To determine whether or not they have a certain desease, 304 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to group the people in groups of 19. The blood samples of the 19 people in each group will be pooled and analyzed together. If the test is negative, one test will suffice for the 19 people (we are assuming that the pooled test will be positive if and only if at least one person in the pool has the desease); whereas, if the test is positive each of the 19 people will also be individually tested and, in all, 20 tests will be made on this group. Assume the probability that a person has the desease is 0.04 for all people, independently of each other, and compute the expected number of tests necessary for the entire group of 304 people.

The given function y = 4(3/8)^x represents exponential decay.

As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

The given function is y = 4(3/8)^x. To determine if the function represents growth, decay, or neither, we need to examine the base of the exponent, which is (3/8).

When the base of an exponential function is between 0 and 1, such as (3/8) in this case, it represents exponential decay. This is because as the exponent (x) increases, the value of the function decreases.

In the given function, the coefficient 4 multiplied by the decaying exponential term (3/8)^x indicates that the function starts with an initial value of 4 and then exponentially decreases. The term (3/8)^x represents the decay factor, where x determines the extent of decay.

Therefore, we can conclude that the given function, y = 4(3/8)^x, represents exponential decay. As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

In summary, the given function y = 4(3/8)^x represents exponential decay.

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The five in 35.76 is 100 times bigger than the five in 26.95.

Here we want to compare the values of the 5's in two different numbers, which are 35.76 and 26.95.

To compare them we need to compare the place value in which each five is.

To compare them, just write the numbers but replacing all the other values by zeros:

35.76 = 05.00 = 5

26.95 = 00.05 = 0.05

Now take the quotient of these two, we will get:

5/0.05 = 100

Thus, the 5 in 35.76 is 100 times bigger than the 5 in 26.95.

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Answer:

1. 4√5

2. 3√5

3. √149

4. √58

Step-by-step explanation:

The Pythagorean theorem states "a^2 + b^2 = c^2",  where "a" and "b" are the legs, while "c" is the hypotenuse.

Knowing this, we can substitute each variable with given values on the triangles

1.  "4" and "8" are legs "a" and "b" and we need to find the hypotenuse "c"

4^2 + 8^2 = c^2

16 + 64 = c^2

80 = c^2

√80 = c

4√5 = c

2. "6" and "3" are legs "a" and "b" and we need to find the hypotenuse "c"

6^2 + 3^2= c^2

36 + 9 = c^2

45 = c^2

√45 = c

3√5 = c

3. "7" and "10" are legs "a" and "b" and we need to find the hypotenuse "c"

7^2 + 10^2 = c^2

49 + 100 = c^2

149 = c^2

√149 = c

4. "3" and "7" are legs "a" and "b" and we need to find hypotenuse "c"

3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

√58 = c

The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.

The number of minutes to read 6.25 pages will be given as,

⇒ 6.25 x 0.8

⇒ 5 minutes

The number of minutes to take the test will be given as,

⇒ 5.5 - 5

⇒ 0.50 minute

⇒ 0.50 x 60

⇒ 30 seconds

The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

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That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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Answer: The area of the new parallelogram is multiplied by 18

Step-by-step explanation: Let the base and the height of the original parallelogram be ' x '

Base of the parallelogram = x

Height of the parallelogram = x

Area of parallelogram = l × b = lb

= x × x = x²

∴ Area of the original parallelogram = x²

∴ The base is multiplied by 3 = 3x

The height is multiplied by 6 = 6x

∴ Area of new parallelogram = 3x × 6x = 18x²

∴ The area of the new parallelogram is multiplied by = 18x²/ x²

= 18

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Answer:

The rational function that might have the given graph is \(y = - \frac{x}{(x+1)\cdot (x-1) }\).

Step-by-step explanation:

This graph shows a rational function whose numerator is a first order polynomial and denominator is a second order, due to the presence of vertical asymptotes at \(x = -1\) and \(x = 1\). The lead coefficient of the numerator must be 1, since horizontal asymptote must be \(y = 0\) and intercept must be \(0\), since \(y(0) = 0\).

Then, we conclude that a rational function that might have the graph is:

\(y = - \frac{x}{(x+1)\cdot (x-1) }\) (1)

We present the proof that given function is appropriate.

Answer:

He will have 2 cups :)

Answer:

he would have 2 cups in it cause 1 pint = 2 cups

A ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

The steps for constructing a copy of an angle:

Step 1: Draw the angle.

Step 2: Place the center of the protractor on the vertex of the angle.

Step 3: Line up the baseline of the protractor with one of the angle's rays.

Step 4: Read the degree measure where the other ray crosses the protractor.

Step 5: Draw a ray from the vertex of the angle to the right.

Step 6: Use a ruler to mark the same distance on the ray that was just drawn.

Step 7: Draw a ray from the vertex through the point just marked on the ray.

This is the copy of the angle's second ray.

Step 8: Use a compass to draw an arc centered at the vertex of the original angle that passes through one of the angle's rays.

Step 9: Without adjusting the compass, draw another arc that intersects the previous arc at a point.

Step 10: Draw a ray from the vertex through the point where the two arcs intersect.

This is the copy of the original angle.

Using a compass, draw an arc centered on the vertex of the original angle passing through one of the angle rays. Place the tip of the

compass on the vertex of the original angle and draw an arc that intersects one of the angle rays.

Draws another arc that intersects the previous arc at a point without adjusting the compass.

Draw a second arc that intersects the first arc at another point, keeping the compass latitude.

Using a ruler or ruler, draw a ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

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Answer: 56.52mm

Step-by-step explanation:

First, you have to find the circumference of the wheel and divide it by 25 since the spokes are equally spaced.

