which is rights answer?

Use a graphing utility to create a scatter plot of the data, with t = 5 corresponding to 2005. Then use the regression feature to find the least square regression line and predict the population of New Jersey in 2045. Round to the nearest whole number.

A) 94,452
B) 17,193
C) 10,475
D) 437,079​

Answer: 946.353 ML in 4 Cups

Step-by-step explanation:

1 ml = 0.00422675284 Cups

a. A Cartesian graph representation of the situation is shown below.

b. The differential equation whose solution is the answer to the question is C(dC/dt) = A(dA/dt) + B(dB/dt).

c. The solution to this equation is 390 mi/h.

In Mathematics and Geometry, Pythagorean's theorem is represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the side lengths of any right-angled triangle.

Part a.

First of all, we would create a graphical representation of the speed of these airplanes flying in the air at the same height by using an online graphing tool as shown in the Cartesian graph below.

Part b.

Assuming the variable C represent the distance between the airplanes, an equation that models the situation can be written as follows;

C² = A² + B²

By taking the first derivative of C with respect to time, we have:

2C(dC/dt) = 2A(dA/dt) + 2B(dB/dt)

By dividing both sides of the equation by 2, we have;

C(dC/dt) = A(dA/dt) + B(dB/dt)

Where:

dC/dt represents the rate of change of the distance between the airplanes.

C = √(A² + B²)

C = √(30² + 40²)

C = √2500

C = 50 miles

Part c.

Now, we can determine the solution to this equation as follows;

50(dC/dt) = (30 × 250) + (40 × 300)

50(dC/dt) = 19500

dC/dt = 19500/50

dC/dt = 390 mi/h.

Read more on Pythagoras theorem and distance here: https://brainly.com/question/15415980

#SPJ1

a. The population mean is the average wage (including benefits) of all judges employed by the state of Florida. Since we do not have data on the entire population, we can estimate the population mean using the sample mean. The point estimate of the population mean is the same as the sample mean, which is $67.00 per hour.

b. To develop a 99% confidence interval for the population mean wage (including benefits), we can use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

The critical value depends on the desired confidence level and the sample size. For a 99% confidence level, the critical value can be obtained from a standard normal distribution table, and it is approximately 2.62 for a sample size of 29 (with a degrees of freedom of 28). The standard deviation is given as $6.17 per hour, and the sample size is 29.

Confidence Interval = $67.00 ± (2.62 * ($6.17 / sqrt(29)))

Calculating this expression will give you the confidence interval for the population mean wage.

c. To estimate the population mean wage with 95% confidence and a margin of $2.00, we need to determine the sample size. The formula to calculate the required sample size is:

n = (z * (sigma / E))^2

Where:

- n is the required sample size

- z is the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of approximately 1.96)

- sigma is the estimated standard deviation

- E is the desired margin of error

In this case, we can use the given standard deviation of $6.17 per hour and the desired margin of $2.00. Plugging these values into the formula will give you the required sample size.

The percentage of residents aged 25 and older in Indiana with a degree is approximately 31%.

To find the percentage of residents aged 25 and older in Indiana with a degree, we need to calculate the total number of residents with a degree and then divide it by the total number of residents aged 25 and older. Finally, we multiply the result by 100 to get the percentage.

The total number of residents with a degree is the sum of residents with an associate's degree, a bachelor's degree, and a graduate or professional degree:

Total residents with a degree = Residents with an associate's degree + Residents with a bachelor's degree + Residents with a graduate or professional degree

Total residents with a degree = 326,036 + 623,200 + 348,807 = 1,298,043

Now, we can calculate the percentage:

Percentage of residents with a degree = (Total residents with a degree / Total residents aged 25 and older) * 100

Percentage of residents with a degree = (1,298,043 / 4,229,138) * 100 ≈ 30.7%

Rounded to the nearest whole number, the percentage of residents aged 25 and older in Indiana with a degree is approximately 31%.

