by-step explanation:
What you do to the denominator, you do the same to the numerator.
[tex]\frac{7}{8} * \frac{3}{3} = \frac{21}{24}[/tex]
[tex]\frac{5}{6} * \frac{4}{4} = \frac{20}{24}[/tex]
[tex]\frac{3}{4} * \frac{6}{6} = \frac{18}{24}[/tex]
Point g is located at (3,6) on the coordinate plane. Point G is reflected over the x-axis to create point G'. Point G' is then reflected over the y-axis to create point G''. What ordered pair describes the location of G''.
-Answer:
(-3. -6)
Step-by-step explanation:
G (3,6)
x axis reflect
G' (3, -6)
y axis reflect
G'' (-3. -6)
Solve the following system
3x+y=9
4x-3y=6
Answer:
multiply the first equation with 3, then add the two equations, you'll get the value of x, by putting the value of x in any of the two equations, find y, answer should be this,
x = 33/13,
y = 18/13
Answer:
Step-by-step explanation:
3x+y=9
y=9-3x
4x-3y=6
4x-6=3y
y=(4x-6)/3
y= 4/3x-2
9-3x=4/3x-2
9+2=4/3x+3x
11=13/3x
x=11*3/13
=2.53
y=9-3*2.53
=1.41
What is the difference between congurent and similar ?
Answer:
When a shape is congruent they are equal in shape, size, and measure. Although if a shape is similar they will be the same shape, but not the same size, instead they will be proportionate.
Step-by-step explanation:
Answer:
CongruentCongruent figures are identical in size, shape and measure. SimilarTwo figures are similar if they have the same shape, but not necessarily the same size.
Step-by-step explanation:
Simplify: 6x^-2
a) 1/6x^2
b) 6/x^2
c) x^2/6
d) 1/36x^2
Answer:
The correct answer choice is option B. 6/x^2
Step-by-step explanation:
Answer:
6/x^2
Step-by-step explanation:
6 * x^-2
We know that a^ -b = 1/a^b
6 * 1/x^2
6/x^2
Mary subscribed to a cell phone plan with a $50 monthly fee and a charge of $0.25 for each minute she talks. Find an equation for the total cost for her plan when she uses minutes.
Answer:
c = 0.25m + 50
Step-by-step explanation:
Let c = cost; let m = number of minutes.
c = 0.25m + 50
Three measurements are made on each of three individuals in a random sample from a population. X 1 = 2, X2 = 8
and
1
1
187
X3 = 4. The distances d(X1, X2)between X1, X, and d(X2, X3) between X2, X3 respectively are (Use Euclidean inner
L5.
product)
Step-by-step explanation:
here is the answer hope it helps
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9 } A= {1, 2, 3, 4} and B= {4, 5, 6, 7}. Draw the Venn diagram of A ∩B. Answer with full explanation and diagram will be marked as brainliest for sure!!!
Step-by-step explanation:
Its mean the same number for both A and B which is only 4.
Find the surface area of the figure round your answer to the nearest tenth if necessary
Answer:
Step-by-step explanation:
S.A. = (6 + 8 + 10) × 4 + 2(8 × 6) ÷ 2 = 144 mi²
ILL GIVE BRAINLIEST
Combine like terms.
4x – 7y + 2x – 4 = [ ? ]x + [ ]y + [ ]
Answer:
[6x] + [-7y] + [-4]
Step-by-step explanation:
There are only two like terms in this expression "4x" and "2x." Since they are like terms we can combine them by adding the coefficients and keeping the variable attached. Therefore we can combine 4x and 2x into 6x. Since there are no more like terms, this expression can be simplified to 6x - 7y - 4.
A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles. Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.
Compute the linear speed on the surface of the planet at 30 degrees north latitude.
Answer:
The velocity is [tex]v = 886.96 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
The period of each revolution is [tex]T = 1\ day = 24 \ hours[/tex]
The angle is [tex]\theta = 30^o[/tex]
The radius is [tex]r = 3387.5 \ miles[/tex]
Generally the linear speed is mathematically represented as
[tex]v = w * r[/tex]
Where [tex]w[/tex] is the angular speed which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 *3.142 }{24}[/tex]
[tex]w = 0.2618 \ rad/s[/tex]
Thus
[tex]v = 0.261833 * 3387.5[/tex]
[tex]v = 886.96 \ m/s[/tex]
There are 30 colored marbles inside a bag. Six marbles are yellow, 9 are red, 7 are white, and 8 are blue. One is drawn at random. Which color is most likely to be chosen? A. white B. red C. blue D. yellow Include ALL work please!
Answer:
red
Step-by-step explanation:
Since the bag contains more red marbles than any other color, you are most likely to pick a red marble
what is square root of 49 over square root of 1250 simplified
im pretty sure its 0.19 because the sqyare root of 49 is 7. the square root of 1250 is 35.35
7/35.35=0.19
3 log2 (x+1) - 2 = 13
Answer:
Hello,
Answer 31
Step-by-step explanation:
[tex]3*log_2(x+1)-2=13\\\\3*log_2(x+1)=13+2\\\\log_2(x+1)=5\\\\\\x+1=2^5\\\\x=32-1\\\\\boxed{x=31}\\[/tex]
Find x and y plz help me show work
Answer:
Sorry but the photo is not clear
Given log32≈0.631 and log37≈1.771, what is log314
Answer:
the log to the base 3 of 14 is 2.402
Step-by-step explanation:
You must find a way to indicate that 3 is the base; you cannot run this '3' together with 2, 7 or 14.
