What are the ACT math formulas that you absolutely have to know?

Median would be a better measure of central tendency to use in the employees perspective, the mean of data set is 12.5 and median is 10, and

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us find the mean and median of the given data set {11,6,32,7,18,4,9,1,15,9,5,27}.

To find mean, we add up all the numbers and divide by the total number of numbers:

(11 + 6 + 32 + 7 + 18 + 4 + 9 + 1 + 15 + 9 + 5 + 27) / 12 = 12.5

So the mean number of years of employment is 12.5.

To find the median, we first need to put the numbers in order:

1, 4, 5, 6, 7, 9, 9, 11, 15, 18, 27, 32

Since there are 12 numbers, the median is the average of the middle two numbers, which are 9 and 11.

So the median is (9 + 11) / 2 = 10.

The median would be a better measure of central tendency to use, because it is less sensitive to extreme values than the mean

Hence, the mean of data set is 12.5 and median is 10, and median would be a better measure of central tendency to use in the employees perspective.

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The most likely production for a rainfall of 40 mm is 56.4 quintals.

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

          Rainfall (mm) Production (quintals)

Mean           35                  50

S.D                5                    8

Coefficient of correlation = 0.8​

First, we need to calculate the regression equation, which is:

y = a + bx

Where

To calculate the intercept and slope, we use the following formulas:

b = r * (SDy / SDx)

a = Ymean - b * Xmean

Plugging in the given values, we get:

b = 0.8 * (8 / 5) = 1.28

a = 50 - 1.28 * 35 = 5.2

Therefore, the regression equation is:

Y = 5.2 + 1.28x

To find the most likely production for a rainfall of 40 mm, we plug in x = 40 into the regression equation:

Y = 5.2 + 1.28 * 40

Y = 56.4

Hence, the most likely production is 56.4 quintals.

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The percent of mice whose response time was 0.8 seconds or more is; Choice B; 50%.

As evident on the box plot; The response time, 0.8 seconds corresponds to the median of the plot.

Since the median represents the 2nd quartile of a distribution or otherwise termed , the 50th percentile;

It can be inferred that the percent of mice who responded in 0.8 seconds or more is; Choice B; 50%.

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Answer: 14π

Step-by-step explanation:

The area of a circle can be expressed as πr^2. In this case, the area is given as 49π m², so we can write:

πr^2 = 49π

Dividing both sides by π, we get:

r^2 = 49

Taking the square root of both sides, we get:

r = 7

The circumference of a circle is given by 2πr, so the circumference in this case would be:

C = 2π * 7 = 14π

So the circumference of the circle with an area of 49π m² is 14π meters.

The inequality that represents the graph is given as follows:

x < 4.

The four inequality symbols, along with their meaning, are presented as follows:

The numbers to the right of 4 that are shaded on the number line are the numbers that are less than 4, with an open interval, due to the open circle at x = 4, hence the inequality is given as follows:

x < 4.

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Answer:

Step-by-step explanation:

To determine how many crates Tom needs to put 1000 bottles into, we can divide the number of bottles by the number of bottles that fit into one crate.

So,

number of crates = 1000 bottles / 24 bottles per crate = 1000 / 24 = 41.67 (approximately 42 crates)

Therefore, Tom needs 42 crates to put 1000 bottles into.

The fraction of water Libby drinks is 1 6/8 more liters of water than Jack.

In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. A fraction is a piece or section of a whole, where the whole can be any number, a particular value, or an object. Let's use an example to better comprehend this idea. A pizza cut into 8 equal pieces is depicted in the following diagram. Now, to describe a single portion of the pizza, we may use the notation 1/8, which indicates that, out of 8 equally sized portions, we are speaking of one portion.

Given that, Libby drinks 2 7/8 liters of water.

Coverting the mixed fraction into improper fraction:

2 7/8 = 2(8) + 7/ 8 = 23/8

Jack drinks 1 1/8 liters of water.

Coverting the mixed fraction into improper fraction:

1 1/8 = 8 + 1/8 = 9/8

The difference between is:

D = 23/8 - 9/8 = 14/8

14/8 = 1 6/8

Hence, Libby drinks 1 6/8 more liters of water than Jack.

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To find the percentage of yield in a calculator, you can follow these steps:

1. Determine the actual yield and the theoretical yield of the reaction. The actual yield is the amount of product that was actually produced in the reaction, while the theoretical yield is the amount of product that should have been produced based on the balanced chemical equation.

2. Divide the actual yield by the theoretical yield to find the decimal form of the percentage yield.

3. Multiply the decimal form of the percentage yield by 100 to find the percentage yield.

For example, if the actual yield of a reaction is 15 grams and the theoretical yield is 20 grams, the percentage yield would be:

(15/20) x 100 = 75%

Therefore, the percentage yield of the reaction is 75%.

