Answer:
HMO
Step-by-step explanation:
Health Maintenance Organization is your answer :D
The heights of American men are normally distributed. If a random sample of American men is taken and the confidence interval is (65.3,73.7), what is the sample mean x¯? Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.
Answer:
69.5Step-by-step explanation:
Given the confidence interval of the heights of american heights given as (65.3,73.7);
Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7
Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]
[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]
Hence, the sample mean is 69.5
objective: Solve applications involving problem-s...
1 of 21 (0
1.1.A-4
Cookies are sold singly or in packages of 8 or 24. With this packaging, how many
ways can you buy 48 cookies?
Step-by-step explanation:
With the packaging of 8
48 cookies = 48 ÷ 8 = 6 boxes
With the packaging of 24
48 cookies = 48 ÷ 24 = 2 boxes
Logs are stacked in a pile. The bottom row has 50 logs and next to bottom row has 49 logs. Each row has one less log than the row below it. How many logs will be there in 5th row? Use the recursive formula.
Answer:
46 logs on the 5th row.
Step-by-step explanation:
Number of logs on the nth row is
n = 50 - (n-1)
n = 51 - n (so on the first row we have 51 - 1 = 50 logs).
So on the 5th row we have 51 - 5 = 46 logs.
The given relation is an arithmetic progression, which can be solved using the recursive formula: aₙ = aₙ₋₁ + d.
The 5th row has 46 logs.
What is an arithmetic progression?An arithmetic progression is a special series in which every number is the sum of a fixed number, called the constant difference, and the first term.
The first term of the arithmetic progression is taken as a₁.
The constant difference is taken as d.
The n-th term of an arithmetic progression is found using the explicit formula:
aₙ = a₁ + (n - 1)d.
The recursive formula of an arithmetic progression is:
aₙ = aₙ₋₁ + d.
How to solve the question?In the question, we are informed that logs are stacked in a pile. The bottom row has 50 logs and the next bottom row has 49 logs. Each row has one less log than the row below it.
The number of rows represents an arithmetic progression, with the first term being the row in the bottom row having 50 logs, that is, a₁ = 50, and the constant difference, d = -1.
We are instructed to use the recursive formula. We know the recursive formula of an arithmetic progression is, aₙ = aₙ₋₁ + d.
a₁ = 50.
a₂ = a₁ + d = 50 + (-1) = 49.
a₃ = a₂ + d = 49 + (-1) = 48.
a₄ = a₃ + d = 48 + (-1) = 47.
a₅ = a₄ + d = 47 + (-1) = 46.
Hence, the 5th row will have 46 logs.
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We can show that ∆ABC is congruent to ∆A′B′C′ by a translation of
CHECK THE ATTACHMENT FOR COMPLETE QUESTION
Answer:
We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 unit(s) Left and a Reflection across the x axis.
Step-by-step explanation:
We were given triangles ABC and A'B'C' of which were told are congruents,
Now we can provide the coordinates of A and A' from the given triangles ΔABC and ΔA'B'C' ,if we choose a point of A from ΔABC and A' from ΔA'B'C' we have these coordinates;
A as (8,8) and A' (6,-8) from the two triangles.
If we shift A to A' , we have (8_6) = 2 unit for that of x- axis
If we try the shift on the y-coordinates we will see that there is no translation.
Hence, the only translation that take place is of 2 units left.
It can also be deducted that there is a reflection
by x-axis to form A'B'C' by the ΔABC.
BEST OF LUCK
Data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20-year-olds consumed alcoholic beverages in 2008.
(a) Suppose a random sample of the ten 18-20-year-olds is taken. Is the use of the binomial distribution appropriate for calculating the probability that exactly six consumed alcoholic beverages?
i. No, this follows the bimodal distribution.
ii. Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.
iii. No, the trials are not independent.
iv. No, the normal distribution should be used.
(b) Calculate the probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink.
(c) What is the probability that exactly four out of the ten 18-20-year-olds have not consumed an alcoholic beverage?