The equation for the circumference of a circle is:

C = 2πr

C = 2 x π x 225

C = 1413

Then, you divide it by 25

1413/25 = 56.52

The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.

The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.

Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.

Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.

Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.

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The probable question may be:

Which cellphone service provider was the first to be established in south africa

Answer:

60

Step-by-step explanation:

Assuming that all 54 shelves hold the same number of books its just a matter of dividing them (or sharing them equally) on each shelf.

3240 / 54 = 60

Each shelf holds 60 books.

Formula for the Sum of Natural Numbers is [n(n+1)]/2, where n is the natural number.

Given that,

We have to find sum of the n natural numbers is .

We know that,

The arithmetic progression formula, where the common difference between the preceding and following numbers is 1, is used to calculate the sum of natural numbers. Natural numbers, which range from 1 to infinity, include 1, 2, 3, 5, 6, and so on.

Therefore, to get the formula for the sum of natural numbers, we use the sum of n terms in the arithmetic progression

Formula for the Sum of Natural Numbers is [n(n+1)]/2, where n is the natural number.

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The correct option for the given sum is option B. The point (2,-9) paired with (2, 3), will make a side equal to this length.

Let the other point of the pentagon will be M(n, o).

The given point be A (a, b)

Also given one of the sides of a pentagon has length 12.

Now, we need to find the distance between the two points,

Distance between two points: |AM| = √\((a-n)^2+(b-o)^2\)

Now,

\(12 = \sqrt{(2-n)^2+(3-o)^2}\)

\((12)^2\) = \((2-n)^2+(3-o)^2\)

\((2-n)^2+(3-o)^2\) = 144 ----------------------------- eq (1)

Now, check every point for the values to match with equation (1)

Option A: \((2-14)^2+(3-15)^2\) = 288. So the option is false.

Option B:

\((2-2)^2+(3-(-9))^2\) =114

0+114 =114

Therefore option B is correct. The other point is (2,-9).

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The wavelength  λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now, the given equation for photon energy, E , is

E = hcλ

Here, h = 6.626×10^−34 J⋅s (Planck's constant) and

c = 2.99×10^8 m/s (the speed of light)

Therefore, we have

E = hcλ

⇒ λ = E/hc

Put the values of E, h and c we get,

λ = 4.26×10^−19 / (6.626×10^−34*2.99×10^8)

Solving we get,

λ = 4.26×10^−19 / 19.81×10^(−34+8)

⇒ λ = 4.26×10^−19 / 19.81×10^-26

⇒ λ = (4.26/19.81)*10^(-19+26)

⇒ λ = 0.215042×10^5 meter

⇒ λ = 21504.29 meter

Thus, the wavelength  λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.

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Step-by-step explanation:

The dressmaker's expected value can be calculated as follows:

E(X) = (1/5) x $76 + (6/11) x (-$31)

E(X) = $15.20 - $16.36

E(X) = -$1.16

Therefore, the dressmaker's expected value is -$1.16, which means that on average, the dressmaker can expect to lose $1.16 for each dress they create.

Answer:

I think the answer might be b.

Step-by-step explanation:

Answer:

Initial balance 500, compounds 4 times at an interest rate of 15%

Step-by-step explanation:

Initial balance 500, compounds 4 times at an interest rate of 15%

Answer:

The term that best describes a figure formed by three segments connecting three non-collinear points is:

Triangle.

Step-by-step explanation:

Step-by-step explanation:

We know that with the help of just one point we can't form any figure.

With the help of two points a line segment can be formed.

And with the help of three points if the three points are collinear a triangle can be formed.

Hence, the term that best describes a figure formed by three segments connecting three non-collinear points is:

Triangle.

Answer:

= - 7.68 I hope this helped you.

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

The value of g(x) is (x^3+5) and g(64) = 262149.

According to the statement

we have given that the

f(x)=√x^3 and (fog)(x)=√(x^3+5) and we have to find the value of the g(64).

So, For find the value of g(64), Firstly we have to find the g(x).

So,

We given that

f(x)=√x^3 and (fog)(x)=√(x^3+5)

And here the formula used is

(f o g)(x) = f (g(x))

here (fog)(x)=√(x^3+5) and f(x)=√x^3

From this we get g(x) is (x^3+5)

So,

g(x) = (x^3+5) and

g(64) = ((64)^3+5)

g(64) = 262149.

So, The value of g(x) is (x^3+5) and g(64) = 262149.

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Question:

If f(x)=√x^3 and (fog)(x)=√(x^3+5). Then find the value of g(64).

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I take this to mean \(f(x) = \sqrt{x^3}\) and \((f\circ g)(x) = \sqrt x\).

Let's first find the inverse of \(f\).

\(f\left(f^{-1}(x)\right) = \sqrt{\left(f^{-1}(x)\right)^3} = x \\\\ \implies \left(f^{-1}(x)\right)^3 = x^2 \\\\ \implies f^{-1}(x) = x^{2/3}\)

(Note that \(f\) is defined only if \(x^3\ge0\), or \(x\ge0\).)

Apply the inverse of \(f\) to \(f\circ g\).

\((f\circ g)(x) = f(g(x)) = \sqrt x \\\\ \implies f^{-1}\left(f(g(x))\right) = f^{-1}(\sqrt x) \\\\ \implies g(x) = \left(\sqrt x\right)^{2/3} = \left(x^{1/2}\right)^{2/3} = x^{1/3} = \sqrt[3]{x}\)

Then

\(g(64) = \sqrt[3]{64} = \sqrt[3]{4^3} = \boxed{4}\)

Answer:

I usseme you already got this answer

Answer:

C. 26 + 4x = 46