A mammogram is used to screen women for breast cancer. False positives are tests that incorrectly show a positive result. 85% of positive mammograms are actually false positives. If 1,000 women receive mammograms, and 200 are told there is an abnormal finding, how many women are likely to actually have breast cancer?

Answer:

14,982,240

Step-by-step explanation:

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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Answer:

the answer is A

Step-by-step explanation:

be my friend please

It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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Just to have fun, I have written a transcript scenario. Your answer is in the paragraph as if I was teaching it! Hope this improves the quality of the answer, if it hasn't just give your review! Have a nice day!

All right. So you want the surface area for this composite figure? So, the surface area, we're going to split into two different shapes. So, I'm gonna do this shape here. That's kind of up. And then I'll do this one. That's kind of flattered. Okay, so when we look at the base, because our surface area formula, let's start with. That is perimeter times high plus two times the area of the base. So, I need the perimeter of this. This is my base, right? I'm thinking about the one that's on the bottom that I can't see. So this is 20 and four. So when you do perimeter, I'm gonna say 20 plus 20 Plus four Plus 4. That's perimeter. The height is eight plus two. And then my area of the base is the two numbers I used in the first parentheses. So four times 20. Okay, so let's see. 20 plus 20 is 40, 40-plus 8 is 48. 48 times eight Is 3 84. Okay. Plus four times 20 is 80, maybe times two is 1 60. If I add all this together And your calculator or do it by hand, you get 5:44. So that is the surface area for the shape that I drew mostly over just now. Let me do it in red for the next one. So my base for this one, I'm actually gonna use 20 and 14 for my perimeter. So the same kind of steps, 20 plus 20 plus 14 plus 14. And then my height is too Plus two times the area of the base. So 20 times 14. So 40 plus 28. Because that's what 14 plus 14 is is 68 68 Times two for the height. So I get 1 36 plus And now 20 times 14 gives you 2 80 times two. It's 5 60 Plus 1 36. So I'm adding these together now And you get 6 96. Alright, We're almost done. Now. We have to take our first answer and add it To our second answer. So 6 96. So 6 96 plus 5 44. You can use your calculator, you get 1240. And if you wanted to use correct units it's centimeters squared. Alright. I hope this helps.

Image attatched is the actual problem.

Answer:

did u guys ever figure it out

Step-by-step explanation:

The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2 is the ordered pair (4.2, -0.2).

In this exercise, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.

Mathematically, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(3(4) + 2(-2))/(3 + 2)],  [(3(-3) + 2(4))/(3 + 2)]

P(x, y) = [(27 - 4)/(5)],  [(-9 + 8)/5]

P(x, y) = [21/5],  [-1/5]

P(x, y) = [4.2, -0.2]

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The equation to represent the situation are as follows:

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

The miles of travel the total cost will be the same is 100 miles.

Your family needs to rent a car for a week while on vacation. Company A charges $3.25 per mile plus a flat fee of $125 per week. Company B charges $3 per mile plus a flat fee of $150 per week.

Therefore, the equation to express the situation is as follows;

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

where

The number of miles the travel will cost the same can be calculated as follows:

3.25x + 125 = 3x + 150

3.25x - 3x = 150 - 125

0.25x = 25

x = 25 / 0.25

x = 100

Therefore, the number of miles is 100 miles.

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Answer:

\(x = 6\)

\(y = 4\)

I'm not sure what type of equations you are looking for but these are the most basic ones.

Step-by-step explanation:

Hope this helps! if you have any questions ask me in the comments.

Answer:

1.59 change

Step-by-step explanation:

2.78*2=5.56

5.56+2.85=8.41

10.00-8.41=1.59

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Answer:

£1.59

Step-by-step explanation:

Cup of Coffee:

=>2 cups of coffee = 2(£2.78)

=> 2 cups of coffee = £5.56

Piece of cake = £2.85

Total cost = 5.56 + 2.85

=> £8.41

Now, the change:

=> £10-£8.41

=> £1.59

We have to make sure that we are taking square roots of non-negative values to stay within the real number system.

You have to make sure x^2-16 ≥ 0 for the inner square root to stay in the real numbers.

You also have to make sure sqrt(x^2-16)-3 ≥ 0 for the outer square root to stay in the real numbers.

Solving x^2-16 ≥ 0 we have that x^2 ≥ 16, so either x≥4 or x≤-4.

Solving sqrt(x^2-16)-3 ≥ 0, we have

     sqrt(x^2-16) ≥ 3

              x^2-16 ≥ 9

                   x^2 ≥ 25

    either x ≥ 5 or x ≤ -5.

Since that second condition is more restrictive that x ≥ 4 or x ≤ -4, we can default to just using

   { x | x ≥ 5 or x ≤ -5 }

   (-infty, -5) U (5, infty)

Answer:

48.8°

Step-by-step explanation:

tangent = opposite / adjacent

tan x = 200 / 175

tan x = 1.143

Take the inverse tangent of both sides

x = 48.8°

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Answer:

HT = 17

<T = 62°

<H = 28°

Step-by-step explanation:

1. Use the Pythagorean Theorem to find the length of the missing side.

a² + b² = c²

15² + 8² = c²

225 + 64 = c²

289 = c²

√289 = c

c = 17

The length of side HT is 17.

