Write the nth term rule for the arithmetic sequence with the given term and common difference. Fill in the formula: a = a₁ + d(n-1) below.
a1=-10 and d=0.5

The solution is y = -5

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Given data ,

Let the function be f ( x ) = y

And , y = x² + 2x - 8

So , f ( x ) = x² + 2x - 8

Substituting the value for x in the equation , we get

When x = -3

f ( -3 ) = ( -3 )² + 2( -3 ) - 8

         = 9 - 6 - 8

         = 9 - 14

f ( -3 ) = -5

When x = 1

f ( 1 ) = ( 1 )² + 2( 1 ) - 8

       = 1 + 2 - 8

       = 3 - 8

f ( 1 ) = -5

Hence , the value of y = -5

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Answer:

Solution given:

5.

we have.

11x=½(16x+16+50)

22x=16x+66

22x-16x=66

6x=66

x=66/6

x=11

6.

118°=½(6x-11+181)

236=6x+170

6x=236-170

x=66/6

x=11°

The total population mean must be close to $47,600 based on statistical inference.

The entire population mean must be close to $47,600. Then the correct option is C.

The mean is the simple definition of the average of a bunch of numbers. In statistics, one of the markers of central tendency is the mean.

The average is referred to as the arithmetic mean.

It's the ratio of the number of real observations to the total number of observations.

The owners of a manufacturing company conducted a survey to determine the mean income of the customers who prefer the company’s brand of clothing.

From a random sample of 100 customers, it was determined that their mean income was $47,600.

Based on statistical analysis, the entire population mean must be close to $47,600.

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Answer:

3 r 2 +9 r − 120

Step-by-step explanation:

Write the problem as a mathematical expression.

3 r ^2 + 9 r− 120

Factor  3  out of  3 r ^2 + 9 r − 120 .

Factor  3 out of  3 r ^2 .

3 ( r ^2 ) + 9 r − 120

Factor  3  out of  9 r .

3 ( r^ 2 ) + 3( 3 r ) − 120

Factor  3  out of  − 120 .

3 r ^2 + 3( 3 r ) + 3 ⋅ − 40

Factor  3 out of  3 r 2 + 3 ( 3 r ) .

3 ( r^2 + 3 r )+ 3 ⋅ − 40

Factor  3 out of  3 ( r 2 + 3 r ) + 3 ⋅ − 40 .

3 ( r^ 2 + 3 r − 40 )

Factor.

Factor  r^ 2 + 3 r − 40 using the AC method.

3 ( ( r − 5 ) ( r + 8 ) )

Remove unnecessary parentheses.

3 ( r − 5 ) ( r + 8 )

Hope this helps! :)

Answer:

Here are the graphs

Step-by-step explanation:

1. Green Line

2. Purple Line

3. Red Line

Answer:

10000 cm²

Step-by-step explanation:

To find the volume of the box you would need to use the equation for volume of a rectangular prism, which is V = l*w*h

V = 25*10*40

V = 10000 cm²

The test statistic for this problem is given as follows:

t = (242 - 250)/(12/sqrt(24))

The equation for the test statistic in the context of the problem is defined as follows:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

In which:

The parameters for this problem are given as follows:

\(\overline{x} = 242, \mu = 250, s = 12, n = 24\)

Hence the test statistic is given as follows:

t = (242 - 250)/(12/sqrt(24))

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The volume for the boxes that are held by Chris will be 80ft³.

Volume refers to the amount of space that a three-dimensional object occupies. It is typically measured in cubic units, such as cubic meters or cubic feet. The volume of an object can be calculated using various formulas depending on the shape of the object.

Volume is an important concept in many fields, including physics, engineering, and architecture. It is also used in everyday life, such as when measuring the amount of liquid in a container or determining the capacity of a storage space.

