Answer:
Explained below.
Step-by-step explanation:
Let X = number of trucks that will be going over the speed limit on I-77 South between Dobson and Elkin.
The probability of X is, p = 0.75.
A random sample of n = 5 trucks are observed on this stretch of I-77.
The random variable X follows a binomial distribution with parameters n = 5 and p = 0.75.
(a)
Compute the mean as follows:
[tex]\mu=n\times p=5\times 0.75=3.75[/tex]
The mean of this probability distribution is 3.75.
(b)
The mean of 3.75 implies that on average 3.75 trucks that will be going over the speed limit on I-77 South between Dobson and Elkin.
(c)
Compute the standard deviation as follows:
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{5\times 0.75\times (1-0.75)}=0.968[/tex]
Thus, the standard deviation of this probability distribution is 0.97.
(d)
Compute the probability that exactly 3 of the observed trucks are speeding as follows:
[tex]P(X=3)={5\choose 3}(0.75)^{3}(1-0.75)^{5-3}\\\\=10\times 0.421875\times 0.0625\\\\=0.263671875\\\\\approx 0.2637[/tex]
Thus, the probability that exactly 3 of the observed trucks are speeding is 0.2637.
(e)
Compute the probability that less than 3 of the observed trucks are speeding as follows:
[tex]P(X<3)=P(X=0)+P(X=1)+P(X=2)\\\\=\sum\limits^{2}_{x=0}{{5\choose x}(0.75)^{x}(1-0.75)^{5-x}}\\\\=0.0009765625+0.0146484375+0.087890625\\\\=0.103515625\\\\\approx 0.1035[/tex]
Thus, the probability that less than 3 of the observed trucks are speeding is 0.1035.
Carlos has saved $19.80. Shaq saved 5/6 of the amount that Carlos saved. Deontae saved 4 times as much as shaq. What is the total saved amount of all threw
please help am confused
Answer:
9%Step-by-step explanation:
432 ÷ 6 = 72
8 = 1% of 800
8 x 9 = 72 = 9%
Step-by-step explanation:
I = P×r%×t
432 = 800 × r/100 × 6
432 = 4800 × r/100
[tex]r = \frac{432 \times 100}{4800} [/tex]
r = 9%
1/3 x + y = 4 solve for y
The simplified answer to the equation is [tex]y=-\frac{1}{3}x+4[/tex]
First, subtract [tex]\frac{1}{3}x[/tex] on both sides.
[tex]y=-\frac{1}{3}x+4[/tex]
You have isolated [tex]y[/tex] by itself, and the equation can't be simplified further, so [tex]y=-\frac{1}{3}x+4[/tex] is your answer.
1 gallon is equal to 4 quarts (conversion factor). How many gallons do you have if you have 18 quarts?
START END CONVERSION FACTOR(s) SOLUTION
Answer:
4.5 gallons
Step-by-step explanation:
18/4
After conversion 18 gallons will be equal to 4.5 quarts .
Given,
1 gallon is equal to 4 quarts
Convert 18 quarts to gallons
Few unit conversions :
Conversion Factors:
1 mile = 5280 feet
1 foot = 12 inches
1 inch = 2.54 cm
1 cm = 10 mm
1 second = 1 s
Now 1 gallon is equal to 4 quarts ,
Here,
1 gallon = 4 quarts
Hence ,
18 quarts = 4.5 quarts .
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in a geometrical progression,the product of the 2nd and 4th term is double the the 5th terms. and the sum of the first four terms is 80 find the G.p
The 15th term of the geometric progression is 9,565,94.
What is the 15th term of the geometric progression?A geometric progression can be expressed as an = a1rn-1 for some a1 and r. You are told that a2 * a4 = 2a5 and a1 + a2 + a3 + a4 = 80.
From the first equation, a2 = a1 r, a4 = a1 r3, and a5 = a1 r4. This tells us that
a1 r a1 r3 = 2 a1 r4
The r's and one a1 cancel leaving a1 = 2.
