If a seed is planted, it has a 90% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that exactly 2 don't grow
Answer:
0.2301 = 23.01% probability that exactly 2 don't grow.
Step-by-step explanation:
For each seed planted, there are only two possible outcomes. Either it grows into a healthy plant, or it does not. The probability of a seed growing into a healthy plant is independent of any other seed, which means that the binomial probability distribution is used to solve this question.
Binomial probability 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.
90% chance of growing into a healthy plant.
This means that [tex]p = 0.9[/tex]
12 seeds are planted
This means that [tex]n = 12[/tex]
What is the probability that exactly 2 don't grow?
So 12 - 2 = 10 grow, which is [tex]P(X = 10)[/tex]. Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{12,10}.(0.9)^{10}.(0.1)^{2} = 0.2301[/tex]
0.2301 = 23.01% probability that exactly 2 don't grow.
Consider the function h(x) =StartFraction 1 Over x EndFraction . Which graph shows h(2x) + 4? On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It goes through (0.5, 1), (1, negative 2), and (2, negative 3). Another curve opens down and to the left in quadrant 3. It goes through (negative 4, negative 4.5) and (negative 2, negative 5). On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It approaches the y-axis in quadrant 1, and then curves down through (0.5, negative 3) and then approaches y = negative 4. Another curves opens down and to the left in quadrant 3. It approaches y = negative 4 and then curves down through (negative 1, negative 4.5). On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (2, 5) and (3, 4.5). Another curve opens down and to the left in quadrants 2 and 3. It goes through (negative 1, 2) and curves down through (negative 0.5, negative 1). On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (1, 4.5) and (4, 4). Another curve opens down and to the left in quadrants 2 and 3. It approaches y = 4 and then curves down and approaches the y-axis in quadrant 3. Mark this and return
Answer:
Graph D
Step-by-step explanation:
correct answer on edge :)
Answer:
D
Step-by-step explanation:
A club of 10 people wants to choose an executive board consisting of president, secretary, treasurer, and three other officers. In how many ways can this be done
Answer:
The number of ways = 151200
Step-by-step explanation:
Below is the calculation of the number of ways:
Total number of people = 10
Total number of posts = 6
The number of ways = 10P6
The number of ways = [tex]\frac{10!}{10! - 6!}[/tex]
The number of ways = 10 x 9 x 8 x 7 x 6 x 5
The number of ways = 151200
If a silver alloy that costs $6.75 an ounce is
going to be mixed with 55 ounces of a silver
alloy that costs $10 an ounce to make a
mixture that costs $8 an ounce, how many
ounces of the $6.75 an ounce alloy must be
used?
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Answer:
88 ounces
Step-by-step explanation:
Let x represent the number of ounces of the less expensive alloy in the mix. Then the cost of the mix will be ...
6.75x +10(55) = 8(55+x)
110 = 1.25x . . . . . . subtract 440+6.75x
88 = x . . . . . . . . divide by 1.25
88 ounces of $6.75/oz silver must be used.
What is the value of x if 2/ 3 - 2 = -4 ?
Answer:
x= -3
Step-by-step explanation:
(2x/3)-2=-4
Add 2 to both sides
2x/3=-2
multiply both sides by 3
2x=-6
divide both sides by 2
x= -3
Answer:
x = -3
Step-by-step explanation:
2x/3 - 2 = -4
Add 2 to both sides.
2x/3 = -2
Multiply both sides by 3/2.
x = -2 * 3/2
x = -3
If U= {1,2,3,......8} , A={1,4,6,7} , B= {2,4,5,7} & C= {3,5,6,7} prove that 1) An( BUC ) = ( AnB) U ( AnC ). 2) AU (BnC)= (AUB) n ( AUC )
Step-by-step explanation:
BUC={2,3,4,5,6,7}
An(BUC)={4,6,7}
AnB={4,7},AnC={6,7}
(AnB)U(AnC)={4,6,7}
Au(BnC)={1,4,5,6,7}
(AUB)n(AUC)= {1,4,5,6,7}
PLEASE I NEED SO MUCH HELP HERE!!!!!!
the old building at the back of the school is badly in need of repair. the company Hsa and the executive are planning to renovate the building to accommodate a new music room. There are 15 rooms in the building and the dimension of the rooms to be redone with tiles are 6m long and 4 m wide. ted the tile man has 500 one meter square tiles.
Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?
How many tiles, each measuring 1 square meter, are needed to cover one room floor?
How many tiles are needed to cover all the floors in the entire building? Show your work?
Answer:
a. If the area of the tiles is greater than or equal to the area of all the rooms.
b. 24
c. 360
Step-by-step explanation:
a. Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?
Ted would have enough tiles if the area of the tiles is greater than or equal to the area of all the rooms. Since we have 500 one meter square tiles, we have 500 m² of tiles.
Since the rooms are 6 m long and 4 m wide, the area of each room is 6 m × 4 m = 24 m². Since there are 15 rooms, the area of all the rooms is 15 × 24 m² = 360 m².
Since the area of the tiles = 500 m² is greater than the area of the rooms = 360 m², Ted would have enough tiles to cover all kitchen floors in the entire apartment building.
b. How many tiles, each measuring 1 square meter, are needed to cover one room floor?
Since the area of each room floor is 24 m² and the area of each tile is 1 m², so the number of 1 square meter tiles needed to cover each floor is n = area of floor/area of tile = 24 m²/1 m² = 24.
c. How many tiles are needed to cover all the floors in the entire building?
Since 24 tiles are needed to cover each floor and there are 15 rooms in the building, we would require 24 tiles/room × 15 rooms/building = 360 tiles.
So we require 360 tiles.
Which graph has a domain of all real numbers?
On Monday, 27 adults visited an amusement park. On Tuesday, 23 adults visited the amusement park. The enterance fee for the adults is Rs. 100. How much amount is collected from the adults in these two days?
PLEASE TELL FULL SOLUTION.
Answer:
5000
Step-by-step explanation:
Add the number of adults first: 27+23=50
Then multiply the number of adults by 100 for the fee.
50*100 = 5000
Answer:
within the two days a total of 5000$ where collected in the two days
Solution:
R= 100 per adult
1 adult = 100
27(R)+ 23(R) = 27(100)+ 23(100)
27(100)+23(100) =5000
or add both 27 and 23 and multiple by 100
50•100 = 5000
Round your number to the nearest hundredth 65 7
The hypotenuse of a 45°, 45°, and 90° triangle is 26 sqrt(2) inches. What is the length of each of the other sides?
(A)13 sqrt(2) inches
(B)13 inches
(C)13 sqrt(3) inches
(D)26 inches
remember the pythagorean theorem:
a² + b² = c²
where c is the hypotenuse.
so:
[tex] {a}^{2} + {b}^{2} = { ( \sqrt{26)}}^{2} [/tex]
the square and the square root cancel each other out, so...
a² + b² = 26
we know that a and b are of equal length given the angles.
so it's
[tex] { \sqrt{13} }^{2} + { \sqrt{13} }^{2} = 26[/tex]
here the squares and square roots also cancel, but to keep the equation from the formula true we need to write them. that makes the difference between optional and B
Option A is correct,
[tex] \sqrt{13} inches[/tex]
You are dealt one card from a 52-card deck. Find the probability that you are dealt a king or a red card.
Answer:
7/13
Step-by-step explanation:
Half the deck is red so there are 26 reds.
There are 4 kings but we already counted two of these in the 26.
So there are 26+2 red or king cards total.
The probability of selecting a king or red is 28/52.
This can be reduced by dividing top and bottom by 4: 7/13.
help me plz----------------------------
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Answer:
A. 5 should have been subtracted in step 4
Step-by-step explanation:
No question is stated, so there is no "answer."
__
If we assume the question is, "What error did Keith make?" then choice A properly describes it.
Step 4 should look like ...
x -5 = 7y . . . . . . . 5 should be subtracted from both sides
and the final result should be ...
g(x) = (x -5)/7
) A patient drank 12 ounces of orange juice. How many milliliters did the patient drink?
Answer:
[tex]Drink = 354.882\ mL[/tex]
Step-by-step explanation:
Given
[tex]Drink = 12oz[/tex]
Required
Equivalent in mL
We have:
[tex]1\ oz = 29.5735\ mL[/tex]
So:
[tex]Drink = 12 * 29.5735mL[/tex]
[tex]Drink = 354.882\ mL[/tex]
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
Demand for Service
Service Strong Weak
Full price $960 -$490
Discount $670 $320
1. What is the decision to be made, what is the chance event, and what is the consequence for this problem?
2. How many decision alternatives are there?
Number of decision alternatives =
3. How many outcomes are there for the chance event?
Number of outcomes =
4. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?
a. Optimistic approach
b. Conservative approach
c. Minimax regret approach
here i attached the answer
The decision to be made is the type of service to be provided. The chance event is the level of demand for the air service.
What is Air Service?The services performed by an airline, as flights between various destinations to transport passengers, freight, and mail.
The decision to be made is the type of service to be provided. The chance event is the level of demand for the air service. The consequence can be considered as the amount of quarterly profit. Full price and discount price services are two decision alternatives. The number of outcomes for chance event is two, which are strong demand and weak demand.
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Solve the inequality. |X-15|>9
Answer:
X<6 or X>24
Step-by-step explanation:
what is the quotient?
Answer:
the result gaven by dividing one number by another
Dr. Smith is interested in the relationship between nicotine and hand steadiness. Two groups participated in the experiment. One group smoked 5 cigarettes in an hour, while another group read during the same hour. Participants are then tested on the hand steadiness apparatus (yielding a score with the number of errors made). What is the independent variable
Answer:
Exposure to nicotine is the independent variable
Step-by-step explanation:
An independent variable is a factor that remains unchanged (by other factors in the experiment) throughout the course of an experiment. It can however be manipulated by the researcher. A dependent variable, on the other hand, is the factor being measured that relies on the independent variable. In the case above, exposure to 1 hr of nicotine intake forms the independent variable while the levels of hand steadiness, which will be measured, form the dependent variable.
A coordinate plane with a line passing through the points (0, negative 1, 0) and (4, 0).
What is the equation of the graphed line written in standard form?
x – 4y = 4
x + 4y = 4
y = y equals StartFraction one-fourth EndFraction x minus 1.x – 1
y = –y equals negative StartFraction one-fourth EndFraction x minus 1.x – 1
Answer:
x-4y=4
Step-by-step explanation:
The equation of a straight line is in slope intercept form:
y = mx + b;
where y and x are variables, m is the slope of the line and b is the y intercept.
The standard form of a line is:
Ax + By = C
where A, B and C are constants, x and y are variables
The equation of a straight line passing through the points (x₁, y₁) and (x₂, y₂) is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\[/tex]
Given that a line passes through the points (0, -1) and (4, 0), the equation of the line is given by:
[tex]y-(-1)=\frac{0-(-1)}{4-0} (x-0)\\\\y+1=\frac{1}{4} x\\\\y=\frac{1}{4} x-1\\\\4y=x-4\\\\x-4y=4[/tex]
Answer:
Step-by-step explanation:
jeremy drove to work with the average speed of 42 miles per hour. if he had driven with the speed of 48 mph, he would have arrived 10 minutes earlier. how far is it from his home to work?
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Answer:
56 miles
Step-by-step explanation:
Let d represent the distance in miles. Then the drive time in hours is ...
d/42 = d/48 +10/60
8d = 7d +56 . . . . . . . . multiply by 336
d = 56
The distance from Jeremy's home to work is 56 miles.
_____
At 42 mph, his commute time is 1 hour 20 minutes.
Can someone help please ??
Answer:
x=40
Step-by-step explanation:
In the picture, it seems that angles BHC, CHD, and DHE form a line, 180 degrees. So to solve, set up an equation:
[tex](2x+5)+55+40=180[/tex]
Take off the parentheses and solve.
Subtract 5, 55 and 40 from both sides, or add them together, then subtract.
5+55+40=100
You get:
[tex]2x=80[/tex]
Divide both sides by 2
You get:
[tex][x=40][/tex]I hope this helps!
PLZ PLZ HELP
Mark is investing $47,000 in an account paying 5.26% interest compounded continuously.
What will Mark's account balance be in 17 years?
O $114,932.80
$114,925.39
$114,921.47
$114.925.46
===============================================
Work Shown:
A = P*e^(r*t)
A = 47000*e^(0.0526*17)
A = 114,932.799077198
A = 114,932.80
Notes:
P = 47,000 is the principal or amount depositedr = 0.0526 is the decimal form of 5.26%The "e" refers to the special constant e = 2.718... which is similar to pi = 3.14... I would let your calculator handle this constant. There should be a button labeled "e".Mark's account balance after 17 years would be $114,932.8
What is the formula for the continuous compounding?[tex]A=Pe^{rt}[/tex]
where,
A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
t = time in years
For given question,
P = $47000, t = 17 years
R = 5.26%
[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]
Using the Continuous Compounding Formula,
[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]
Therefore, Mark's account balance after 17 years would be $114,932.8
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Which sequence is geometric?
O 1,5, 9, 13, ….
O 2, 6, 8, 10, ...
O 5, 7, 9, 11, ....
O 4, 8, 16, 32, ….
Answer:
4, 8, 16, 32, ...
Step-by-step explanation:
8 / 4 = 2
16 / 8 = 2
32 / 16 = 2
Common ratio is 2
So, The sequence 4, 8, 16, 32, …. is geometric.
Peter is 8 years younger than Alex. In 9 years time, the sum of their ages will be 76 . How old is Alex now?
Answer:
Peter is a-8 in 9 years, (a-8)+ 9+ a+ 9= 76
Answer:
P = 25
A = 33
Step-by-step explanation:
P + 8 = A
P + 9 + A + 9 = 76
P + A = 58
~~~~~~~~~~~~~~
P = 58 - A
P = 58 - P - 8
2 P = 50
P = 25
A = 33
How to solve this problem what do I do
=================================================
Explanation:
We undo the "minus 6" by adding 6 to both sides.
Also, we undo the "+s" by subtracting s from both sides
-----------
So we have these steps
P = r+s-6
P+6 = r+s-6+6 .... adding 6 to both sides
P+6 = r+s
r+s = P+6
r+s-s = P+6-s ..... subtracting s from both sides
r = P + 6 - s
Answer:
P+6-s=r
Step-by-step explanation:
Hi there!
We are given the equation P=r+s-6 and we need to solve for r
To do that, we need to isolate r onto one side, and have everything else on the other.
Here is the equation:
P=r+s-6
start by adding 6 to both sides to clear it from the right side
P+6=r+s
now subtract s from both sides to clear it from the right side
P+6-s=r
now everything that isn't r is on the left side, and r is by itself on the right side. P+6-s=r is the answer.
Hope this helps!
what Is an equation of the line that passes through points (-12 -8) (-17 -16)
anyone have sna pc hat ??
mine is rince9253
Answer:
Yeah the answer is n o .
Answer:
yes i do have but i dont use it
6. Two cell phone companies charge a flat fee plus an added cost for each minute or part of a minute used. The cost is represented by C and the number of minutes is represented by t.
Call-More: C = 0.40t + 25 Talk-Now: C = 0.15t + 40
a) Which company is cheaper if a customer talks for 50 minutes. (1 mark)
b) Under what conditions do the two companies charge the same? (3 marks)
c) Under what conditions is Talk-Now better? Explain
Answer:
Call More is cheaper at 50 minutes
The two companies would charge the same for 60 minutes of use.
Talk Now is cheaper the more minutes you talk. At some point the rate of change of Call More makes it more expensive. That point is just after their costs are even.
Step-by-step explanation:
If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
Answer:
The possible values are a = -2.5 or a = 4.5.
Step-by-step explanation:
Composite function:
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this case:
[tex]f(x) = 4x^2 - 8x - 20[/tex]
[tex]g(x) = 2x + a[/tex]
So
[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]
Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So
[tex]4a^2 - 8a - 20 = 25[/tex]
[tex]4a^2 - 8a - 45 = 0[/tex]
Solving a quadratic equation, by Bhaskara:
[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]
The possible values are a = -2.5 or a = 4.5.
