There are approximately 2,720 people per square mile in Charlotte. If


Charlotte is 297. 7 square miles, approximately how many people live in


Charlotte?


Round to the nearest person.

\(\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}\)

▪ \( \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}\)

▪ \( \sf{Area = 72 yd^2}\)

▪ \( \sf{BD = 6yd}\)

\(\leadsto\) Substitute the values:

\(\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}\)

\(\leadsto\) Solve for AC:

\(\longrightarrow \sf{72=8\times AC}\)

\(\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}\)

\(\longrightarrow \sf{AC=9}\)

\(\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}\)

\(\large \bm{AC= \: 9 yd}\)

BD = 16 yd

Area of ABCD = 72 yd²

AC = ?

Area of rhombus, using diagonal:

\( \frac{1}{2} \times d1 \times d2\)

Therefore:

\( \frac{1}{2} \times 16 \times ac = 72\)

Then:

\( \frac{16ac}{2} = 72\)

Cross multiply the above into:

\(16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144\)

Divide by the coefficient of AC:

\( \frac{16ac}{16} = \frac{144}{16} \)

Final answer is 9 yd

The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

For each function f(z), compute g(x) = lim h→0. The functions are:\(f(x) = 7f(x)= 1/(3-x)²\)

Solution:1) Calculation of g(x) for f(x) = 7

We need to find the value of g(x) for\(f(x) = 7.g(x) = lim h→0 {f(x+h) - f(x)}/hf(x) = 7f(x+h) = 7; f(x) = 7g(x) = lim h→0 {7 - 7}/h= lim h→0 0/h= 0So, g(x) = 0 for f(x) = 72)\)

Calculation of g(x) for f(x) = 1/(3-x)²

We need to find the value of g(x) for \(f(x) = 1/(3-x)².g(x) = lim h→0 {f(x+h) - f(x)}/h\)

First, let's calculate\(f(x + h)f(x + h) = 1/ (3 - (x + h))²\)

On simplifying the above expression, we get,\(f(x + h) = 1/ (9 - 6xh - h²)\)

Next, we need to find f(x)f(x) = 1/ (3 - x)²

On simplifying the above expression, we get,\(f(x) = 1/ (9 - 6x + x²)\)

Now, let's calculate \({f(x + h) - f(x)}/h{f(x + h) - f(x)}/h = {1/ (9 - 6xh - h²) - 1/ (9 - 6x + x²)}/h\)

Multiplying the numerator and denominator by \((9 - 6x + x²)(9 - 6xh - h²) - (9 - 6x + x²) = -6xh - h²\)

Now, substituting the values in g(x), we get,\(g(x) = lim h→0 {-6xh - h²}/h= lim h→0 (-6x - h)= -6x\)

Therefore,\(g(x) = -6x for f(x) = 1/(3 - x)².\)

To know more about function

https://brainly.com/question/11624077

#SPJ11

Answer:

1350 cubic inches

Step-by-step explanation:

9*10*15

Step-by-step explanation:

To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:

m = (9 - 2) / (8 - (-2))

= 7 / 10

= 0.7

The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:

tan(θ) = 0.7

Taking the inverse tangent of both sides, we find:

θ = arctan(0.7)

Using a calculator, we can evaluate this to be approximately:

θ ≈ 35.87 degrees

Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.

Answer:

The independent variable.

A random sample is a sample that is drawn from a population in such a way that each member of the population has an equal chance of being selected. The mean is a measure of central tendency that represents the average value of a set of data.

In this scenario, a simple random sample of size n was drawn from a population that is normally distributed. The sample mean, X, was found to be 112, and the sample standard deviation, s, was found to be 10.

(a) To construct an 80% confidence interval about us if the sample size, n, is 13, we can use the formula:

CI = X ± t(α/2, n-1) * s/√n

where t(α/2, n-1) is the critical value for the t-distribution with (n-1) degrees of freedom and α is the level of significance. For an 80% confidence interval, α = 0.2 and t(α/2, n-1) = 1.340. Thus, the confidence interval is:

CI = 112 ± 1.340 * 10/√13
CI = (103.76, 120.24)

(b) To construct an 80% confidence interval about p if the sample size, n, is 24, we can use the formula:

