In a chemistry experiment, 50,000
independent samples need to be tested for the presence of a chemical compound. To decrease the amount of testing, 5 samples at a time are combined and tested together. A combined sample will result in a negative test only if each of the five component samples is negative for the chemical compound.

If the probability of an individual sample testing positive is 0.2, what is the probability that a combined sample tests positive?

To find the volume of a triangular prism, you will need to use the formula V = (1/2)bhL, where V is the volume, b is the base of the triangular prism, h is the height of the triangular prism, and L is the length of the triangular prism.

Here is a step-by-step explanation on how to find the volume of a triangular prism:

Step 1: Find the base of the triangular prism. This will be one of the sides of the triangular base.

Step 2: Find the height of the triangular prism. This will be the distance from the base to the opposite vertex.

Step 3: Find the length of the triangular prism. This will be the distance between the two triangular bases.

Step 4: Plug in the values for the base, height, and length into the formula V = (1/2)bhL.

Step 5: Simplify the equation to find the volume of the triangular prism.

For example, if the base of the triangular prism is 4, the height is 3, and the length is 6, the volume would be:

V = (1/2)bhL

V = (1/2)(4)(3)(6)

V = 36

So, the volume of the triangular prism is 36.

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Answer:

To find f(4), we simply need to substitute 4 for x in the equation for f(x):

f(x) = -x + 2

f(4) = -(4) + 2

f(4) = -2

Therefore, f(4) = -2.

Step-by-step explanation:

With the sequence having sum of four consecutive integers as 198 , the fourth integer in the sequence is calculated to be 51.

Let's call the first integer in the sequence "x". Since the integers are consecutive, the next three integers in the sequence would be "x + 1", "x + 2", and "x + 3". The sum of these four integers can be represented as:

x + (x + 1) + (x + 2) + (x + 3) = 198

Expanding and simplifying the left side of the equation, we get:

4x + 6 = 198

Subtracting 6 from both sides of the equation, we get:

4x = 192

Dividing both sides of the equation by 4, we get:

x = 48

So the first integer in the sequence is 48. To find the fourth integer in the sequence, we add 3 to the first integer:

x + 3 = 48 + 3 = 51

So the fourth integer in the sequence is 51.

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Answer: y = 6x

Step-by-step explanation:

Answer:

y = 6x

In real-world terms
x = number of sandwiches

y = total cost of x sandwiches in dollar amounts

Step-by-step explanation:

The first piece of advice I have for you is to have confidence in yourself that you will succeed. That is what learners and tutors here at brainly are for. To help out.

Now to explanation of the problem and solution
The linear equation of a graph can be written in a couple of ways. On ios the standard form which is of the form
Ax + By = C where A, B and C are constants

The other is in slope-intercept form which is written as
y = mx + b

Here m is the slope which is also referred to as rise/run. I will explain these terms as we solve the problem

b is the y-intercept. This is the y-value at which the line crosses the y-axis. It corresponds to the value of y when x = 0

Sometimes the graph will not show the complete line so we cannot determine where the line crosses the y-axis. In this case this determination is a cinch

Looking at the graph, we see the line crosses the y-axis at (0,0) which is the origin

Therefore the y-intercept is 0 and hence b=0

Hence we get the line equation as

y = mx + b
==> y = mx + 0
==> y = mx

Let's find m, the slope:
Take any two points on the line. Here two points have been identified as (1, 6) and (4, 24)

The difference in y-values for these two points is 24 - 6 = 18.
This difference in y-values is known as the rise since it is measured vertically

The corresponding difference in x values is 4  - 1 = 3
This is referred to as run because it is measured horizontally

The slope m = rise/run
Here m = 18/3 = 6

Therefore plugging in m = 6 the equation in slope-intercept form is
y = 6x

Slope has another meaning. It signifies the rate of change
In this particular case in real-world terms it means that the cost of sandwiches is proportional to the number of sandwiches