For more questions on whole number, click on:

https://brainly.com/question/30765230

#SPJ8

I think it is the question:

A 2010 U.S. Census Bureau report indicated there are 4,229,138 residents of Indiana aged 25 and older. What percentage of the residents aged 25 and older have a degree if there are 326,036 residents with an associate's degree, 623,200 with a bachelor's degree, and 348,807 with either a graduate or professional degree? Write your answer as a percent rounded to the nearest whole number.

Answer:

b=7

Step-by-step explanation:

17 = opp b = adj so TOA

17 x tan(23) = 7.216071876

= 7 (to the nearest integer)

The total estimated number of retirees at the senior center in retirement community in Florida in March  is 1,740.

To estimate the total number of retirees at the senior center in March, round each weekly attendance to the nearest tens place and add them together:

To the nearest tens, we have

First week: 346 ≈ 350

Second week: 412 ≈ 410

Third week: 293 ≈ 290

Fourth week: 689 ≈ 690

Add the estimated values

350 + 410 + 290 + 690

= 1,740

Therefore, the total estimated number of retirees at the senior center in March is 1,740.

Learn more on Retirees on https://brainly.com/question/28128413

#SPJ1

Answer:

yes

Step-by-step explanation:

Because

3x - 5 = 1

3x = 1 + 5

3x = 6

So, yes, 3x - 5 = 1 implies that 3x = 6

True. Given the statement '3x-5=1 implies that 3x=6' is true. 3x-5=1 is a linear equation in one variable as its highest degree is 1 with a single variable x.

For the given question,

An algebraic equation 3x-5=1 is given.

An algebraic expression with an equality sign is called an equation. An equation has 2 parts: The left-hand side[LHS] and The right-hand side[RHS].

An equation is solved by bringing all the variables to one side and the numbers to the other side. There is a reversal of sign from LHS to RHS and vice-versa.

Thus, Taking the -5 from the LHS to the RHS makes it +5.

Thus, 3x=1+5

∴3x=6.

x=6/3

x=3.

Therefore by solving the given equation, the value of x is found to be 3.

In mathematics, the degree of an equation is the highest power of the variable. An equation with degree 1 is a linear equation. With degree 2 is a quadratic equation and with degree 3 is a cubic equation. When the degree is more than 3, it is known as a polynomial.

To know more about algebraic equations:

https://brainly.com/question/19297665

Answer:

Not a function

Step-by-step explanation:

This is not a function. It will fail the vertical line test.  For any value of x, there are two different y values.  This tells us that it is not a function

The correct statement that describes the horizontal line test is:

B: If any horizontal line touches the function more than once, the function is not a function.

The horizontal line test is defined as a mathematical test that checks if a function is one-to-one. A one-to-one function has only one x-value for each y-value. If a horizontal line passes through a graph more than once, the function can't be one-to-one.

The horizon line test is a graphical test used to determine if a function is one-to-one or has an inverse function. Tests show that a horizontal line does not have to intersect a function's graph more than once for the function to be one-to-one (and have an inverse). If the horizontal line intersects the function's graph at multiple points, the function fails the horizontal line test, indicating that it is not one-to-one and has no inversion. 

Thus, option B is correct.

Read more about Horizontal Line Test at: https://brainly.com/question/30241436

#SPJ1

The coordinates of point G are (1.5, -4). The reflection of point G across x-axis and y-axis lies in quadrant II, and the coordinates of that point are (-1.5, 4). ​

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

Based on the, the coordinates of point G are located at (1.5, -4) in quadrant IV.

By applying a reflection over the x-axis to the coordinates of point G, we have the following coordinates of the image G';

(x, y)                              →      (x, -y)

Point G (1.5, -4)             →      G' (1.5, -(-4)) = G' (1.5, 4)

By applying a reflection over the y-axis to the coordinates of point G', we have the following coordinates of the image G";

(x, y)                            →      (-x, y)

Point G' (1.5, 4)           →      G" (-1.5, 4), which is located in quadrant II.

