The probability mass function of X( -3, -1, 1 ,3) is P(X) 1/8 3/8 3/8 1/8.
A fair coin is flipped 3 times and the random variable X is defined as follows:
X = 3 times the number of heads - 2 times the number of tails
To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.
The Possible outcomes are as shown:
3 heads (X = 3)
2 heads, 1 tail (X = 1)
1 head, 2 tails (X = -1)
3 tails (X = -3)
And the Probabilities are:
P(X = 3) = 1/8
P(X = 1) = 3/8
P(X = -1) = 3/8
P(X = -3) = 1/8
Therefore, the probability mass function of X is:
X( -3, -1, 1 ,3) is P(X) 1/8 3/8 3/8 1/8
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c) assume that 25% of the defendants in the state are innocent. in a certain year 200 people put on trial. what is the expected value and variance of the number of cases in which juries got the right decision?
The expected value of cases in which juries got the right decision is 150, and the variance is 375.
1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.
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gamboa, inc. sold 110 selfie sticks for $10 each. if producing the selfie sticks had an average cost of $3 , how much profit did the company make?
The company made a profit of $770
How much profit did the company make?Profit is the difference between revenue and costs. In this scenario, the revenue from selling 110 selfie sticks is $10 × 110 = $1100.
Therefore, the costs of producing the same number of selfie sticks are
110 × $3 = $330
So, the profit that Gamboa, Inc. made is
$1100 - $330 = $770.
As we can see, based on the number of selfie sticks together with their production, we managed to obtain a profit of $770.
Hence, the company made a profit of $770.
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parabola a and parabola b both have the x-axis as the directrix. parabola a has its focus at (3,2) and parabola b has its focus at (5,4). select all true statements.
a. parabola A is wider than parabola B
b. parabola B is wider than parabola A
c. the parabolas have the same line of symmetry
d. the line of symmetry of parabola A is to the right of that of parabola B
e. the line of symmetry of parabola B is to the right of that of parabola A
In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.
The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.
Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.
Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.
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A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.
In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.
a) The probability that an individual will wait more than 7 minutes can be found as follows:
Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.
Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.
b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.
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A number is increased by 70% and the result is 42.5. What is the number?
A. 29.75
B. 27.5
C. 25
D. 17
E. 12.75
Can someone help me with this please?
To solve the question asked, you can say: So, the other angle of the figure is 49 degree.
what are angles?In Euclidean geometry, an angle is a shape consisting of two rays, known as sides of the angle, that meet at a central point called the vertex of the angle. Two rays can be combined to form an angle in the plane in which they are placed. Angles also occur when two planes collide. These are called dihedral angles. An angle in planar geometry is a possible configuration of two rays or lines that share a common endpoint. The English word "angle" comes from the Latin word "angulus" which means "horn". A vertex is a point where two rays meet, also called a corner edge.
here the given angles are as -
107 + (180-156) + x = 180
as total angle sum of a triangle is 180
so,
x = 180 - 131
x = 49
So, the other angle of the figure is 49 degree.
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What’s the area?
7 yd
4 yd
7 yd
3 yd
The area is 49 square yards.
555 centigrams = 55.5 ________
decigrams
grams
decagrams
hectograms
555 centigrams = 55.5 GRAMS
The metric system is based on multiples of 10, where each unit is 10 times larger or smaller than the previous one. In this system, "centi-" means one hundredth, so 1 centigram is one hundredth of a gram. Therefore, 555 centigrams is equal to 5.55 grams (since there are 100 centigrams in 1 gram).
On the other hand, "deci-" means one-tenth, so 1 decigram is one-tenth of a gram. Therefore, 555 centigrams is also equal to 55.5 decigrams (since there are 10 decigrams in 1 gram).
In summary, 555 centigrams is equal to:
55.5 decigrams
5.55 grams
555 centigrams is equal to = 55.5 decigrams
Solution:1 cg is equal to 10 dg, therefore 555 cg is equivalent to 55.5 dg.
