Solving 2 step equations
5 ( x + 4 ) = 30

The length of the microorganism in millimeters is 0.005 mm.

The theory behind converting length units from one unit to another is based on the conversion factor principle. In the International System of Units (SI), the conversion factor between two units of length can be obtained by comparing the number of meters represented by each unit. For example, 1 millimeter is equal to 0.001 meters, and 1 micrometer is equal to 0.000001 meters.

To convert from one unit of length to another, we multiply the length by the appropriate conversion factor. In this case, to convert from micrometers to millimeters, we multiply the length in micrometers by 0.001 to obtain the length in millimeters.

To convert the length of the microorganism from micrometers (μm) to millimeters (mm), we divide by 1000.

5 μm / 1000 = 0.005 mm

Therefore, the length of the microorganism in millimeters is 0.005 mm.

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It is stated that y = 10x + 60 is the equation for the line of greatest fit for all of this data set. indicating that the third choice is the right one.

How can I get the formula for the best fit line?

It is stated that a linear function has the following slope-intercept definition:

y = mx + b.

which contains the following coefficients:

The slope, or m, shows how quickly the function's output changes in relation to its input.

The y-intercept, or b, represents the value that the input function assumes to be zero.

Since the function passes through the given point (0,60), the following is the line's b-intercept:

b = 60.

When x rises by two from zero to two, y rises by twenty from sixty to eighty.

Consequently, the slope m is determined as follows:

m = 20/2 = 10.

Therefore, the following is the line of fit:

y = 10x + 60.

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It is stated that y = 10x + 60 is the equation for the line of greatest fit for all of this data set. indicating that the third choice is the right one.

How can I get the formula for the best fit line?

It is stated that a linear function has the following slope-intercept definition:

y = mx + b.

which contains the following coefficients:

The slope, or m, shows how quickly the function's output changes in relation to its input.

The y-intercept, or b, represents the value that the input function assumes to be zero.

Since the function passes through the given point (0,60), the following is the line's b-intercept:

b = 60.

When x rises by two from zero to two, y rises by twenty from sixty to eighty.

Consequently, the slope m is determined as follows:

m = 20/2 = 10.

Therefore, the following is the line of fit:

y = 10x + 60.

Answer:

21+9=27+x

30=27+x

30-27=x

x = 3

Answer: 20 cars and then send the rest of showrooms iin New York

Step-by-step explanation:

The number of polynomials that can be formed with -2 and 5 as zeroes are more than 1.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.x² -3x - 7 is an illustration of a polynomial with a single indeterminate x.

Given that the zeros of a polynomial are -2 and 5.

The polynomial that has a and b as zeors is p(x) = k[x² + (a+b)x + ab].

where k is a real number.

The polynomial that has -2 and 5 zeros is

p(x) = k[x² + (-2 + 5)x + (-2)×5]

p(x) = k[x² + 3x - 10]

Where k is a real number.

The number of real numbers is infinity.

The number of polynomials is infinity.

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Using the properties of Isosceles Triangle we get that When the line containing the vertex of an isosceles triangle is drawn from the vertex angle perpendicular to the base, it bisects the vertex angle and the base.

Based on the length of the sides of the triangle, there are three types of equilateral triangles . , isosceles triangle, unequal triangle. An isosceles triangle is a triangle with two sides of equal length and corresponding angles are equal.

Statement : -

Let ABC be an isosceles triangle such that AB=AC.

Let AD be the bisector of ∠A.

we have to prove:- BD=DC

Proof :-

In △ABD&△ACD

AB=AC(∵△ABC is an isosceles triangle)

∠BAD=∠CAD(∵AD is the bisector of ∠A)

AD=AD (Common)

By S.A.S.(side angle side)

△ABD≅△ACD

By corresponding parts of congruent triangles-

⇒BD=DC

Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.

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Complete question:

Prove that if a line containing a vertex of an isosceles triangle is perpendicular drawn from the vertex angle to the base bisect the vertex angle and the base.

Answer:B

Step-by-step explanation:

A0. The best estimate of the proportion of adults who believe that immediate government action is required.

The bost estimate of the proportion of adults who believe that immediate government action is required is given by the following formula:

P-hat = (Number of individuals who responded yes to the question) / (Total number of individuals polled)

= 957/1661

= 0.576 (rounded to three decimal places)

Therefore, the best estimate of the proportion of adults who believe that immediate government action is required is 0.576.

A research poll is a process of collecting data by asking questions or gathering information from a group of people. It is commonly used to determine public opinion or to evaluate attitudes towards specific topics. In general, research polls are conducted by sampling a small proportion of the population that is representative of the entire group.

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Answer:

ok so its 9 times a number plus 13 this is shown as c

9y+13

Answer:

ok so its 9 times a number plus 13 this is shown as c

9y+13

Step-by-step explanation:

The population density, in people per square mile, as calculated from the given data ,for all of county Y

=8.25/ square mile

Population density of district A = No of people/ Area

                                                    = 370/30

                                                     =12.3

Population density of district B = No of people/ Area

                                                    = 290/50

                                                     = 5.8

Now ,

Population density for the country Y will be,

=No of people/ Area

= (370+ 290 )/ 30 + 50

=  8 . 25 / square mile

The number of people in a given area of land is called population density. Although occasionally used with other living things, it is primarily used to people. It is a significant geographic term.

Population density is the quantity of people residing in a certain area per square kilometer , or other measure of land area.

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Answer:

Check pdf

Step-by-step explanation:

Answer:

4ft

Step-by-step explanation:

circumference of circle = π r^2

=> circumference = 50.25 ft

=> πr^2 = 50.25 ft

=> r^2 = 50.25/3.14 = 16 ft

=> r = √16

=> r = 4 ft

hope it helps

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

Number 3 is 10

Step-by-step explanation:

16+13(10)=146

14(10)+6=146

Answer:

See answer below.

Step-by-step explanation:

# 3  x = number of boxes

     $16 + 13x = Tracy cost

     $6 + 14x = Brendan cost

     The costs are equal.  

    16 + 13x = 6 + 14x

     10 + 13x = 14x

      10 = x

#4   First plan                                                            second plan

      x = number of people at a table          x = number of people at a table

      y = number of people at a booths        y = number of people at a booths    

24x + 21y = 270       multiply by 23   ⇔   552x + 483y = 6210

 14x + 23y = 222      multiply by -21   ⇔ -294x  - 483y = -4662

                                                                   258x    =     1548

                                                                          x  = 6

Six people at each tables

 24 (6)  + 21y = 270                                      

   144 + 21y = 270

         21y = 126

            y = 6      

Answer: 6 people at each table; 6 people at each booth.

Answer:

5,31,616 bacteria

Step-by-step explanation:

Solution:

Here, Principal (P) = 5,06,000, Rate of Interest (R) = 2.5%, Time (n) = 2 hours

After 2 hours, number of bacteria,

Amount (A) = P\left(1+\frac{R}{100}\right)^nP(1+100R)n

= 506000\left(1+\frac{2.5}{100}\right)^2506000(1+1002.5)2

= 506000\left(1+\frac{25}{1000}\right)^2506000(1+100025)2

= 506000\left(1+\frac{1}{40}\right)^2506000(1+401)2

= 506000\left(\frac{41}{40}\right)^2506000(4041)2

= 506000\times\frac{41}{40}\times\frac{41}{40}506000×4041×4041

= 5,31,616.25

Hence, number of bacteria after two hours are 531616 (approx.).

Answer:

x-intercept: none

y-intercept: 4.5

linear

slope: 0

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:39

Step-by-step explanation:

Yrust me bro

The Dimension Index is 0.322.

The Dimension Index is calculated using the formula:

\[ \text{Dimension Index} = \frac{\text{Actual Value} - \text{Minimum Value}}{\text{Maximum Value} - \text{Minimum Value}} \]

Given that the Actual Value is 8.5, the Minimum Value is 4.0, and the Maximum Value is 19.3, we can plug these values into the formula:

\[ \text{Dimension Index} = \frac{8.5 - 4.0}{19.3 - 4.0} = \frac{4.5}{15.3} \approx 0.294 \]

So, the Dimension Index is approximately 0.294.

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Answer:

3 + 2k

Step-by-step explanation:

1/5(15+10k)

distribute

1/5 * 15 + 1/5 * 10k

3 + 2k

Answer:

3 + 2k

Step-by-step explanation:

First, I am going to explain what the distributive property is. Lets say he had the expression a(b + c). We can "distribute" the a to the b and c:

a(b + c) = ab + ac

We can apply the distributive property to the expression 1/5(15 + 10k):

1/5(15 + 10k)

= (1/5)(15) + (1/5)(10k)

= 3 + 2k

By using the distributive property, we found the expression 3 + 2k.

I hope you find my answer helpful.

Answer:

Step-by-step explanation:

Dhddhhfjvjvmx,sfkiritifkflf,gjgi*jfckblhog

The length of one leg of the right triangle is 5√10

The leg of a right triangle can be found as follows;

Therefore, using trigonometric ratios,

sin 45 = opposite / hypotenuse

sin 45 = x / 10√5

1 / √2 = x / 10√5

cross multiply

10√5 = x√2

divide both sides by √2

x = 10√5 / √2

x = 10√5 / √2 × √2 / √2

x = 10√10 / 2 = 5√10

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The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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Residual Plot A indicates that the linear model is not appropriate because the fanned pattern shows that the model's predicting power decreases as the values of the explanatory variable increases. Residual Plot B indicates that the linear model is appropriate because the scattered residuals suggest a linear relationship.

Residual Plot A shows a fanned pattern which indicates that the linear model is not appropriate. This means that the model's predicting power decreases as the values of the explanatory variable increases. This suggests that the relationship between the dependent and independent variables is not linear and a different model may be necessary. Residual Plot B, on the other hand, shows a scattered pattern which suggests that the linear model is appropriate. The scattered pattern indicates that the data points are randomly distributed, which is a sign of a linear relationship. This indicates that the linear model is an appropriate fit for the data.

the complete question is :

Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

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In a fictional alphabet with 20 letters, there are 8,000 different 3-letter words possible.

To solve this problem, we can use the formula for permutations, which is n!/(n-r)!, where n is the number of letters in the alphabet and r is the number of letters in the word.

In this case, n = 20 and r = 3, so the formula would be 20!/(20-3)!. Simplifying the equation, we get:

P = 20!/(17!)

P = (20*19*18)/(1*1*1)

P = 8,000

Therefore, there are 8,000 different 3-letter words possible in a fictional alphabet with 20 letters.

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Answer:

15

Step-by-step explanation:

-3 x -5 = 15

=======================================

The commutative property of addition is where we can add two numbers in any order we want. Example: 2+3 = 5 and 3+2 = 5.

In general, the rule is x+y = y+x.

In our case, 2x and 15 can be added in any order. So that's why 2x+15 is the same as 15+2x.

-------

Side note: a similar rule applies for multiplication as well. This is called the commutative property of multiplication. Example: 9*3 = 27 and 3*9 = 27. So we can say x*y = y*x.

the ramp gets further away from the step, the angle it has with the ground decreases.

θ = \(tan^{-1}\)(0.515 / (48 + x))

Assuming that the ramp remains the same height as the step, we can use trigonometry to find the angle that the ramp would make with the ground if it starts farther away from the step.

First, let's convert the distance from feet to inches, since the height of the step is given in inches: 4 feet = 48 inches.

Next, we can use the tangent function to find the angle theta:

tan(θ) = opposite / adjacent

where opposite is the height of the step (5 inches) and adjacent is the horizontal distance from the base of the step to the point where the ramp meets the ground (48 inches * tan(5.9°) = 5.514 inches).

So, tan(θ) = 5 / 5.514, which gives us θ = 41.2°.

Now, let's say the ramp starts at a distance x from the base of the step. We can use the same formula, but with a different value for adjacent:

tan(θ) = 5 / (48 + x) * tan(5.9°)

We can simplify this expression by substituting the value of tan(5.9°) as approximately 0.1032:

tan(θ) = 0.515 / (48 + x)

Solving for theta, we get:

θ = \(tan^{-1}\)(0.515 / (48 + x))

As a result, we can see that the denominator of the fraction within the arctan function gets larger as x increases (i.e., the ramp starts further from the step), resulting in a smaller fraction and, consequently, a smaller angle theta. To put it another way, as the ramp gets further away from the step, the angle it has with the ground decreases.

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the third side must be greater than 8 and less than 16.

To determine the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So, for a triangle with sides of 4 and 12, the third side must satisfy:

12 - 4 < third side < 12 + 4

which simplifies to:

8 < third side < 16

what is triangle?

A triangle is a geometric shape with three sides and three angles. It is formed by connecting three non-collinear points in a plane. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measures.

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