Read more on reflection here: brainly.com/question/27912791

#SPJ1

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

Para aprender más sobre ecuaciones algebraicas: https://brainly.com/question/20307002

#SPJ1

There are a total of 50 + 10 + 8 + 10 + 10 + 7 = 95 customers who were older than 32

A stem-and-leaf plot is a method of data representation that aids in the visualisation of statistical data. It is a convenient and simple method of recording, analysing, and understanding data with a numerical range. The stem-and-leaf plot displays data in a way that shows how often specific data values occurred.
In the given stem-and-leaf plot, each number is broken into two parts: the stem, which is the left-side digit(s), and the leaf, which is the right-side digit(s).The digits on the left side of the stem are known as the stems, and the digits on the right side of the stem are known as the leaves. The stem represents the tens digit, and the leaves represent the units digit.```
3 | 1 3 5 6 7
4 | 2 2 4 6 6 7 7
5 | 0 1 2 5 6 8 9
6 | 1 2 3 4 6 6 7 7 8 8
7 | 0 2 3 3 4 5 5 7 9 9
8 | 0 1 3 4 6 6 7
```To calculate the number of customers who were older than 32, we must first determine the values in the stem-and-leaf plot that are greater than 3. The stem is 3, and the values in the leaves are greater than 2, which indicates that they are all greater than 32. So we can count the values in the stem-and-leaf plot to find out the number of customers older than 32.
- 5 values in the stem 3 (31, 33, 35, 36, 37)
- 10 values in the stem 4 (42, 42, 44, 46, 46, 47, 47, 52, 56, 57)
- 8 values in the stem 5 (50, 51, 52, 55, 56, 58, 59, 59)
- 10 values in the stem 6 (61, 62, 63, 64, 66, 66, 67, 67, 68, 68)
- 10 values in the stem 7 (70, 72, 73, 73, 74, 75, 75, 77, 79, 79)
- 7 values in the stem 8 (80, 81, 83, 84, 86, 86, 87)

For more such questions on customers

https://brainly.com/question/24553900

#SPJ8

The meaning of the absolute value in this problem is given as follows:

The temperature decreased 1.2 degrees.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

The number for this problem is -1.2, hence:

More can be learned about the absolute value of a number at https://brainly.com/question/24368848

#SPJ1

Answer:

circumference

Step-by-step explanation:

The maximum volume of water that the pool can contain is approximately 2,000,703.6 cm³.

The length of the security fence needed around the pool is 618 cm.

Catalina purchased a cylindrical pool with a diameter of 206 cm and a depth of 60 cm for her garden. Additionally, she plans to construct a cemented area and a security fence around the pool. Let's calculate the maximum volume of water the pool can hold and the length of the security fence.

To find the maximum volume of water the pool can contain, we can use the formula for the volume of a cylinder:

V = πr²h

Given the diameter of the pool is 206 cm,we can calculate the radius (r) by dividing the diameter by 2:

r= 206 cm / 2 = 103 cm

The depth of the pool is 60 cm, so the height (h) in the formula is 60 cm.

Now, substituting the values into the formula:

V = π(103 cm)²(60 cm)

V ≈ 3.14(10609 cm²)(60 cm)

V ≈ 3.14(636540 cm³)

V ≈ 2000703.6 cm³

Next, let's calculate the length of the security fence. The formula for the circumference (C) of a circle is:

C = 2πr

Using the given value of π (approximately 3) and the radius (r = 103 cm), we can calculate the circumference:

C = 2(3)(103 cm)

C = 6(103 cm)

C = 618 cm

for such more question on volume

https://brainly.com/question/6204273

#SPJ8

Answer:

Step-by-step explanation:

To calculate the distances between celestial bodies in our Solar System using astronomical units (AU), we can represent the distances using exponents. One astronomical unit (AU) is approximately the average distance from the Earth to the Sun, which is about 93 million miles or 150 million kilometers.

Let's calculate the distances between five celestial bodies in AU and arrange them in ascending and descending order.

Celestial bodies:

1. Mercury - Average distance from the Sun: 0.39 AU

2. Venus - Average distance from the Sun: 0.72 AU

3. Earth - Average distance from the Sun: 1 AU

4. Mars - Average distance from the Sun: 1.52 AU

5. Jupiter - Average distance from the Sun: 5.20 AU

Now, let's calculate the distances using exponents:

1. Mercury: 0.39 AU

2. Venus: 0.72 AU

3. Earth: 1 AU

4. Mars: 1.52 AU

5. Jupiter: 5.20 AU

Arranging in ascending order:

1. Mercury: 0.39 AU

2. Venus: 0.72 AU

3. Earth: 1 AU

4. Mars: 1.52 AU

5. Jupiter: 5.20 AU

Arranging in descending order:

1. Jupiter: 5.20 AU

2. Mars: 1.52 AU

3. Earth: 1 AU

4. Venus: 0.72 AU

5. Mercury: 0.39 AU

Therefore, in ascending order, the distances between the five celestial bodies in AU are: Mercury (0.39 AU), Venus (0.72 AU), Earth (1 AU), Mars (1.52 AU), and Jupiter (5.20 AU). In descending order, the distances are: Jupiter (5.20 AU), Mars (1.52 AU), Earth (1 AU), Venus (0.72 AU), and Mercury (0.39 AU).

Fοr functiοn y = 4x + 2, this statement is true.

Thus, the cοrrect οptiοn is C.

A functiοn is a reIatiοnship οr expressiοn invοIving οne οr mοre variables. There is a list of its inputs and outputs.

A) [tex]\text{y}=2(4)\text{x}=8\text{x}[/tex]

if x = a

[tex]\text{y}(\text{a})=8\text{a}[/tex]

and nοw with x = a + 2

[tex]\text{y}(\text{a}+2)=8(\text{a}+2)=8\text{a}+16[/tex]

The answer increased by 16. It is nοt the right οptiοn.

B) [tex]\text{y}=2(8\text{x)}=16\text{x}[/tex]

if x = a

[tex]\text{y}(\text{a})=16\text{a}[/tex]

and nοw with x = a + 2

[tex]\text{y}(\text{a}+2)=16(\text{a}+2)=16\text{a}+32[/tex]

The answer increased by 32. It is nοt the right οptiοn.

C) [tex]\text{y}=4\text{x}+2[/tex]

if x = a

[tex]\text{y}=4\text{a}+2[/tex]

and nοw with x = a + 2

[tex]\text{y}(\text{a}+2)=4(\text{a}+2)+2=4\text{a}+8+2=4\text{a}+10[/tex]

This time, between [tex]4\text{a}+2[/tex] and [tex]4\text{a}+10[/tex] there is a difference οf 8.

Sο fοr this functiοn, the statement is true.

To knοw more about Functions, visit:

https://brainly.com/question/31062578

Complete Question:

When x increases from a to a + 2, y increases by a difference of 8.

For which functions is this statement true?

A) y = 2(4)x

B) y = 2(8)x

C) y = 4x + 2

Answer:

Step-by-step explanation:

They're are all perfect cube.

a=19

b=45

c=63

The probability that;

i). two are red and 1 is blue is 0.0257

ii). at least 2 are white is 0.1144

iii). 1 of each colour is drawn is 0.0343

The probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.

Total possible outcome = 3 + 7 + 8 = 18

i). probability that two are red and 1 is blue = 7/18 × 6/17 × 3/16

probability that two are red and 1 is blue = 7/272

probability that two are red and 1 is blue = 0.0257

ii). probability that at least 2 are white = 8/18 × 7/17 × 7/16 + 8/18 × 7/17 × 3/16

probability that at least 2 are white = 70/612

probability that at least 2 are white = 0.1144

iii). probability that 1 of each colour is drawn = 7/18 × 8/17 × 3/16

probability that 1 of each colour is drawn = 7/204

probability that 1 of each colour is drawn = 0.0343

Therefore, the probability that; two are red and 1 is blue, at least 2 are white and 1 of each colour is drawn are approximately 0.0257, 0.1144 and 0.0343 respectively.

Read more about probability here:https://brainly.com/question/20140376

#SPJ1

The probability that an MP3 player manufactured in Fort Meyers is defective is 0.37%.

To calculate the probability that an MP3 player is defective, we need to consider the manufacturing plants and their respective defect rates.

Given:

Plant at Memphis manufactures 50% of the MP3 players, and 1% of those manufactured at that plant are defective.

Plant at Fort Meyers manufactures 20% of the MP3 players, and 3% of those manufactured at that plant are defective.

