Answer:
D. 91%
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Less than 15 minutes.
Event B: Less than 10 minutes.
We are given the following probability distribution:
[tex]f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5[/tex]
Simplifying:
[tex]f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}[/tex]
Probability of arriving in less than 15 minutes:
Integral of the distribution from 5 to 15. So
[tex]P(A) = \int_{5}^{15} = \frac{375}{t^4}[/tex]
Integral of [tex]\frac{1}{t^4} = t^{-4}[/tex] is [tex]\frac{t^{-3}}{-3} = -\frac{1}{3t^3}[/tex]
Then
[tex]\int \frac{375}{t^4} dt = -\frac{125}{t^3}[/tex]
Applying the limits, by the Fundamental Theorem of Calculus:
At [tex]t = 15[/tex], [tex]f(15) = -\frac{125}{15^3} = -\frac{1}{27}[/tex]
At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]
Then
[tex]P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}[/tex]
Probability of arriving in less than 15 minutes and less than 10 minutes.
The intersection of these events is less than 10 minutes, so:
[tex]P(B) = \int_{5}^{10} = \frac{375}{t^4}[/tex]
We already have the integral, so just apply the limits:
At [tex]t = 10[/tex], [tex]f(10) = -\frac{125}{10^3} = -\frac{1}{8}[/tex]
At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]
Then
[tex]P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}[/tex]
If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087[/tex]
Thus 90.87%, approximately 91%, and the correct answer is given by option D.
Which linear inequality is represented by the graph?
O y < 3x + 2
Oy> 3x + 2
Oy< 1/3x + 2
O y>1/3x+2
Answer:
[tex]y> 3x + 2[/tex]
Step-by-step explanation:
Hope it is helpful....
The linear inequality that represents the given graph is y > 3x + 2.
The solutions to the graph of the inequalities is given as;
(x, y) = (0, 2)
(x, y) = (-3, -7)
To determine the inequality represented in the graph;
Using option A, when x = 0, y < 2 (this is not same as the graph)Using option B, when x = 0, y > 2 ( same as the graph)Using option B, when x = -3, y > -7Thus, the linear inequality that represents the given graph is y > 3x + 2.
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What are the coordinates of the point that is 3/8 of the way from A(-8, -9) to B (24, -1)
(-6,4)
(-2,4)
(4,-6)
(12,-4)
Answer:
C. (4, -6)
Hope it helps :)
PLEASE CAN SOMEONE HELP ME??????????????
Answer: 180 degrees rotation, center (1.5, -0.5)
=====================================================
Explanation:
Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)
Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2
--------------
Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11
--------------
We have this system of equations
[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]
Equate the right hand sides and solve for x
7x-11 = x-2
7x-x = -2+11
6x = 9
x = 9/6
x = 3/2
x = 1.5
which leads to
y = x-2 = 1.5-2 = -0.5
or
y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5
Either way, x = 1.5 leads to y = -0.5
We get the ordered pair (x,y) = (1.5, -0.5)
This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)
Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that
AD = A''D
BD = B''D
CD = C''D
PLZ HELPPP I need to pass this!!
Answer:
x=-1
Step-by-step explanation:
the middlepoint is where its symetrical, and so you take the x part of the point. the point is (-1,4), and all we need is x, so you have x=-1
27,On a coordinate grid, the vertices
of Marie's garden are at
(0.8), (5,2), (0, 2), and (5, 8).
What is the shape of the patio?
O
y-axis
ه ه ه ه و يا د ا م م
0 1 2 3 4 5 6 7 8 9 10
x-axis
A rectangle
B trapezoid
C square
D rhombus
nince of stained
Answer:
Rectangle
Step-by-step explanation:
Given the points :
(0, 8), (5,2), (0, 2), and (5, 8).
Based on the vertices given :
If we mark the points on a graph and then join the points, we'll Obtain a rectangle ; this is because the length and with are not equal, with a length of 6 unit and width of 5 unit
Attached below is a rough sketch if the plot created in a notebook.
PLS HELP I WILL GIVE BRAINLIEST
Answer:
a) correct
b) 70 degrees
Step-by-step explanation:
since in the triangle BXC the sides BX and XC have the same length, they must also have the same angles with the baseline BC.
so, we know, XBC = 55 degrees.
and therefore BCX = 55 degrees.
the sum of all angles in a triangle is always 180 degrees.
so,
BXC = 180 - 55 - 55 = 70 degrees
Question number 7 only
Answer:
the answer is (4)
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The equation represents the total resistance, r, when two resistors
whose resistances are r1 and r2 are connected in parallel. Find the total
resistance when r1 is x and r2 is x + 1.
Answer:
[tex]R = \frac{x(x+1)}{2x+1}[/tex] --- total resistance
Step-by-step explanation:
Given
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]
Required
Find R when
[tex]R_1 = x[/tex]
[tex]R_2 = x+1[/tex]
So, we have:
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]
Substitute values for both R's
[tex]\frac{1}{R} = \frac{1}{x} + \frac{1}{x+1}[/tex]
Take LCM
[tex]\frac{1}{R} = \frac{x+1+x}{x(x+1)}[/tex]
Collect like terms
[tex]\frac{1}{R} = \frac{x+x+1}{x(x+1)}[/tex]
[tex]\frac{1}{R} = \frac{2x+1}{x(x+1)}[/tex]
Inverse both sides
[tex]R = \frac{x(x+1)}{2x+1}[/tex]
The product of three consecutive numbers is divisible by
Answer:
6
Step-by-step explanation:
The product of three consecutive numbers is divisible by 6
Let us say the numbers are x, x+1 , x+2
if x = 1,
Product of the three consecutive numbers,
(1)(2)(3)
=> 6, which is divisible by 6
if x = 2,
Product of the three consecutive numbers,
(2)(3)(4)
=> 24, which is divisible by 6
Similarly if we take any 3 consecutive numbers their product will be divisible by 6.
please help me please help me please help me please help me please help me please help me please
Answer:
2025 is not a perfect cube
Explain why the work is not correct.
arithematic mean between 2-x and 2+x
Answer:
2
Step-by-step explanation:
The mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{2-x+2+x}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
12. Three fifths of the children at my party like chocolate ice cream. How many of the 20 children at my party do not like chocolate ice-cream ? …8 children don't like choc ice cream…………………….
13. I have to pack 296 apples into 8 boxes. How many apples will there be in a box if each box contains the same number of apples? There will be 37
14. If I share 123 sweets equally among amongst 7 children, how many sweets will each child get?
……………………………………..
15. One soccer ball costs $4.50. How much will the soccer will balls in the picture cost?
Answer:
12. if 3/5 of them like chocolate ice cream 2/5 don't and 2/5 of 20 is 8.
A=8
13. 296 divided by 8 is 37
A=37
14. 123 divided by 7 is 17.5714285714 so each child will get 17 sweets and there will be 4 left over.
A=17 remainder of 4
15. umm i don't know just multiple 4.50 by the amount of soccer balls
A=?
16. srry i don't realy know there not enough of the pattern
Brainlest please
Your Welcome
BIFFY OUT!!!
The sum of two numbers is 19 and there differnce is 5
Answer:
x = 12 , y = 7
Step-by-step explanation:
Let the numbers be x and y
Sum of the numbers, x + y = 19 -------- ( 1 )
Difference of the number , x - y = 5 -------- ( 2)
( 1 ) + ( 2 ) => 2x = 24
x = 12
Substitute : x in ( 2 ) => 12 - y = 5
=> 12 - 5 = y
=> 7 = y
When a baseball park owner charges $3.00 for admission, there is an average attendance of 100 people. For every $0.10 increase in the admission price, there is a loss of 2 customers from the average number.
1. What admission price should be charged in order to maximize revenue?2. What is the maximum revenue?
Answer:
$1
max rev = 80(4) = $320
Step-by-step explanation:
let us do this in pennies
R = (100 - x/5)(300 + x)
d/dr = -2x - 200
5
(-2x-200)/5 = 0
-2x = 200
x = 100
An amount of $320 is the admission price that should be charged in order to maximize revenue.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, Let x represent the revenue function.
Hence, We can formulate;
x = (3 + 0.1(x))(100 - 2x)
x = 300 - 6x + 10x - 0.2x²
x = 300 + 4x- 0.2x²
x' = 4 - 0.4x
Generally, a maximum revenue occurs when x' = 0:
x' = 4 - 0.4x = 0
4 = 0.4x
x = 4 / 0.4
x = 10
Hence, The admission price,
= 3 + 0.1x
= 3 + 0.1 x 10
= 3 + 1
= $4
Thus, The Maximum revenue is,
= $4 (100 - (10 x 2)
= $4 (100 - 20)
= $4 x 80
= $320
In conclusion, the amount of $320 is the admission price that should be charged in order to maximize revenue.