CI = p ± z(α/2) * √(p(1-p)/n)

where z(α/2) is the critical value for the standard normal distribution and p is the sample proportion. Since the population is normally distributed, we can assume that the sample proportion is also normally distributed. For an 80% confidence interval, α = 0.2 and z(α/2) = 1.282. Thus, the confidence interval is:

CI = 112/24 ± 1.282 * √(112/24 * (1-112/24)/24)
CI = (0.38, 0.68)

(c) To construct a 95% confidence interval about p if the sample size, n, is 13, we can use the same formula as in (b), but with α = 0.05 and z(α/2) = 1.96. Thus, the confidence interval is:

CI = 112/13 ± 1.96 * √(112/13 * (1-112/13)/13)
CI = (0.38, 0.78)

(d) Yes, we could have computed the confidence intervals using the formulas provided, as long as the assumptions of normality and independence were met. However, if the sample size was small or the population was not normally distributed, we would need to use different methods, such as the t-distribution or non-parametric tests.

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ11

Answer:

so there are 3825 worker in total

Step-by-step explanation:

675=15%

women=85%

how much workers are 5%=675/3 =225

225=5%

how many workers is 85%= 85/5=17

                                    85%=225x17=3825

Answer:

d = 14

Step-by-step explanation:

\( \sin \: 45 \degree = \frac{a}{7 \sqrt{2} } \\ \\a = 7 \sqrt{2} \sin \: 45 \degree \\ \\ a = 7\sqrt{2} \times \frac{1}{ \sqrt{2} } \\ \\ a = 7 \\ \\ \sin \: 30 \degree = \frac{a}{d} \\ \\ \frac{1}{2} = \frac{7}{d} \\ \\ d = 2 \times 7 \\ \\ d = 14\)

Answer:14

Step-by-step explanation:opposite angle

The 5 arithmetic means between 18 and -12 are; ​-7, -2, 3, 8, 13

Arithmetic Means is defined as the branch of mathematics that deals with the properties as well as the manipulation of numbers.

The formula for the nth term of an arithmetic mean is;

an = a + (n - 1)d

where;

a is first term

d is common difference

n is position of term

In this case, we want 5 terms between 18 and -12 and this means we have a total of 7 terms. Thus;

a = -12

a₇ = 18

18 = -12 + (7 - 1)d

18 + 12 = 6d

30 = 6d

d = 5

a₂ = -12 + (2 - 1)5

a₂ = -12 + 5

a₂ = -7

a₃ = -12 + (3 - 1)5

a₃ = -12 + 10

a₃ = -2

a₄ = -12 + (4 - 1)5

a₄ = 3

Thus;

a₅ = 8

a₆ = 13

Read more about arithmetic mean at; https://brainly.com/question/20118982

#SPJ1

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its Denominator, or to eliminate denominators from a radical expression.

To rationalize the denominator 1/7 + 3√2,

A rational number is a number that can be expressed as a ratio of two integers, with the denominator not equal to zero. The fraction 4/5, for example, is a rational number since it can be expressed as 4 divided by 5.

Step-by-Step SolutionTo rationalizes the denominator 1/7 + 3√2, we'll need to follow these steps.

Step 1: First, we need to create a common denominator for the two terms. The common denominator is 7. Thus, we can convert the expression to the following form:(1/7) + (3√2 × 7)/(7 × 3√2).

Step 2: Simplify the denominator to 7. (1/7) + (21√2)/(21 × 3√2).

Step 3: The numerator and denominator can now be simplified. (1 + 21√2)/(7 × 3√2).Step 4: Simplify further. (1 + 21√2)/(21√2).We have successfully rationalized the denominator!

The final answer is (1 + 21√2)/(21√2).

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its denominator, or to eliminate denominators from a radical expression.

For more questions on Denominator.

https://brainly.com/question/20712359

#SPJ8

The causes of variation which are large in magnitude and are not part of the normal variation are known as Outliers.

What is an Outlier? An outlier is a value that is far greater or less than the majority of other values in a given dataset. These may be due to a variety of factors, including statistical errors or data entry mistakes, but they may also represent actual phenomena that have an impact on the overall results. These causes are not typically part of the normal variation of the process. Thus, outliers are not considered a part of the normal variation.