Every sandwich you purchase will cost you $6 more

So the cost per sandwich is $6

For 1 sandwich -→ $6,

For 2 sandwiches → $12

For 7 sandwiches → $42

and all this is clearly evident in the graph

Hope that helps you and good luck on all your subjects

The equation which represents the number of tickets sold in advance is 0.35 × 800

Total tickets sold for a play = 800

Percentage of tickets sold in advance= 35%

Number of tickets sold in advance= Percentage of tickets sold in advance × Total tickets sold for a play

= 35% × 800

= 0.35 × 800

= 280 tickets

In conclusion, 280 tickets were sold in advance.

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The length of line FG is 16 units

The length of FG is equal to length GH that is to say

line FG = line GH

From the problem, we have that

FG = x  + 11

GH = 3x + 1

Equation both lines

x + 11 = 3x + 1

collecting like terms

11 - 1 = 3x - 1

10 = 2x

rearranging and isolating x

2x = 10

x = 5

The line FG = x + 11 = 5 + 11 = 16 units

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Answer:

Answer is 1/2. Box plot is split into quarters. So 1/4 + 1/4 = 1/2

The total area of the composite figure can be found to be 24. 52 cm ²

First, find the area of the first triangle :

= 1 / 2 x base x height

= 1 / 2 x 3 x 2. 7

= 4. 05 cm ²

The area of the second triangle :

= 1 / 2 x 3 . 4 x ( 6. 8 - 2 . 7 )

= 6. 97 cm ²

Then the area of the rectangle :

= 5 x 2. 7

= 13. 5 cm ²

The total area of the composite shape is :

= 13.5 + 6.97 + 4. 05

= 24. 52 cm ²

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Number of seconds in a year riddle will be 31,536,000 seconds in a year ((24 x 60 x 60) x 365).

To calculate number of seconds in year riddle, we need to calculate the no. of seconds in each month.

There are a total 12 months and each month consists of 31, 30 and 28 days respectively.

Now, calculating the number of seconds in each month multiplying the count of months with respect to the number of days in that month.

In January, March, May, July, August, October, December : 31x24x60x60=26,78,400x7=1,87,48,800

In Feb: 28X24x60x60=24,19,200

In April, June, September, November: 30x24x60x60=25,92,000x4=1,03,68,000

Now add all the values: No of Seconds in year riddle = 1,87,48,800+24,19,200+1,03,68,000

Totally the value will be equal to 3,15,36,000 seconds.

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To properly measure the volume of water in a calibrated glass device such as a graduated cylinder, follow these steps:

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The probability of rolling a 9 or higher on the 3rd roll is 4/27, or approximately 14.8%.

Probability is a branch of mathematics that deals with determining the likelihood or chance of an event occurring. It is often expressed as a fraction or a percentage.

Conditional probability is the probability of an event happening given that another event has already happened.

The probability of not rolling a 9 or higher on the first roll is 8/12 or 2/3, as there are 8 numbers on the cube that are less than 9.

The same is true for the second roll, so the probability of not rolling a 9 or higher on the first two rolls is (2/3) * (2/3) = 4/9.

The probability of rolling a 9 or higher on the third roll is 4/12 or 1/3, as there are 4 numbers on the cube that are 9 or higher.

So, the probability of rolling a 9 or higher on the third roll given that the previous two rolls did not result in a 9 or higher is

=> (4/9) * (1/3) = 4/27

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Graph of y = cosec x is attached below.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Given function,

y = cosecx

when x = (π/2)

y = cosec (π/2)

y = 1

when x = π

y = cosec π

y = ∞

when x = 3π/2

y = cosec 3π/2

y = -1

By the calculation, graph of y = cosecx is drawn as follows.

Hence, graph of y = cosecx is attached below.

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The requried expression that describes the cost of a talk-and-texting plan for one month, given x minutes over 600 is 35 + 0.35(x) + 20.