Example:
log to the base 3 of 2 = 0.631
log to the base 3 of 7 = 1.771
Note that 2 times 7 is 14. Thus, to obtain the log to the base 3 of 14, we must ADD the two logs shown above:
0.631
+1.771
----------
2.402
Thus, the log to the base 3 of 14 is 2.402.
Check: Does 3^2.402 = 14? YES
A ladder 10 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 6 ft/sec, how fast is the height of the top changing (this will be a negative rate) when the lower end is 6 feet from the wall?
Answer:
-4.5ft per sec
Step-by-step explanation:
Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).
This forms a triangle with the ladder as the hypothenus of length 10ft
We have dy/dt = 6ft per sec
According to Pythagoras law the relationship between x and y is
(x^2) + (y^2) = (hypothenus ^2) = 10^2
When we differentiate both sides of the equation
2x(dx/dt) + 2y(dy/dt) = 0
dy/dt = (x/y) * (dx/dt)
y= √(10^2) - (6^2) = 8ft
So dy/dt = (6/8)* (6/1)= -4.5 ft per sec
It is a negative rate
Sally's paycheck this week was $100. She spent $220.45 for a shirt, $12.95 for a CD, $15 for gasoline, and put the balance in the bank.
a. What percent of her total pay was spent on the shirt?
b. What percent of her total pay did she put in the bank?
Answer:
A) 220.45%
B) 0%
Step-by-step explanation:
A) 220.45 / 100 = 2.2045 * 100 = 220.45%
B) Costs exceeded her paycheck, so 0% of her pay was leftover and put in the bank.
Answer: A) 22.045% , B) 75.16%
I guess its a typo and weekly salary was $1000
So weekly salary = 1000
Spent on shirt = $220.45
Spent on CD = $12.95
Spent on Gasoline = $15
A) 220.45/1000×100
= 22.045%
B) Total spent = 220.45 + 12.95 + 15
= $248.4
Total left with her = 1000 - 248.4
= $751.6
Total percent of pay she put in bank = 751.6/1000×100
= 75.16%
Must click thanks and mark brainliest
Find the missing side or angle round to the nearest tenth b=15 a=30 c=29 A=[?]°
Answer: 79
Step-by-step explanation:
i just did it on acellus and its right
HELP ASAP!!
The equation (blank) has no solution
Answer:
Just to recap, an equation has no solution when it results in an incorrect "equation".
For example:
Equation: x+3 = x+4
Subtract x: 3 = 4???
But clearly, 3 is not equal to 4, so this equation has NO SOLUTION.
Now onto our problem:
13y+2-2y = 10y+3-y
11y+2 = 9y+3
2y=1
y=1/2
9(3y+7)-2 = 3(-9y+9)
27y+61 = -27y+27
54y = -34
y = -34/54
32.1y+3.1+2.4y-8.2=34.5y-5.1
34.5-5.1=34.5y-5.1
5.1=5.1
infinite solutions
5(2.2y+3.4) = 5(y-2)+6y
11y+17 = 11y-10
17 = -10??
That's not true, so the option "5(2.2y+3.4) = 5(y-2)+6y" has no solution.
Let me know if this helps
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?
(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5
Answer:
(A) 37.5 miles
Step-by-step explanation:
The trains x and y are travelling on tracks starting simultaneously from a from opposite ends of 100 miles roads.
Translate these information into a simple represention to visualize the problem. (Picture below)
■■■■■■■■■■■■■■■■■■■■■■■■■■
First let's calculate the velocity of both trains.
The velocity formula is:
● V = d/t
d is the distance travelled and t is the tile needed to do it.
● V(x) = 100/5 = 20 miles per hour
● V(y) = 100/3 = 33.33.. wich is approximatively 33 after rounding to the nearest unit.
■■■■■■■■■■■■■■■■■■■■■■■■■■
After calculateingboth velocities, Let's find when the trains meet.
First understand what does it mean matematically when both trains meet.
Go back to the representation and notice what happens when the trains meet.
Let t be that moment.
When x and y reches the meeting point at t, the sum of the distances they have travelled is equal to the total distance wich is 100 miles .
We khow that V = d/t so d = V×t
Let's find the expression of the distances both trains travelled when they have met each other.
● d = V(x) × t
● d' = V(y) × t
■■■■■■■■■■■■■■■■■■■■■■■■■■
So the equation will be:
● V(x) × t + V(y) × t = 100
Factor using t
● t (V(x) + V(y) ) = 100
Replace V(x) and V(y) by their values
● t (20+33) = 100
● 53 t = 100
Divide both sides by 53
● 53t /53 = 100/53
● t = 1.88
■■■■■■■■■■■■■■■■■■■■■■■■■
Replace t in the expression of the distance that train x has travelled when meeting y.
● d = V(x) × t
● d = 20 × 1.88
● d = 37.6 wich is approximatively 37.5 miles