-2≤x<7 what is the equivalent interval notation

Answers

Answer 1

Answer:

576482670576482670576482670576482670576482670576482670576482670576482670576482670576482670

Step-by-step explanation:


Related Questions

Championship T-shirts sell for $22 each.

What point(s) MUST be on the graph for the quantities to be proportional to each other?

Answers

The points that must be on the graph for the quantities to be proportional to each other are (2, 44), (3, 66) and (4, 88)

How to determine the points that must be on the graph?

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

Championship T-shirts sell for $22 each.

The above parameter means that

The unit rate of a T-shirt = $22

This can be represented as

Unit rate = 22

The interpretation of the above rate is that:

The number of n T-shirts is the unit rate multiplied by n

So, we have the following equation

Cost of n shirts = Unit Rate * n

When the number of shirts is 2, we have

Cost of 2 shirts = 22 * 2

Cost of 2 shirts = 44

When the number of shirts is 3, we have

Cost of 3 shirts = 22 * 3

Cost of 3 shirts = 66

When the number of shirts is 4, we have

Cost of 8 shirts = 22 * 4

Cost of 4 shirts = 88

So, the points are (2, 44), (3, 66) and (4, 88)

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What is the area of 300 meters by 200 meters in sq kilometers

Answers

Answer: 0.06 sq km

Step-by-step explanation:

We first convert each dimension from meters to kilometers. 300 meters is equal to 0.3 kilometers. 200 meters is 0.2 kilometers. We now compute the area: 0.3 km * 0.2 km = 0.06 sq km.

How do you think you can find f(3) without using a graph?

Answers

Answer:

f(3)=13

Step-by-step explanation:

f(x)=5x-2

f(3)=5(3)-2

 =15-2

 =13

can someone help me with, expand 4(3x-5)?

Answers

Answer:

Step-by-step explanation:

12x-20

Answer:

Answer: 4 ∙ 3x - 4 ∙ 5

Step-by-step explanation:

5)
What is the mean of 14, 7, 10 and 5?

Answers

[tex]\stackrel{\textit{\LARGE arithmetic mean}}{\cfrac{14+7+10+5}{\underset{\textit{number of data elements}}{4}}\implies \cfrac{36}{4}\implies \text{\LARGE 9}}[/tex]

Answer:

the mean is 9 .

Step-by-step explanation:

i did this & got it correct .

A credit union client deposits $2,500 in an account earning 7% interest, compounded annually. What will the balance of the account be at the end of 21 years?

Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.

Balance ≈ $______________ after 21 years.

Answers

The balance of the account at the end of 21 years, given the deposit amount and the interest rate is $10, 351. 41

How to find the balance on the account?

The balance on the account at the end of 21 years is the future value of the amount in the account today. This means that this balance can be found by the formula:
= Amount deposited x ( 1 + rate) ^ number of years

The balance on the Credit union client's account after 21 years is therefore:
= 2, 500 x ( 1 + 7%) ²¹

= $10, 351. 41

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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(0) = 2
B.
g(-4) = -11
C.
g(7) = -1
D.
g(-13) = 20

Answers

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, the statement that could be true for g is: D. g(-13) = 20.

What is a range?

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

From the information provided, the domain and range of this function g(x) in interval notation is given by:

Domain = [-20, 5]Range = [-5, 45]

How to determine the true statement?

Function g(0) = 2 is false because it was stated that g(0) = -2. Also, g(-4) = -11 is outside the scope of the given range for this function.

Furthermore, function g(7) = -1 is not within the domain for the given function. However, g(-13) = 20 is within the domain for the given function and produces an output that is within the scope of the given range for this function.

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Which equation represents the transformation formed by vertically stretching the graph of f(x)=√x by a factor of 6 and then vertically shifting the graph 7 units up?

g(x)=6√x +7
g(x) = √6x +7
g(z) = √1/6x +7​

100 brainly points

Answers

Please open the image to see the answer so the first one

Brenda deposited $2,059 in an account earning 1% interest compounded annually.
To the nearest cent, how much will she have in 1 year?

Answers

Answer: $2,079.59

Steps:
A = P ( 1 + r/n )^nt

A = 2059 ( 1 + 0.01/1 )^1•1

A = 2079.59

Work out
198.02% of £83.02
83.02
Give your answer rounded to 2 DP

Answers

The value of 198.02 percent of £83.02 is £164.40

How to calculate the value?

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

The value will be illustrated thus:

198.02% × £83.02

= 1.9802 × £83.02

= £164.3962

= £164.40

The value is £164.40.

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WILL ASSIGN BRAINLIEST
determine the quadratic function of the form f(x)=a(x-h)^2+k
Whose graph is given below




Graph shows -3,8 and 0,-19








Answers

The quadratic function of the given graph is y = (x + 3)² + 8.

Quadratic function:

Basically, the standard form of the quadratic function is written as,

f(x) = a(x - h)² + k,

And a not equal to zero.

Here if a is positive, the graph opens upward, and if a is negative, then it opens downward. And the line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Given,

Here we have the graph and we have to find the quadratic function of the graph.

While we looking in to the given graph,

We have identified then the graph is opening the upward direction, So, the value of a is positive.

Now, we have to find the value of a which is 1.

And the vertex of the graph is (-3, 8).

So, the standard form of the quadratic function of the graph is written as,

=> y = (x + 3)² + 8.

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ANSWER THIS QUESTION WILL MARK BRAINLIEST

Answers

The probability that Jordan will win in three or fewer matches if they play 5 matches using binomial probability distribution is; 0.95636

How to solve Binomial probability distribution problems?

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula for binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring

x = the number of expected successful outcomes

n = the number of trials you perform

nCx = the number of different combinations for x items you test in n trials

We are given probability that Jordan wins the match as 1/3. Thus;

p = 1/3 = 0.333

Thus, probability that Jordan will win in three or fewer matches if they play 5 matches is;

P(X ≤ 3) = P(0) + P(1) + P(2) + P(3)

From online binomial probability calculator, we have;

P(X ≤ 3) = 0.95636

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

y=7000(1.97)

Answers

The given exponential function is increasing so it will be growth and the percentage increase is 97%.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given function,

y = 7000(1.97)^x

As x increase the 1.97^x will be increased thus, y will be increased so it will be growth.

Suppose x = 0

y = 7000

Suppose x = 1

y = 1.97 x 7000

% increase = (1.97 x 7000 - 7000)/7000

% increase = 97 %

Hence "The given exponential function is increasing so it will be growth and the percentage increase is 97%".

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the mean systolic blood pressure of all healthy adults is less than 122 mm Hg. Simple data for 281 healthy adults, the mean systolic blood pressure level is 119.87 mm Hg and the standard deviation is 15.21 mm Hg. Complete part a and b. express the original claim in symbolic form. Let the parameter represent a value with respect to systolic blood pressure for a healthy adult

Answers

a) The claim is given as follows:

[tex]\mu < 122[/tex]

b) The null and the alternative hypothesis are given as follows:

Null hypothesis: [tex]H_0: \mu \geq 122[/tex].Alternative hypothesis: [tex]H_0: \mu < 122[/tex].

What are the null and the alternative hypothesis?

The claim in this problem is given as follows:

The mean systolic blood pressure of all healthy adults is less than 122 mm Hg.

Symbolically, the claim is given as follows:

[tex]\mu < 122[/tex].

As:

The symbol [tex]\mu[/tex] represents the mean.The symbol < represents less than.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_0: \mu \geq 122[/tex].

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, that is, enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_1: \mu < 122[/tex].

Missing Information

The questions are given by the image at the end of the answer.

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Multiple Choice You are taking guitar •lessons. The cost of the first lesson is twice the cost of each additional lesson. You spend $360 for 8 lessons. How much did the first lesson cost'7 A $40 (C $50 (E $80 B) $45 (D $60

Answers

The first guitar lesson will cost (E $80

How to know the cost of the first lesson'

The cost of the first lesson is solved by comparing the costs

Since the cost of the first lesson is twice the cost of each additional lessons, double counting the first lesson makes the total number of lesson to be 9

if 9 lessons costs $360 then 1 lesson will cost

9 = 360

1 = ?

cross multiplying

8 * ? = 360 * 1

? = 360 / 9

? = 40

The unit cost is 40 taking the double counts makes the first lesson to be 2 * 40 = $80 then other lessons are 40

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Over the interval [0,2π ), what are the solutions tosin (2 x)=sin (x)? Check all that apply. 0 π/3 2π/3 π 4π/3 5π/3

Answers

The solutions to the trigonometric equation sin(2x) = sin(x) on the first quadrant is given as follows:

0.π/3.π.5π/3.

How to obtain the solutions to the trigonometric equation?


The trigonometric equation in this problem is defined as follows:

sin(2x) = sin(x).

To verify the solutions, we replace each possible solution into each side of the equation, and verify if they are equal, as follows:

sin(2(0)) = sin(0) -> sin(0) = sin(0) -> 0 is a solution.sin(2π/3) = sin(π/3) = sqrt(3)/2, as they are equivalent angles, hence it is a solution.sin(4π/3) = -sqrt(3)/2 = -sin(2π/3), hence it is not a solution.sin(2π) = sin(π) = 0, hence it is a solution.sin(8π/3) = sqrt(3)/2 = -sin(4π/3), hence it is not a solution.sin(10π/3) = -sqrt(3)/2 = sin(5π/3), hence it is a solution.

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4x +5 what do I times and add

Answers

Answer:

to be real i don´t think you can do anything because they´re not like terms. you can´t combine them (add) because they don´t have anything in common

Step-by-step explanation:

So if this formula is the like equation y=Mx+b, then u can use to find coordinates of the line on the graph. So it’ll be something like: y= 4x +5
So if x=0 then y will be 4*0 +5 which is 5
If x = 1 then y will be 4*1 + 5 which is 9
Or if x = 2 then y will be 4*2 + 5 which is 13


And u also do it the other way around in order to find X,
For example, if y = 0 then x will be 0=4x+5, so x will be (when solved for x) -5/4
If y = 1 then x will be 1=4x+5, so x will be -1
If y = 2 then x will be 2=4x+5, so x will be -3/4



Conclusion: So by itself you do not really times things, but you use it to find linear coordinates. (e.g. (1,3), (4,6))

The nth term of a series is represented by an=4n/5^n+1 ⋅n.

Otto correctly applies the ratio test to determine whether the series converges or diverges.

Which statement reflects Otto's conclusion?

Answers

The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

Given that, the nth term of a series represented by [tex]a_n=\frac{4^n}{5^{n+1}.n}[/tex].

What is the series converges or diverges?

A convergent series is a series whose partial sums tend to a specific number, also called a limit. A divergent series is a series whose partial sums, by contrast, don't approach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Next term in the series is [tex]a_{n+1}=\frac{4^{n+1}}{5^{n+2}.(n+1)}[/tex]

Now, the ratio is [tex]|\frac{a_{n+1}}{a_n}| =|\frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} | \frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |\frac{4^{n+1}}{4^n}.\frac{5^{n+2}}{5^{n+1}} .\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |4.\frac{1}{5}} .\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+\frac{1}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+0|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= 0.8[/tex]

Since 0.8 < 1 so the series converges.

The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

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Answer:

From the ratio test, r = 0.8. The series converges.

Step-by-step explanation:

TTT

Karen needs to buy plastic forks. Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.

Find the unit price for each brand. Then state which brand is the better buy based on the unit price.


Round your answers to the nearest cent.

Answers

The unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

Given that, Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

The cost of each fork of brand A

= 2.17/42

= $0.0517

The cost of each fork of brand B

= 3.97/48

= $0.0828

Therefore, the unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

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Which of the following fractions rounds most closely to 0? 7/12 10/11 5/10 1/5

Answers

Answer: 1/5

Step-by-step explanation:

Answer: 5/10

Step-by-step explanation:5/10 is the smallest answer here you et get to 0 concluding your answer to 5/10

How would y-x2=5 be written in function notation

Answers

Hope this helped alot ok

Darrien is building a model of the Globe Theatre stage using a scale of 1in:3 feet. On the model, the width of the stage is 15 inches. What is the actual width, in feet, of the stage?

a. 2.5 feet
b. 45 feet
c. 180 feet
d. 540 feet

Answers

Answer:

b. 45 ft

Step-by-step explanation:

The scale is 1 in : 3 ft.

1 inch in the model equals 3 feet real.

To go from the model size to the real size, multiply the model inch measurement by 3 and change to feet.

15 inch model size = 15 × 3 ft real size

Answer: 45 ft

The answer is 45 all u gotta do is multiply 15 times 3

My-Lien has enough room in her truck to move 3.385 tons of gravel. Her father has asked her to move 3 5/16 tons. My-Lien will have enough room to move the amount of gravel her father has asked her to.
I need this by tonight :) pls my little brother made me make this account for his homework help

Answers

Answer:

  True

Step-by-step explanation:

You want to know if My-Lien has enough room in a truck with a capacity of 3.385 tons to move 3 5/16 tons of gravel.

Space available

The empty space can be found by subtracting the load from the capacity of the truck. The attached calculator output shows there is room for an addition 0.0725 tons.

My-Lien will have enough room to move the gravel.

__

Alternate solution

You can convert 3 5/16 to a decimal: 3.3125. Clearly, this amount is less than 3.3850.

Find the length of AC and ED.

Answers

Answer:

A and C = 13 and D and E = 24

Step-by-step explanation:

more than 3.2% of homes have only a landline telephone and no wireless phone. sample data: A survey by the national center for health statistics showed that among 15800 homes 5.81% had landline phones without wireless phones. Complete parts a and b . Express the originall claim in symbolic form. Let the parameter represent a value with respect to homes that have only a landscape telephone and no wireless phone

Answers

a) The original claim expressed in symbolic form is; p > 0.032

b) The hypotheses are defined as;

Null hypothesis; H₀: p ≤ 0.032

Alternative hypothesis; Hₐ: p > 0.032

How to define the hypotheses?

A hypothesis is defined as an educated guess while using reasonable thinking, about the answer to a scientific question.

a) We are told that the claim is that more than 3.2% (0.032) of homes have only a landline telephone and no wireless phone. Thus, the original claim in symbolic form is; p > 0.032

b) From the sample survey that we see, it is clear that among 15800 homes, 5.81% had landline phones without wireless phones. This would be the sample proportion.

This means that we can define the alternative hypothesis as;

Hₐ: p > 0.032

Null hypothesis is;

H₀: p ≤ 0.032

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For a hypothesis test where H0: μ=μ0, Ha: μ≠μ0, α=0.10 , and n=50, which of the following test statistics reject H0?

Answers

The test statistics that reject the null hypothesis are given as follows:

t such that |t| > 1.6766.

When is the null hypothesis rejected?

The null hypothesis is rejected when the test statistic is out of the accept done, defined by the critical value.

The critical value is obtained considering these three features are follows:

The significance level.The number of degrees of freedom.The tail.

These parameters in this problem are given as follows:

Significance level of 0.10.50 - 1 = 49 degrees of freedom.Two-tailed test, as we are testing if the mean is less than a value.

Using a t-distribution calculator, the critical value is given as follows:

t = 1.6766.

Hence, as we have a two-tailed test, test statistics with absolute value greater than the critical value reject the null hypothesis.

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need help with this math problem; think I have the answer but not quite sure

Answers

Answer:

0

-7+7 = 0  0/82=0   0x8-3=0

Please help will mark Brainly

Answers

The graph of g(x) = f(x - 5) has a slope of 1 and the y-intercept is -5

How to interpreted the graph

A graph is a pictorial representation of data and the graph presented represents g(x) = f(x - 5) is attached

The graph shows a linear function written in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Comparing the equation with the above we can see that

m = 1

y intercept, c

this is a point where the graph cuts the y axis

c = -5

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please refer to picture and answer all parts for brainliest ​

Answers

The value of the given limits [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e.

What is the limit?

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

Because the value of that function at that point doesn't define.

a)

[tex]\lim_{x \to \infty} 1/x^2[/tex] by substitute limit 1/∞² = 0

b)

[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] here (x² - 4)/(x - 2) = (x - 2)(x + 2)/(x - 2) = (x + 2)

Putting x = 2 will give the limit as 2 + 2 = 4.

c)

[tex]\lim_{x \to \pi} sinx\\[/tex] herer put x to π so sinπ = 0.

c)

[tex]\lim_{x \to \55} e[/tex] here no variable thus e will be the answer.

Hence "The value of [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e".

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How many metric tons are in 230.2 g

Answers

The conversion of 230.2 g to metric ton is given by 0.0002302 metric tons.

How to convert grams to metric tons?

Grams (g) and metric ton (MT) are the SI units of mass. Scientist measure various things with different units. The following are measures and their units;

Temperature: Fahrenheit, Celsius, KelvinLength: Meters, centimeters, millimeters etcWeight: Kilograms, milligrams, gramsTime: seconds, minutes, hours.

Convert metric ton to grams:

1 metric ton = 1,000,000 grams

230.2 g = 230.2 ÷ 1,000,000

= 0.0002302 metric tons

Therefore, it can be said that 230.2 g is equivalent to 0.0002302 metric tons

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Five Star Retro Video rents VHS tapes and DVDs to the same connoisseurs who like to buy LP record albums. The store rents new videos for $3.00 a night, and oldies for $2.00 a night.Write a program that the clerks at Five Star Retro Video can use to calculate the total charge for a customers video rentals.The program should prompt the user for the number of each type of video and output the total cost.An example of the program input and output is shown below:Enter the number of new videos: 3Enter the number of oldies: 2The total cost is $13.0 a grassland biome select one: a. consists of mostly coniferous trees. b. has nutrient-rich soil. c. has a long growing season. d. is warm and dry. e. consists of moss and lichen. Garnett, Inc. has a required rate of return on new projects of 12%. The Western division of Garnett is currently earning a combined return on investment (ROI) of 14.5% on the projects in its division. The manager of the Western division is considering a project that is projected to earn 13.25%. Which of the following statements regarding the manager's decision are correct? Which civic responsibility is most closely related to voting? What are the president's powers as chief executive ?. What 3 shoe companies are mentioned as having sponsor deals? how many countries does each sponsor?. Three of the exterior angles of an n-sidedpolygon are 50 each,two of its interiorangles are 127 and 135,and the remaininginterior angles are 173 each. Find the value of n. What makes a triangle congruent by HL?. Can someone please please write me a myth about the creation of the internet.Will give BRAINLIEST PLEASE What's considered a developing country?. Can a fixed mortgage rate increase?. What section of Title 21 of the Code of Federal Regulations 21 CFR provides the procedures for performance standards development?. Directions - Use the compound interest formula to calculate the final balance.*Formula: P (1+7Compound Interest Formula: P$300 compounded quarterly at 5% for 8 years.Final balance = $(if necessary, round to two decimal places) What are some ways we can increase voter turnout ?. Cotton Hotel Corporation recently purchased Emporia Hotel and the land on which it is located with the plan to tear down the Emporia Hotel and build a new luxury hotel on the site. The cost of the Emporia Hotel should be A) depreciated over the period from acquisition to the date the hotel is scheduled to be torn down B) capitalized as part of the cost of the land. C) capitalized as part of the cost of the new hotel. D) written off as an extraordinary loss in the year the hotel is torn down. Suppose you need to know an equation of the tangent plane to a surface S at the point P(4, 1, 4). You don't have an equation for S but you know that the curves r1(t) = 4 + 2t, 1 t2, 4 5t + t2 r2(u) = 3 + u2, 2u3 1, 2u + 2 both lie on S. Find an equation of the tangent plant at P What is the solution to the trolley problem?. which is the correct statement to increase the maximum number of rows to display the entire dataframe if it has 799 rows? a 1 kg ball is hung at the end of a rod 1 m long. if the system balances at a point on the rod 0.25 m from the end holding the mass, what is the mass of the ro A company that recently changed its slogan is hosting an optional company picnic. Some members of the marketing team are eating together at the picnic and sharing their thoughts on the new slogan. They find that 80 % 80%80, percent of them like the new slogan. For which population is 80 % 80%80, percent a legitimate estimate of the percent of employees who like the new slogan?.