(d) What is the probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages?
Answer:
(a) Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.
(b) The probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is 0.203.
(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is 0.203.
(d) The probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is 0.167.
Step-by-step explanation:
We are given that data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20-year-olds consumed alcoholic beverages in 2008.
(a) The conditions required for any variable to be considered as a random variable is given by;
The experiment consists of identical trials.Each trial must have only two possibilities: success or failure.The trials must be independent of each other.So, in our question; all these conditions are satisfied which means the use of the binomial distribution is appropriate for calculating the probability that exactly six consumed alcoholic beverages.
Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.
(b) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 10 people
r = number of success = exactly 6
p = probability of success which in our question is % 18-20
year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.
So, X ~ Binom(n = 10, p = 0.697)
Now, the probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is given by = P(X = 6)
P(X = 3) = [tex]\binom{10}{6}\times 0.697^{6} \times (1-0.697)^{10-6}[/tex]
= [tex]210\times 0.697^{6} \times 0.303^{4}[/tex]
= 0.203
(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is given by = P(X = 4)
Here p = 1 - 0.697 = 0.303 because here our success is that people who have not consumed an alcoholic drink.
P(X = 4) = [tex]\binom{10}{4}\times 0.303^{4} \times (1-0.303)^{10-4}[/tex]
= [tex]210\times 0.303^{4} \times 0.697^{6}[/tex]
= 0.203
(d) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 5 people
r = number of success = at most 2
p = probability of success which in our question is % 18-20
year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.
So, X ~ Binom(n = 5, p = 0.697)
Now, the probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 3)
= [tex]\binom{5}{0}\times 0.697^{0} \times (1-0.697)^{5-0}+\binom{5}{1}\times 0.697^{1} \times (1-0.697)^{5-1}+\binom{5}{2}\times 0.697^{2} \times (1-0.697)^{5-2}[/tex]
= [tex]1\times 1\times 0.303^{5}+5 \times 0.697^{1} \times 0.303^{4}+10\times 0.697^{2} \times 0.303^{3}[/tex]
= 0.167
Suppose that c (x )equals 5 x cubed minus 40 x squared plus 21 comma 000 x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.
Answer
X= 64.8 gives the minimum average cost
Explanation:
The question can be interpreted as
C(x)= 5x^3 -40^2 + 21000x
To find the minimum total cost, we will need to find the minimum of
this function, then Analyze the derivatives.
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 58.2 σ=58.2. You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.
Answer:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
Step-by-step explanation:
Let's define some notation
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=58.2[/tex] represent the population standard deviation
n represent the sample size
[tex] ME =1[/tex] represent the margin of error desire
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
A rectangle has a length of x and a width of 5x^3+4-x^2. What is the polynomial that models the perimeter of the rectangle
Answer:
[tex] L= x[/tex]
And the width for this case is:
[tex] W= 5x^3 +4 -x^2[/tex]
And we know that the perimeter is given by:
[tex] P= 2L +2W[/tex]
And replacing we got:
[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]
And symplifying we got:
[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]
Step-by-step explanation:
For this problem we know that the lenght of the rectangle is given by:
[tex] L= x[/tex]
And the width for this case is:
[tex] W= 5x^3 +4 -x^2[/tex]
And we know that the perimeter is given by:
[tex] P= 2L +2W[/tex]
And replacing we got:
[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]
And symplifying we got:
[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]
Tension needs to eat at least an extra 1,000 calories a day to prepare for running a marathon. He has only $25 to spend on the extra food he needs and will spend it on $0.75 donuts that have 360 calories each and $2 energy drinks that have 110 calories. This results in the following system of equations:
0.75d+2e≤25
360d+110e≥1,000
where d is donuts and e is energy drinks. Can Tension buy 8 donuts and 4 energy drinks?
Select the correct answer below:
Yes or No
Answer:
Yes, he can buy 8 donuts and 4 energy drinks.
Step-by-step explanation:
If Tension is able to buy 8 donuts and 4 energy drinks, then both inequalities would be valid when we use these numbers as inputs. Let's check each expression at a time:
[tex]0.75*d + 2*e \leq 25\\0.75*8 + 2*4 \leq 25\\6 + 8 \leq 25\\14 \leq 25[/tex]
The first one is valid, since 14 is less than 25. Let's check the second one.
[tex]360*d + 110*e \geq 1000\\360*8 + 110*4 \geq 1000\\2880 + 440 \geq 1000\\3320 \geq 1000[/tex]
The second one is also valid.
Since both expressions are valid, Tension can buy 8 donuts and 4 energy drinks and achieve his goal of having a caloric surplus of at least 1000 cal.
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = (b) Find an expression for the number of cells after t hours. P(t) = (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr
Answer:
a) k=2.08 1/hour
b) The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
c) 977,435,644 cells
d) 2.033 billions cells per hour.
e) 2.81 hours.
Step-by-step explanation:
We have a model of exponential growth.
We know that the population duplicates every 20 minutes (t=0.33).
The initial population is P(t=0)=58.
The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
For t=0, we have:
[tex]P(0)=Ce^0=C=58[/tex]
If we use the duplication time, we have:
[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]
Then, we have the model as:
[tex]P(t)=58e^{2.08t}[/tex]
The relative growth rate (RGR) is defined, if P is the population and t the time, as:
[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]
In this case, the RGR is k=2.08 1/h.
After 8 hours, we will have:
[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]
The rate of growth can be calculated as dP/dt and is:
[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]
For t=8, the rate of growth is:
[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]
(2.033 billions cells per hour).
We can calculate when the population will reach 20,000 cells as:
[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]
If 2x+9<32 then x could be
Answer:
x < 11.5
Step-by-step explanation:
2x + 9 < 32
(2x + 9) - 9 < 32 - 9
2x < 23
2x/2 < 23/2
x < 11.5
Answer:
x < 11 1/2
Step-by-step explanation:
2x+9<32
Subtract 9 from each side
2x+9-9 < 32-9
2x<23
Divide by 2
2x/2 <23/2
x < 11 1/2
X is any number less than 11 1/2
In a race, Brian Collins has to cross 10 hurdles. The probability that he clears a hurdle is 2/3. Find P(clears all hurdles).
Answer:
1024/59049
Step-by-step explanation:
P( clear hurdle) = 2/3
There are 10 hurdles
P ( clear all hurdles) = P( clear hurdle) * P( clear hurdle)...... 10 times
= 2/3 * 2/3 *....... 10 times
= (2/3) ^ 10
=1024/59049
Answer:
1024/59049, 1.7%
Step-by-step explanation:
One way to do it would to be simply multiply 2/3 by itself 10 times
2/3 x 2/3 x 2/3 x 2/3 and so on
That would be a really long equation so instead we can use exponents to shorten it. We can simply just do 2^10/3^10
2^10=1024
3^10=59049
1024/59049, 1.7%
15% as a fraction in its lowest terms is:
-3/20
-5/100
-1/15
-3/100
Answer:
3/20
Step-by-step explanation:
15%
15/100
/5 /5
3/20
Which set of numbers can represent the lengths of the sides of a triangle? A. {1,2,3} B. {3,5,7} C. {3,9,14} D. {4,4,8}
The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.
What is a triangle?Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.
That is to say, 3+5 = 8 is greater than the third side which is 7.
Therefore, the set of numbers the would represent a triangle are 3,5,7.
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Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3
Answer:
99% confidence interval for the mean of college students
A) 112.48 < μ < 117.52
Step-by-step explanation:
step(i):-
Given sample size 'n' =150
mean of the sample = 115
Standard deviation of the sample = 10
99% confidence interval for the mean of college students are determined by
[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]
Step(ii):-
Degrees of freedom
ν = n-1 = 150-1 =149
t₁₄₉,₀.₀₁ = 2.8494
99% confidence interval for the mean of college students are determined by
[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]
on calculation , we get
(115 - 2.326 , 115 +2.326 )
(112.67 , 117.326)
Find the indicated conditional probability
using the following two-way table:
P( Drive to school | Sophomore ) = [?]
Round to the nearest hundredth.
Answer:
0.07
Step-by-step explanation:
The number of sophmores is 2+25+3 = 30.
Of these sophmores, 2 drive to school.
So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.
Answer:
[tex]\large \boxed{0.07}[/tex]
Step-by-step explanation:
The usual question is, "What is the probability of A, given B?"
They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"
We must first complete your frequency table by calculating the totals for each row and column.
The table shows that there are 30 students, two of whom drive to school.
[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]
whats 1 and 1/2 + 2 and 3/10
Answer:
[tex]3\frac{4}{5}[/tex]
Step-by-step explanation:
You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.
10/10-->1
1/2--> 5/10
2--> 20/10
3/10, the denominator is already 10, so don't need to change.
10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]
Answer:
3 4/5
Step-by-step explanation:
hopefully this helped :3
PLEASE HELP ME!!!!!! Consider what would happen if you were to slice a face at a vertex (cut a corner) of a particular polyhedron. You would see a new polygonal face where the old vertex used to be. What type of polygon would a slice of a cube at a vertex create? Explain how you know.
Answer:
See below.
Step-by-step explanation:
There are 3 edges and 3 faces projecting out from a vertex of a cube.
So the polygon produced would be a triangle.
Answer:
A triangle.
Step-by-step explanation:
As shown above, the plane which slices a corner intersects the polyhedron in [tex] n [/tex] faces which depend on the particular polyhedron.
Here it is a cube, and it intersects three faces. Since the intersection of two planes is a line and there are three planes to intersect with, there are three sides of the polygon.
Hence the polygon is a triangle.
The area of a rectangular horse pasture is 268,500 square yards. The length of the pasture is 5 yards less than three times the width. What is the width of the pasture in yards? Do not include units in your answer. Please help right away! Thank you very much!
Answer: width = 300
Step-by-step explanation:
Area (A) = Length (L) x width (w)
Given: A = 268,500
L = 3w - 5
w = w
268,500 = (3w - 5) x (w)
268,500 = 3w² - 5w
0 = 3w² - 5w - 268,500
0 = (3w + 895) (w - 300)
0 = 3w + 895 0 = w - 300
-985/3 = w 300 = w
Since width cannot be negative, disregard w = -985/3
So the only valid answer is: w = 300
4. In ABC, AB = 8,BC = 10, and AC = 7
Order the angles of the triangle from smallest to largest.
a.
b.
C.
d.
Answer:
B, C, A
Step-by-step explanation:
If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.
Draw the triangle.
AC (7) is opposite from B
AB (8) is opposite from C
BC (10) is opposite from A
From smallest to largest: 7>8>10
7, 8, 10
or
B, C, A
Find the area of this parallelogram.
6 cm
11 cm
Step-by-step explanation:
given,
base( b) = 6cm
height (h)= 11cm
now, area of parallelogram (a)= b×h
or, a = 6cm ×11cm
therefore the area of parallelogram (p) is 66cm^2.
hope it helps...
Factor the trinomial!! PLEASE HELP and if possible please explain how to do this!!
Answer:
d. a = 39
Step-by-step explanation:
Question:
for which value of "a" will the trinomial be factorizable.
x^2+ax-40
For the expression to have integer factors, a = sum of the pairs of factors of -40.
-40 has following pairs of factors
{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }
meaning that the possible values of a are
+/- 39, +/- 18, +/- 6, +/- 3
out of which only +39 appears on answer d. a=39
Which of the following graphs is described by the function given below?
y = 2x^2 + 8x + 3
Answer:
Option A
Step-by-step explanation:
Equation of the given quadratic function is,
y = 2x² + 8x + 3
y = 2(x² + 4x) + 3
= 2(x² + 4x + 4 - 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5
By comparing this equation with the equation of a quadratic function in vertex form,
y = a(x - h)² + k
Here (h, k) is the vertex of the parabola
Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)
Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.
Option (A). Graph A will be the answer.
how many types of progression in mathematics?
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 27 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
Answer:
The probability is 12.66%.
This is a low probability, so it is unlikely for such a combined sample to test positive.
Step-by-step explanation:
If the probability of being infected is 0.005, the probability of not being infected is 0.995.
Then, to find the probability of at least one of the 27 people being infected P(A), we can find the complementary case: all people are not infected: P(A').
[tex]P(A') = 0.995^{27}[/tex]
[tex]P(A') = 0.8734[/tex]
Then we can find P(A) using:
[tex]P(A) + P(A') = 1[/tex]
[tex]P(A) = 1 - 0.8734[/tex]
[tex]P(A) = 0.1266 = 12.66\%[/tex]
This is a low probability, so it is unlikely for such a combined sample to test positive.
Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your player, each of the 12 songs is played once in random order. Find the probability that among the first two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)-(c) if a song can be replayed before all 12 songs are played.
Answer:
The answer is below
Step-by-step explanation:
We have the following information:
Number of songs you like = 2
Total number of songs = 12
a) P(you like both of them) = 2/12 x 1/11 = 0.015
This is unusual because the probability of the event is less than 0.05
b) P(you like neither of them) = 10/12 x 9/11 = 0.68
c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30
d) If a song can be replayed before all 12,
P(you like both of them) = 2/12 x 2/12 =0.027
This is unusual because the probability of the event is less than 0.05
P(you like neither of them) = 9/12 x 9/12 = 0.5625
P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25
how many are 4 x 4 ?
16, think of 4 plus 4 plus 4 plus 4.
Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?
Got the explanation from classmates
N=??? I/Y=5 PV=1000000 PMT=-65000 FV=0
It will last 27 years.
Answer:
27 years
Step-by-step explanation:
The formula for the number of payments can be used:
N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03
There will be a couple thousand dollars left after the 27th payment.
The winnings will last 27 years.
The perimeter of a triangle is 82 feet. One side of the triangle is 2 times the second side. The third side is 2 feet longer than the second side. Find the length of each side.
Answer:
Side 1: 40 feet
Side 2: 20 feet
Side 3: 22 feet
Step-by-step explanation:
Side 1 is twice the length of side 2 and side 2 is 20 feet, which means side 1 is 40 feet. Side 3 is the the length of the second side plus 2, which means it has a length of 22 feet.
Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 6 p plus 3 x plus 2 pxequals69. Suppose also that p and x are both functions of time, measured in days. Find the rate at which x is changing when xequals3, pequals5, and StartFraction dp Over dt EndFraction equals1.5.
Answer:
[tex]\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]
Step-by-step explanation:
The price p, in dollars, and the number of sales, x, of a certain item follow the equation: 6p+3x+2px=69
Taking the derivative of the equation with respect to time, we obtain:
[tex]6\dfrac{dp}{dt} +3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}+2x\dfrac{dp}{dt}=0\\$Rearranging$\\6\dfrac{dp}{dt}+2x\dfrac{dp}{dt}+3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}=0\\\\(6+2x)\dfrac{dp}{dt}+(3+2p)\dfrac{dx}{dt}=0[/tex]
When x=3, p=5 and [tex]\dfrac{dp}{dt}=1.5[/tex]
[tex](6+2(3))(1.5)+(3+2(5))\dfrac{dx}{dt}=0\\(6+6)(1.5)+(3+10)\dfrac{dx}{dt}=0\\18+13\dfrac{dx}{dt}=0\\13\dfrac{dx}{dt}=-18\\\dfrac{dx}{dt}=-\dfrac{18}{13}\\\\\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]
The number of sales, x is decreasing at a rate of 1.3846 sales per day.