an obese man, 5'0 tall and 160 pounds, sets a long-term goal to lose 40 pounds. What is a reasonable benchmark he might set for himself​

(a) The chance that a person actually has the disease given a positive test result is approximately 91.67%.

(b)  The probability that a person is disease-free given a negative test result is approximately 91.15%.

(c)  The probability that a person who tests positive actually has the disease for a rarer disease with a prevalence rate of 0.1% is approximately 9.01%.

(d) Upon plotting, we find that as the prevalence rate (p) increases, the probability of a person actually having the disease given a positive test result also increases.

(a) To determine the probability that a person actually has the disease given a positive test result, we can use Bayes' theorem. Let's denote the probability of having the disease as P(D) and the probability of testing positive given that the person has the disease as P(Pos|D).

P(D) = 0.10 (prevalence rate)

P(Pos|D) = 0.99 (sensitivity)

Using Bayes' theorem, we can calculate the probability that a person actually has the disease given a positive test result:

\(P(D|Pos) = (P(Pos|D) \times P(D)) / P(Pos)\)

P(Pos) can be calculated as:

\(P(Pos) = P(Pos|D) \times P(D) + P(Pos|D') \times P(D')\)

Since P(D') (complement of having the disease) is 1 - P(D), we can substitute and calculate:

\(P(Pos) = (0.99 \times 0.10) + (1 - 0.98) \times (1 - 0.10) = 0.108\)

Now we can calculate P(D|Pos):

\(P(D|Pos) = (0.99 \times 0.10) / 0.108 = 0.9167\)

(b) Given a negative test result, we want to calculate the probability that the person is disease-free. Let's denote the probability of testing negative given that the person is disease-free as P(Neg|D').

P(D') = 1 - P(D) = 0.90

P(Neg|D') = 0.98 (specificity)

Using similar calculations as in part (a), we can calculate the probability that a person is disease-free given a negative test result:

\(P(D'|Neg) = (P(Neg|D') \times P(D')) / P(Neg)\)

P(Neg) can be calculated as:

P(Neg) = P(Neg|D') * P(D') + P(Neg|D) * P(D)

P(Neg) = (0.98 * 0.90) + (1 - 0.99) * 0.10 = 0.0192

Now we can calculate P(D'|Neg):

P(D'|Neg) = (0.98 * 0.90) / 0.0192 = 0.9115

(c) For a rarer disease with a prevalence rate of 0.1%, we can repeat the calculations from part (a) and part (b) using the new prevalence rate:

P(D) = 0.001

P(D') = 1 - P(D) = 0.999

Using the same values for sensitivity (0.99) and spe\(P(Neg) = P(Neg|D') \times P(D') + P(Neg|D) \times P(D)\)

\(P(Pos) = (0.99 \times 0.001) + (1 - 0.98) \times 0.999 = 0.01098\\P(D|Pos) = (0.99 \times 0.001) / 0.01098 = 0.0901\)

(d) To plot the answer to part (a) as a function of p (prevalence rate), we can use the same calculations and vary the  value of p. The plot will show the relationship between the prevalence rate and the probability of a person actually having the disease given a positive test result.

This relationship is expected because a higher prevalence rate leads to a higher probability of true positive cases, which in turn increases the probability of a positive test result being accurate. However, it's important to note that even with high sensitivity and specificity, the probability of a positive test result indicating the presence of the disease can be significantly influenced by the prevalence rate.

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Range = \(-3 < y \le 3\)

===================================================

Explanation:

The range is the set of all possible y values of a function.

The lowest point happens when y = -3. We exclude this y value because of the open hole.

The highest point is at y = 3 which is included because of the filled in circle.

The range can be written as \(-3 < y \le 3\) meaning y is between -3 and 3, excluding -3 but including 3.

Side note: The range in interval notation is (-3, 3].

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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Answer:

1,092 feet

Step-by-step explanation:

set up a proportion, then cross multiply:

let 'x' = actual length, in feet

\(\frac{1}{120}\) = \(\frac{9.1}{x}\)

The length of the given aircraft with the given scale factor will be 108 feet.

You must specify the extent of the shape's enlargement when describing one.

For example, 50 meters is very big so we cannot measure it but if we can convert it into 50 mm such that the scale ratio is maintained then it will be easy to draw.

Suppose the aircraft's actual length is L.

The ratio of actual length to blueprint

L/(9 1/10) = L/0.9

As per the given scale factor,

1 inches = 120 feet

120 feet = 1440 inches

i inches = 1440 inches

Thus, 1440/1 = L(0.9)

L = 1296 inches = 108 feet

Hence "The length of the given aircraft with the given scale factor will be 108 feet".

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Answer:for #21(d)#22(b)  

sorry cant give u the rest

Step-by-step explanation:

To determine which location yields the higher profit per year, we need the specific data for the annual profit in each location. Please provide the annual profit values for the locations in question, and I will be able to calculate and compare the profit per year.

Without the necessary information regarding the annual profits of the locations, it is not possible to determine which location yields the higher profit per year. To make a meaningful comparison, we need the specific profit figures for each location. Once the annual profit values are provided, we can calculate the profit per year by dividing the total profit by the number of years.

Once the profit per year is calculated for each location, we can compare the values to determine which location has the higher profit per year. However, as the specific data regarding the annual profit in each location is missing, it is not feasible to provide a conclusive answer at this time. Please provide the annual profit figures for the locations in question, and I will be able to assist you further in determining which location yields the higher profit per year.

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Answer: 5.3

Step-by-step explanation:

\(12.6-(5.1+2.2)\\\\=12.6-7.3\\\\=5.3\)

Answer:

false

Step-by-step explanation:

The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Given the expression:

At y = 3, it means that we substitute all the y variables in the expression into 3.

We get,

Therefore, the answer is -4.

To determine the number of high fives that will be exchanged, we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person .

To calculate the number of unique pairs, we can use the formula for combinations, which is nC2, where n is the number of people .So, for Ronnie's class with 20 people, the number of high fives exchanged is:20C2 = (20 * 19) / (2 * 1) = 190.Therefore, a total of 190 high fives will be exchanged in Ronnie's class on National High Five Day. we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person needs to give a high five to every other person, excluding themselves.

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After 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We know the decay can be as:

\(\rm C = a(1-r)^t\)

We have:

a = 470 grams

r = 3% = 0.03

t = 6 hours

\(\rm C = 470(1-0.03)^6\)

C = 391.49 grams

Thus, after 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.

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Answer:

Five students wear glasses.

Step-by-step explanation:

20 percent of 25 is 5

We are given that 25 students in the class and 20% wear glasses.

Take 20% of 25 to calculate how many students wear glasses.

\(25 \times 20 \%=25 \times 0.20\)

\(= 5\)

5 students in class 2-11 wear glasses. Let me know if you have any questions, thanks!

The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.

The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;

(x²+3) (x³+4x) (x²+x-i-xi) = 0.

Hence, by further factorisation; we have;

x(x²+3) (x²+4) (x-i) (x+1) = 0.

The possible values of x are therefore;

x = 0;

x²+3 = 0; x = ±√3i

x² +4 = 0; x = ±2i

x -i = 0; x = i.

x +1 = 0; x = -1

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Answer:

225

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

numbers greater than 200 and less than 300 is 201-299

square numbers between such are

15^2 - 225

16^2 - 256

17^2 - 289

multiples of 5 end in 0 or 5.

225 ends in 5, whereas the other numbers do not.

the number Dave is thinking of is 225

hope this helps:)

Answer:

56mph

Step-by-step explanation:

Speed = distance/ time

= 224/4

= 56

56mph

Answer:

56mph

Step-by-step explanation:

Hello! In order to determine if the equation has a solution, we need to check if the determinant of the matrix A is equal to zero. The equation in question is given by Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix.

If A is an invertible matrix, then its determinant is not equal to zero. Hence, the equation will have a solution. To find x, we can use the inverse of A. The solution is given by x = A^(-1) * b, where A^(-1) is the inverse of A.

To summarize:
1. Calculate the determinant of matrix A.
2. If the determinant is not equal to zero, the equation has a solution.
3. Find the inverse of A, denoted as A^(-1).
4. Compute the solution using x = A^(-1) * b.

Remember to substitute the actual matrices A and b into the equation to find the specific solution.

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6 integers that satisfy the given condition are 10,11,12,13,14,15.

Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

we have the number X

Of which the square root is greater than 3 and less than 4

so,

\(3 < \sqrt{X} < 4\)

on squaring both sides

\(3^2 < (\sqrt{X})^{2} < 4^2\)

\(9 < X < 16\)

so the integer that satisfies the condition is 10,11,12,13,14,15.

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Answer:

6

Step-by-step explanation:

Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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Answer:

x = -12

Step-by-step explanation:

−10x + 1 + 7x = 37

Combine like terms

-3x+1 = 37

Subtract 1 from each side

−3x + 1 -1 = 37-1

-3x = 36

Divide each side by -3

-3x/-3 = 36/-3

x = -12

The area of the shaded region is 319 square inches in the squares.

The area of larger square

The side length of the square which is larger is 20 in

Area of square = side ×side

=20×20

=400 square inches

The side length of the square which is smaller is 9 in

Area of square =9×9

=81 square inches

To find the area of shaded region we have to find the difference between two squares

Difference=400-81

=319 square inches

Hence, the area of the shaded region is 319 square inches in the figure which has squares.

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the equation of a line that has a y-intercept of 4 and is perpendicular to y = x - 1 is y = -x + 4.

To find the equation of a line that has a y-intercept of 4 and is perpendicular to y = x - 1, we can use the fact that perpendicular lines have opposite reciprocal slopes.

The given equation y = x - 1 has a slope of 1, since it is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of a line that is perpendicular to this one, we need to take the negative reciprocal of the slope of the given line. That is, the slope of the new line will be -1/1, or just -1.

We also know that the y-intercept of the new line is 4. So we have the slope (-1) and the y-intercept (4), and we can use the slope-intercept form of a line to write the equation:

y = mx + b

y = -x + 4

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second one is correct

mark me brainlist

Answer:

-1,6 are the answers for the question

Step-by-step explanation:

please give me brainlest

Answer:8r squared -16

Step-by-step explanation:

By using the formula of a geometric sequence, the 14th term will be 125/1024

We have, the Fourth term of geometric sequence T_4= 125 and T_10 = 125/64

Let's find the first term and common ratio of the geometric sequence.

Using the formula of the nth term of a geometric sequence, we get,

T_4 = a * r^3 = 125 ....(1)

and,

T_10 = a * r^9 = 125/64 ...(2)

On dividing eq. (2) by eq. (1), we get,

(r^6) = (125/64) / 125 ⇒ 1/64

Taking the sixth root of both sides, we get:

r = (1/64)^(1/6)

r = 1/2

Now that we know the common ratio, we can use the equation for the nth term of a geometric sequence:

T_n = a * r^(n-1)

To find the 14th term, we substitute n=14 and solve:

T_14 = a * (1/2)^(14-1) ⇒ a * (1/2)^13

We don't know the value of a yet, but we can use the fact that the 4th term is 125 to solve for it:

a * r^3 = 125

a * (1/2)^3 = 125

a = 125 * 2^3

a = 1000

Substituting this value for a, we get:

T_14 = 1000 * (1/2)^13

T_14 = 1000 * 1/8192

T_14= 125/1024

Therefore, the 14th term of the geometric sequence is 125/1024.

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Answer: wait I was wrong I saw thinking about something else

yes that is a unit rate.

Answer:

Yes

Step-by-step explanation:

A unit rate always has 1 as the second value, in this case 1 hour.

Answer :

y = \(\frac{2}{5} ( x - 3)\)

Step-by-step explanation:

6 + 5y = 2x

or, 5y + 6 - 6 = 2x - 6

or, 5y = 2x - 6

or, 5/5 y = 2 ( x - 3) / 5

or, y = 2/5 ( x - 3)

therefore, y = \(\frac{2}{5} ( x - 3 )\)

Simplified expressiοn οf given : f(x) = 15 x +7 and r=4 is f(rx) = 15(rx) + 7 = 15rx + 7.

What is algebraic expressiοn?

An algebraic expressiοn is a cοmbinatiοn οf variables, cοnstants, and mathematical οperatiοns, such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. It may alsο cοntain expοnents and parentheses.

The variables and cοnstants can represent numbers, quantities, οr any οther mathematical οbjects. Algebraic expressiοns are used tο represent mathematical relatiοnships and can be used tο sοlve equatiοns οr simplify cοmplex calculatiοns.

Examples οf algebraic expressiοns include 3x + 5, 2y - 7, and 4a² + 2b - 3c.

r f(x) = 4(15x + 7) = 60x + 28

f(x)+r = 15x + 7 + 4 = 15x + 11

f(x-r) = 15(x-4) + 7 = 15x - 53

f(rx) = 15(rx) + 7 = 15rx + 7

Therefοre, simplified expressiοn οf given : f(x) = 15 x +7 and r=4 is

f(rx) = 15(rx) + 7 = 15rx + 7.

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