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The value of the expression for the given p and r value is 136.3.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 9.3p + 8.9.

Here, p=7 and r=8

Substitute p=7 and r=8 in 9.3p + 8.9r, we get

9.3×7+8.9×8

= 136.3

Therefore, the value of the expression is 136.3.

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A bell-shaped histogram is a type of graph that displays a normal distribution, which is a probability distribution that is symmetrical and has a characteristic bell shape.

The bell-shaped histogram is created by plotting the data on a horizontal axis and the frequency or probability on a vertical axis. The data points are grouped into intervals called bins, and the number of data points that fall into each bin is plotted as a bar. The bars are typically drawn adjacent to one another and connected with lines to create a continuous curve that represents the normal distribution.

The resulting histogram will have a characteristic bell shape, with a high point at the mean, and decreasing frequency or probability as the values move away from the mean in either direction. The width of the curve is determined by the standard deviation of the data, with wider curves indicating greater variation in the data.

The bell-shaped histogram is commonly used in statistical analysis to represent normally distributed data, such as the heights or weights of a population, test scores, or other measurements that tend to cluster around a central value with a predictable range of variation.

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Answer:

0.25%

Step-by-step explanation:

Answer:

0.25%

Step-by-step explanation: you`re welcome :)

Answer: 13.5, 3.5, and 119

Step-by-step explanation:

To find these percentages, we can use the formula:percentage = (percentage value / 100) x (original value)Using this formula, we can calculate:30% of 45:

percentage = (30 / 100) x 45

percentage = 0.3 x 45

percentage = 13.5

5% of 70:

percentage = (5 / 100) x 70

percentage = 0.05 x 70

percentage = 3.5

35% of 340:

percentage = (35 / 100) x 340

percentage = 0.35 x 340

percentage = 119

Answer:

Answers below :D

Step-by-step explanation:

1. 30% of 45:

Write 30% as 30/100

Since, finding the fraction of a number is same as multiplying the fraction with the number-

30/100 of 45 = 30/100 × 45

Therefore, the answer is 13.5.

2. 5% of 70:

Write 5% as 5100

Use same reason above to multiply-

5/100 of 70 = 5/100 × 70

Therefore, the answer is 3.5.

3. 35% of 340:

Write 35% as 35/100

Multiply-

35/100 of 340 = 35/100 × 340

Therefore, the answer is 119.

Answer:

Rhonda's: 32$ Joel's: 128$ Joel has 96 more dollars than Rhonda.

Step-by-step explanation:

4+1=5

5x=160

x=32

Rhonda's: 32$

Joel's: 128$

Joel has 96 more dollars than Rhonda.

Answer:

Step-by-step explanation:

y=9700(0.909)^x

# If the base of an exponential function is an element of the set (0,1) the function is decreasing as the value of 'x' is increasing from negative infinity to positive infinity.

the function y=9700(0.909)^x is an exponential function with a coefficient 9700 and base 0.909, as we increase the value of x from negative infinity to positive infinity, the value of y decreases. So the change between two consecutive 'y' values as 'x' increases indicate decay rather than growth.

And it can be written as y=9700(1-0.091)^x, therefore the percentage decrease is 9.1%

Answer:

B. 20x + 4

Step-by-step explanation:

Perimeter of a rectangle = 2 × (Length + Width)

                                         = 2 × [(4x + 2) + 6x]

Expand the brackets and bring like terms together:
                                         = 2 × [4x + 2 + 6x]

                                         = 2 × [4x + 6x + 2]
                                         = 2 × [10x + 2]

Expand the brackets by applying the Distributive Law:

                                        = 20x + 4

                                        Option B.

On solving for (x), we get -

x = ±i√(a/72).

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the equation as -

- 72x² = a

The given equation is -

- 72x² = a

x² = -a/72

x = ±i√(a/72)

Therefore, on solving for (x), we get -

x = ±i√(a/72).

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The missing numerator are 7, 3, 6, 6, and 2

The Numerator is the number the at top of a fraction.

From the question, the numerators are

21) 2/3 x 7/5 = 14/15

The missing numerator here is 7

22) 5/6 X 3/7 = 5/14

The missing numerator here is 3

23) 3/4 X 6/7 = 9/14

The missing numerator here is 6

24) 6/9 X 2/4 = 1/2

The missing numerator here is 6

25) 9/10 X 2/3 = 3/5

The missing numerator here is 2

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Answer:

-------------------------

Substitute ? with x and solve each equation.

21)

22)

23)

24)

25)

Answer:

Arc Length=∫ba√1+[f′(x)]2dx. Note that we are integrating an expression involving f′(x), so we need to be sure f′(x) is integrable. This is why we require f(x) to be smooth.

Step-by-step explanation:

have a nice day

Answer:

75.

Step-by-step explanation:

The mean = (78 + 64 + 74 + 92 + 67) / 5

                 = 375 / 5

                 = 75.

Answer:A.75

Step-by-step explanation:

i did it in class

Answer:

Step-by-step explanation:

First, we need to calculate the cost of each car after 60 months.

For the Ford Mustang:

Y = 275X + 2500

Y = 275 * 60 + 2500

Y = 16500

For the Dodge Charger:

Y = 250X + 1500

Y = 250 * 60 + 1500

Y = 15000

Next, we can compare the total cost of each car to determine which is the better deal.

In this case, the Dodge Charger is the better deal as it costs $1500 less than the Ford Mustang over the course of 60 months.

It's important to keep in mind that these calculations are based on the assumption that Junior will only make the minimum payments of $250 per month. If he decides to make larger payments or pay off the car early, the total cost of each car will be different.

Additionally, there may be other factors, such as the reliability and maintenance costs of each car, insurance costs, fuel efficiency, and driving experience, that should also be considered before making a decision. Junior should research and weigh all these factors before making a final decision.

In conclusion, the calculation of the cost of each car after 60 months is just one aspect of the decision-making process when buying a car. Junior should consider all relevant factors and weigh the pros and cons of each option before making a final decision.

The value of x is -29

It is important to note that;

We have the diameters as;

-9x + 104 and 3x + 82

Also note that angles at the center is 360 degrees

This is then represented as;

-9x + 104 + 3x + 82 = 360

collect the like terms

-6x = 360 - 186

subtract the values

-6x = 174

Make 'x' the subject of formula, we get;

x = 174/-6

x = -29

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Area of the parallelogram is 65 square meter.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Area of the parallelogram = Base × Height

From the figure,

Length of base = AB = 3 m + 10 m = 13 m

Height is also given as 5 m.

Area of the parallelogram ABCD = 13 m × 5 m

                                                      = 65 m²

Hence the required area of the parallelogram is 65 m².

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The solutions of the system are y = -8 and x = 9.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

A system of equations,

5x + 6y = -3   {Equation 1}

8x + 8y = 8     {Equation 2}.

Multiply 8 into equation 1 and multiply by 5 into equation 2,

and subtract the equation,

we get,

40x + 48y - 40x - 40y = -24 - 40

8y = -64

y = -8 and x = 9

Therefore, the solutions are y = -8 and x = 9.

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For {K} = 12, the image will remain preserved.

Given is the scale factor of {K} = 12.

We can write the scale factor as -

reduction  {for K < 1}

enlargement  {for K > 1}

preserved  {for K = 1}

For {K} = 12, the image will remain preserved.

Therefore, for {K} = 12, the image will remain preserved.

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For length of 50 yards , the width is 60 yards, for length of 40 yards , the width is 75 yards, for length of 48 yards, the width is 62.5 yards , for length of 36 yards, the width is 83.33 yards, they are inversely proportional.

The formula for the area of a rectangle is: Area = Length * Width.

So, for the given case, we have:

Area = 3000 square yards

Length = 50 yards, 40 yards, 48 yards, or 36 yards

Therefore, the width of the plot in each case can be calculated as:

For Length = 50 yards,

Width = Area / Length

= 3000 / 50

= 60 yards

For Length = 40 yards,

Width = Area / Length

= 3000 / 40

= 75 yards

For Length = 48 yards,

Width = Area / Length

= 3000 / 48

= 62.5 yards

For Length = 36 yards,

Width = Area / Length

= 3000 / 36

= 83.33 yards

Therefore, the width of the plot depends on the length chosen and they are inversely proportional. When the length increases, the width decreases, and when the length decreases, the width increases.

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Answer: 79 kilograms is equal to 173.776 pounds.

Step-by-step explanation:

To convert kilograms to pounds, you can multiply the number of kilograms by 2.20462.

So, to convert 79 kilograms to pounds:

79 kg * 2.20462 = 173.776 lbs

Therefore, 79 kilograms is equal to 173.776 pounds.

240 gallons of a 50% antifreeze solution must be mixed with 80 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

Let's call the amount of 50% antifreeze solution that we want to mix with the 80 gallons of 10% antifreeze "x".

The total volume of the mixture after mixing x gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution is given by (x + 80) gallons.

The concentration of antifreeze in the mixture is given by the weighted average of the antifreeze concentrations in the two solutions, where the weight for each solution is proportional to its volume:

(0.5x) + (0.1 * 80) = (0.4 * (x + 80))

Expanding and solving for x, we get:

0.5x + 8 = 0.4x + 32

0.1x = 24

x = 240

Therefore, we need to mix 240 gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution to get a mixture that is 40% antifreeze.

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