Answer:
4,320 times
Step-by-step explanation:
12 x 6 = 72 beats per minute
72 x 60 = 4320 beats in 60 minutes
Answer: 840 in 30 minuets
Step-by-step explanation:
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.
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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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:
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%.
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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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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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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F(x)=-(x+3)(x+10) pls help
Answer:
Zeros: x = -10 and x = -3
Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]
Step-by-step explanation:
Pre-SolvingWe are given the following function:
f(x) = -(x+3)(x+10)
We want to find the zeros and the vertex of the parabola.
SolvingZerosThe zeros are the values of the function where f(x) = 0.
So, in order to find the zeros, we can set f(x) = 0.
0 = -(x+3)(x+10)
We can divide both sides by -1, to get:
0 = (x+3)(x+10)
To solve this, we will use zero product property.
Split and solve:
x+3 = 0
x = -3
x+10=0
x = -10
Vertex
Now, to find the vertex, we first get the average of the zeros.
Add the values of the zeros together, then divide by two:
[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]
Now, we plug this in for x to get the y value (found through f(x)) of the vertex.
[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]
So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]
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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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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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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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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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.
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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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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Whats 21 square root of 98 divided by 7 square root of 21
The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407
A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.
Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.
Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.
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Find the first 4 terms of the sequence represented by the expression 3n + 5
The first 4 terms of the sequence represented by the expression 3n + 5
is 8, 11, 14 and 17.
Sequence:
In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.
According to the Question:
Given, aₙ = (3n+5).
First four terms can be obtained by putting n=1,2,3,4
a 1=(3×1+5) = 8
a 2 =(3×2+5) = 11
a 3 =(3×3+5) = 14
a 4 =(3×4+5) = 17
First 4 terms in the sequence are 8, 11, 14, 17.
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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.
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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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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the sides of a triangle have lengths 15, 20, 25. find the length of the shortest altitude of the triangles.
The length of the shortest altitude of the triangles is 15 units by using Heron’s formula.
We have, The sides of a triangle have lengths of 15, 20, and 25.
To find, The length of the shortest altitude of the triangle.
Steps to solve the problem:
Let us assume that the length of the b is h.According to the property of triangles, the area of the triangle can be calculated as:Area = 1/2 * base * height
We can choose any side as the base of the triangle, let us assume that 20 is the base of the triangle, and its corresponding height is h.Area of the triangle = 1/2 * 20 * h ⇒ 10h
Using Heron’s formula, the area of the triangle can be calculated as:A = √(s(s-a)(s-b)(s-c))
Where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle.
According to the given problem, the sides of the triangle are 15, 20, and 25.
s = (a + b + c)/2
= (15 + 20 + 25)/2
= 30
Therefore, the area of the triangle can be calculated as:
A = √(30(30-15)(30-20)(30-25))
= √(30*15*10*5)
= 150 sq. units
Therefore, we can write the formula for the area of the triangle as:
150 = 10 h
h = 15 units
Therefore, the length of the shortest altitude of the triangle is 15 units.
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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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If you run towards a faraway friend at 5 miles per hour and she bikes towards you at 15 miles per hour, how many miles closer are you to each other after 1 hour?
Using the unitary method we calculate that the friend would be 20 miles closer in an hour.
If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:
5 miles / hour - (- 15 miles / hour) = 20 miles / hour
Also, we know that
speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,
20 miles/hour × 1 hour = 20 miles
Therefore, you would be 20 miles closer to each other after 1 hour.
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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
=
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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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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How to find x? I am not sure what equation to use to get the correct answer?
Each angle of a regular polygon is 1680. How
many sides has it? What is the name of this
polygon?
Answer: 2 solutions
Step-by-step explanation:
To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)
Setting them equal, we get (180n-360)/n = 1680.
Multiplying by n on both sides, we get 180n-360 = 1680n.
Solving, we get 1500n = 360.
n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.
The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.
Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.
Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.
Evaluate the expression shown below and write your answer as a fraction in simplest form.
-0.25 + 0.3 - ( - 3/10 ) + 1/4
The evaluation of the expression -0.25 + 0.3 - ( - 3/10 ) + 1/4 is 3 / 5.
How to solve expression?An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Therefore, let's solve the expression as follows:
-0.25 + 0.3 - ( - 3/10 ) + 1/4
let's convert it to fraction
- 1 / 4 + 3 / 10 + 3 / 10 + 1 / 4
Hence,
3 / 10 + 3 / 10 + 1 / 4 - 1 / 4
3 + 3 / 10
6 / 10 = 3 / 5
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True or false (with a counterexample if false)?(a) The vectors that are not in the column space form a subspace.(b) If contains only the zero vector, then is the zero matrix.(c) The column space of equals the column space of .(d) The column space of equals the column space of .
(a) False; A subspace is formed by the set of vectors that do not belong to the column space.
(b) True; If the matrix contains solely the zero vector, then it is the zero matrix.
(c) True; The column space of a particular matrix is equivalent to the column space of another specified matrix.
(d) False; The column space of one matrix is identical to the column space of another matrix.
(a) False; if A = [1 0; 0 0], then the column space of A is { e1 }, where e1 is the standard unit vector in the plane. If v is not in the column space of A, but w is not in the column space of A, then v + w is not in the column space of A.
Therefore, the set of vectors that are not in the column space of A does not form a subspace.
(b) True; if every vector in Rn is in the null space of A, then in particular, every standard unit vector is in the null space of A. Thus, the ith column of A is zero for i = 1, . . . , n, so A is the zero matrix.
(c) True; the column space of A is generated by the columns of A, while the column space of AB is generated by linear combinations of the columns of AB. By definition of matrix multiplication, the columns of AB are linear combinations of the columns of A, so the column space of AB is a subspace of the column space of A. Conversely, let b be in the column space of A. Then there is an x in Rm such that Ax = b. Thus, ABx = A(Bx), so b is in the column space of AB. Therefore, the column space of A is a subspace of the column space of AB. Hence the two column spaces are equal.
(d) False; if A = [1 0; 0 0] and B = [0 0; 0 1], then the column space of A is { e1 }, while the column space of B is { e2 }. The column space of AB is { 0 }, so it is not equal to either column space.
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