Volume = area of the base × height

V= L× w × h =B × h

The volume for one box = 1 1/3 × 10

                                     = 40/3 = 13 1/3

The volume for 6 boxes=  6 × 13 1/3 = 80 ft³

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Total Volume in cubic feet and express answer in mixed fraction

chris has 6 identical boxes. The rectangular base of each box has an area 1 1/3 ft 3. The height of each box is 10 inches. What is the total volume of all the boxes in cubic feet?

Answer:

\(2x + 4 = 22\)

\(or \: 2x = 22 - 4\)

\(or \: 2x = 18\)

\(or \: x = \frac{18}{2} \)

\(therefor \: x = 9\)

Answer:

x = 9

Step-by-step explanation:

Since M is the midpoint of AC then

AM = MC , that is

2x + 4 = 22 ( subtract 4 from both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Answer:

29.25

Step-by-step explanation:

15x1.95= 29.25

Hope this helps :)

if 1 article = 1.95

then if u want to find how much 15 articles = to

you just have to multiply 1.95 * 15 which is equal to 29.25

hope this helps

:)

The triangle ABC undergoes a dilation of scale factor 2 centered at the origin.

Dilation About the Origin

Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).

If we are given the dilated point, then we can find the original point by dividing by the scale factor.

Triangle ABC was dilated by a scale factor of 2 about the origin mapping it to triangle A'B'C' with vertices A'(-4,4), B'(-4,6), and C(2,4).

The coordinates of triangle ABC are:

A=(-4/2,4/2) = (-2,2)

B=(-4/2,6/2) = (-2,3)

C=(2/2,4/2) = (1,2)

The coordinates of ABC are respectively (-2,2), (-2,3), and  (1,2).

Hence the answer is the triangle ABC undergoes a dilation of scale factor 2 centered at the origin.

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Answer:i'm pretty sure it's the one to the right of the example

Step-by-step explanation:

Answer:

3/40 hours.

Step-by-step explanation:

hope this helps !

Wehave the following:

according to the statement we have the following equation

where d is the distance and p is gas cost

replacing when p is 2

Therefore he was able to travel a total of 310 miles

The chores overshadowed the joy of our Reunion, learned a valuable lesson about managing time and prioritizing obligations

Embarking on a bike ride to visit a friend who lives 3 miles away, little did I know that a looming sense of forgotten chores would soon disrupt my plans. Determined to fulfill my obligations, I mustered the strength to continue riding towards my friend's house, albeit with a heavy heart.

I pedaled towards my destination, the weight of my impending chores grew heavier with each passing moment. Thoughts of unfinished tasks occupied my mind, and I knew that I couldn't stay for long once I reached my friend's place. However, in my haste, a newfound urgency propelled me forward, and I found myself pedaling at a speed 5 mph faster than my initial journey.

With this increased velocity, the return trip promised to be swifter, yet time was slipping away. My mind raced as I calculated the implications of my predicament. The total round trip, comprising both the journey to my friend's house and the hurried return, needed to be accomplished within a tight time frame of 30 minutes.

As I approached my friend's house, I realized that I had no choice but to deliver my news swiftly and immediately turn back around. The momentary joy of reunion would be overshadowed by the pressing chores that awaited me. Regrettably, I bid my friend a hasty farewell, explaining the circumstances that compelled my premature departure.

Once on my bike again, I kicked up the pace, utilizing the extra speed to my advantage. The wind rushed past my face as I hurriedly retraced my path, pushing myself to complete the return trip as swiftly as possible. The seconds ticked away relentlessly, as the pressure mounted to make it back within the allocated timeframe.

In a flurry of determination, I managed to reach home just in the nick of time, fulfilling my duties and responsibilities. Exhausted but relieved, I contemplated the whirlwind of events that had transpired within the span of this half-hour adventure.

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Note the question be like :

A company is hosting a team-building event and has allocated a total of 4 hours for various activities. If Activity A takes 1 hour, Activity B takes 2 hours, and Activity C takes 45 minutes, what is the maximum amount of time that can be dedicated to Activity D while still staying within the allocated 4-hour timeframe?