1 Centigram = 1 x 10 = 10 Milligrams
555 Centigrams = 555 / 10 = 55.5 Decigrams
Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.
Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
HELPPPPPPP PLEASEEEEEEEEEEEEEEE
y=mx+b
The required equation of straight line is y = 0.03x + 20.
What is an equation?
A mathematical equation states that two quantities or values are identical. Equations are used when more than one factor has to be examined in order to fully understand or explain a situation.
The general form of an equation is y = mx + b, where m is the slope of equation and b is a constant.
From the given graph we get 2 points.
i.e., (0, 20) and (2000, 80)
Slope of the line is
[tex]m=\frac{80-20}{2000-0}\\\ \ = \frac{60}{2000}\\ = \frac{6}{200} \\= \frac{3}{100}[/tex]
Then the equation will be
[tex]y-20=\frac{3}{100}(x-0)\\\Rightarrow y-20=0.03x\\\Rightarrow y-0.03x-20=0\\\Rightarrow y = 0.03x+20[/tex]
Therefore, the required equation is y = 0.03x + 20, calculating with the help of given graph.
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=
Suppose that a new employee starts working at $7.32 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y = $7.32(1.04). Find
the amount of time after which he will be earning $10.00 per hour.
After what amount of time will the employee be earning $10.00 per hour?
years (Round to the nearest tenth of a year as needed.)
HELP PLEASE
Using the equation [tex]y = $7.32(1.04)^t[/tex], the amount of time after which the employee will be earning $10.00 is about 9.64 years, or approximately 9 years and 8 months.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
We can start by setting up the equation for the employee's hourly wage y after t years -
[tex]y = $7.32(1.04)^t[/tex]
We want to find the amount of time t after which the employee will be earning $10.00 per hour, so we can set y equal to 10 and solve for t -
[tex]10 = $7.32(1.04)^t[/tex]
Dividing both sides by $7.32, we get -
[tex]1.367 = 1.04^t[/tex]
Taking the natural logarithm of both sides, we get -
[tex]ln(1.367) = ln(1.04^t)[/tex]
Using the property of logarithms that [tex]ln(a^b) = b ln(a)[/tex], we can simplify the right-hand side -
ln(1.367) = t ln(1.04)
Dividing both sides by ln(1.04), we get -
t = ln(1.367)/ln(1.04) ≈ 9.64
Therefore, the employee will be earning $10.00 per hour after about 9.64 years.
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what is the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 ? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 0.9378
First, we should find the total number of chips in the box. The box contains 225 chips numbered from 1 to 225. Therefore, the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 211/225.
The probability can be expressed as a simplified fraction or a decimal rounded to four decimal places. The probability is rounded to four decimal places is 0.9378.
The probability of drawing a chip number that is smaller than 212 from the box is 211/225 or 0.9378 (rounded to four decimal places).
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the answer i need is Another pair it could be (_,10)
and every y value is _ every x value
Answer:
Another order pair could be (30,10).
Every y value is "one-third of" every x value.
Two percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 95% detection rate for carriers and a 3% detection rate for noncarriers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual. A. What is the probability that both tests yield the same result?
The probability that both tests yield the same result is 7.7%.
Simply put, probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
It is predicated on the likelihood that something will occur. The justification for probability serves as the primary foundation for theoretical probability. For instance, the theoretical chance of receiving a head when tossing a coin is 12.
Let's break it down:-
90% don't have of those 99%
5% will be positive
1% positive of those 1%
90% positive
10% negative.
Well we need it to be the same, so 99*(.05*.05+.95*.95)+.01*(.9*.9+.1*.1)= 90.4%.
