The Probability of red light is 0.3
P(red) = 0.3
The probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light be 0.25.
P(exactly three get stopped by red light)=0.25
The correct option is (d) P(red)=.3,P(exactly 3 get stopped)=.25
What is Binomial distribution?
A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.
The occurrence,
Red light= 15 sec, Yellow light= 5 sec, Green light= 15 secp= probability of a red light
=[tex]\frac{15}{15+5+30}[/tex]
= [tex]\frac{15}{50}[/tex]
= 0.3
Hence, Probability of getting red light be,
P (red)= 0.3
Now, the Binomial distribution formula,
Probability=( [tex]_r^nC[/tex])[tex]\;p^{r} \;q^{n-r}[/tex]
where, r = number of times for a specific outcome within n trials
[tex]_r^nC[/tex] = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trial
According to question,
r= 3 (Exactly three)n=8 (eight eastbound)p(red) =0.3q= 1 -p= 1- 0.3
= 0.7
Now using the formula, ( [tex]_r^nC[/tex])[tex]\;p^{r} \;q^{n-r}[/tex]
P( exactly 3 get stopped) = ( [tex]_3^8C[/tex])[tex]\;(0.3)^{3} \;(0.7)^{8-3}[/tex]
= [tex]\frac{8!}{3!(8-3)!}[/tex] [tex](0.027) \; (0.7)^{5}[/tex]
= [tex]\frac{8!}{3!(5)!}[/tex][tex](0.027) \; (0.16807)[/tex]
= [tex]\frac{8 * 7 * 6 }{3 * 2}[/tex] x 0.027 x 0.16807
= 56 x 0.00453789
= 0.25412184
≈ 0.25
Hence, Probability of next eight eastbound so that exactly three will stopped by a red light be 0.25.
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Look at the image for the instructions! I need this asap! I will give points, 5 stars and brainliest ((:
(This is an essay)
Answer:
1. one is smaller by 5 cm and one is larger by 5 cm
2. well they are similar to each other, but one is dilated and isn't
Draw a right trapezoid with bases of 8 and 10 cm
Answer:
Here is a picture of a right trapezoid with bases of 8 and 10 cm
Solve the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5), Dg=(-∞,4)
For the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5) the solution is mathematically given as
1 ≤ x < 6
What is the following inequalities g(5-x^2)≤g(3x-5)?
Generally, the equation for the inequalities is mathematically given as
g(5-x^2)≤g(3x-5)
therefore,
x^2<5x+6
-1< x <6
In conclusion, the solution to the inequalities are
1 ≤ x < 6
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Can you please help me really quick I need help with this
Check the picture below.
Adult tickets for the evening show at XD Theater are $16 and children's tickets are $8. If the theater seats 282 people, how many adult
tickets must be sold for $2416 of total sales?
please solve for x 3x + 22
Answer:
The x intercept is [tex](-\frac{22}{3} ,~0)[/tex]
The y intercept is [tex](0,~22)[/tex]
find the are of the shape below
Answer:
Area is 235
Step-by-step explanation:
Split the shape evenly so 11 x 14 and 9 x 9then multly and add
when slpitting up the number some times you have to add or subtract so to get 9 x 9 we just take 20 then take away 11 due to the line going through 20 and 20 - 11 = 9
9 x 9 = 81
11 x 14 = 154
81 + 154 = 235
or
Simular to the first one but the cutting line is different. this time the line cuts through 14
9 x 20 = 180
11 x 5 = 55
180 + 55 = 235
lily and Aiko think of a whole number aiko's numbers of 2000 when rounded to the nearest 1000 lily's number 1900 when rounded to 100 Aiko says "my number larger than Lily's!" is Aiko correct?
he has a higher chance of having the larger number but that does not make him correct
Step-by-step explanation:
Aikos number can be any where from 1501 all the way to 2499 while lily's number would have to be between 1851 and 1949.
What is the length of the missing leg? If necessary, round to the nearest tenth
Answer:
Solution
Here,
H=?
P=3
b=6
H=√p2+B2
=√6×6+3×3
=√36+9
=√45
=3√5
Answer:
23
Step-by-step explanation:
a^2 + b^2=c^2
3=a^2
6=b^2
3×3= 9
6x6=36
36+9=45
45÷2=22.5
Let p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x. Define r(x) = p(x) \cdot q(x).
Find all values of x for which r(x) = 0.
The roots of the entire polynomic expression, that is, the product of p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x, are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6.
How to solve a product of two polynomials
A value of x is said to be a root of the polynomial if and only if r(x) = 0. Let be r(x) = p(x) · q(x), then we need to find the roots both for p(x) and q(x) by factoring each polynomial, the factoring is based on algebraic properties:
r(x) = (x + 6) · (x + 2) · x · (x² + 5 · x - 6)
r(x) = (x + 6) · (x + 2) · x · (x + 3) · (x + 2)
r(x) = x · (x + 2)² · (x + 3) · (x + 6)
By direct inspection, we conclude that the roots of the entire polynomic expression are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6. [tex]\blacksquare[/tex]
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5. Which side lengths form a right triangle?
Check all that apply.
Answer:
=> 6.5, 7.2 , 9.7
Step-by-step explanation:
By using Pythagorean theoram
H² = P² + B²
=> (9.7)² = (7.2)² + (6.5)²
=> 94.09 = 51.84 + 42.25
=> 94.09 = 94.09
The tank of a car holds 10 gallons of gas.
How many liters does the tank hold? Round to the nearest tenth.
Answer:
37.9 liters
Step-by-step explanation:
Multiply the number of gallons by 3.785 to convert to liters
Multiplying by ten moves the decimal point over to the right
3.785 * 10 = 37.85
The tenths place is where the 8 is, and since 5 is [tex]\geq[/tex] (greater than or equal to) 5 that makes the 8 round up to a 9
resulting in...
10 gallons = 37.9 liters
hope this helps:)
Last year the depth of the river was 4.2 feet deep. This year it dropped 9% Find the depth of the river this year
Answer: 3.822
Step-by-step explanation: 9/100 × 4.2 = 0.378
Deduct from 4.2
what is the median in 72 77 75 72 70 69 71 78 75 68 62 69 65 63 68 53 57 79 77 75 80 73 71 64 71 64 50 50 55 55
Answer:
The median is 69.5
Step-by-step explanation:
The median is also known as the middle value. To find the median, you first arrange your data in numerical order.
Numerical order:
50, 50, 53, 55, 55, 57, 62, 63, 64, 64, 65, 68, 68, 69, 69, 70, 71, 71, 71, 72, 72, 73, 75, 75, 75, 77, 77, 78, 79, 80
There are 30 numbers, which means that the median is between the 15th and 16th value (69 and 70).
69 + 70 = 139
139/2 = 69.5
Therefore, the median of this data set is 69.5
Hope this helps!
6. A rectangle with a length of 15 feet has a
diagonal that measures 17 feet. Find the
perimeter of the rectangle.
Answer:
46 feet
Step-by-step explanation:
it is a 8-15-17 Pythagorean Triple (or you can use the Pythagorean theorem)
P=8+8+15+15=46
The perimeter of the rectangle with a length of 15 feet and has a diagonal that measures 17 feet is: A. 46 feet.
What is the Perimeter of a Rectangle?To find the perimeter of the rectangle, we need to know the width of the rectangle. Let's call the width of the rectangle W.
In a rectangle, the diagonal, length, and width are related by the Pythagorean theorem:
Diagonal² = Length² + Width²
In this case, the diagonal (D) is 17 feet, and the length (L) is 15 feet. So we have:
17² = 15² + W²
289 = 225 + W²
Now, let's solve for W:
W² = 289 - 225
W² = 64
W = √64
W = 8 feet
Now that we know the width is 8 feet, we can calculate the perimeter (P) of the rectangle:
Perimeter = 2 * (Length + Width)
= 2 * (15 + 8)
= 2 * 23
Perimeter = 46 feet
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27
5
to a mixed number
a
decimal.
Answer: 5.4 and 5⅖
Step-by-step explanation:
27/5 to a mixed number 5⅖
Decimal 5.4
A sample of students is taken from the school's A honor roll. The school
estimates that there are 360 students on the A honor roll. Using this sample,
how many students on the A honor roll are 8th graders?
Answer:
There are 126 8th grade A honor roll students.
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
c
Step-by-step explanation:
because 3 x 3 = 9
1 x 5 = 5
simplest form will be 1 4/5
16 Select the correct answer. Jonathan opened an auto repair shop. In the first month, 11 cars were serviced at his shop. After the first month, the total number of cars serviced at Jonathan's shop increased by 9 cars per month. How many total cars were serviced at Jonathan's shop at the end of the 7th month? O A 75 cars OB. 86 cars Oc 74 cars OD 65 cars Reset Net l rights reserved.
I just need help please
Answer:
65 cars
Step-by-step explanation:
In the first month, there are 11, then the cars increased by 9 for the last 6 months, meaning you can do 6*9=54
You can then add that to 11, which is 11+54=65
Help pls
What is the value of RS?
Answer:
RS = 16
Step-by-step explanation:
If a line is parallel to a side of a triangle and intersects the other 2 sides , it divides those sides proportionally.
PR is such a line , then
[tex]\frac{QR}{RS}[/tex] = [tex]\frac{QP}{PT}[/tex] ( substitute values )
[tex]\frac{32}{RS}[/tex] = [tex]\frac{42}{21}[/tex] = 2 ( multiply both sides by RS )
32 = 2 RS ( divide both sides by 2 )
16 = RS
Answer:
Your answer is, RS- 16.
Step-by-step explanation:
I hope this helps you :)
pls mark brainleist :P
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W/ <3...
Tori
‼️⚠️⚠️‼️ HELP PLEASE WILL GIVE POINTS
Answer:
m∠ABC=42°
Step-by-step explanation:
m∠ABD=70°
⇒m∠ABD=m∠ABC+m∠CBD
⇒70°=(3x+33°)+(5x+13°)
70°=8x+46°
70°-46°=8x
24°=8x⇒x=3°
x=3°
Then,
m∠ABC=3x+33°
put x=3°, we get
m∠ABC=3×3°+33°=9°+33°
m∠ABC=42°
Which equation represents the graphed function? –3x 2 = y –x 2 = y x – 3 = y 2x – 3 = y
Answer:
C) 3/2x-3=y
Step-by-step explanation:
-3 because that is the Y- intercept and 3/2 is the slope of the line. Y= mx +b is the formula and m is the slope and b is the y intercept.
- A new rectangular lawn has a
perimeter of 298 ft. and a width of
67 ft. A bag of grass seed will cover
285 ft2 of ground. How many bags
of grass seed are needed to seed
the new lawn?
The number of bags of grass seed that are needed to seed the new rectangular lawn is approximately 19 bags .
Perimeter of a rectangle
The perimeter of a rectangle is the sum of the whole sides of the rectangle.
Therefore,
perimeter of the rectangle = 298 ft
The width is 67 ft.
Hence
perimeter of rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
298 = 2 ( l + 67)
298 = 2l + 134
298 - 134 = 2l
164 = 2l
l = 164 / 2
l = 82 ft
Therefore,
area of the rectangle = 82 × 67 = 5494 ft²
285 ft² = 1 bag of grass seed
5494 ft² = ?
cross multiply
number of bag of grass seed to fill the new rectangular lawn = 5494 / 285
number of bag of grass seed to fill the new rectangular lawn = 19.2771929825
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Don't Send links, don't Write random things and get the points for free.
Answer:
2,714in^3
Step-by-step explanation:
V = pi*r^2*h
V = 3.14*6^2*24
V = 3.14*36*24
V = 2,714
The volume of the cylindrical fish tank is 2,714 inches cubed.
Answer:
Option A, [tex]2714\ in^3[/tex]
Step-by-step explanation:
Step 1: Determine the volume of the cylinder
[tex]V=\pi r^2h[/tex]
[tex]V=\pi *(12\ in/2)^2*24\ in[/tex]
[tex]V=\pi *(6\ in)^2*24\ in[/tex]
[tex]V=\pi * 36\ in^2 *24\ in[/tex]
[tex]V = \pi *864\ in^3[/tex]
[tex]V=2,714\ in^3[/tex]
Answer: Option A, [tex]2714\ in^3[/tex]
f x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?
What's the range of f(x)=x+6 if x ∈(-4,-1)
Answer:
the range of is (2 , 5)Step-by-step explanation:
f(x)=x+6
f is an increasing function then the range of is
f(-4,-1) = (f(-4) , f(-1))
f(-4) = -4 + 6 = 2
f(-1) = -1 + 6 = 5
Therefore
the range of is f(-4,-1) = (2 , 5)
What expression is equivalent to 4 (3x-2)
Answer:
12x-8
Step-by-step explanation:
In order to take away the parentheses, we have to multiply all terms inside the parentheses by 4. 4*3x = 12x, and -2*4 = -8. So we can determine at 4(3x-2) = 12x-8.
Sally's soccer team played 25
games this season and lost 9 of
those games. What percent of the
games did the team win?
Answer:
64%
Step-by-step explanation:
25 - 9 = 16, so 16 of the games were won by Sally's team.
16/25 = 64% of the games were won
What are the y-intercept and the horizontal asymptote of g(x) = 7x + 2?
(0, 3) ; y = 2
(0, 4) ; y = 7
(0, 7) ; y = 2
(0, 9) ; y = 7
please hurry
Put x =0 to find y intercept
7(0)+20+22Y intercept:-
(0,2)Horizontal asymptote=y=2
30 points pls helppp
Select the equation of the line that passes through the point (2, –1) and has slope 3 in point-slope form.
(y + 1) = 3(x – 2)
(y – 1) = 3(x + 2)
(x + 2) = 3(y – 1)
(x – 2) = 3(y + 1)
Answer:
(y + 1) = 3( x +2)
Step-by-step explanation:
from equation,
y - y1 = m( x - x1)
given x1=2, y1= -1
m = 3 (slope)
substitute
y - (-1) = 3( x - 2)
ans: y+1= 3(x+2)