40 x 7 = _________ x 10 x 7

280 = ? x 70

280 = 4 x 70

check: 280 = 280

4 goes in the blank

Answer:

4

Step-by-step explanation:

40×7=280

10×7=70

280:70=4

Answer: x<4

Step-by-step explanation:

Let's solve the inequality step-by-step.

2x<8

Step 1: Divide both sides by 2.

2x2<82

x<4

Answer:

x<4

Answer:

Thanks for the points loser

Answer:

B. 5.22×10⁸

Step-by-step explanation:

Answer:

38.40

Step-by-step explanation:

I just took the test

There are 8 observations with x1 values greater than 30, when the data is sorted in ascending order the first observation has x1 value of 10, x2 value of 1 and x3 value of 1.

After sorting the data in ascending order,

Value of x1 - 10

Value of x2 - 1

Value of x3 - 1

c. Sort the data by xi and x2 both in descending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of X1 - 35

Value of x2 - 10

Value of x3 - 5

d. How many missing values are there in x1, x2, and x3?

The number of missing values in X1 - 0

The number of missing values in X2 - 0

The number of missing values in X3 - 0

a. How many observations have x1 values greater than 30? Number of observations - 8

b. Sort the data by x1, x2, and then x3 all in ascending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of x1 - 10

Value of x2 - 1

Value of X3 - 1

c. Sort the data by xi and x2 both in descending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of X1 - 35

Value of x2 - 10

Value of x3 - 5

d. How many missing values are there in x1, x2, and x3? The number of missing values in X1 - 0

The number of missing values in X2 - 0

The number of missing values in X3 - 0

There are 8 observations with x1 values greater than 30, when the data is sorted in ascending order the first observation has x1 value of 10, x2 value of 1 and x3 value of 1. When the data is sorted in descending order, the first observation has x1 value of 35, x2 value of 10 and x3 value of 5. There are no missing values in x1, x2, and x3.

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0.0006 .

The probability that both systems of an atomic reactor will fail simultaneously is 0.0006.

This is calculated by multiplying the probability of cooling system A failing (0.02) by the probability of cooling system B failing (0.03) which results in 0.0006, rounded to four decimal places.

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Answer:

(-8,-71)

Step-by-step explanation:

I assume by turning point it means the vertex:

\(y=x^2+16x-7\\y+71=x^2+16x-7+71\\y+71=x^2+16x+64\\y+71=(x+8)^2\\y=(x+8)^2-71\)

Now that we converted our equation to vertex form \(y=(x+h)^2+k\), we can see our vertex, or turning point, is (h,k)=(-8,-71)

Fishermen in the region experienced hardships due to a massive fish death. A student was assigned to investigate this occurrence. The student used water sampling and Fish Necropsy to analyze the cause of the fish's death. Through Fish Necropsy, the student dissected the fish to determine the cause of death. Fresh dead fish have clear eyes, red to pink gills, good coloration, and no bad odor.

The analysis of water quality and fish necropsy revealed that the depletion of dissolved oxygen and fish lesions were the main reasons for the fish's death. The students used a LABSTER simulation to confirm the findings of the biological material in the water by looking at it through a microscope. The purpose of the laboratory experiment was to determine the fundamental etiology of the fish's death.The objective of the research was to determine the cause of the fish's sudden death.

The research aims to find out how the depletion of dissolved oxygen levels and fish lesions led to the death of the fish. It would also establish the range of dissolved oxygen and other environmental factors necessary for the survival of fish. The scope of the study covered the entire region affected by the massive death of fish. It involved the use of scientific methods to analyze water quality and fish necropsy to understand the cause of death of the fish.

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Answer:

1

Step-by-step explanation:

Answer:

$91

Step-by-step explanation:

20% of 120= 96

96-5=91