If both tests are positive, we have:-
0.99*0.05*0.05 and 0.01*0.9*0.9 for being positive, so :-
[tex]\frac{carrier}{positive} = \frac{0.01*0.9*0.9}{(0.99*0.05*0.05+0.01*0.9*0.9)} = 7.7[/tex]
hence, the probability of the two tests yield the same result is 7.7%.
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a pastry chef accidentally inoculated a cream pie with six s. aureus cells. if s. aureus has a generation time of 60 minutes, how many cells would be in the cream pie after 7 hours?
After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.
How many cells would be in the cream pie after 7 hours?Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.
The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.
If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.
The number of generations (n) in seven hours is calculated as:
n = t/g
n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations
The number of cells in the cream pie after 7 hours is calculated as :
N = N₀ × 2ⁿ
N = 6 cells × 2⁷
N = 768 cells
Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.
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Which state is located at point C?
a map of the United States. New York, Indiana, and Kansas are labeled. There is an A marking the state south of New York along the Atlantic coast. There is a B marking the state east of Indiana. There is a C marking the state north of Indiana. There is a D marking the state northeast of Kansas. There is an E marking the state south of Kansas.
New Jersey
Ohio
Michigan
Iowa
According to the information provided, the state is at point C, Michigan.
Based on the information provided, the state located at point C is Michigan.
What is logical thinking?Logical reasoning consists of aptitude questions that require logical analysis to arrive at a suitable solution. Most of the questions are conceptual, the rest are unconventional.
Logical thinking follows he is divided into two types.
Oral reasoning:
It is the ability to logically understand concepts expressed in words and solve problems. Oral reasoning tests your ability to extract information and meaning from sentences. Non-verbal thinking:
It is the ability to logically understand concepts represented by numbers, letters, and combinations of numbers and words and solve problems. Nonverbal reasoning tests your ability to reason and guide the logic and implications of information in a problem.
Much of the logic curriculum can be classified into his two types above.
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7. What is the greatest whole number that satisfies the inequality
3x - 1 < 8 ?
Answer:
2
Step-by-step explanation:
3(2)-1<8
6-1<8
5<8
if you go up to 3 as the whole number then the equation ends up 8<8, and the sign is less than (<) not less than or equal to.
So 2 would be the answer.
What is the quotient of 6. 208 × 10^9 and 9. 7 × 10^4 expressed in scientific notation?
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
Quotient:
The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.
Based on the given conditions, Formulate:
6.208× 10⁹ /9.7×10⁴
Simply using exponent rule with same base:
[tex]a^n. a^m = a^(n+m)[/tex]
= 6.208 × 1/9.7
Now,
the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³
Now solving, we get:
6.208/9.7 × 10¹³
Converting fraction into decimal, we get:
0.64× 10¹³
⇒ 6.4 × 10¹²
Therefore,
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
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cosθ(1+tanθ)=cosθ+sinθ
Answer:
Starting with the left side of the equation:
cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)
= cosθ + sinθ
Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.
1.3. The Dow Jones average (a stock market share index) dropped from 12 837 to 12 503 in one week in July 2012. 1.3.1. Calculate the drop in the share index. 1.3.2. If the price continued to drop at the same rate, calculate the Dow Jones average after 4 more weeks.
The Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
What is average?
Average, also known as mean, is a measure of central tendency that represents the typical or common value in a set of data. It is calculated by adding up all the values in a data set and then dividing the sum by the total number of values.
To calculate the drop in the Dow Jones average, we subtract the initial value from the final value:
Drop = Final Value - Initial Value
Drop = 12,503 - 12,837
Drop = -334
So the Dow Jones average dropped by 334 points in one week.
If the price continued to drop at the same rate for 4 more weeks, then the total drop after 5 weeks would be:
Total Drop = 5 x Drop
Total Drop = 5 x (-334)
Total Drop = -1670
To calculate the Dow Jones average after 4 more weeks, we need to subtract the total drop from the initial value:
New Dow Jones Average = Initial Value - Total Drop
New Dow Jones Average = 12,837 - 1,670
New Dow Jones Average = 11,167
Therefore, the Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.
How to determine the true statement from the optionsBy comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.
Comparing the probabilities of the three players, we can see that:
Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.
Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.
Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.
Therefore, the statement that is true is: Player 2 has the of getting a hit in their at-bats.
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simplest form please
hmmm what we do is firstly make the recurring part a variable, then we multiply it such that, the recurring digits move over from the decimal point to the left, so we'd multiply it by some power of 10, in this case power of 3, because we have three digits to move, 246, so let's do all that
[tex]0.\overline{246}\hspace{5em}x=0.\overline{246}\hspace{5em} \begin{array}{llll} 1000x&=&246.\overline{246}\\\\ &&246+0.\overline{246}\\\\ &&246+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 1000x=246+x\implies 999x=246\implies x=\cfrac{246}{999}\implies x=\cfrac{82}{333}[/tex]
A dolphin was swimming 6 feet below sea level. The number line shows the
location of the dolphin. It then swam down 3 feet. Describe how to use the
number line to find the new location of the dolphin.
-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
OA. On the number line, move 3 units to the left. End at -9. The dolphin
was 9 feet below sea levelsm
OB. On the number line, move 3 units to the right. End at 9. The dolphin
was 9 feet above sea level.
OC. On the number line, move 3 units to the left. End at 3. The dolphin
was 3 feet above sea level.
OD. On the number line, move 3 units to the right. End at -3. The
dolphin was 3 feet below sea level.
On the number line, move 3 units to the left. End at -9. The dolphin was 9 feet below sea level.
What is location?
Location refers to the specific position or coordinates of an object or point in space or time. It can refer to the physical location of an object or place on Earth, such as a building or city, or the position of an astronomical object in the universe.
In a mathematical context, location is often expressed as a set of coordinates or points in a coordinate system.
Location is an important concept in various fields, including geography, cartography, astronomy, and mathematics, and is often used to describe and locate objects, places, or events in a precise and accurate manner.
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16 ft
Find the area.
20 ft
12 ft
10 ft
15 ft A = [?] ft²
Round to the nearest
hundredth.
then the area would be: [tex]Area=\frac{(a+b)}{2*h}[/tex] = (16 ft + 10 ft)/2 x 15 ft = 150 ft²
What is area?Area is a mathematical term that refers to the measurement of the size or extent of a two-dimensional region or surface. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²). The area of a shape is determined by multiplying the length and width of the shape in the case of a rectangle or square, or by using more complex formulas for irregular shapes such as circles, triangles, or polygons. The concept of area is important in various fields such as mathematics, geometry, physics, engineering, and architecture, among others.
by the question.
. If we assume that these are the dimensions of a rectangle, then the area would be:
Area = length x width = 20 ft x 12 ft = 240 ft²
However, if we assume that the area is a trapezoid with a height of 15 ft, and the parallel sides of length 16 ft and 10 ft.
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To compare the pain control offered by two different analgesics in pediatric patients, the authors selected the Wong-Baker FACES pain rating scale as the primary end point. Before beginning the clinical trial, the authors sought to validate this ordinal scale by showing a correlation with a previously validated visual analog scale. Which one of the following statistical test is most appropriate to assess whether a correlation exists between these two measurements?
A. Pearson correlation
B. Analysis of variance (ANOVA)
C. Spearman rank correlation
D. Regression analysis
The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.
What is correlation?Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.
Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".
The formula for Spearman's rank correlation coefficient:
Rs = 1 - {6Σd₂}/{n(n₂-1)}
Where, Σd₂ = the sum of the squared differences between ranks.
n = sample size
Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.
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Levi's investment account accrues interest biannually. The function below represents the amount of money in his account if the account is left untouched for
t years.
f(t) = 2000 (1.03)2t
The amount of money in the account ( increases or decreases )
by (2 , 3 or 103)
% (every six months, each year, or every two years)
Answer:
The amount of money in the account increases by 3% every six months, or biannually.
To see why, we can break down the function f(t) = 2000(1.03)^(2t):
The base amount in the account is $2000.The term (1.03)^(2t) represents the interest accrued over time.Since the interest is compounded biannually, the exponent of 2t indicates the number of six-month periods that have elapsed. For example, if t = 1, then 2t = 2, which means two six-month periods have elapsed (i.e., one year).
Each time 2t increases by 2, the base amount is multiplied by (1.03)^2, which represents the interest accrued over the two six-month periods.
Thus, the amount of money in the account increases by 3% every six months, or biannually.
As for the second part of the question, the amount of increase is not 2%, 3%, or 103%.
Question 70 Approximately 38 percent of people living in on Whave the blood type o positive. A random sample of 100 people from region veled people in the samed the Contra Hypothesis test to vestigate whether the percent of people in thegion with positive blood is different from that of tegen wWwth of the following is the property for the H-0.35 He0.35 с Hep -0.35 D Hp 0.35 H: 0.38
Answer: The null hypothesis (H0) is the statement that there is no significant difference between the proportion of people in the region with the O positive blood type (p) and the population proportion (p0) of 0.38.
The null hypothesis is usually denoted as:
H0: p = p0
In this case, p0 is given as 0.38, so the correct answer is:
H0: p = 0.38
Step-by-step explanation:
If the pyramids below are similar, what is the
ratio of their surface area?
21 in
14 in
A. 3:2
B. 6:4
C. 9:4
D. 27:8
The required ratio of the surface area of the given pyramids is (A) 3:2.
What are ratios?A ratio can be used to show a relationship or to compare two numbers of the same type.
To compare things of the same type, ratios are utilized.
We might use a ratio, for example, to compare the proportion of boys to girls in your class.
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
So, the given surface area is:
- 21 in
- 14 in
Now, calculate the ratio as:
= 21/14
= 3/2
= 3:2
Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.
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Tonia sells seashells to tourists throughout the year. During the summer
months her sales are very high and she makes a considerable profit. As the
seasons change it gets colder less people come to the beach and the less
foot traffic she has causes her to earn less. This cycle repeats every year.
Tonia's situation can be modeled through a(n)
function.
Tonia's situation can be modeled through a seasonal function, specifically a periodic function. This is because her sales and profits vary over time in a predictable pattern that repeats each year.
What is a seasonal function?A seasonal function is a type of mathematical function that models a repeating pattern or a cyclical behavior that occurs over a fixed interval of time. Seasonal functions are used to analyze and forecast patterns in time series data that have a clear seasonality or periodicity
One common type of periodic function is a sine or cosine function. These functions oscillate back and forth between two extreme values in a smooth, periodic way. In Tonia's case, her sales and profits might be modeled as a sine or cosine function that oscillates between high values during the summer months and lower values during the winter months.
Other types of periodic functions include sawtooth functions and square wave functions, which have a more abrupt change between their high and low values.
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X is a Poisson RV with parameter 4. Y is a Poisson RV with parameter 5. X and Y are independent. What is the distribution of X+Y? A. X+Y is an exponential RV with parameter 9 B. X+Y is a Poisson RV with parameter 4.5 C. X+Y is a Poisson RV with parameter 9
The distribution of C) X+Y is a Poisson RV with parameter 9.
This is because the sum of two independent Poisson distributions with parameters λ1 and λ2 is also a Poisson distribution with parameter λ1 + λ2. Therefore, X+Y follows a Poisson distribution with parameter 4+5 = 9.
Option A is incorrect because an exponential distribution cannot arise from the sum of two Poisson distributions. Option B is also incorrect because the parameter of X+Y is not the average of the parameters of X and Y. Option C is the correct answer as explained above.
In summary, the distribution of X+Y is Poisson with parameter 9.
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