1. (20 marks) A survey database shows that 20 percent of the adults in country A have been tested for HIV at some point in their life. (a) Suppose that an adult who has been tested for HIV at some point in his life is needed in a study. Some adults are randomly selected from the population of country A in the selection process until the one who has been tested for HIV is found. Let X be the number of adults selected in this process. Show that the cumulative probability P(X≤x)=1−0.8 x . (4 marks) (b) Using the formula of P(X≤x) in (a), find the probability that the number of adults selected in the process are: (i) Three, (ii) Less than five, (iii) Between five and nine, inclusive, (iv) More than five, but less than 10, (v) Six or more. (5 marks) (c) Find the mean and variance of the number of people selected in the above process. (3 marks) (d) Consider a simple random sample of 18 adults. Find the probability that the number of adults who have been tested for HIV in the sample would be: (i) Three, (ii) Less than five, (iii) Between five and nine, inclusive, (iv) More than five, but less than 10 , (v) Six or more. ( 5 marks) (e) Find the mean and variance of the number of people tested for HIV in the sample. (3 marks)

The power consumed by resistor R3 is 0.79 watts.

The rate at which energy is transferred or converted is known as Power. It is a measure of how much work can be done in a given amount of time. Power is typically measured in watts and is a key factor in determining the efficiency of machines and systems.

To determine the power consumed by resistor R3, we need to first find the current flowing through it.

E₁ = I(R₁ + R₂ + R3 + R4)

I = E₁ / (R₁ + R₂ + R3 + R4)

= 30 / (152 + 202 + 252 + 102)

= 0.056 A

Now that we know the current flowing through R3, we can use Ohm's Law again to find the power consumed by it:

P = I²R3

= (0.056)² x 252

= 0.79 W

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Answer: 7.4

Step-by-step explanation:

Considering the figure, the missing lengths are

In geometry, the phrase "similar triangles" refers to triangles whose respective sides are proportionate and whose corresponding angles are congruent.

Hence, if the triangle's corresponding angles are congruent, the side should be in proportion.

The proportions are as follows

say the side on top of 10 (in horizontal line) is y

y / (10 + 15 + 12.5) = 10 / (10 + 15)

y / 37.5 = 10 / 25

cross multiplying  

25y = 37.5 * 10

25y = 375

y = 15

say the side below side 10 (in horizontal line) is x

x / 10 = 10 / (10 + 15)

x / 10 = 10 / 25

cross multiplying  

25x = 100

x = 4

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Answer:

5^x+x

Step-by-step explanation:

5^x+1+5^x-1

First of all 1- 1 = 0

so we are here with 5^x +5^x

Step-by-step explanation:

94 - 50% * 94   =

             94 - .50 * 94  =

                              94 - 47 =  47  

Answer:

47

Step-by-step explanation:

50 × 94 ÷ 100 =

47,00 ÷ 100=

47

a) Tοtal squares shaded is 4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)

b) The expressiοn gives the tοtal number οf squares.

Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn.  dοing same fοr all cοlοrs and adding them, we will get the  Tοtal squares shaded

c) On simplifying the expressiοn, we get  138  squares

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a cοmplete sentence. Any οne οf the fοllοwing mathematical οperatiοns can be used. A sentence has the fοllοwing structure: Number/variable, Math Operatοr, Number/Variable is an expressiοn.

In each cοlumn, there are 10 squares

The first grid has 4 cοlumns and 6 squares shaded green

=> 4*10+(1*6) = 46  green squares

On the same grid, 6 squares and 4 cοlumns are shaded red.

=> 4*10+(1*6) = 46   red squares

On the same grid, 8 squares are shaded blue. => (1*8) blue squares

On the secοnd 10 by 10 grid, 3 cοlumns and 8 squares are shaded blue.

=> 3*10+(1*8) blue squares

a)Tοtal squares shaded

= shades οn first grid +  shades οn secοnd grid

= ( green squares + red squares +  blue squares ) + ( blue squares )

=  4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)

b)   The expressiοn gives the tοtal number οf squares.

Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn.  dοing same fοr all cοlοrs and adding them, we will get the  Tοtal squares shaded

c)  On simplifying the expressiοn, we get

= 46+46+8+38

= 138  squares

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Answer:

D.) 3.14/2

Step-by-step explanation:

Answer:

34m

Step-by-step explanation:

To find:-

Answer:-

We are here given that Elizabeth climbed up the mountain vertically 30m , and the distance between frank and the bottom of the mountain is 30m .

We are interested in finding out the distance between frank and Elizabeth. For that we will have to use Pythagoras theorem , in which;

[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]

Where h is the longest side of the triangle and a and b are two other sides. here we need to find out the longest side ( see attachment) .

So on substituting the respective values, we have;

[tex]\rm\implies h^2 = (16m)^2+(30m)^2 \\[/tex]

[tex]\rm\implies h^2 = 256m^2 + 900m^2 \\[/tex]

[tex]\rm\implies h^2 = 1156m^2\\[/tex]

[tex]\rm\implies h =\sqrt{1156 \ m^2} \\[/tex]

[tex]\rm\implies \red{h = 34 m} \\[/tex]

Hence the distance between Elizabeth and Frank is 34m .

Answer:

[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find an \underline{equivalent expression}.}[/tex]

[tex]\textsf{This expression is set up to allow us to use the \underline{Distributive Property}.}[/tex]

[tex]\Large\textsf{What is the Distributive Property?}[/tex]

[tex]\textsf{The \underline{Distributive Property} is a property that allows us to distribute.}[/tex]

[tex]\large\underline{\textsf{For this problem;}}[/tex]

[tex]\textsf{We can use the Distributive Property to distribute the 8 into values in the Parentheses.}[/tex]

[tex]\large\underline{\textsf{Distribute:}}[/tex]

[tex]\mathtt{8(2y+\frac{1}{4} )}[/tex]

[tex]\mathtt{(8 \times 2y) + (8 \times \frac{1}{4}) .}[/tex]

[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]

Answer:

16y + 2

Step-by-step explanation:

Now we have to,

→ Find the equivalent expression.

The expression is,

→ 8(2y + (1/4))

Let's simplify the expression,

→ 8(2y + (1/4))

→ 8(2y) + 8(1/4)

→ 16y + (8/4)

→ 16y + 2

Hence, the answer is 16y + 2.

Answer : 6 Dollars

Explanation :  4.00 × 20/100 = 0.8 + 4 = 4.8 * 25/100 = 6

Answer : 6 doolarz                ThanK me

The integer that satisfies all of these conditions is -4.

Exponentiating -4 gives 16, which is less than -1.

The y-coordinate of -4 on the coordinate plane is above 2.

The x-coordinate of -4 on the coordinate plane is greater than -3.

And, the sum of the absolute values of the coordinates of -4 is 7, which is equal to five.

Answer:

The sum of a number and 9 can be written as:

x + 9

where "x" represents the number being referred to.

Alternatively, if we want to use a different variable, we can write it as:

n + 9

where "n" represents the number being referred to.

Hope this helped, if not I'm sorry! If you need more help, feel free to ask! :]

Answer:

9, 20 and 4

Step-by-step explanation:

Swimming only 9

Track only 20

All 3 events

14 did track and field

10 did track and swimming

Those who sis all 14- 10 = 4

The answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

Given that, a school sports team contains 68 students. 33 do field events, 40 do track events, 23 go swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events,

Please refer to picture attached

Therefore,

15+a+c+d = 33.......1

b+c+d+e = 40.........2

a+b+d+f = 23..........3

c+d = 14...............4

a+d = 8.............5

b+d = 10.............6

Now, solving for variables,

From 1 and 4,

a = 4

Therefore, from 5,

d = 4

From 6,

b = 6

Put these in eq 3,

f = 9

c = 10

e = 20

Therefore,

Swimming only = 9

Track events = 20

All three = 4

Hence, the answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4

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Answer:

Ill help you figure out how to graph.

Step-by-step explanation:

The value in front of x (like 2x or 7x) is the slope (rise over run) rise is how much the line goes up, and run is how much it goes to the side. the second number (in the bottom left graph, it is -5) is the y intercept. it is where the line crosses the y axis. (in this case on -5) Here is an example. (of the problem y=x-5)

Answer:

The answer you're looking for is x = 6, and the missing angle is 30º

Step-by-step explanation:

In order to find the answer we need to find out what the angle amount actually is. We can use the equation 180º = 110+ 40 + (8x-18).

Now there are two ways to solve this equation you could solve it by starting with the equation actually is or you can find out the missing angle using another equation.

First Method:

Using 180º = 110+ 40 + (8x-18), you first need to do is to combine like terms such as combining 110, 40, and -18, giving you 132.

Now you have 180 = 132 + 8x.

Then you will have to make sure that 8x is left by itself so do the opposite operation and to keep the equation balanced you do it on both sides giving you 48 = 8x. The only step left to do is to do the opposite operation on both sides which is dividing by 8, giving you 6 = x

Now with that, you replace x, with 6, and go from there.
(8x-18) = (8×6-18) = (48 - 18) = 30.

With that, we are finished with the equation.

However, the other method you could use, which is easier in my opinion, can be found below.

Second Method:

The first thing we do is find out immediately what the missing angle (m) is using the equation 180 = 110 + 40 + m.

You combine like terms 110 and 40, giving 150 and then get,
180 = 150 + m.

You then do the inverse of operations, which is subtracting 150 from both sides and you get 30 = m.

Now that we complete that we start with our other equation which is:
30 = 8x-18. You then do inverse of -18, which adds 18 to both sides giving: 48 = 8x.

Finally doing the inverse operation of multiplying is dividing 8 by both sides giving 6 = x as the correct answer.

The 3 sides to a right triangle are:

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (called the legs) is equal to the square of the length of the longest side (called the hypotenuse).

So, if we have three sides of a triangle and we want to know if it forms a right triangle, we can use the Pythagorean Theorem in the following three ways:

Check if a² + b² = c², where a and b are the lengths of the two legs and c is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.

Check if b² + c² = a², where b and c are the lengths of the two legs and a is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.

Check if a² + c² = b², where a and c are the lengths of the two legs and b is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.

If none of these equations are true, then the triangle is not a right triangle.

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The Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.

a. In order to find each person's optimal number of art works, one must solve for the point at which the marginal benefit and the marginal cost intersect. For Alice, that point is when N = 7 and MBA = MCA, resulting in an optimal number of works of art of 7. For Bianca, the intersection point is when N = 14 and MBB = MCB, resulting in an optimal number of works of art of 14. For Claire, the intersection point is when N = 8.3 and MBC = MCC, resulting in an optimal number of works of art of 8.3.

b. Without considering altruism, Alice will contribute 7 works of art, Bianca will contribute 14 works of art, and Claire will contribute 8.3 works of art.

c. With altruism, the optimal number of art works for each individual can be calculated in the same way as without altruism, but with the warm-glow benefit added to their respective total marginal benefits. For Alice, that point is when N = 7.3 and TMBA = MCA, resulting in an optimal number of works of art of 7.3. For Bianca, the intersection point is when N = 14.6 and TMBB = MCB, resulting in an optimal number of works of art of 14.6. For Claire, the intersection point is when N = 8.7 and TMBC = MCC, resulting in an optimal number of works of art of 8.7.

d. With altruism, Alice will contribute 7.3 works of art, Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.

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To simplify the given expression, we can first evaluate each term inside the square root, and then add them up. Using basic algebraic operations, we get:

T = √(2023^2)(4046) + (2023^2) + 0

T = √(2023^2)(4046 + 1)

T = √(2023^2)(4047)

T = 2023√4047

Therefore, the simplified expression for T is 2023√4047.

The maximum value of the objective function is 33, which occurs at the corner point (3, 3)

According to the question we have to maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3).Linear programming is a mathematical method that aims to maximize or minimize an objective function subject to a set of linear constraints. In this problem, we are asked to maximize the objective function 6x + 5y subject to the constraints given by the inequalities 1, 2, and 3.

The inequalities 1, 2, and 3 define a feasible region in the xy-plane, which is a region that satisfies all the constraints. The feasible region can be found by graphing the three inequalities and shading in the region that satisfies all of them.
In this case, the feasible region is a triangle with vertices (0, 0), (3, 3), and (4, 1), as shown below:

The objective function 6x + 5y is evaluated at each corner point as follows:
At (0, 0), 6(0) + 5(0) = 0,  At (3, 3), 6(3) + 5(3) = 33, At (4, 1),  6(4) + 5(1) = 29. Thus, the optimal solution is x = 3 and y = 3, and the maximum value of the objective function is 33.

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Answer:

Step-by-step explanation:

To see which bag is the better buy, calculate how much each pound of rice would cost.

To do that divide the price by the amount of costs for each then compare those numbers

$2.25/3 = $0.75 per pound

$6.66/9 = $0.74 per pound

So the 9 pound bag of rice would cost 1 cent less per pound making it the better buy.

Answer:

DE's length is 1/2 of BC's length, due to it being a mid segment (13)((You can tell it is a mid segment due to the congruency lines)). AD's length is 12, due to there being a midpoint. EC's length is 10, also due to the congruency lines.

Answer:

[tex]\boxed{ \$600}[/tex]

Step-by-[tex]\boxed{/$600}[/tex]step explanation:

El enunciado nos dice que toda la tienda cuenta con 20% de descuento, así que por cada artículo paga el 80% de su valor (100%-20%).

Una forma rápida de resolver el ejercicio es con regla de 3.

[tex]\$750 \Rightarrow 100 \% \newline x \Rightarrow 80\%[/tex]

para encontrar [tex]x[/tex]:

[tex]x=\frac{80*750}{100} \\x=\$600[/tex]

Por lo que la cantidad que termina pagando por el vestido es de $600.00

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer: x = π - π/4 = 3π/4

Step-by-step explanation:

If sec(x) = -√2 and x is in the second quadrant (between π/2 and π), we can use the identity:

sec^2(x) - 1 = tan^2(x)

to find the value of tan(x):

sec^2(x) - 1 = tan^2(x)

(-√2)^2 - 1 = tan^2(x)

2 - 1 = tan^2(x)

1 = tan^2(x)

Taking the square root of both sides, we get:

tan(x) = ±1

Since x is in the second quadrant, the angle that satisfies tan(x) = 1 is π/4. Therefore, we have:

x = π - π/4 = 3π/4

Note that the angle that satisfies tan(x) = -1 is in the fourth quadrant, so it is not relevant to this problem.

Cross-sectional area of the dam can be calculated without using calculus as explained below:

Step 1: Draw the cross-section of the dam on a graph paper and divide it into simple shapes like triangles, rectangles, and circles.

Step 2: Calculate the area of each shape separately using the appropriate formulae. For example, the area of a rectangle is length times width, area of a triangle is 1/2 times base times height and the area of a circle is pi times radius squared.

Step 3: Add the areas of all the shapes to find the total cross-sectional area of the dam. This gives an approximate value of the area since the actual shape of the cross-section is not perfectly regular.If we take a concrete example of a dam with a cross-section of a trapezoid,

we can calculate the cross-sectional area using the above steps:

Step 1: Draw the cross-section of the dam on a graph paper as shown below. The cross-section of the dam can be divided into a rectangle and a triangle.

Step 2: Calculate the area of the rectangle and the triangle separately using the formulae for the area of the rectangle and the triangle respectively.Area of the rectangle = base times height = 10 m times[tex]4 m = 40 m²[/tex]Area of the triangle = 1/2 times base times height = 6 m times 4 m = 12 m²

Step 3: Add the areas of the rectangle and the triangle to get the total cross-sectional area of the dam.Area of the cross-section = area of rectangle + area of triangle= [tex]40 m² + 12 m²= 52 m²[/tex]The area found using the above method is not exact since it is an approximation of the actual area of the cross-section of the dam. It can be more accurate by dividing the cross-section into smaller and simpler shapes and calculating their areas individually.

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25 bottles every minute are filled using a filling and capping machine in [tex]11700[/tex]

Even though both pressures and movements are involved in a machine's functioning, one of its principal functions can either be force amplification or motion modification. A lever essentially adds force, but a gearbox often acts as a speed reducer.

A machine diagram represents a function operation on a variable x to create a variable output y diagrammatically. If x falls inside the scope of the f(x, the machine will accept x as an input and output y in accordance with the function's rules.

[tex]25 bottles/minute * 20 minutes = 500 bottles.[/tex]

During the remaining [tex]280[/tex] minutes, both machines are running and together they fill

[tex]25 bottles/minute + 15 bottles/minute = 40 bottles/minute[/tex]

So, the total number of bottles filled during this period is

[tex]40 bottles/minute * 280 minutes = 11,200 bottles.[/tex]

[tex]500+ 11,200= 11,700[/tex]

None of the given options represents this equation.

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Answer:

1 . x(x+1)
2.(3a-1)(5a+8)
3.(4x + 3y) ( 3x - 3y)
4.(a+b)

Answer:

769

764 + 3 + 2 = 769

1. She can do   764 + 3 = 767   767 + 2 = 769

2. OR She can do   2 + 3 = 5   5 + 764 = 769