2. Use SOHCAHTOA to find the measure of <T. Since we know the measure of two sides, opposite (15) and adjacent (8), use the formula for tangent as tangent is opposite/adjacent.

Tangent = \(\frac{opposite}{adjacent}\)  = \(\frac{15}{8}\) = 1.875

Use the tan⁻¹ button on the calculator to find the value for <T.

tan⁻¹(1.875) = 61.9°

<T = 62°

3. To find the measure of <H, you can either add up the two angles and subtract from 180° or use SOHCAHTOA.

90° + 61.9° + x = 180°

151.9° + x = 180°

x = 28°

or

We know two sides: opposite (8) and adjacent (15). So, we will use tangent.

Tangent = \(\frac{opposite}{adjacent}\) =  \(\frac{8}{15}\) = 0.5333333333

Take the tan⁻¹ to get the measure of <H.

tan⁻¹(0.5333333333) = 28.07 = 28°

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Answer:

ANSWER

Step-by-step explanation:

Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.

If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).

For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.

Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.

The cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.

To find the cost per pound of each type of meat, we can set up a system of equations based on the given information.

Let's denote the cost per pound of rib steak as 'x' and the cost per pound of hamburger meat as 'y'.

From the first statement, we know that:

2x + 6y = 12.30 ---(Equation 1)

From the second statement, we know that:

3x + 2y = 9.70 ---(Equation 2)

Now we can solve this system of equations to find the values of 'x' and 'y'.

Multiplying Equation 1 by 3 and Equation 2 by 2 to eliminate the 'x' term, we get:

6x + 18y = 36.90 ---(Equation 3)

6x + 4y = 19.40 ---(Equation 4)

Subtracting Equation 4 from Equation 3, we get:

14y = 17.50

Dividing both sides by 14, we find:

y = 1.25

Substituting the value of 'y' back into Equation 1, we can solve for 'x':

2x + 6(1.25) = 12.30

2x + 7.50 = 12.30

2x = 4.80

x = 2.40

Therefore, the cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.

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Answer:

f(x) = 2x - 6

Step-by-step explanation:

positive slope = 2

y- intercept = -6

Answer:A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

B) 2

/////////////////

Answer:

x=5

Step-by-step explanation:

10x + 3 = 9 x -2

10•x + 3 = 9•x -2

Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

explaination ::

principle (p) = $890

rate (r) = 4.25%

time (t) = 2 years

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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Answer:

-26

Step-by-step explanation:

did this help

Answer:

The football team gained 9 yards on their first play. On the next play they lost 17 yards. By how many yards did their position change?

Answer:-8

Step-by-step explanation:

Given:

The average price of gas Johannesburg is about 19.24 ZAR per liter.

a) The equivalent amount in US dollars is,

b) The rate in US dollars per gallon is,

Answer:

7.5

Step-by-step explanation:

because 7.5 x 16 = 120

The true similarity statement are using Right Triangle Altitude Theorem :

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

By the Right Triangle Altitude Theorem,

If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.

Using this,

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.

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The complete question is given below.

Answer:

b = 54; A = 34.7°; C = 19.3°

Step-by-step explanation:

To solve the triangle means that we have to calculate the values of the missing angles and the missing sides.

We are given;

B = 126°, a = 38, and c = 22

Using law of cosines, we can find side b.

So;

b² = a² + c² - 2ac*cosB

Thus;

b² = 38² + 22² - 2(38 × 22)cos 126

b² = 1444 + 484 - 1672(-0.5878)

b² = 2910.8016

b = √2910.8016

b = 53.9518 ≈ 54

Using Law of sines, we can find the other 2 angles a and c.

Thus;

a/sin A = b/sinB = c/sinC

Thus, for A;

a/sin A = b/sin B

38/sin A = 53.9518/sin 126

sinA = (38 × sin 126)/53.9518

sinA = 0.5698

A = sin^(-1) 0.5698

A = 34.7363° ≈ 34.7°

Likewise;

b/sinB = c/sinC

53.9518/sin 126 = 22/sinC

sinC = (22 × sin 126)/53.9518

sinC = 0.3299

C = sin^(-1) 0.3299

C = 19.2627 ≈ 19.3°

If the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. Then 192 grams of zinc does it contain

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that,

In a certain​ chemical, the ratio of zinc to copper is 4 to 11.

i.e 4:11 or 4 /11

If A jar of the chemical contains 528 grams of copper

We need to find how many grams of zinc does it contain.

Let us consider it as x.

Form a equation,

4/11=x/528

4×528=11x

2112=11x

Divide both sides by 11

192=x

Hence 192 grams of zinc does it contain.

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