A student earned the scores in the data set in one course.

{78, 64, 74, 92, 67}

What is the mean of the scores?

75
74
64
28

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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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.

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 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: The relationship between the distance a car has traveled in miles, d, and the amount of gas left in the tank in gallons, x, can be represented by the equation:

d = r * m

where r is the fuel efficiency of the car in miles per gallon and m is the amount of gas consumed in gallons.

Since x is the amount of gas left in the tank, we can write:

x = m_0 - m

where m_0 is the initial amount of gas in the tank.

Combining the two equations, we get:

d = r * (m_0 - x)

This equation represents the relationship between the distance the car has traveled in miles, d, and the amount of gas left in the tank in gallons, x.

Step-by-step explanation:

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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The function 2y = -4x is linear and the graph is given below.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Here the given function is 2y = -4x.

The function is linear since the exponent of the two variables x and y are 1.

This can be written as,

y = -4x / 2

y = -2x

This is a proportional function with slope -2.

Graph will be a decreasing function.

The points on the graph includes (-2, 4), (-1, 2), (0, 0), (1, -2) and (2, -4).

Hence the graph of the function is given below.

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The difference in the medians is 1/3 times the IQR.

Mathematically, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) for Speed Slide = Q₃ - Q₁

Interquartile range (IQR) for Speed Slide = 12 - 6

Interquartile range (IQR) for Speed Slide = 6.

For the interquartile range (IQR) for Wave Machine, we have:

Interquartile range (IQR) for Wave Machine = 14 - 8

Interquartile range (IQR) for Wave Machine = 6.

For the required expression, we have the following:

2 = 6x

x = 2/6

x = 1/3.

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Answer:

The difference in the medians is 1/3 times the IQR.

Step-by-step explanation:

hope this helps!

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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Answer:

Step-by-step explanation:

x% OF 7200 = 288

x/100*7200 = 288

x=288/72=4

4% was donated

Verifying trig identities can be difficult because they involve manipulating complex equations with multiple trigonometric functions that have various associated angles and coefficients.

For example, the Pythagorean Identity states that sin2θ + cos2θ = 1, which must be verified by using the identity sin2θ = 2sinθcosθ and substituting it into the equation. This results in a complex equation: 2sinθcosθ + cos2θ = 1, which must then be simplified and rearranged in order to show that it is true for all values of θ. Furthermore, trig identities can involve multiple steps that involve multiple functions and angles, which can make verifying them even more difficult.

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Step-by-step explanation:

I suspect this to be a trick question.

because 2 statements are correct :

B and C.

according to the definition, two triangles are similar if their corresponding angles are congruent (identical) and corresponding sides are proportional (the ratio between the length of corresponding sides is equal for all pairs of corresponding sides, or, in other words, there is one scale factor for all 3 pairs of corresponding sides).

in fact, each criteria alone is sufficient.

if all 3 corresponding angles are identical between both triangles, the corresponding pairs of sides will be proportional.

if all 3 pairs of corresponding sides are proportional, then the corresponding angles are identical.

and the triangles are similar.

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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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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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 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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65 kg is equivalent to approximately 143.3 pounds and both are unit of measurement of weight.

To convert kilograms to pounds, we multiply the weight in kilograms by the conversion factor of 2.20462. Therefore, to convert 65 kg to pounds, we can multiply 65 by 2.20462, which gives us approximately 143.3 pounds.

It's important to note that kilograms and pounds are both units of weight, but they are used in different parts of the world. Kilograms are the standard unit of weight in most countries, while pounds are commonly used in the United States and some other countries.

Converting between units of measurement is a valuable skill, especially when communicating or traveling internationally. Knowing how to convert from kilograms to pounds, or vice versa, can help you understand weight measurements in different contexts.

Online conversion tools or calculators can be useful resources to quickly and accurately convert between units of measurement as needed.

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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.

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.

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:

0.25%

Step-by-step explanation:

Answer:

0.25%

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

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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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.

The percentage of sales tariff is 8.06%. Then the second item cost before the tariff will be $124.

Any product's quantity is given as if it were a percentage of one hundred. The ratio can be written as 100. The word "%" means "100%" in English. The sign for it is the letter "%".

The percentage is given as,

[tex]\text{Percentage (P) }= \dfrac{ \text{Final value - Original value}}{\text{ Original value }} \times 100[/tex]

An item that costs $310 before the tariff carries a $25 sales tariff. The sales tax % is then provided as,

[tex]\rm P = \left ( \dfrac{25}{ 310} \right ) \times 100[/tex]

P = 0.0806 x 100

P = 8.06%

The sales tax on a second object is $10. Then the second object cost before the tariff is given as,

⇒ $10 / 0.0806

⇒ $124

The percentage of sales tariff is 8.06%. Then the second item cost before the tariff will be $124.

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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 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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