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33. The perimeter of a room is 22m.lf
the length of the room is 6.5m,
what is its width?
The formula for perimeter is 2(Length) + 2(width)
Fill in the known information:
22 = 2(6.5)+ 2(width)
Simplify:
22 = 13 + 2(width)
Subtract 13 from both sides:
9 = 2(width)
Divide both sides by 2:
Width = 4.5m
Can someone please help please.you will get 48 points
Answer:
x = 20
Step-by-step explanation:
We can use a ratio to solve
10 14
------ = ----------
x 28
Using cross products
10 * 28 = 14*x
280 = 14x
Divide by 14
280/14 = 14x/14
20 =x
Answer:
20 cm
Step-by-step explanation:
It says that both of these shapes are similar. If we divide 28/14=2.
Then we can also multiply 10 cm by 2 cm to get 20 cm .
x= 20 cm
Hope this helps!
When doctors prescribe medicine, they must consider how much the drug’s effectiveness will decrease as time passes. If each hour a drug is only 95% as effective as the previous hour, at some point the patient will not be receiving enough medicine and must be given another dose. If the initial dose was 250 mg, what will the level of the dose be after 3 hours?
Please hurry!
Answer:
ok so this is what we have to do
250*0.95*0.95*0.95
ok so
214.34375
so about 214.3
Hope This Helps!!!
A large population has skewed data with a mean of 70 and a standard deviation of 6. Samples of size 100 are taken, and the distribution of the means of these samples is analyzed. a) Will the distribution of the means be closer to a normal distribution than the distribution of the population?
b) Will the mean of the means of the samples remain close to 70?
c) Will the distribution of the means have a smaller standard deviation?
d) What is that standard deviation?
a. Yes.
b. Yes.
c. Yes.
d. 0.6.
Answer:
a) Yes
b) Yes
c) Yes
d) 0.6
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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 large population has skewed data with a mean of 70 and a standard deviation of 6.
This means that [tex]\mu = 70, \sigma = 6[/tex]
Samples of size 100
This means that [tex]n = 100[/tex]
a) Will the distribution of the means be closer to a normal distribution than the distribution of the population?
According to the Central Limit Theorem, yes.
b) Will the mean of the means of the samples remain close to 70?
According to the Central Limit Theorem, yes.
c) Will the distribution of the means have a smaller standard deviation?
According to the Central Limit Theorem, the standard deviation of the population is divided by the sample size, so yes.
d) What is that standard deviation?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{100}} = \frac{6}{10} = 0.6[/tex]
So 0.6.
09:30 to 17:00 minus 30 minutes
How many hours is that ?
Answer:
7 hours
Step-by-step explanation:
9 : 30 to 17:00 = 7 hours 30 minutes
Minus 30 minutes = 7 hours
Hi if you have a 65% grade can a 80% bring it up to a C 70%
Answer:
Ask your Teacher if you are missing any work and if you are do it and do some things for extra credit
Step-by-step explanation:
Answer: yes,it depends on the points
if you have 65% and you score a 80 on a 45 point assingment it can go up to a c
+ep explanation:
Which fact is not used to prove that ABC is similar to DBE?
is 16 the decimal value of 1000
Answer:
0.016
Step-by-step explanation:
Answer:
0.016
Step-by-step explanation:
in a right triangle ABCD prove that angle abc is equal to angle CAD
From 22 potential women jurors and 25 potential men jurors, a jury of 12 is chosen at random. Let X be the number of women selected. Find the probability mass function of X.
Answer:
The probability mass function is:
[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]
Step-by-step explanation:
The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability mass of the hypergeometric probability distribution is given by:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
22 + 25 = 47 jurors, so [tex]N = 47[/tex]
22 are women, which means that [tex]k = 22[/tex]
Jury of 12, which means that [tex]n = 12[/tex].
Thus
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]
Which is the probability mass function.
Solve the equation.
(X-5)(x + 7) = 0
X=
-D
(Use a comma 6 separate answers as needed.)
9514 1404 393
Answer:
x = -7, 5
Step-by-step explanation:
The equation is written as a product equal to zero. The "zero product rule" tells us that a product is zero if and only if one or more factors are zero. Each factor will be zero when x takes on a value equal to the opposite of the constant in that factor.
x -5 = 0 ⇒ x = 5
x +7 = 0 ⇒ x = -7
The solutions to the equation are x = -7, 5.
The recursive formula for a geometric sequence is:
(a, = 5
[an = ans (3)
What is the 3rd term of this sequence?
A. 125
B. 11
C. 45
D. 15
9514 1404 393
Answer:
C. 45
Step-by-step explanation:
Apparently, your recursive definition is ...
[tex]a_1=5\\a_n=a_{n-1}\cdot3[/tex]
Each term is 3 times the previous one, so the sequence starts ...
5, 15, 45, 135, 405, ...
The 3rd term is 45.
PLEASE HELP ME WILL MARK YOU JF YOU HELP ME PLEASE!!!
Answer:
2, 3, 4, 7, 8, 10 I hope
Answers
Congruent by AAS (shown in the example)Congruent by SASCongruent by SSSCongruent by ASANot enough info (shown in the second example)Congruent by AASCongruent by SASCongruent by SSSCongruent by AASNot congruent=================================================
Explanations:
As the example shows, we have two pairs of congruent angles and a pair of congruent sides. The side are not between the angles in question. So AAS is slightly different from ASA.We have two pairs of congruent sides, and a pair of congruent angles. The angles are between the sides. So we use SAS which is a valid congruence theorem. Recall that SSA is not a valid theorem, so the order matters.We have three pairs of congruent sides, so we go with SSS. The order doesn't matter here.Similar to problem 1, but now the sides are between the angles. So we go with ASA this time instead of AAS.We unfortunately don't have enough info to determine if the triangles are congruent or not. We need to know something about the side lengths to determine congruency.As the hint suggests, marking the vertical angles will produce the other pair of congruent angles. So that's why we go for AAS (the side is not between the angles).This is similar to problem 2, as both use SAS. Note the unmarked vertical angles which are congruent.This is similar to problem 3. We use SSS here because we have 3 pairs of congruent sides as indicated by the tickmarks.The unmarked vertical angles can get double arcs to show they are congruent. We have a pair of congruent sides that are not between the two pairs of congruent angles, so we go for AAS (problems 1 and 6 also use AAS).For the triangle on the left, the arc is between the tickmarked sides. The triangle on the right has the arc not between the tickmarked sides. So there's no way the triangles are the same. The arc needs to be between the marked sides for each triangle, if we wanted them to be congruent (using SAS).---------------
Acronyms
SSS = side side side
SAS = side angle side
ASA = angle side angle
AAS = angle angle side
A parallelogram has base (2x - 1) metres and height (4x - 7) metres.
The area of the parallelogram is 1 m?.
(1) Show that 4x? - 9x + 3 = 0.
Answer (a)(i)
(*) Solve the equation 4x² – 9x + 3 = 0.
Show all your working and give your answers correct to 2 decimal places.
Answer:
0.4069 ; 1.843
Step-by-step explanation:
Given:
Base of parallelogram, b = (2x - 1)
Height = (4x - 7)
Area = 1
Area of parallelogram = Base * height
Area of parallelogram = (2x - 1) * (4x - 7)
(2x - 1) * (4x - 7) = 1
8x² - 14x - 4x + 7 = 1
8x² - 18x + 7 - 1 = 0
8x² - 18x + 6 = 0
Divide through by 2
4x² - 9x + 3 = 0
Solving the quadratic equation :
Using the formula
-b ± √(b² - 4ac) / 2a
a = 4 ; b = - 9 ; c = 3
Plugging in the values :
-(-9) ± √((-9)² - 4(4)(3)) / 2(4)
9 ± √(81 - 48) / 8
9 ± √33 / 8
(9 ± 5.7445626) / 8
(9 - 5.7445626) / 8) = 0.4069
(9 + 5.7445626) / 8 = 1.843
6x = 1/2(2x + 5)
Solve for x step by step
Please answer quickly
Answer:
x = 1/2
hope it helps
have a nice day
Answer:
maybe x=3.5
Step-by-step explanation:
6x= 1/2 (2x+5)
we take the 1/2 and distribute it into (2x+5) so we end up with
6x= 1x (or just x) + 2.5
We subtract 2.5 from both sides of the equation and we end up with
3.5x= 1x
we then need to isolate the x, so we divide both sides of the equation by x
and then we end up with
3.5= x/x, which ends up just being
3.5=x