Now, plugging similarly into a1 + a2 + a3 + a4 = 80,
2 + 2r + 2r2 + 2r3 = 80
r3 + r2 + r + 1 = 40
In general, the easiest way to solve a cubic is by graphing, but here you know the answer will be a small integer, so just try a few. If we try r=3, we get 27 + 9 + 3 + 1 = 40 so r = 3.
So the geometric sequence here is an = 2 3n-1. The 15th term is then:
a15 = 2*3^14
a15 = 9,565,938.
Full question:
A G.P, the product of the 2nd and the 4th term is double the 5th term, and the sum of the first 4th terms is 80. find the 15th term.
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Which expression is equivalent to one over five m − 20? (4 points)
A one over five (m − 4)
B one over five (m − 100)
C 5(m − 4)
D 5(m − 100)
HELP ASAP
Answer:
The equivalent to one over five m − 20 is one over five (m − 100) ⇒ B
Step-by-step explanation:
Let us solve the question
∵ One over five means [tex]\frac{1}{5}[/tex]
∴ One over five m - 20 = [tex]\frac{1}{5}[/tex] m - 20
→ By using the distributive property, take one over five as a common factor
from both terms
∴ [tex]\frac{1}{5}[/tex] m - 20 = [tex]\frac{1}{5}[/tex] [tex](\frac{\frac{1}{5}m}{\frac{1}{5}}[/tex] - [tex]\frac{20}{\frac{1}{5}})[/tex]
→ Simplify the bracket
∵ [tex]\frac{1}{5}[/tex] m ÷ [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{5}[/tex] m × 5 = m
∵ 20 ÷ [tex]\frac{1}{5}[/tex] = 20 × 5 = 100
∴ [tex]\frac{1}{5}[/tex] [tex](\frac{\frac{1}{5}m}{\frac{1}{5}}[/tex] - [tex]\frac{20}{\frac{1}{5}})[/tex] = [tex]\frac{1}{5}[/tex] (m - 100)
∴ [tex]\frac{1}{5}[/tex] m - 20 = [tex]\frac{1}{5}[/tex] (m - 100)
The equivalent to one over five m − 20 is one over five (m − 100)
Someone help me pls , i really wouldn’t like to fail :(
Answer:
the answer to that is gonna be B
Step-by-step explanation:
i just looked at the x's and divided them by 2 and compared the answers to y and those were the only ones that seemed to work lol..
A basketball team played five games. In those games, the team won by 7 points, lost by 3, won by 4, lost by 2, and won by 9. What was the mean difference in game scores over the five games? The mean difference in game scores over the five games was
Given:
A basketball team played five games.
In those games, the team won by 7 points, lost by 3, won by 4, lost by 2, and won by 9.
To find:
The mean difference in game scores over the five games.
Solution:
Total number of games = 5
Scores in 5 matches are 7, -3, 4, -2, 9.
Positive sign is used for winning and negative sign is used for losing the game.
We know that,
[tex]Mean=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
[tex]Mean=\dfrac{7-3+4-2+9}{5}[/tex]
[tex]Mean=\dfrac{20-5}{5}[/tex]
[tex]Mean=\dfrac{15}{5}[/tex]
[tex]Mean=3[/tex]
Therefore, the mean difference in game scores over the five games was 3.
ILL MARK BRAINLIST IF YOU SHOW YOUR WORK and get it right ....... Simplify 42/70
Find the GCF(Greatest Common Factor) of 42 and 70: 14
Divide numerator and denominator by the GCF.
42 ÷ 14 = 3
70 ÷ 14 = 5
3/5
Answer:
3/5
Step-by-step explanation:
Think of the GCF of 42 and 70
which is 14 divide by 14 which you will get 3/5
(Alternate method)
If you don't know how to do that I will try to divide by the prime numbers like: 2,3,5,7 etc
until you get to a answer that can't be divided anymore
Hope this helps!
The ratio of men to woman working for a company id 5 to 8. if there are 208 woman working for the company, what is the total numbers of employees
The ratio 0f men to worm is 5 to 8, so for every 8 women there are 5 men.
Divide the total woman by 8 and then multiply that by 5.
208/8 = 26 x 5 = 130
There is 130 men.
-6=2/3x What does x equal
Answer:
x = -9 :)
Step-by-step explanation:
solve for x by simplifying both sides of the equation then isolating the equation
brainliest pls if correcto
Plz help!!! Will mark brainliest!!!!!!
0.6×100 is equal to
Answer:
60
Step-by-step explanation:
.6 x 100 = 60
Which theorem correctly justifies why the lines m and n
are parallel when cut by transversal k?
converse of the corresponding angles theorem
converse of the alternate interior angles theorem
converse of the same side interior angles theorem
converse of the alternate exterior angles theorem
Name a point non-complanar to plane K
Answer:
did you attach an image?
Step-by-step explanation:
We have a figure given in question.
We have to find a point non-coplanar to plane K.
What is Coplanarity of points?Two or more points are coplanar if they lie on the same plane in the three dimensional coordinate system. If they don't lie on the same plane, then they are called non - coplanar.
According to the question, we have to find a point non-coplanar to
plane K.
All the points except points W and Y lie on plane K. Hence, W and Y are the two points that do not lie on the K - plane.
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HIN
The cliff dwellings in Mesa Verde
National Park are accessible to visitors
only when accompanied by a park
ranger. Billy is at a cliff dwelling in
Mesa Verde National Park. So, Billy
(is, may be, is not) with a park ranger.
Deductive reasoning
Answer: Be careful !
Billy is with a park ranger. Should be correct BUT
It is not given that Billy is visiting the cliff dwelling.
Billy may be the Park Ranger.
So Billy may be with a park ranger.
Step-by-step explanation:
Can you also tell me if the others are right? please?
Answer:
the others are right
Step-by-step explanation:
good work keep going
20 POINTS! HELP ME PLZZ I NEED HELP WITH THIS! IS THIS RIGHT!
Answer:
A
Step-by-step explanation:
can a triangle have an exterior angle that is obtuse at two vertices? Explain
Answer:
Yes
Step-by-step explanation:
An obtuse triangle will have two obtuse angle at its exterior.
Take for instance, the angles in the triangle are 100, 40 and 40.
The exteriors would be 80, 140, 140 (this is gotten by subtracting each interior angles from 180).
So, using the above analysis, we can conclude that the statement is possible.
A fish population, p, can be represented by the equation p = 800 . 1/2 where t is time in years since the beginning of 2015. What was the fish population at the beginning of 2012? A. 100 B. 800 C. 2,400 D. 6,400
Answer:
D. 6,400
Step-by-step explanation:
I got it right
The fish population at the beginning of 2012 is 100.
GivenA fish population, p, can be represented by the equation;
[tex]\rm P =800 \left (\dfrac{1}{2} \right)^t[/tex]
Where t is time in years since the beginning of 2015.
How to determine the population at the beginning of 2012?The expression represents the number of population in the year 2015 so first take the difference between the year 2015 and 2012 which is 3 then substitute the 3 in the given equation and solve.
The difference between year 2015 and 2012 is;
t = 2015 - 2012 = 3
Substitute the value of t in the equation
[tex]\rm P =800 \left (\dfrac{1}{2} \right)^t\\\\\rm P =800 \left (\dfrac{1}{2} \right)^3\\\\P = 800 \times \dfrac{1}{8}\\\\P = 100[/tex]
Hence, the fish population at the beginning of 2012 is 100.
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The ratio of money in Terry's bank account to Faye's bank account was 3:7.
Terry then put £220 in his account and Faye withdrew £300 from her account.
They now had the same amount in their accounts.
How much did Terry initially have?
Answer:
£390
Step-by-step explanation:
The ratio of money in bank:
Terry : Faye
3 : 7
Terry put £220 in his account
Faye withdrew £300 from her account
Unknown:
Initial amount Terry had = ?
Solution:
Let the real amount terry has = 3x
Faye will have = 7x
Now;
3x + 220 = 7x -300
Solving this equation:
3x + 220 = 7x -300
3x - 7x = -300 - 220
-4x = - 520
4x = 520
x = 130
Originally, Terry has 3x = 3 x 130 = £390
Which table was created using the equation y = 4x +4?
Answer:
x -2, -1, 0 1 2
y-4 0 4 8 12
Step-by-step explanation:
i think...