To learn more about outliers visit : https://brainly.com/question/3631910

#SPJ11

Answer:

Step-by-step explanation:

Density of copper = 9.86 g / cm^3 = 9860 kg / m^3

= 9.86 x 1 / 1000 kg / cm^3 = 9.86 / 1000 Kg / cm^3

= 0.00986 kg / cm^3

= 9.86 x 1 / 1000 kg (1 / 100 m)^3

= 9.86 x 1000000 / 1000 kg / cm^3

Mass "m" = 9860 kg / m^3

thus the mass of copper in solid form is m =  9860 kg / m^3

True. The is subset() method is used to check if all elements of set1 are present in set2, which means set1 is a subset of set2 if the is subset() method returns true.

True. The "is subset()" method can be used to determine whether set1 is a subset of set2. If all elements of set 1 are present in set 2, then set 1 is considered a subset of set 2. The method returns `True` if set1 is a subset of set2 and `False` otherwise.
In mathematics, if all the elements of A are also elements of B, then the set A is one of the set B; then B is a superset of A. A and B may be equal; if they are not, A is a necessary condition of B. A relationship in which one group is one of the other is called existence (or sometimes existence). A is part of B, it can also indicate that B contains (or contains) A, or that A contains (or contains) B. A k-subset is a subset with k elements.

A linked subset defines the partial order of a set. In fact, intersection and union give intersection and intersection, with subsets of the given set being Boolean algebra in the relationship, and the link itself is a Boolean coverage relationship.
Example usage:
```python
set1 = {1, 2, 3}
set2 = {1, 2, 3, 4, 5}

result = set1.issubset(set2)
print(result) # Output: True
```

Learn more about subset:

brainly.com/question/24138395

#SPJ11

Answer:

Step-by-step explanation:

"Undefined terms are those terms that don't require a formal definition. The four terms are point, line, plane, and set. A point is quite simply, a dot. Points are labeled with one capital letter."

Based on the calculation below, the amount of vanessa’s down payment is $9,314.45.

First, we have to calculate the balance after deducting vanessa’s down payment using the formula for calculating the present value (PV) of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or balance after deducting vanessa’s down payment = ?

P = Monthly payment = $1,595.85

r = Monthly interest rate = 6.25% / 12 = 0.0625 / 12 = 0.00520833333333333

n = number of months = 30 * 12 = 360

Substitute the values into equation (1), we have:

PV = $1,595.85 * ((1 - (1 / (1 + 0.00520833333333333))^360) / 0.00520833333333333) = $259,185.55

Now, the amount of vanessa’s down payment can be calculated as follows:

Vanessa’s down payment = Cost of the house – PV = $268,500 - $259,185.55 = $9,314.45

Learn more about the present value of an ordinary annuity here: https://brainly.com/question/17112302.

#SPJ4

Answer:

Step-by-step explanation:

Is the given equation factorable?

(x - 7)(x - 2) = x^ - 9x + 14 That doesn't work.

-7 * - 2  = 14 but the middle term is - 9 not - 5

x - 7 is not a factor  of x^ - 5x + 14

What is?

Something very ugly (x - 2.5 +/- 2.783 i )

The following distributions has a mean that varies

II. The distribution of sample data

III. The sampling distribution of the sample mean

The correct answer is option v) II and III."

Here, we have,

In the context of statistical distributions:

I. The population distribution refers to the distribution of a specific variable within the entire population. The mean of the population distribution which is fixed and does not vary.

II. The distribution of sample data refers to the distribution of a variable within a specific sample. The mean of the sample data can vary from one sample to another.

III. The sampling distribution of the sample mean refers to the distribution of sample means taken from multiple samples of the same size from a population. The mean of the sampling distribution of the sample mean is equal to the population mean, but the individual sample means can vary from sample to sample.

Therefore, the mean varies in both the distribution of sample data (II) and the sampling distribution of the sample mean (III), but not in the population distribution (I).

To learn more on distribution click:

brainly.com/question/14651443

#SPJ4

In Milgram's first study of obedience, the majority of teachers initially complied but refused to deliver more than slight levels of shock.

In Milgram's first study of obedience, participants were assigned the role of 'teacher' and were instructed to administer electric shocks to a 'learner' whenever they answered a question incorrectly. The shocks ranged from mild to severe, with the highest level labeled as 'XXX.' The learner was actually an actor, and no real shocks were administered.

The study found that the majority of teachers initially complied with the experimenter's orders and delivered shocks, but they refused to deliver more than slight levels of shock. This suggests that while they were willing to follow the instructions to some extent, they had moral reservations about causing significant harm to another person.

It is important to note that the study has been criticized for ethical concerns and the potential psychological harm it may have caused to participants. However, it remains a significant contribution to our understanding of obedience and the power of authority figures.

About Milgram's first study of obedience here:

https://brainly.com/question/30462620

#SPJ11

The probabilities for all values of k (18 to 25), and then sum them up to find the exact probability of getting 18 or more heads in 25 tosses of a coin.

To find the exact probability of getting 18 or more heads in 25 tosses of a coin, we can use the binomial probability formula. The formula is:

P(X=k) = (n choose k) * \(p^{k} *(1-p)^{n-k}\)

where P(X=k) is the probability of getting k successes, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which is the number of ways to choose k successes out of n trials.

In this case, we want to find the probability of getting 18 or more heads in 25 tosses of a coin. The probability of getting a head on any one toss of a fair coin is 1/2, so p = 1/2. The total number of trials is 25, so n = 25. Therefore, we can calculate the probability as follows:

P(X ≥ 18) = Σ P(X=k) from k=18 to 25

= Σ (25 choose k) * \((\frac{1}{2} )^{25} *(\frac{1}{2} )^{25-k}\) from k=18 to 25

Using a calculator or software, we can calculate each term of the sum and add them up. The exact probability of getting 18 or more heads in 25 tosses of a coin is approximately 0.035.

This means that out of all possible sequences of 25 coin tosses, only about 3.5% of them will have 18 or more heads.

In summary, to find the exact probability of getting 18 or more heads in 25 tosses of a coin, we can use the binomial probability formula.

The calculation involves finding the sum of several terms, which can be done using a calculator or software. The resulting probability is relatively low, indicating that getting 18 or more heads in 25 tosses of a coin is not a common occurrence.

Know more about   binomial probability   here:

https://brainly.com/question/14984348

#SPJ11

Answer:

[I didn't do it right]

Step-by-step explanation:

[Deleted since it has been said to be wrong and I would not like to spread misinformation]

To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.

Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)

Plugging in the values:

n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67

Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.

To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:

n = (Z^2 * p * q) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.

In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03

Now, we can plug these values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65

Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.

Learn more about Z-score at: brainly.com/question/31871890

#SPJ11

The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

Learn more about simple interest here:

https://brainly.com/question/25793394

#SPJ1

Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

if you roll a regular 6-sided die once then the  odds of rolling either a 3 or a 6 is 2:5, option a is correct.

When rolling a regular 6-sided die once, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6.

Out of these six outcomes, two of them (3 and 6) meet the condition of interest.

Therefore, the probability of rolling either a 3 or a 6 is 2 out of 6, which can be simplified to 1 out of 3 or 1:3.

the odds of rolling either a 3 or a 6 is 2:5 because we can take 3 or 6 as one outcome.

So the possible outcomes are 5.

The odds of rolling either a 3 or a 6 is 2:5.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ12

The angle of depression of the escalator is approximately 10.1 degrees.

To find the angle of depression, we need to draw a right triangle where the vertical distance is the opposite side, the horizontal distance is the adjacent side, and the angle of depression is the angle opposite the hypotenuse.

Let's call the angle of depression θ. Then we have

tan(θ) = opposite/adjacent

We know the vertical distance (opposite) is 194.7 feet and the horizontal distance (adjacent) is the length of the escalator, which is 1085.5 feet. So we can plug in these values and solve for θ:

tan(θ) = 194.7/1085.5

θ = tan^-1(194.7/1085.5)

θ ≈ 10.1 degrees

Learn more about angle of depression here

brainly.com/question/13697260

#SPJ4

Answer:

266.66666667%

Step-by-step explanation:

240 / 90 = 266.666666666667%

The angle B in the triangle is 67.5 degrees.

The sum of angles in a triangle is 180 degrees. A triangle is a polygon that three sides.

Therefore, let's find the angle B in the triangle as follows:

Hence, let's find x

2x + 3x + 3x  = 180

8x = 180

divide both sides of the equation by 8

x = 180 / 8

x = 22.5

Therefore,

angle B = 3(22.5)

angle B = 67.5 degrees.

learn more on triangle here: brainly.com/question/29984805

#SPJ1