Answer:
a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.
b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.
Step-by-step explanation:
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
To use the Poisson approximation for the binomial, we have that:
[tex]\mu = np[/tex]
1 in every 2500 automobiles produced has a particular manufacturing defect.
This means that [tex]p = \frac{1}{2500} = 0.0004[/tex]
a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.
This is [tex]P(X = 4)[/tex] when [tex]n = 7000[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558[/tex]
0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.
(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.
Using the approximation:
[tex]\mu = np = 7000*0.0004 = 2.8[/tex]. So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557[/tex]
0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.
the missing exponent 1,728 =12 (?)
Answer:
x=144
Step-by-step explanation:
Under her cell phone plan, Lily pays a flat cost of $55.50 per month and $4 per
gigabyte. She wants to keep her bill at $63.10 per month. Write and solve an equation
which can be used to determine x, the number of gigabytes of data Lily can use while
staying within her budget.
equation:
answer x=
Answer:
Equation : y = 4x + 55.50
x = 1.9 gigabytes
Step-by-step explanation:
Given that:
Flat fee per month = $55.50
Cost per gigabyte = $4
Let,
x be the number of gigabytes.
y be the total cost
y = 4x + 55.50
Lily wants to keep her bill $63.10
63.10 = 4x + 55.50
63.10 - 55.50 = 4x
4x = 7.60
Dividing both sides by 4
[tex]\frac{4x}{4} = \frac{7.60}{4}\\x=1.9[/tex]
Hence,
Equation : y = 4x + 55.50
x = 1.9 gigabytes
Answer:
Equation: 4x+55.5=63.1
Answer: x=1.9
Follow the steps and write the equation represented by this graph.
Step 1: Write the general equation.
Step 2: Identify b, the Y intercept (x = 0) b=
Step 3: The second point from graph (x, y) P=
,
Step 4: Define m as ratio of rise / run m = rise /
Step 5: Put coordinates into ratio and get (7 -
) / (
- 0)
Step 6: Perform subtraction; get slope
/ 1
Step 7: Substitute values into y = mx + b
Step 8: Write answer y =
x +
Answer:
y = 4x + 3
Step-by-step explanation:
Step 1: Write the general equation
y = mx + b
Step 2: Identify b, the Y intercept (x = 0)
b is the value of y when x = 0.
From the graph, when x = 0, y = 3.
Therefore, b = 3
Step 3: The second point from graph (x, y):
P = (1, 7)
Step 4: Define m as ratio of rise / run:
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Step 5: Put coordinates into ratio:
Using the two coordinates, (0, 3) and (1, 7), we would have,
[tex] m = \frac{7 - 3}{1 - 0} [/tex]
Step 6: Perform subtraction to get slope:
[tex] m = \frac{4}{1} [/tex]
m = 4
Step 7: Substitute values into y = mx + b:
Thus, plug in the values of m and b into the slope-intercept equation.
b = 3, m = 4, therefore:
y = (4)x + (3)
Step 8: Write answer:
y = 4x + 3
what is the square root of 430
Answer:
√430 or 20.74
Step-by-step explanation:
√430
Prime factorize 430
√2 · 5 · 43
There are no pairs to take out of the root, so the most simplified form of √430 is √430.
If you want the decimal form, it is 20.74
Please mark me Brainliest :)
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
Y = 0 , X = - 3/2
Step-by-step explanation:
Answer:
just give the brainliest to him
Step-by-step explanation:
9/45 how to simplify to it lowest term
Answer:
1/5
Step-by-step explanation:
divide numerator and denominator by 9.
(Because that will go into both 9 and 45.)
9/45 = 1/5
I WILL GIVE BRAINLIEST PLS I NEED HELP, The scale drawing of a field in the shape of a triangle is shown below.
What is the actual area, in square meters, of this field?
Answer:
20
Step-by-step explanation:
A delivery company has 18 vehicles in its fleet.
It has 8 vans and 10 trucks.
All 18 vehicles are on the road every working day.
The company is reviewing its fuel expenses and therefore
gathers some information about each type of vehicle.
Average distance Average distance
Type of vehicle
travelled ber day (in km) travelled per litre (in km) All the vehicles use the
Van
198
9
same type of fuel at
£1.29 per litre.
Truck
620
6.2
Use this information to work out the total fuel bill for 1 working day.
You must show all your working.
Answer: £1517.04
Step-by-step explanation:
The fuel expenses for the vans will be calculated as:
Vans:
Since the average distance travelled per day is 198km and the average distance travelled per litre is 9km, the van would use:
= 198/9
= 22 litres
Since there are 8 vans, they'll use:
= 22 × 8 = 176 liters
Trucks:
Since the average distance travelled per day is 620km and the average distance travelled per litre is 6.2km, the truck would use:
= 620/6.2
= 100
Since there are 10 trucks, they'll use:
= 100 × 10 = 1000 liters
The amount of liters for both the van and the truck will be:
= 176 liters + 1000 liters
= 1176 liters
The fuel cost will then be:
= 1176 × 1£1.29
= £1517.04
What type of table has the largest area
Answer:
The Rectangular Table Has The largest area of 1460 in^2
Which expression has a value greater than 4^3?
Answer:
(-3)^4
Step-by-step explanation: We just have to evaluate
So, the only expression that exceeds 4^3 is (-3)^4:
what expression is equal to 632
Answer:
2^3(3x5^2+2^2) = 632
Step-by-step explanation:
i big brain
Answer:
Step-by-step explanation:
Jefferson is plotting the vertices of an isosceles triangle on a coordinate graph. He has plotted the two points shown. Where would he plot the three point?
Answer:
4,2
Step-by-step explanation:
Answer:
It is 4, 2
Step-by-step explanation:
Trust me
is -9 greater thank or less than 8
find the value of x in the figure below
Answer:
24
Step-by-step explanation:
cuz its an iscosceles triangle so the angles are the same so
2x-4=44 and solve
A circular mirror has a radius of 6 inches what is the circumference of the mirror
Answer:
37.68
Step-by-step explanation:
pie = 3.14
3.14 x 2 = 6.28
6.28 x 6 = 37.68
Answer: 37.68
Step-by-step explanation:
Sarah used 3 pound of blueberries to make 1 cup of jam. How many pounds of blueberries would she need
42
to make a cup of jam?
Answer:
126 pounds of blueberries
Step-by-step explanation:
1cup of jam=3pounds of blueberries
42cups of jam=?
42 X 3=126
PLSSSSS HELP I HAVE BEEN STUCK ON THIS FOR THE PAST HOUR!!!!!!!!!!!!!!!!!!!!!!!!!
Take a factor out of the square root and simplify the expression:
[tex]-0.05*\sqrt{28,800}[/tex]
Answer:
[tex] - 6 \sqrt{2} [/tex]
Step-by-step explanation:
simplify
[tex] \sqrt{28800} [/tex]
to
[tex]120 \sqrt{2} [/tex]
then
-0.05 × 120 = -6
then we have our answer
-6√2
2y-11=25 solve the equation
Answer:
18
Step-by-step explanation:
25 + 11 = 36
36/2 = 18
hope this helps
Find the zeros of the function.
Enter the solutions from least to greatest.
f(x) = 5x^2 - 20
lesser x =
greater x =
Answer:
lesser x = -2
greater x = 2
Step-by-step explanation:
The values of a function f(x) are the values of x for which f(x) = 0.
In this question:
[tex]f(x) = 5x^2 - 20[/tex]
So, finding the zeros:
[tex]5x^2 - 20 = 0[/tex]
[tex]5x^2 = 20[/tex]
[tex]x^2 = \frac{20}{5}[/tex]
[tex]x^2 = 4[/tex]
[tex]x = \pm \sqrt{4}[/tex]
[tex]x = \pm 2[/tex]
So
lesser x = -2
greater x = 2
A man needed to sell a car. He priced it at 3500 the first day. The second day he reduced the price by 15%. What was the price of the car after this reduction?
Answer:
Step-by-step explanation:b
Holiday dinners at June’s house are always a festive occasion. One particular holiday, June has 16 guests.
June offers the guests apple pie and blueberry pie. While any guest can have slices of both pies, June never serves a particlar guest more than one slice of each pie and each guest is allowed to decline any slice of pie they don’t care for.
June serves a total of 10 slices of apple pie and a total of 11 slices of blueberry pie.
June serves 8 guests slices of both pies.
How many guests had no pie at all?
a. 3
b.2
c.0
Answer:
a. 3
Step-by-step explanation:
We solve this question gathering the information given in the question.
June serves 8 guests slices of both pies.
This is soon going to be used
June serves a total of 10 slices of apple pie
This includes the 8 guests which got served both pieces. So 10 - 8 = 2 guests were served only apple pie.
11 slices of blueberry pie.
By the same logic as above, 11 - 8 = 3 guests were served only blueberry pie.
So
8 + 2 + 3 = 13 guests were served at least one pie.
16 - 13 = 3 guests had no pie at all.
solve the following equation.
2x=4
Answer:
2
Step-by-step explanation:
Which expression is equal to 27 when x = -6?
A (-x)2 - 9
B (-2x)2 - 120
C 10(-x) +33
D 3(x-4) + 3
Answer:
C
Step-by-step explanation:
i got C & D to both be -27 but I think I made a mistake in C w the negatives so I believe it is C.
I hope this helps, have a great day/ night :)
Factor the algebraic expression.
30a + 25
Answer:
5(6a+5)
Step-by-step explanation:
SOLVE FOR X AND Y !! WILL GIVE BRAINLIEST
Answer:
x=21, y=17
Step-by-step explanation:
180-42= 138
2x+138=180
2x= 42
x= 21
8y+2+2x=180
8y+2 + 42=180
8y= 136
y= 17
Answer:
x=21, y=68
Step-by-step explanation:
We're given that the quadrilateral on the left is a parallelogram as indicated by the arrow markings on the sides. We're also told that the angle on the right is 42 degrees. So, we can find the bottom right angle in the parallelogram by subtracting 42 from 180, because it forms a straight angle. 180-42 is 138. By the alternate interior angles theorem, 8y+2=138, because 138 is also the angle measure of the opposite corner. we also know that the bottom left angle in the parallelogram is the same as 2x. by the alternate interior angles theorem. Notice how the sides of the parallelogram with two arrow markings are parallel, which means that the bottom left angle and the 42 degree angle are congruent, or have the same measure, because of the parallel lines. This means that 2x=42, and the bottom left angle is 42. We can solve for x and y with simple algebra now. 8y+2=138, 8y=138-2, 8y=136, y=68. 2x=42, x=42/2, x=21. So, x is 21 and y is 68.
How many 1 1/2 -pound loaves of bread can be made from 9 pounds of dough?
Answer:
6
Step-by-step explanation:
You divide 9 by 1 1/2.
Why does 3x4 and 3x4 the same answer?
Answer:
bc the are both the same numbers. So the answer is 12. :>
Step-by-step explanation:
Answer:
because thay are the same problom
Step-by-step explanation:
3x4 is 12
Help ME PLSSS HURRY!!!!!!
Answer:
None of them are proportiionsal
Step-by-step explanation:
Answer:
i don't even see any proportiionsal
Step-by-step explanation:
Over the course of 6 days Tonda ran 17.22 miles She ran the same distance each day How far did Tonga run each day ?
Work Progress: 17.22mile/6 days = 2.87
Tonda ran 2.87 miles each day.
Answer:
103.32
Step-by-step explanation:so what you need to do is times the decimals so: 17.22 x 6 = 103.32
For what value of x is the rational expression below equal to zero?
X-4
X5
A. -6
B. -4
C. 6
D. 4