Answer:
X Y
1 8
2 12
3 16
4 20
5 24
Step-by-step explanation:
I'm not seeing a table so I assume you need to creat one
there are 49 mangoes and 63 avocado's to be sold as part of the fair is school. the organizer wants the same number of items of fruits in each bag. mangoes and avocado's should not be mixed. what is the greatest number of each fruit that can be placed in a bag? A) 7 B) 8 C) 9 D) 10
Answer:
9
Step-by-step explanation:
Anita is filling a small pool for her kids. Currently, there are 60 gallons of water in the pool and she is filling the pool at a rate of 50 gallons every 5 minutes. The pool holds 200 gallons of water.
Which equation represents the amount of minutes (m) that it will take to fill the pool?
-10m + 200 = 60
50m +200 = 60
-10m + 140 = 60
-50m +140=60
Answer:
M/140 = 50/60
Step-by-step explanation:
Since the total is 200 it will be the denominator but we already have 60 gallons so we do 200-60=140
the ratio is 50 per 60
Mrs adeolu spent 1/4 of her monthly income at a shopping mall 1/3 at a open market and 2/5 of the remaining amount at a mechanic workshop. if she had 225,000 naira left .
find her monthly income
find the amount spent at the open market
Answer: it's c
Step-by-step explanation:
Suppose the parallelogram JKLM has vertices:
J (2, 1)
K (7, 1)
L (6, −3)
M (1, −3)
Write each transformation in function notation and find the new coordinates of each point.
1. J' if the parallelogram is rotated counterclockwise 270° about the origin?
2. K' if the parallelogram is rotated counterclockwise 180° about the origin?
3. L' if the parallelogram is rotated counterclockwise 90° about the origin?
4. M' if the parallelogram is rotated counterclockwise 90° about the origin?
I NEED HELP
Answer:
1. For a rotation of 270° counterclockwise about the origin the coordinates of J' is (1, -2)
2. For a rotation of 180° counterclockwise about the origin the coordinates of K' is (-7, -1)
3. For a rotation of 90° counterclockwise about the origin the coordinates of L' is (3, 6)
4. For a rotation of 90° counterclockwise about the origin the coordinates of M' is (3, 1)
Step-by-step explanation:
The coordinates of the vertices of the parallelogram are given as follows;
J(2, 1), K(7, 1), L(6, -3), M(1, -3)
1. We have, for a rotation of 270° counterclockwise about the origin we have
f(x, y) = (y, -x)
Therefore, we have for the vertices;
f(J(2, 1)) = J'(1, -2)
Therefore, we have the coordinates of J' as (1, -2);
2. We have, for a rotation of 180° counterclockwise about the origin we have
f(x, y) = (-x, -y)
Therefore, we have for the vertex point K;
f(K(7, 1)) = K'(-7, -1)
3. We have, for a rotation of 90° counterclockwise about the origin we have
f(x, y) = (-y, x)
Therefore, we have for the vertex point L;
f(L(6, -3)) = L'(3, 6)
4. We have, for a rotation of 90° counterclockwise about the origin we have
f(x, y) = (-y, x)
Therefore, we have for the vertex point M;
f(M(1, -3)) = M'(3, 1)
4 x 105 in standard notation
Answer:
Lol its 420
Step-by-step explanation:
11a − 2a = 9 what does a=
Answer:
a=1
Step-by-step explanation:hhqhhahehh
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2a equals negative 2 and StartFraction 3 Over 4 EndFraction. when a = –2a equals negative 2 and StartFraction 3 Over 4 EndFraction.. Which equation represents this direct variation between a and b?
Answer:
B
Step-by-step explanation:
The equation that represents this direct variation between a and b is:
b = -a. See explanation below.
What is a Direct variation?
Direction Variation is best defined as an equation in which one variable equals a constant times the other can be used to express a mathematical relationship between two variables.
Hence it is correct to state that The equation that represents this direct variation between a and b is: b = -a
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1. Transform pentagon BEARS According to (x,y) → (x + 6, y + 8). Write the coordinates for
pentagon B'E'A'R'S' and sketch pentagon B'E'A'R'S' on the same coordinate plane
Answer:
2,1
Step-by-step explanation: