When creating a serial dilution from 1/10 to 1/1000, the first dilution will be [a] part sample and [b] parts diluent (what you dilute the sample in). The second dilution will be one part [c] and nine parts [d]. The final dilution will be one part [e] and nine parts diluent.

The next three terms in the following arithmetic sequence -4, 5, 14, 19 … include the following:

Term 5 = 32.

Term 6 = 41

Term 7 = 50

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 5 - (-4)

Common difference, d = 9

Next, we would determine the next three terms as follows:

a₅ = a₁ + (n - 1)d

a₅ = -4 + (5 - 1)9

a₅ = 32

a₆ = a₁ + (n - 1)d

a₆ = -4 + (6 - 1)9

a₆ = 41

a₇ = a₁ + (n - 1)d

a₇ = -4 + (7 - 1)9

a₇ = 50

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The AB intersects circle P if PA is 7mm and PB is 3mm it must exit the circle, and it has 2 contact points.

PA is longer than the radius of the circle so Point A must be outside of the circle.

Two or more circles intersect at one point. Two circles can be tangent to each other in two different ways.

here, we have,

We have given that,

AB lies in the same plane as circle P, which has a radius of 6 mm.

PB is less than the radius of the circle so Point B must be inside the circle.

Since the ray is going from A to B it is coming inside the circle and continuing in the other direction.

Therefore, it must exit the circle, giving us 2 contact points.

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Answer:

4.6%

Step-by-step explanation:

3500+175 = 3675

(175/3675)×100 = 4.6%

The Cylinder can hold 138, 160 cm³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.

Given:

Height= 1.1 m = 110 cm

Radius= 20 cm

Now, Volume of Cylinder

= πr²h

= 3.14 x 20 x 20 x 110

= 3.14 x 44000

= 138, 160 cm³

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Answer:

  √576 = 24

Step-by-step explanation:

You want to find the square root of 576 by the long division method.

The attachment shows the result of applying the method.

The root of 576 is 24.

Answer:

To find the radius of a ball that holds 66 cubic centimeters of air:

1. Substitute the given volume into the equation r= (3v/4π): r = (3*66/4π).

2. Simplify the equation: r = (198/4π).

3. Calculate the value of 4π: 4π = 12.57.

4. Divide 198 by 12.57: r = 15.75.

5. The radius of the ball that holds 66 cubic centimeters of air is 15.75 cm.

Answer:

Step-by-step explanation:

To find the radius of a sphere that holds 66 cubic centimeters of air, we can use the formula provided in the question:

r = (3v/4π)

where v is the volume of the sphere. We are given that the volume of the sphere is 66 cubic centimeters, so we can substitute this value into the formula:

r = (3 x 66) / (4 x π)

Simplifying this expression:

r = 198 / (4π)

Using a calculator to evaluate this expression:

r ≈ 15.8267

Therefore, the radius of the sphere that holds 66 cubic centimeters of air is approximately 15.8267 centimeters.

Answer:5/8

Step-by-step explanation:

Lowest common denominator is 24

15/24 > 8/24

5/8>1/3

Answer:

y=-0.25x+3.5

Step-by-step explanation:

Ik this

The value of 77 degrees Fahrenheit (°F) is equal to 25 degrees Celsius (°C).

The conversion from Fahrenheit to Celsius involves a simple mathematical formula, which is as follows:

°C = (°F - 32) x 5/9

In this formula, °F represents the temperature in degrees Fahrenheit, while °C represents the temperature in degrees Celsius.

To convert 77 degrees Fahrenheit to Celsius, we first plug in the value of 77 for °F:

°C = (77 - 32) x 5/9

Next, we simplify the expression inside the parentheses:

°C = 45 x 5/9

We can simplify this further by multiplying 45 and 5/9:

°C = 225/9

We can then simplify this fraction by dividing both the numerator and denominator by the greatest common factor, which is 9:

°C = 25

Therefore, we conclude that 77 degrees Fahrenheit is equivalent to 25 degrees Celsius.

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Step-by-step explanation:

What notes are you speaking of?

Answer:

  112

Step-by-step explanation:

You want the number of 3-digit "dropdown numbers".

A "dropdown number" has distinct digits, one of which is the average of all digits.

We can count the number of dropdown numbers by considering the digit that is the average of the rest. For that digit (n), the number of possible choices of the other digits is the lesser of (n) or (9-n). For example, for n=2, we can have other digit pairs of (0, 4) or (1, 3). For n=6, we can have other digit pairs of (5, 7) or (4, 8) or (3, 9).

The value of n may range from 1–8, inclusive, so the number of digit triples will be 2(1 +2 +3 +4) = 20. Each triple of digits can be arranged 6 ways, for a total of 20·6 = 120 numbers of 3-digits.

Of those, 8 numbers will have a leading 0, so may not count as 3-digit numbers. That leave a total of 120 -8 = 112 3-digit dropdown numbers.

__

Additional comment

The first 5 in numerical order are ...

  102, 120, 123, 132, 135

The last 5 are ...

  957, 963, 975, 978, 987

In general, a number on the list, m, has a corresponding number 999-m also on the list. The exceptions are numbers that have a leading digit of 0.

True, the standard deviation is a resistant measure of spread.

The standard deviation is calculated as the square root of the variance of the data set. Variance is calculated as the average of the squared differences between each data point and the mean of the data set. The standard deviation is the square root of this average.

In mathematical terms, the standard deviation can be calculated using the following formula:

σ = √(1/n ∑(x - μ)²)

Where σ is the standard deviation, n is the number of data points in the data set, x is the value of the i-th data point, and μ is the mean of the data set.

The standard deviation is an important measure because it gives an idea of how much the individual values in a data set differ from the mean.

In summary, the standard deviation is a resistant measure of spread because it gives a robust measure of the spread of the data in a set and is not easily influenced by outliers or extreme values.

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-3/4 is slope of the linear equation 3x+4y=5.

Two or more expressions with an Equal sign is called as Equation.

The standard form for linear equations in two variables is Ax+By=C.

3x+4y=5 is a linear equation in standard form.

4y=5-3x

Divide both sides by 4

y=5/4-3/4x

y=-3/4x+5/4

The slope of the equation is -3/4.

Hence, the  slope of the linear equation is -3/4.

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The complete question is given below:

Find the slope of  linear equation 3x+4y=5?

Answer:

Step-by-step explanation:

Divide 20 by 0.50. This gets you 40 meaning she can buy 40 candy bars with her $20 if they are $0.50 each. In order to have $7 left over then she would buy 14 candy bars.

The measure of the angle formed by 2 secants that have a common point outside a circle is 1/2 the difference of the measure of the further intercepted arc and the closer intercepted arc. That means that half of the the measure of arc ABC - measure of arc XYZ is the measure of angle X. Substituting the given values gives you the equation x = 1/2 (125-45)

Then you can solve.

x = 1/2 (80)

x = 40

The measure of angle X is 40 degrees

The fourth term in the sequence is 7.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

Given is the first term of a sequence.

c(1) = 56

Also, there is given an nth term of the sequence.

c(n) = c(n - 1) [tex]\frac{1}{2}[/tex]

This means that every term in the sequence is the half of the preceding term.

So this is a geometric sequence with a common ratio of 1/2.

nth term of a geometric sequence = a. rⁿ⁻¹, where a is the first term and r is the common ratio.

Given, first term = 56 and we found r = 1/2

c(4) = 56 × ([tex]\frac{1}{2}[/tex])⁴⁻¹ = 7

Hence the fourth term in the given sequence is 7.

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Answer:

6w by 9L

Step-by-step explanation:

24 x 1/4=6

36 x 1/4=9

Yhe volume of both the prism and the pyramid are the same. The right response is B, which states, "The volume of both shapes is the same."

What is the straightforward meaning of volume?

Three-dimensional space is occupied by everything. Here, the volume of the space is calculated. A three-dimensional object's volume is the area included inside its bounds. It is also referred to as an object's capability occasionally.

[tex]\mathrm{h_{py} = 3 \times h_p}[/tex]

The volume of the prism is given by:

[tex]V_p[/tex] = base area × height = 4 cm² × [tex]h_p[/tex]

The volume of the pyramid is given by:

[tex]\mathrm{V_{py}}[/tex] = (1/3) * base area * height = (1/3) * 4 cm² * [tex]h_{py[/tex]

Using the equation for [tex]h_{py[/tex] from above, we can substitute:

[tex]\mathrm{V_{py}}[/tex]  = (1/3) * 4 cm² * 3 *  [tex]h_p[/tex] = 4 cm² *  [tex]h_p[/tex] = [tex]V_p[/tex]

So the volume of both the prism and the pyramid are the same. The right response is B, which states, "The volume of both shapes is the same."

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The solution of the equation is,

⇒ x = - 2/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

a) Now, We can solve the expression by using change of base formula:

⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]

Hence, We get;

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

Take log both side we get;

⇒ log 5³ˣ⁻² = log 5⁶ˣ

⇒ (3x - 2) log 5 = 6x log 5

⇒ (3x - 2) = 6x

⇒ - 2 = 6x - 3x

⇒ - 2 = 3x

⇒ x = - 2/3

b) Solve for another method as;

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

By comparing,

⇒ 3x - 2 = 6x

⇒ 3x - 6x = 2

⇒ - 3x = 2

⇒ x = - 2/3

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Answer:

1. 7 or S

2. 2 or E

3. 5 or A

4. 3 or I

5. 9 or the shaded-in letter

6. 11 or T

7. 20 or E

Step-by-step explanation:

1. 7 times 2 is 14, and 7 times 3 is 21

2. 2 times 5 is 10, and 2 times 6 is 12

3. 5 times 3 is 15, and 5 times 5 is 25

4. 3 times 2 is 6, and 3 times 5 is 15

5. 9 times 4 is 36, and 9 times 3 is 27

6. 11 times 2 is 22, and 11 times 3 is 33

7. 20 times 3 is 60, and 20 times 1 is 20.

There are two imaginary roots and one real root of the equation

Generally, In mathematics, the root of an equation is a value that satisfies the equation. In other words, it is the value of the variable for which the equation is true. For example, in the equation x^2 - 4 = 0, the roots are +2 and -2, because when either of these values is substituted for x, the equation becomes true.

There are different methods for finding roots of an equation, depending on the type of equation. For example, some equations can be solved by factoring, while others require the use of more advanced techniques such as the quadratic formula or numerical methods like the Newton-Raphson method.

In general, finding the roots of an equation is an important task in mathematics and has many practical applications in fields such as engineering, physics, and finance.

The roots of the equation  are

x=-2,3+2 i, 3-2 i

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The statements which are true about Micah's survey are;

As evident in the task content; Micah wants to know the most common style of surfboard used at Breakers Point.

Hence, it can be inferred that the population of the survey in this context is; all people that surf at Breakers Point.

Also, since Micah only surveys surfers between 8:00 AM and 12:00 PM, it follows that; Micah will not get a representative sample.

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Answer:

W > 28

W has to be greater than 28

The compound inequality is x < 1 or x >= 3

From the question, we have the following parameters that can be used in our computation:

The number line

From the number line, we have the following readings

x is less than 1 (exclusive of 1)

x is greater than or equal to 3 (inclusive of 3)

Using the above as a guide, we have the following:

x < 1 or x >= 3

Hence, the solution is x < 1 or x >= 3

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By the help of inequality properties The maximum number of interviews is 644.

Let x = number of undergraduate students hired, y = number of graduate students hired, z = number of faculty members hired, n = number of interviews

The objective function is:

Maximize n = 30x + 32y + 33z

The constraints are:

x + y + z ≤ 20

100x + 150y + 200z ≤ 3200

x, y, z integers and ≥ 0 The solution is x = 0, y = 16, z = 4, n = 644

0 undergraduate students, 16 graduate students, and 4 faculty members should be hired to maximize the number of interviews. The maximum number of interviews is 644.

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By using the function rule, the missing values in table should be completed as follows;

x       -2       -1      0      1       2

y       -16      -6     4      14     24

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = -2, the y-value of this linear function is given by;

-10x + y = 4

y = 10x + 4

y = 10(-2) + 4 = -16.

When the value of x = -1, the y-value of this linear function is given by;

y = 10x + 4

y = 10(-1) + 4

y = -6.

When the value of x = 0, the y-value of this linear function is given by;

y = 10x + 4

y = 10(0) + 4

y = 4.

When the value of x = 1, the y-value of this linear function is given by;

y = 10x + 4

y = 10(1) + 4

y = 14.

When the value of x = 2, the y-value of this linear function is given by;

y = 10x + 4

y = 10(2) + 4

y = 24.

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Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.

The implied value of an asset as of a particular date in the future based on a growth rate assumption is known as the Future Value (FV). This area of mathematics examines how random events happen. The value might be between 0 and 1. The mathematical idea of probability aids in predicting the possibility of specific events. In general, probability relates to how probable something is to happen. The interest rate assumption, or the rate of return on the initial amount of capital invested, or the present value, determines the projected future value (PV).

Calculation of the value:

The initial deposit is $1.200

The rate of interest is 5%

Now the future value be like

 [tex](1200\times\frac{(1+0.05)^9-1}{0.05} )\times(1+0.05)+1,200\\\\\(1200\times(\frac{1.5513-1}{0.05} )\times(1+0.05)+1,200\\\\(1200\times11.0265)\times(1.05)+1,200\\\\13893.4711+1,200\\$15,093.47[/tex]

Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.

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Answer:

The answer is B.

Step-by-step explanation:

Method #1 use point slope formula to solve for m of slope.

Method #2 Plug in x-values into option A or B to see you get your dots.

Answer:

we can't find it by herons formula. but here is your answer.....

Step-by-step explanation:

[tex]\\\sqrt{22}\\\\we can do by long division method \\ the actual value of \sqrt{22} = 4.69041575982343.\\well \sqrt{22} itself is in the simplest form[/tex]