Answer:
0.8343
Step-by-step explanation:
From the question, we have the following values:
Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75
Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25
P = 0.25
n = number of random variables = 9
The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:
P < 4 = P ≤ 3
n = 9
P(x) = n!/(n - x)! x! × p^x × q^(n - x)
x = 3
p = 0.25
q = 0.75
P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)
P(x) =0.8343
The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.
Given information:
75% of the vehicles passing through a checkpoint are from within the state.
So, the probability that the vehicle is from within the state is 0.75.
The probability that the vehicle is from outside the state will be 1-0.75=0.25.
Now, let x be the random variable. So, the value of n=9. and x<4
It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.
So, [tex]x< 4[/tex], p=0.25 and q=0.75.
So, the required probability can be calculated as,
[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]
Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.
For more details, refer to the link:
https://brainly.com/question/14282621
The length and width of a rectangle are measured as 58 cm and 45 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
Error in calculated area = [tex]\pm 10.3 cm^2[/tex]
Step-by-step explanation:
x = 58 cm
y = 45 cm
A = x*y
delta A
= delta (x*y)
= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)
= 45(0.1) + 58(0.1)
= 103(0.1)
= 10.3 cm^2
List the sides of ΔRST in ascending order (shortest to longest). m∠R=2x+11°, m∠S=3x+23°, and m∠T=x+42°
Answer:
ST, RS, RT
Step-by-step explanation:
Angles of a triangle add up to 180°.
2x + 11° + 3x + 23° + x + 42° = 180°
6x + 76° = 180°
x = 17⅓
m∠R = 2x+11° = 45⅔°
m∠S = 3x+23° = 75°
m∠T = x+42° = 59⅓°
The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.
ST, RS, RT
Can you please me with the word problem thank you so much
Answer:
4. 53
5. 66
6. 89
7. 31
Step-by-step explanation:
4. 14 + 18 + 21
^ ^
33 + 21
53
5. 86 - 20
66
6. 34 + 55
89
7. 14 + 11 + 6
^ ^
25 + 6
31
The equation| x + 4| = x has solution a. X = -2 b. X = 2 c. X = -4 d. X = 4
Answer:
B) 2
/////////////////
What is the measure of m?
Answer:
√245
Step-by-step explanation:
altitude on hypotenuse theorem:
m^2=7*35
m^2=245
m=√245
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced? Answer: A= the cube with side length 6 cm, B= the cube with side length 8 cm, C= the cube with side length 10 cm, D= the cube with side length 12 cm. On one side of the scale : , on the other side of the scale
Answer: The cube with side length of 12cm is alone in one plate, the other 3 cubes are in the other plate.
Step-by-step explanation:
We have 4 cubes with side lengths of:
6cm, 8cm, 10cm and 12cm.
Now, some things you need to know:
If we want a scale to be balanced, then the mass in both plates must be the same.
The volume of a cube of side length L is:
V = L^3
And the mass of an object of density D, and volume V is:
M = D*V.
As all the cubes are of the same material, all of them have the same density, so the fact that we do not know the value of D actually does not matter here.
Then we want to forms two groups of cubes in such a way that the total volume in each plate is the same (or about the same), the volumes of the cubes are:
Cube of 6cm:
V = (6cm)^3 = 216cm^3
Cube of 8cm:
V = (8cm)^3 = 512cm^3
Cube of 10cm:
V = (10cm)^3 = 1000cm^3
cube of 12cm
V = (12cm)^3 = 1728cm^3
First, if we add the volumes of the first two cubes, we have:
V1 = 216cm^3 + 512cm^3 = 728cm^3
Now we can see that we add 1000cm^3 the volume will be equal to the volume of the larger cube, so here we can also add the cube with side length of 10cm
Then the volume of the 3 smaller cubes together is:
V1 = 216cm^3 + 512cm^3 + 1000cm^3 = 1728cm^3.
Then, if we want to have the same volume in each plate, then we need to have the 3 smaller cubes in one plate, and the larger cube in the other plate.
32 to 34 Directions: Given the following set of
numbers find the mean, median, and mode.
12, 13, 15, 15, 16, 19, 19, 19, 20, 21, 25
39.
32. Mean =
a. 17.64
b. 19
c. 15
40. 1
33. Median
a. 17.64
b. 19
c. 15
Answer:
32. A
33. B
Step-by-step explanation:
32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is
33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end
A sports club was formed in the month of May last year. The function below, M(t), models the number of club members for the first 10 months, where t represents the number of months since the club was formed in May. m(t)=t^2-6t+28 What was the minimum number of members during the first 10 months the club was open? A. 19 B. 28 C. 25 D. 30
Answer:
A: 19
Step-by-step explanation:
For this, we can complete the square. We first look at the first 2 terms,
t^2 and -6t.
We know that [tex](t-3)^2[/tex] will include terms.
[tex](t-3)^2 = t^2 - 6t + 9[/tex]
But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:
[tex]m(t) = (t-3)^2 - 9 +28[/tex]
[tex]m(t) = (t-3)^2 +19[/tex]
Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.
Find X using the Angle Sum Theorem
Answer:
Step-by-step explanation:
x + 30 + 25 = 180
x + 55 = 180
x = 125
y + 125 = 180
y = 55
How many solutions does the system have? x+2y=2 2x+4y=−8
Answer:
Step-by-step explanation:
x + 2y = 2
2x + 4y = -8
-2x - 4y = -4
2x + 4y = -8
0 not equal to -12
no solution
6. Sam is buying tickets to a movie
online. The price of one ticket is $8.50.
An equation showing the total cost is
C = 8.50t +3.50 where t is the
number of tickets and $3.50 is a
convenience fee. What is the total cost
if he buys 4 tickets?
Which term best describes a figure formed by three segments connecting three non Collin ear points
Answer:
Triangle
Step-by-step explanation:
PLS HELP! VERY URGENT PICTURE INCLUDED!!
Answer:
y = 6x ^2 - 6x + 9
Step-by-step explanation:
hopefully it's visible
:)
A recipe says to use 2/3 cup milk to make 4/5 serving of pudding. How many cups of milk are in one serving?
Answer:
[tex]\frac56[/tex] cups
Step-by-step explanation:
The serving size is proportional to the amount of milk used, so we have
[tex]\frac{2/3}{4/5}=\frac x1[/tex]
where [tex]x[/tex] is the amount of milk needed for 1 serving. The right side is simply [tex]x[/tex]. We now simplify
[tex]x=\frac23\cdot\frac54=\frac{10}{12}=\frac56[/tex]
Therefore [tex]\frac56[/tex] cups of milk are needed for 1 serving.
Select the graph of the solution. Click until the correct graph appears.
Answer:
convert the 27 degree into grades
A children's rectangular pool holds 480 cubic feet of water. What is the depth of the pool of its length is 30 feet and it's width is 16 feet
Answer:
1 ft
Step-by-step explanation:
1, 480/30=16
2, 16/16=1
3, 1 ft
A chemical company makes two brands of antifreeze. The first brand is
55%
pure antifreeze, and the second brand is
80%
pure antifreeze. In order to obtain
130
gallons of a mixture that contains
70%
pure antifreeze, how many gallons of each brand of antifreeze must be used?
9514 1404 393
Answer:
52 gallons of 55%78 gallons of 80%Step-by-step explanation:
Let x represent the quantity of 80% solution. Then the quantity of 55% solution is (130-x) and the total amount of antifreeze in the mix is ...
0.55(130 -x) +0.80(x) = 0.70(130)
0.25x +71.5 = 91 . . . simplify
0.25x = 19.5 . . . . . . subtract 71.5
x = 78 . . . . . . . . . . . divide by 0.25; amount of 80%
130-78 = 52 . . . . amount of 55%
52 gallons of the 55% brand, and 78 gallons of the 80% brand must be used.
You catch an expected number of 1.51.5 fish per hour. You can catch a fish at any instant of time. Which distribution best characterizes the number of fish you catch in one hour of fishing
Answer:
The distribution is Poisson distribution
Step-by-step explanation:
From the question we are told that
An expected number of fish was caught per hour is 1.5
The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution
This because generally the Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time
When the scale factor is one what is the ratio of the side length of the side opposite angle a and the length of the hypotenuse
Answer:
me ajuda por favor matemática
The highest mountain in earth is 29,028 ft. The lowest under sea trench is -35,840ft. Which has the highest absolute value
Answer:
undersea trench
Step-by-step explanation:
Absolute value is the distance from zero
The highest mountain trench is |29028| or 29028 ft from zero
The lowest under sea trench is | -35840| of 35840 ft from zero
The highest absolute value is the undersea trench
Height always be positive .
Highest mountain in earth=29028ftAbsolute value:-
[tex]\\ \sf\longmapsto |29028|=29028ft[/tex]
Lowest undersea trench=-35840ftAbsolute value:-
[tex]\\ \sf\longmapsto |-35840|=35840ft[/tex]
Use Lagrange multipliers to minimize the function subject to the following two constraints. Assume that x, y, and z are nonnegative. Question 18 options: a) 192 b) 384 c) 576 d) 128 e) 64
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option C is the correct option
Step-by-step explanation:
From the question we are told that
The equation is [tex]f (x, y , z ) = x^2 +y^2 + z^2[/tex]
The constraint is [tex]P(x, y , z) = x + y + z - 24 = 0[/tex]
Now using Lagrange multipliers we have that
[tex]\lambda = \frac{ \delta f }{ \delta x } = 2 x[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta y } = y[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta z } = 2 z[/tex]
=> [tex]x = \frac{ \lambda }{2}[/tex]
[tex]y = \frac{ \lambda }{2}[/tex]
[tex]z = \frac{ \lambda }{2}[/tex]
From the constraint we have
[tex]\frac{\lambda }{2} + \frac{\lambda }{2} + \frac{\lambda }{2} = 24[/tex]
=> [tex]\frac{3 \lambda }{2} = 24[/tex]
=> [tex]\lambda = 16[/tex]
substituting for x, y, z
=> x = 8
=> y = 8
=> z = 8
Hence
[tex]f (8, 8 , 8 ) = 8^2 +8^2 + 8^2[/tex]
[tex]f (8, 8 , 8 ) = 192[/tex]
Find the value of x show your work
Answer:
x≈13.08
Step-by-step explanation:
We use the pythagora's theorem
[tex]a^{2} +b^2=c^2\\a=5\\b=x\\c=14\\5^2+x^2=14^2\\x^2=196-25\\x^2=171\\x=3\sqrt{19} =13.08[/tex]
opposite rays form a?
line
ray
point
plane
Answer:
ray is the answer for this
opposite rays form a line because they provide the two opposite directions in which the line extends infinitely.
Opposite rays form a what?Opposite rays are two rays that have the same endpoint but extend in opposite directions. When these opposite rays are extended infinitely in both directions, they form a straight line. A line is a set of points that extends infinitely in both directions, and opposite rays provide the two distinct directions in which the line can be extended.
The concept of opposite rays is derived from the concept of a line. A line can be defined as a straight path that extends infinitely in both directions. Opposite rays are a pair of rays that share a common endpoint and extend infinitely in opposite directions along this line.
For example, consider a line segment AB. If we extend one side of the line segment from point A and the other side from point B, we obtain two opposite rays: one from point A to infinity and the other from point B to infinity. Together, these opposite rays form the line on which the line segment AB lies.
Learn more about lines at:
https://brainly.com/question/24607467
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Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
power sharing helps the ruling party to retain power for a long time. tick or wrong
please solve it fastand give the correct answer pleaseeeeee
Answer:
a. False b. True c. True d. False e. False
Step-by-step explanation:
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 15/ms2. If the same force acts upon another object whose mass is
10kg, what is this object's acceleration?
Answer:
[tex]a = 6m/s^2[/tex]
Step-by-step explanation:
Given
When mass = 4kg; Acceleration = 15m/s²
Required
Determine the acceleration when mass = 10kg, provided force is constant;
Represent mass with m and acceleration with a
The question says there's an inverse variation between acceleration and mass; This is represented as thus;
[tex]a\ \alpha\ \frac{1}{m}[/tex]
Convert variation to equality
[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)
Make F the subject of formula;
[tex]F = ma[/tex]
When mass = 4kg; Acceleration = 15m/s²
[tex]F = 4 * 15[/tex]
[tex]F = 60N[/tex]
When mass = 10kg; Substitute 60 for Force
[tex]F = ma[/tex]
[tex]60 = 10 * a[/tex]
[tex]60 = 10a[/tex]
Divide both sides by 10
[tex]\frac{60}{10} = \frac{10a}{10}[/tex]
[tex]a = 6m/s^2[/tex]
Hence, the acceleration is [tex]a = 6m/s^2[/tex]
About 10% of 8900 commuters carpool to work. Find the number of commuters who carpool.
How many commuters carpool?
Answer: 890 commuters carpool
Step-by-step explanation:
10% of 8900 = 890
8900/10= 890
Note: 10% to decimal form is 10
Answer:
10% of 8900
10/100×8900
=890
hope this is helpful
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find area of an older 35-inch television whose screen has an aspect ratio of 4:3
Greetings from Brasil...
The TV format is 4:3.
4 ÷ 3 = 1.33...
Let's assign the smallest side of the TV screen as X. Since the ratio between the sides is 4:3 = 1.33, then the other side (the largest) will be 1.33 times larger than the smaller side X, that is
smaller side = X
bigger side = 1.33X
The diagonal expression of the rectangle is:
D = √(base² + height²)
35" = √[(1.33X)² + X²]
35" = √(1.7689X² + X²) squaring both members
(35")² = 1.7689X² + X²
1225" = 2.7689X²
X² = 1225/2.7689
X² = 442.414
X = √442.414
X ≅ 21"
Tthe bigger side:
1.33X
1.33 · 21 ≅ 28"
Rectangle Area = base × height
Rectangle Area = 28 × 21
Rectangle Area = 588Fill in the following blanks to prove that n 2^1 n < 2^n n+1 < 2^(n+1) is Box 3 Options: True | False Next, assume that Box 4 Options: 1 < 2^1 k + 1 < 2^(k+1) k < 2^k as we attempt to prove Box 5 Options: k < 2^k k + 1 < 2^(k+1) 2 < 2^1 Therefore, we can conclude that Box 6 Options: k < 2^k k + 1 < 2^(k+1) 2^1 < 2^k k + 2 < 2^(k+2)
Answer:
see below
Step-by-step explanation:
n < 2^n
First let n=1
1 < 2^1
1 <2 This is true
Next, assume that
(k) < 2^(k)
as we attempt to prove that
(k+1) < 2^(k+1)
.
.
.
Therefore we can conclude that
k+1 < 2^(k+1)
Answer:
Step-by-step explanation:
Hello, please consider the following.
First, assume that n equals [tex]\boxed{1}[/tex]. Therefore, [tex]\boxed{1<2^1}[/tex] is [tex]\boxed{\text{True}}[/tex]
Next, assume that [tex]\boxed{k<2^k}[/tex], as we attempt to prove [tex]\boxed{k+1<2^{k+1}}[/tex]
Since .... Therefore, we can conclude that [tex]\boxed{k+1<2^{k+1}}[/tex]
The choice for the last box is confusing. Based on your feedback, we can assume that we are still in the step 2 though.
And the last step which is not included in your question is the conclusion where we can say that we prove that for any integer [tex]n\geq 1[/tex], we have [tex]n<2^n[/tex].
Hope this helps.
Do not hesitate if you need further explanation.
Thank you