No information is provided about the defect rate of the third plant.

To find the overall probability of an MP3 player being defective, we need to consider the probability of selecting a defective player from each plant and then weigh it by the probability of selecting a player from each plant.

Let's calculate the overall probability:

Probability of selecting a defective player from Memphis plant = 50% * 1% = 0.50% or 0.005 (since 50% is equivalent to 0.50 in decimal form)

Probability of selecting a defective player from Fort Meyers plant = 20% * 3% = 0.60% or 0.006 (since 20% is equivalent to 0.20 in decimal form)

To calculate the overall probability, we need to weigh these probabilities by the probability of selecting an MP3 player from each plant:

Probability of selecting from Memphis plant = 50% = 0.50 (decimal form)

Probability of selecting from Fort Meyers plant = 20% = 0.20 (decimal form)

Overall probability of selecting a defective MP3 player is given by:

Overall probability = (Probability from Memphis plant * Probability of selecting a defective player from Memphis) + (Probability from Fort Meyers plant * Probability of selecting a defective player from Fort Meyers)

Overall probability = (0.50 * 0.005) + (0.20 * 0.006) = 0.0025 + 0.0012 = 0.0037 or 0.37%

Therefore, the probability that an MP3 player, manufactured in Fort Meyers, is defective is 0.37%.

For more question on  probability visit:

https://brainly.com/question/25839839

#SPJ8

Answer:

option D: BC = EF

Step-by-step explanation:

as according to SAS their corresponding sides should also be same if the angles between them is congruent

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains.

In conclusion, this piecewise-defined function has a jump discontinuity.

Read more on piecewise function here: brainly.com/question/18670055

#SPJ1

The algebric expression [tex]cot(sin^{(-1)}\sqrt{(x^2}[/tex]simplifies to sqrt(1 - |x|^2) / |x|.

The expression "cot(sin^(-1)(sqrt(x^2)))" involves trigonometric and square root functions. Let's break it down step by step to simplify the expression.

Inside the square root: x^2.

The square root of x^2 is |x| (the absolute value of x), as the square root eliminates the square and keeps the positive value.

The expression sin^(-1)(sqrt(x^2)) is equivalent to arcsin(sqrt(x^2)).

Since we already know that the square root of x^2 is |x|, we can rewrite the expression as arcsin(|x|).

Now, we have cot(arcsin(|x|)).

The cotangent (cot) of an angle is equal to the reciprocal of the tangent (tan) of the same angle.

So, cot(arcsin(|x|)) can be written as 1 / tan(arcsin(|x|)).

Using the inverse trigonometric identity, tan(arcsin(x)) = x / sqrt(1 - x^2), we can simplify further.

In our case, x = |x|.

Therefore, tan(arcsin(|x|)) = |x| / sqrt(1 - |x|^2).

Substituting this result back into the expression, we have 1 / (|x| / sqrt(1 - |x|^2)).

To divide by a fraction, we multiply by its reciprocal.

Hence, the final simplification of the expression is sqrt(1 - |x|^2) / |x|.

For more such question on algebric expression visit:

https://brainly.com/question/4344214

#SPJ8

Answer:

Step-by-step explanation:

The correct answer for this question is Phil can swim 90 meters in 2 minutes.

According to the given question, Phil can swim 15 meters in 20 second.

So, in 1 second, Phil can swim: 15 meters/20 second=0.75 m/s

In other words, the speed of swimming of Phil is 0.75 m/s.

So, in 2 minutes i.e. in 120 second, the distance Phil can travel:

Distance= Speed x Time

Distance= 0.75 m/s x 120 s

Distance= 90 meters.

Hence, Phil swimmed 90 meters in 2 minutes. The speed of Phil is 0.75 m/s which can be used to determine further distances travelled with time if the motion is uniform.

Answer:

Elements, that are part of the universal set, that don't belong to A or B in any way

The maximum revenue is $342,784.

To find the maximum revenue, we need to determine the ticket price that will maximize the number of seats sold. Let's break down the information provided: - The arena has 7,722 seats. - All seats are sold if the ticket price is $45 each. - For each $1 increase in ticket price, 62 fewer seats are sold. To find the maximum revenue, we need to determine the ticket price that maximizes the number of seats sold.

An equation to represent the relationship between the ticket price and the number of seats sold: Revenue = Ticket Price x Number of Seats Sold We know that the number of seats sold decreases by 62 for every $1 increase in ticket price. So, if we let "x" represent the number of $1 increases from the base price of $45, the equation becomes: Number of Seats Sold = 7,722 - 62x Now, let's express the revenue in terms of "x": Revenue = (Ticket Price + $1 increase) x Number of Seats Sold = (45 + x) x (7,722 - 62x) To find the maximum revenue, we need to find the value of "x" that maximizes the Revenue equation.

A graph the equation or use calculus techniques such as finding the maximum of a quadratic function. For the sake of simplicity, let's use a graphing calculator to find the maximum revenue. By graphing the Revenue equation, we can visually identify the maximum point. After graphing the equation, we find that the maximum revenue occurs when "x" is approximately 58.

This means that the ticket price should increase by $58 from the base price of $45. Now, let's calculate the maximum revenue: Revenue = (45 + 58) x (7,722 - 62(58)) = $103 x 3,328 = $342,784 Therefore, the maximum revenue is $342,784. It's important to note that this solution assumes a linear relationship between the ticket price and the number of seats sold.

Know more about linear relationship here:

https://brainly.com/question/13828699

#SPJ8

Answer:

1230

Step-by-step explanation:

Sum of integers from 1 to n:

(n)(n + 1)/2

Find the sum of integers from 1 to 50 and subtract the sum of integers from 1 to 9.

(50)(51)/2 - (9)(10)/2 = 1230

Answer:

1230

Step-by-step explanation:

Counting numbers, also known as natural numbers, are the set of positive integers starting from 1 and continuing indefinitely.

To find the sum of 41 counting numbers starting from 10, we can use sum of an arithmetic series formula.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{n}{2}[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

We want to find the sum of 41 counting numbers, so n = 41.

The first term is 10, so a = 10.

The common difference between consecutive terms is 1, so d = 1.

Substitute these values into the formula and solve.

[tex]\begin{aligned}S_{41}&=\dfrac{41}{2}\left[2(10)+(41-1)(1)\right]\\\\&=\dfrac{41}{2}\left[20+(40)(1)\right]\\\\&=\dfrac{41}{2}\left[20+40\right]\\\\&=\dfrac{41}{2}\left[60\right]\\\\&=\dfrac{2460}{2}\\\\&=1230\end{aligned}[/tex]

Therefore, the sum of the counting numbers from 10 to 50 is 1230.

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:The total of the areas under the standard normal curve to the left of z₁ and to the right of z₂ is 0.1236.

Finding the area under the normal curve:

The total area under the standard normal curve to the left of and to the right of z₂ is equal to the sum of the area to the left of z₁ and the area to the right of z₂.

Here we have

z₁  = -1.54 and z₂ = 1.54

Using a standard normal distribution table,

The area to the left of z₁ = -1.54 is 0.0618, and

The area to the right of z₂ = 1.54 is also 0.0618

(since the standard normal distribution is symmetric about 0).

Hence,

The total area under the standard normal curve to the left of z₁ and to the right of z₂ can be calculated as

=> 0.0618 + 0.0618 = 0.1236

Therefore,

The total of the areas under the standard normal curve to the left of z₁ and to the right of z₂ is 0.1236.

Step-by-step explanation: