Answer: After 1 year = $15085.85168
After 5 years = $20339.34789
After 10 years = $29549.21947
After 25 years = $90609.34284
Step-by-step explanation:
14000e^.0747 (however many years)
Answer:
The balance after 1 year, 5 years, 10 years, 25 years are 15085.85, 20339.35, 29549.22 and 90609.34 respectively.
Step-by-step explanation:
It is given that the principle amount is $14,000 and interest rate is 7.47%.
The formula for amount is
[tex]A=Pe^{rt}[/tex]
Where, P is principle, r is rate of interest and t is time in years.
Substitute P=14000 and r=0.0747 in the above equation.
[tex]A=14000e^{0.0747t}[/tex] ..... (1)
Substitute t=1 in equation (1) to find the balance after 1 year.
[tex]A=14000e^{0.0747(1)}=15085.851678\approx 15085.85[/tex]
Substitute t=5 in equation (1) to find the balance after 5 year.
[tex]A=14000e^{0.0747(5)}=20339.3478896\approx 20339.35[/tex]
Substitute t=10 in equation (1) to find the balance after 10 year.
[tex]A=14000e^{0.0747(10)}=29549.2194696\approx 29549.22[/tex]
Substitute t=25 in equation (1) to find the balance after 25 year.
[tex]A=14000e^{0.0747(25)}=90609.3428426\approx 90609.34[/tex]
Therefore the balance after 1 year, 5 years, 10 years, 25 years are 15085.85, 20339.35, 29549.22 and 90609.34 respectively.
In a survey, 22 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $32 and standard deviation of $17. Construct a confidence interval at a 98% confidence level.
Answer:
[tex]19.22\:<\:\mu\:<\:44.78[/tex]
Step-by-step explanation:
Tthe population is normally distributed and the sample size is [tex]n=22\:<\:30[/tex].
Since the population standard deviation [tex]\sigma[/tex] is unknown and the sample standard deviation [tex]s[/tex], must replace it, the t distribution must be used for the confidence interval.
Hence with degrees of freedom of 21, [tex]t_{\frac{\alpha}{2} }=3.527[/tex].(Read from the t distribution table)
The 98% confidence interval can be constructed using the formula:
[tex]\bar X-t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )\:<\:\mu\:<\:\bar X+t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )[/tex].
From the question the sample mean is [tex]\bar X=32[/tex]dollars and the sample standard deviation is [tex]s=17[/tex] dollars.
We substitute the values into the formula to get
[tex]32-3.527(\frac{17}{\sqrt{22} } )\:<\:\mu \:<\:32+3.527(\frac{17}{\sqrt{22} } )[/tex]
[tex]19.22\:<\:\mu\:<\:44.78[/tex]
Therefore, we can be 98% confident that the population mean is between is between 19.22 and 44.78 dollars.
There are a total of 20 dogs and cats at a kennel. if the ratio of the number of dogs to the number of cats at the kennel is 3 to 2, how many cats are at the kennel?
Answer:
Number of cats in the kennel = 8
Step-by-step explanation:
Let
c denote the number of cats and
d be the number of dogs
Given that the ratio of dogs to cats is 3 to 2
So,
d:c=3:2
Sum of ratio is 5.
And the total number of cats and dogs is 20.
So in order to find the number of cats, following formula will be used:
[tex]Numbr\ of\ cats=\frac{ratio\ of\ cats}{sum\ of\ ratio}*Total\ number\ of\ animals\\ =\frac{2}{5}*20\\ =2*4\\=8[/tex]
So, there are 8 cats in the kennel ..
The number of cats in the kennel can be found using the given ratio of dogs to cats, 3 to 2. Each part in this ratio represents 4, since the total number of animals is 20. Therefore, since the number of cats is represented by 2 parts in the ratio, there are 2 * 4, or 8 cats.
Explanation:This question can be solved using the concepts of ratios and proportions. In this case, the ratio of the number of dogs to the number of cats at the kennel is given as 3 to 2. This means for every 3 dogs, there are 2 cats.
The total number of dogs and cats at the kennel is given as 20. We need to find out how many of these are cats.
To find the number of cats, we first find the total parts of the ratio by adding 3 (for dogs) and 2 (for cats), which equals 5 parts. Since the total number of animals is 20, each part in the ratio represents 20 divided by 5, which is 4. Therefore, since the number of cats is represented by 2 parts in the ratio, the number of cats is 2 multiplied by 4, which equals 8.
Therefore, there are 8 cats in the kennel.
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Victor is a mechanic who wants to ensure he has enough funds during his old age. Which account will be of benefit to Victor?
A.
checking account
B.
savings account
C.
money market account
D.
individual retirement account
Answer:
D.
individual retirement account
Step-by-step explanation:
The account that will be beneficial to Victor, to ensure he has enough funds during his old age, is the individual retirement account(IRA).
Answer:
The most appropriate answer option is D. Individual Retirement Account.
Step-by-step explanation:
We know that Victor is a mechanic and he wants to make sure that he has enough funds during his old age.
For this purpose, an Individual Retirement Account (IRA) would be the most suitable and beneficiary for him.
An Individual Retirement Account is a type of account that is tax advantaged and aims to help people save for their post retirement life.
nnnnneeedd help
1.Find the residual if you know the actual number is 5.2 and the predicted value is 4.8
Answer:
0.4-2Step-by-step explanation:
The residual is the difference between the actual value and that predicted by the model.
1. actual - predicted = 5.2 - 4.8 = 0.4
__
2. actual - predicted = 20 - (4·3 +10) = 20 -22 = -2
Express in exponential form.
log(base 2) 16=4
Answer:
[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]
Step-by-step explanation:
[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]
[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]
Keep in mind that a log is an exponent.
When you are asked for the log base 2 of 16, you are being asked for the exponent you need to raise 2 to, to get 16. The base in the log is the same base as in the exponential form.
In other words, the question "what is log base 2 of 16?" is the same as the question "what exponent do you raise the base 2 to to get 16?"
Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents.
(b^4)^2
[tex]\bf (b^4)^2\implies b^{4\cdot 2}\implies b^8[/tex]
In a group of 40 students, 23 take the AP Psychology class, 18 take the AP Calculus class, and 8 take both classes. What is the probability that a student takes AP Psychology or AP Calculus?
Answer:
Im not this sure but i think its 25/40 so its 62.5%
Step-by-step explanation:
23 Take psychology but 8 takes both so 23-8=15
18-8=10
7 dont take any
this is where im not sure, im not sure if i add the 8 who take both of the classes. I Didnt so its
15+10=25
25/40
Hope this help??
Answer:
Step-by-step explanation:
This is a Venn Diagram problem.
23 - 8 = 15 take just AP Psychology
18 - 8 = 10 take just AP Calculus
I think this question is likely done by adding all three areas together to get 33
15 + 10 + 8
33
The probability is therefore 33/40 = 0.825
Need help with a math question
Answer:
[tex]x =38.7\°[/tex]
Step-by-step explanation:
By definition, the tangent of a x-angle is defined as
[tex]tan(x) =\frac{opposite}{adjacent}[/tex]
For this case
[tex]opposite = 8[/tex]
[tex]adjacent = 10[/tex]
Therefore we have that
[tex]tan(x) =\frac{8}{10}[/tex]
[tex]x =arctan(\frac{8}{10})[/tex]
The answer is:
[tex]x =38.7\°[/tex]
I need help with my geometry homework! Thank you! I will mark brainliest!!!!
Answer:
The first choice is the one you want
Step-by-step explanation:
Use geometric means to solve for a first. The formula is
[tex]8^2=15a[/tex] and 64 = 15a and a = 64/15
That one was quite easy. Finding b is a bit more difficult.
The formula for finding b is
[tex]\frac{a}{b}=\frac{b}{15+a}[/tex]
Solving for b:
[tex]b^2=a(15+a)[/tex]
Filling in we have
[tex]b^2=15(\frac{64}{15})+(\frac{64}{15})^2[/tex] and
[tex]b^2=64+\frac{4096}{225}[/tex] and
[tex]b^2=\frac{18496}{225}[/tex] so b = 136/15
Very important! help needed! timed!
Use the dot product to find [v] when v = -6i.
a.0
b.-6
c.36
d.6
Answer:
6
Step-by-step explanation:
I think you mean |v|... you wouldn't need dot product for that...
It is just sqrt(6^2)=6
Answer:
d
Step-by-step explanation:
You cannot use the dot product on a single vector
To find the magnitude of v = - 6i, then
| v | = [tex]\sqrt{(-6)^2}[/tex] = [tex]\sqrt{36}[/tex] = 6 → d
For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation:
Answer:
Table C
Step-by-step explanation:
we have
[tex]y=-4x^{2}[/tex]
The quadratic equation in standard form is equal to
[tex]ax^{2}+bx+c=0[/tex]
so
In this problem
[tex]a=-4, b=0,c=0[/tex]
The y-intercept is the value of y when the value of x is equal to zero
[tex]y=-4(0)^{2}=0[/tex]
The y-intercept is the point (0,0)
The coefficient a is negative, therefore the parabola open down
Answer:
C
Step-by-step explanation:
Edge2021
How would you find out how many sixth through eighth grade students are interested in joining a running club? Explain how to choose a sample that will give you a good representation of a whole population.
Answer:
The sample should be a random sample from the entire set of students and should include enough students to be reliable. Small samples have more variation, which leads to less reliable inferences.
To find out how many sixth through eighth grade students are interested in joining a running club, you can conduct a survey among these students. Choose a sample by randomly selecting a certain number of students from the list, ensuring diversity. Contact the selected students to ask about their interest in joining the club and calculate the percentage of interested students.
Explanation:To find out how many sixth through eighth grade students are interested in joining a running club, you would need to conduct a survey or questionnaire among the students in these grades. Here's how you can choose a sample that will give you a good representation of the whole population:
Start by listing all the sixth through eighth grade students in your school.You can then use a random sampling method, such as drawing names out of a hat or using a random number generator, to select a certain number of students from the list.Ensure that the sample includes a diverse group of students, representing different genders, ethnicities, and interests.Contact the selected students and ask them if they would be interested in joining a running club.Record their responses and calculate the percentage of students who are interested in joining the club.GEOMETRY HELP PLSSSSS
A = (-3, 2) → (-3 + 2, 2 - 4) → (-1, - 2)
B = (1, 5) → (1 + 2, 5 - 4) → (3, 1)
C = (2, -3) → (2 + 2, -3 - 4) → (4, -7)
A’ = (-1, -2)
B’ = (3, 1)
C’ = (4, -7)
For the function f(x)=x^2+8x+2and g(x)= -5x+9, find (f•g)(x) and (f•g)(1)
Answer: (f·g)(x) = -5x³ - 31x² + 62x + 18
(f·g)(1) = 44
Step-by-step explanation:
f(x) = x² + 8x + 2 g(x) = -5x + 9
(f·g)(x) = (x² + 8x + 2)(-5x + 9)
= -5x³ + 9x²
- 40x² + 72x
- 10x + 18
= -5x³ - 31x² + 62x + 18
(f·g)(1)= -5(1)³ - 31(1)² + 62(1) + 18
= -5 - 31 + 62 + 18
= 44
Why is the metric system called a decimal system of measurement
Answer:
The metric system is a called a decimal-based system because it is based on multiples of ten.
Can someone help me with this problem it’s question number 6
Answer:
[tex]\frac{57}{16}[/tex] lb
Step-by-step explanation:
[tex]\frac{7}{8} +1\frac{3}{4} +\frac{15}{16}[/tex]
Change the mixed fraction into an improper fraction,
[tex]\frac{7}{8} +\frac{7}{4} +\frac{15}{16}[/tex]
Now convert the denominator to 16 (since 8 and 4 are factors of 16)
And remember that what you do to the denominator, you must do the same to the numerator!
[tex]\frac{14}{16} +\frac{28}{16} +\frac{15}{16}[/tex]
Now that we have all fractions with the same denominator, we can simply add all the numerators together,
= [tex]\frac{57}{16}[/tex]
It cannot be simplified any further, so this is your answer!
Hope this helped!!
HELP ME
Drag the labels to the correct locations on the table. Not all tiles will be used.
Match each attribute of a parabola to the correct quadratic function.
Answer:
1. C, E, G
2. A, D, H
Step-by-step explanation:
Compare each equation to the form ...
f(x) = 1/(4p)(x -h)^2 +k
In this form, p is the distance from the vertex to the focus (positive is up), and (h, k) is the location of the vertex. The focus is (h, k+p); the directrix is y=k-p.
1. The equation tells us ...
(h, k) = (1, 4)
1/(4p) = (-1) . . . ⇒ . . . p = -1/4
So, we have ...
vertex: (1, 4) . . . . . . . . (G)focus: (1, 3 3/4) . . . . . (C)directrix: y=4 1/4 . . . . (E)--
2. The equation tells us ...
(h, k) = (-1, 4)
1/(4p) = 2 . . . ⇒ . . . p = 1/8
So, we have ...
vertex: (-1, 4) . . . . . . . . (A)focus: (-1, 4 1/8) . . . . . . (H)directrix: y = 3 7/8 . . . (D)Answer:
Step-by-step explanation:
Kate wants to post three parcels each parcel costs ?1.20 to post how much change should she get from a ?10 note
Answer:
$6.40
Step-by-step explanation:
We first multiply 1.20 by 3 so we can find the price for 3 parcels. We then subtract the result by 10 to get the change Late should get
10-3(1.20)
=10-3.60
=6.40
The required change is $ 6.40
How to find how much change should she get from a $10 note?We first multiply 1.20 by 3 so we can find the price for 3 parcels.So price of 3 parcels = $3(1.20) = $ 3.60
We then subtract the result by 10 to get the change Late should getSo, the change = $ { 10-3.60 }
= $ 6.40
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y = 8x − 9 y = 4x − 1 Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)
Answer:
This is the answer
SORRY IF CAM QUALITY ISNT GOOD ENOUGH...PLZ TRY TO FIGURE OUT...
PLZ MARK BRAINLISEST
Step-by-step explanation:
This question is really confusing me, it talks about unknown angle problems with Algebra.
Help, I need help!!
Answer:
20
Step-by-step explanation:
The two given and marked angles add up to 90.
A = x
B = 3x + 10
A + B = 90 Substitute for A and B. A and B are just letters I gave things.
x + 3x + 10 = 90 Combine the left
4x + 10 = 90 Subtract 10 from both sides.
4x +10-10 = 90-10 Combine
4x = 80 Divide by 4
4x/4=80/4
x = 20
Answer:
x=20
Step-by-step explanation:
The two angles are complementary angles. Complementary angles add to 90 degrees
x + 3x+10 = 90
Combine like terms
4x+10 = 90
Subtract 10 from each side
4x+10-10 = 90-10
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
Which is not a correct way to rewrite this expression using the distributive
property?
Answer: I think the correct answer is B
Step-by-step explanation:
Answer:
The correct option is A.
Step-by-step explanation:
The given expression is
[tex](4x^2+3x-7)(x-2)[/tex]
If a ,b, c are three real number, then by distributive property,
[tex]a(b+c)\Leftrightarrow ab+ac[/tex]
Using distributive property, then given expression can be written as
[tex](4x^2+3x-7)(x)+(4x^2+3x-7)(-2)[/tex]
Option A is not a correct way to rewrite the given expression and option C represents a correct way to rewrite the given expression.
Using distributive property, then given expression can be written as
[tex](4x^2)(x-2)+(3x)(x-2)+(-7)(x-2)[/tex]
Option D represents a correct way to rewrite the given expression.
Again using distributive property in the above expression, we get
[tex](4x^2)(x)+(4x^2)(-2)+(3x)(x)+(3x)(-2)+(-7)(x)+(-7)(-2)[/tex]
Option B represents a correct way to rewrite the given expression.
Therefore the correct option is A.
The distance between two points (x1,y1) and (x2,y2) is √(x1-x2)2+(y1-y2)2 . Determine the distance between (1,3) and (5,2) .
Let the point (1,3) be (x1, y1)
Let the point (5,2) be (x2, y2)
The distance between the two points would be √((x2-x1)²+(y2-y1)²)
Substitute the numbers into the points
distance: √((5-1)²+(2-3)²)
=√(4²+(-1)²)
=√(16+1)
=√17
Answer:5 but its probaly not right bc im just looking for points
Step-by-step explanation:
If y=x^2, then which expression is equivalent to -y?
a: (-x)^2
b: -x^2
c: -x
d: x^-2
e: x
Answer:
Step-by-step explanation:
D
Which best describes the transformation from the graph of f(x) = x2 to the graph of f(x) = (x – 3)2 – 1? left 3 units, down 1 unit left 3 units, up 1 unit right 3 units, down 1 unit right 3 units, up 1 unit
Answer:
right 3 units and down 1 unit
Step-by-step explanation:
we know that
[tex]f(x)=x^{2}[/tex]
Is the equation of a vertical parabola open upward with vertex at (0,0)
and
[tex]f(x)=(x-3)^{2}-1[/tex]
Is the equation of a vertical parabola open upward with vertex at (3,-1)
so
The rule of the translation of
(0,0) -----> (3,-1)
is equal to
(x,y) -----> (x+3,y-1)
That means ----> the translation is right 3 units and down 1 unit
Answer:
C.right 3 units and down 1 unit
Step-by-step explanation:
Aaron bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow him to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on?
Answer:
19 inches each I believe but I'll stand corrected if Im wrong.
Step-by-step explanation:
Answer:
Scale factor is [tex]\frac{1}{2}[/tex]
Dimension for each channel is 46 in × 38 in
Step-by-step explanation:
Given,
The original dimension of television = 92 in × 76 in
Let A represents the area of the television,
So, after splitting the screen of television into 4 channels,
The area of each channel = [tex]\frac{A}{4}[/tex]
We know that, the scale factor is equal to the square root of the ratio of areas of the figures ( new over old ),
If x represents the scale factor,
[tex]\implies x=\sqrt{\frac{A/4}{A}}=\sqrt{\frac{1}{4}}=\frac{1}{2}[/tex]
Hence, scale factor in the given situation is [tex]\frac{1}{2}[/tex]
Also, the dimension of each channel will get after multiplying each dimension of the TV by the scale factor ( i.e. 1/2 ),
Therefore, the dimension of each channel would be 46 in × 38 in
Find the measure of Angle 7.
measure of angle 7 = 2x+15
measure of angle 8 = 3x
Angles 8 and 7 are adjacent angles, meaning that their sum is 180 degrees. Knowing this you can make a formula like so...
2x + 15 + 3x = 180
Now you must combine like terms. Like terms are numbers that have matching variables OR are numbers with out variables. In this case the like terms are 2x and 3x, since they both have the variables "x" attached.
2x + 3x = 5x
so...
5x + 15 = 180
Now bring 15 to the left side by subtracting 15 to both sides (what you do on one side you must do to the other). Since 15 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
5x + 15 - 15 = 180 - 15
5x + 0 = 165
5x = 165
Next divide 5 to both sides to finish isolating x. Since 5 is being multiplied by x, division (the opposite of multiplication) will cancel 5 out (in this case it will make 5 one) from the left side and bring it over to the right side.
5x / 5 = 165 / 5
x = 33
x is 33.
To find measure of angle 7, plug in 33 for x in 2x + 15 and solve
2(33) + 15
66 + 15
81
Measure of angle 7 is 81 degrees
Hope this helped!
~Just a girl in love with Shawn Mendes
Combine like terms to create an equivalent expression. 20(−1.5r+0.75)20(-1.5r+0.75)20(−1.5r+0.75)20, left parenthesis, minus, 1, point, 5, r, plus, 0, point, 75, right parenthesis
Answer:
The combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].
Step-by-step explanation:
Consider the provided expression:
[tex]20(-1.5r+0.75)[/tex]
Use the distributive property: [tex]a(b + c) = ab + bc[/tex]
[tex]-30r + 15[/tex]
After using distribution property there are no more like terms. Thus, [tex]-30r + 15[/tex] is the simplest form.
Hence, the combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].
Based on the information, the simplified expression is -30r + 15.
How to solve the expressionGiven expression:
20(-1.5r+0.75)
Applying the distributive property:
= 20(-1.5r) + 20(0.75)
= -30r + 15
Therefore, the simplified expression is -30r + 15.
Use the distributive property to distribute the 20 to each of the terms inside the parentheses.
Simplify the expression by combining the like terms.
The simplified expression is -30r + 15.
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D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m∠DEF? A. 30° B. 45° C. 60° D. 90°
Answer:
Option D. 90°
Step-by-step explanation:
we have
[tex]D(5, 7),E(4, 3),F(8, 2)[/tex]
Plot the vertices
see the attached figure
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance DE
[tex]D(5, 7),E(4, 3)[/tex]
substitute
[tex]d=\sqrt{(3-7)^{2}+(4-5)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]
[tex]DE=\sqrt{17}\ units[/tex]
step 2
Find the distance EF
[tex]E(4, 3),F(8, 2)[/tex]
substitute
[tex]d=\sqrt{(2-3)^{2}+(8-4)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(4)^{2}}[/tex]
[tex]EF=\sqrt{17}\ units[/tex]
step 3
Find the distance DF
[tex]D(5, 7),F(8, 2)[/tex]
substitute
[tex]d=\sqrt{(2-7)^{2}+(8-5)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(3)^{2}}[/tex]
[tex]DF=\sqrt{34}\ units[/tex]
step 4
The triangle DEF is a right triangle because satisfy the Pythagoras theorem
so
[tex](\sqrt{34})^{2}=(\sqrt{17})^{2}+(\sqrt{17})^{2}[/tex]
[tex]34=34[/tex] -----> is true
therefore
The measure of angle DEF is a right angle
Given f(t) = 282 - 53 +1, determine the function value f(2). Do not include f(z) = in your answer
Answer:
230
Step-by-step explanation:
The function simplifies to ...
f(t) = 230
This will be the value for any value of t, so ...
f(2) = 230
The probability of success is 0.6 for each trial. Find the probability of each:
13 successes in 24 trials
9 successes in 20 trials
6 failures in 12 trials
Please help! Honestly clueless. Only have a few days of school left.
Answer:
1. 0.1367
2. 0.0709
3. 0.1766
Step-by-step explanation:
The probability of success is p=0.6, then the probability of a failure is q=1-0.6=0.4.
1. The probability that there are exactly 13 successes in 24 trials is
[tex]C^{24}_{13}p^{13}q^{24-13}=\dfrac{24!}{13!(24-13)!}\cdot (0.6)^{13}\cdot (0.4)^{11}\approx 0.1367[/tex]
2. The probability that there are exactly 9 successes in 20 trials is
[tex]C^{20}_{9}p^{9}q^{20-9}=\dfrac{20!}{9!(20-9)!}\cdot (0.6)^{9}\cdot (0.4)^{11}\approx 0.0709[/tex]
3. The probability that there are exactly 6 failures in 12 trials is
[tex]C^{12}_{6}q^{6}p^{12-6}=\dfrac{12!}{6!(12-6)!}\cdot (0.4)^{6}\cdot (0.6)^{6}\approx 0.1766[/tex]