To receive a C grade, a student must average more than 77 but less than or equal to 85 . If Ethan received a C in the course and had five grades of 78 , 79 76 , 64 , and 85 before taking the final exam, what were the possible grades for his final if there were 100 points possible?

Answer:

The required function -  [tex]g(x)=\frac{1}{2}(3)^{-x}[/tex]

Step-by-step explanation:

Given : Function represents g(x), a reflection of [tex]f(x) =\frac{1}{2}(3)^x[/tex] across the y-axis

To find : Which function represents the g(x)?

Solution :

The function [tex]f(x) =\frac{1}{2}(3)^x[/tex]

The function f(x) reflected across y-axis to form g(x)

The reflection of the point (x,y) across  the y-axis is the point (-x,y).

f(x,y)→f(-x,y) , the graph of f(x) is reflected across y-axis.

Let [tex]y=\frac{1}{2}(3)^x[/tex]

After reflection across y-axis is

[tex]g(x)=\frac{1}{2}(3)^{-x}[/tex]

The required function.

Refer the attached graph below.

Answer:

2W²-W-28 = 0

Step-by-step explanation:

To convert the number 1,340,000 into scientific notation, move the decimal point 6 places to the left to get 1.34, then place this as an exponent on 10 to get 1.34 x 10^6.

In scientific notation, large numbers are simplified by moving the decimal point to the left until we have a number between 1 and 10. We then use an exponent on 10 to indicate how many places the decimal point has been moved. If you take a look at the number 1,340,000, the decimal point is technically at the end of the number right now. In order to express this number in scientific notation, we move the decimal point 6 places to the left, which gives us 1.34. The number of places we moved the decimal point to the left becomes the exponent on 10. Therefore, 1,340,000 in scientific notation is 1.34 x 10^6.

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Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline. To find the cost per gallon, divide the total cost by the number of gallons, resulting in a cost of $2.90 per gallon of regular gasoline at Greg's gas station.

To determine the cost per gallon for regular gasoline, we need to divide the total amount spent by Mr. Adams at Greg's gas station by the number of gallons of gasoline he purchased. In this case, Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline.

Step-by-step calculation:

Write down the total cost of gasoline: $36.25.

Write down the total gallons of gasoline purchased: 12.5 gallons.

Divide the total cost by the number of gallons to find the cost per gallon: $36.25 \/ 12.5 gallons.

Perform the division: $36.25 \/ 12.5 gallons = $2.90 per gallon.

Therefore, the cost per gallon for regular gasoline at Greg's gas station is $2.90.

multiply the 2 numbers

9 1/2 * 1 3/4 =

19/2 * 7/4 = 133/8 = 16 5/8 miles

Answer:

9.65×10¹⁴

Step-by-step explanation:

The 9 of 9.65 has been moved 14 places to the left to get to its position in 965,000,000,000,000. That is, its value has been multiplied by 10¹⁴.

_____

If you were to write 965,000,000,000,000 in expanded form, you would write it as ...

... 9×10¹⁴ +6×10¹³ +5×10¹² +0×10¹¹ +... +0×10⁰ = 9.65×10¹⁴

The first term of this sum is a clue as to how the number is written in scientific notation,

the answer is 9.65×10¹⁴

To calculate the interquartile range (IQR) of the data set, the ordered values are split by the median to find Q1 and Q3. The difference between Q3 and Q1 gives the IQR which is 2.65 for this data set.

The interquartile range (IQR) is the measure of the middle 50 percent spread in a data set and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). To find the IQR for the provided data set (6.2, 5.0, 4.3, 7.4, 5.8, 7.2, 8.4, 1.2, 6.3), we first need to order the data from smallest to largest and then identify Q1 and Q3. Using the median to split the ordered data into two halves and finding the medians of these two halves gives us Q1 and Q3, and their difference gives us the IQR.

We want to get a quadratic equation by knowing its tangent line at a point. Remember that the tangent line is given by the derivative of the equation.

We will find that the parabola is:

y = 3*x^2  - 4*x

We start with the tangent line:

y₂ = 8*x - 12

The slope of this tangent line is equal to the derivative of our parabola evaluated in x = 2.

Our parabola is y = a*x^2 + b*x

Derivating we get:

y' = 2*a*x + b

Then we have:

2*a*2 + b = 8

And we also know that our parabola passes through the point (2, 4), then we must have:

4 = a*2^2 + b*2

Then we have a system of equations:

2*a*2 + b = 8

4 = a*2^2 + b*2

First we can simplify the equations:

4*a + b = 8

4 = 4*a + 2*b

We can isolate 4*a in the first equation to get:

4*a = 8 - b

Now we can replace it in the second equation:

4 = (8 - b) +  2*b

4 = 8 + b

4 - 8 = b

-4 = b

Now that we know the value of b, we can use

4*a  = 8 - b

4*a = 8 + 4 = 12

a = 12/4 = 3

Then the equation of the parabola is:

y = 3*x^2  - 4*x

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To find the number of notepads bought, we can set up an equation by subtracting the cost of the magazine from the total cost and equating it to the cost of the notepads. By solving the equation, we find that you bought 4 notepads.

To solve this problem, we can start by setting up an equation. Let's assume the number of notepads bought is 'x'. We know the magazine cost $6, so the cost of the notepads is $18 - $6 = $12. Since each notepad costs $3, the equation becomes 3x = 12. To find the value of 'x', we can divide both sides of the equation by 3. So, x = 12/3 = 4.

Therefore, you bought 4 notepads.

Option 'C' is an example of an observational study because it involves recording data without manipulation from the researcher, fitting the definition of observing the natural state or habits of a situation over time.

You have correctly identified option 'C' as an example of an observational study. In an observational study, researchers merely observe and record data without manipulating or intervening in the study environment or subjects. Option 'C', which involves recording the daily output of a balloon factory for 6 months, fits this description as it simply measures and records data over time without any intervention from the researcher.

It is different from a controlled experiment where variables are manipulated to assess the effect of treatments, as in option 'B', which compares survival rates between different treatments for bone cancer. Similarly, options 'A' and 'D' involve asking for opinions, which might be part of a broader observational study but are not observational studies by themselves.

In summary, an observational study is characterized by the purposeful absence of manipulation by the researcher and is designed to observe the natural state or habits of the subject or situation being studied.

If your equation is ...

[tex]t-122=3t^2-3[/tex]

then it has no real solutions, and certainly no integer solutions.

_____

The attached graph show the left side is never equal to the right side of this equation for any real values of t.

the correct answer is actually 3

i just got done with the quiz and the answer was 3