The expression model is described as the model of the given situation in the form of an equation using variables and constants.

here,
The cost of a talk-and-texting plan for one month can be expressed as:

= 35 + 0.35(x) + 20

where x is the number of minutes over the 600 minutes included in the plan. The first two terms represent the cost of talk time, while the last term represents the cost of unlimited texting.

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the mean of Xochitl's finishing times is 84 seconds and the standard deviation is 2.5 seconds, so the interval that represents the middle 68% of her finishing times is:

[84 - 2.5, 84 + 2.5] = [81.5, 86.5]

So, we can conclude that the middle 68% of Xochitl's finishing times in the 400 meter race fall between 81.5 and 86.5 seconds.

Step-by-step explanation:

Answer:

y = -3x + 10

where y = Value and x = Position

or

Value = - 3(Position) + 10

Step-by-step explanation:

We can determine a linear equation for this table in slope-intercept form

The slope intercept form of a linear equation is

y = mx + b

y is referred to as the dependent variable and x the independent variable

Here m is the slope which is the rate of change of y with respect to x

b = y-intercept which is the value of y when x = 0

For the given table it appears that the value is dependent on the position

So the independent variable, let's call it x, is position

The dependent variable, y, is value

Plugging values of x, y into the generalized equation

y = mx + b

At x(position) = 1, we get y = 7
==> 7 = m(1) + b  
==> 7 = m + b
== m + b = 7         ............................. (1)

At x = 3, y = 1

==> 1 = m(3) + b
==> 1 = 3m + b
==> 3m + b = 1       ..............................(2)

If we subtract  equation 1 from equation (2) we get
(3m + b) - (m + b) = 1 - 7

3m - m + b - b = -6

2m + 0 = -6

2m = -6

m = -6/2 = -3

So we now know m = -3 we can write the equation as

y = -3m + b

To find b, plug in any value of x and corresponding y from the table and solve for b. remember that x is position and y is value

Let's choose the last entry x = 9, y = -17

Plugging these into y = -3x + b gives

-17 = -3(9) + b

-17 = -27 + b

Switch sides:
- 27 + b = -17

Add 27 to both sides:
- 27 + 27 + b = -17 + 27

b = 10

So the equation for the table is

y = - 3x + 10

or in terms of the table
Value = - 3(Position) + 10

You can check this is correct by choosing a value for position from the table and seeing the equation value is consistent with the given value

The value of x is 8 units by using Pythagorean theorem.

If x and 6 are the lengths of the legs of a right triangle and the length of the hypotenuse is 10, then we can use the Pythagorean theorem to find the value of x.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

So in this case:

x^2 + 6^2 = 10^2

Expanding the squares and solving for x:

x² + 36 = 100

x² = 100 - 36

x² = 64

x = [tex]\sqrt{64}[/tex]

x = 8

So the value of one leg of x is 8 units and other which is given is 6 units.

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____ The given question is incomplete, the correct question is given below:

What is the value of x?

Enter your answer in the box.

x=

A right triangle. The legs are labelled x and six, and the hypotenuse is labelled ten.

Answer:

If you are asking if y = 4x is proportional, the answer is yes.  It is linear and it goes through the origin.

Step-by-step explanation:

A frequency distribution usually has equal bin widths is the true statement.

All the line charts are not used for the purpose of cross-sectional data. A scatter plot is very useful in this process of visualizing trends over time. A scatter plot essentially requires two quantitative variables (i.e., not categorical data).

The difference of the maximum and minimum values is divided by the number of bins.

1. Identify the maximum and minimum values of the quantitative data.

2. Subtract the minimum value from the maximum value to get the difference

3. Divide the difference by the number of bins to get the approximate width of each bin

The width of the bins in a frequency distribution of quantitative data can be estimated by dividing the difference between the maximum and minimum values of the data by the desired number of bins. This will provide an approximate size for each bin, that can then be used to construct the frequency distribution.

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Answer: 8y=2h

Step-by-step explanation: you have to subtract the first 2 numbers then add the others and then add letters and boom

The only coordinate solution in the table is (8, -9), the other coordinates are not a solution.

A linear equation is an equation that has a leading degree of 1.  Given the linear equation below:

4x + 5y = -13.

We are to determine the coordinates that form a solution.

For (8, -9)

4(8) + 5(-9) = 32 - 45

4(8) + 5(-9) = 13

Hence the coordinate (8, -9) is a solution

The other given coordinates are not a solution since the result on substituting their coordinate will not result in. -13

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The number of possible ways in which we can select 3 elements from 7 elements are  given in option d. 35.

There are a total of 7 elements and we can to select 3 elements out of them.

We have to apply the permutation and combination here in order to find the answer,

The formula is ⁿCₐ

Where, C represents combination,

n is the total number of combination,

a is the number of selections that we have to do,

ⁿCₐ = n!/(n-a)!a!

Now, putting n = 7 and a = 3,

ⁿCₐ = 7!/(4)!3!

ⁿCₐ = 35

So, the total number of ways possible are 35.

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The two figures (i.e. triangles) are similar triangles

Let's create a triangle with the following coordinates:

A = (0, 0)

B = (3, 0)

C = (0, 4)

To get the new coordinates, we need to multiply the y-coordinate of each point by 4:

A' = (0, 0 * 4)

B' = (3, 0 * 4)

C' = (0, 4 * 4)

So the new points are:

A' = (0, 0)

B' = (3, 0)

C' = (0, 16)

To determine if the two figures are similar, we need to check if they have the same shape but different sizes.

Specifically, the new triangle is four times larger in the vertical direction but has the same shape and angles as the original triangle.

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Answer:

23 degrees

Step-by-step explanation:

Sum of interior angles in a triangle = 180°

∴Sum of interior angles in the right- angled triangle in the question:
    67° + 90° + ? = 180°

= ? = 180° - 90° - 67°

∴ ? = Missing angle measurement = 23°

                                                           = 23 degrees

V(x) = (10 - 2x)(17 - 2x)(x)

To find the volume of an open-top box, we need to find the product of its length, width, and height. In this case, the length and width of the box will be the original dimensions of the cardboard minus twice the side length of the square cutouts, and the height will be the side length of the square cutouts.

a) The expression for V(x) can be written as:

V(x) = (10 - 2x)(17 - 2x)(x)

b) To find the volume of the box when x = 3, we simply need to plug in the value of x into the expression for V(x) and simplify:

V(3) = (10 - 2(3))(17 - 2(3))(3)

V(3) = (10 - 6)(17 - 6)(3)

V(3) = (4)(11)(3)

V(3) = 132

Therefore, the volume of the box when x = 3 is 132 cubic centimeters.

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The value of length WZ is 7.5 in and angle Y is 45°

Similar shapes are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio. E.g. These two rectangles are similar shapes.

therefore;

WZ /QT =WX/QR

represent WZ by x

x/3 = 5/2

2x = 15

x = 15/2

x = 7.5

therefore the value of WZ = 7.5 in

Since the two quadrilaterals are similar angle Y is 45°

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Answer:

ranalllldooo

Step-by-step explanation:

suiiiiiii

The brand that is the better buy based on their unit price is; Brand A

A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can be used to compare the same type of goods sold in varying weights and amounts.

It is also referred to as a product's average price which is the result of dividing the product's total sales revenue by the total units sold.

Thus;

Unit price of Brand A = 8.77/24 =$0.365 per pencil

Unit price of Brand B = 9.84/26 = $0.378 per pencil

The cheaper one is the better buy which is Brand A.

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Answer: The equivalent expression to Sarah's expression is:

6.25(x + y) + 242.78

This expression takes into account the total number of hours worked by James (x) and Sarah (y) and adds it to the sum of their tips, which is $242.78. The expression multiplies the total number of hours worked by 6.25, which is their hourly wage.

Step-by-step explanation: