To the nearest year, it will take about years to double the original investment.

Answer:

1. 128.2 mm^2

2. 144 mm^2

Answer:

73

Step-by-step explanation:

Because the sum of all the angles in a triangle is 180°, we can subtract 34 from 180.

\(180-34\\146\\\)

In an isosceles triangle there are two congruent angles (base angles theorem), so we can divide 146 by 2.

\(146/2\\73\)

There company would make 3696000$ more in 2005

Step-by-step explanation:

11×4=44 44% of 8.4millon is 3696000 therefore the answer is 3696000

Answer:

$10.9 million

The percentage of 322 out of 450 using the percentage formula was found out to be approximately 71.56%.

To find the percentage of 322 out of 450, we can use the following formula:

percentage = (part/whole) x 100

where, "part" is the value we want to express as a percentage (in this case, 322), "whole" is the total value (in this case, 450), and "x" means "multiply".

Using the formula mentioned above, we get:

percentage = (322/450) x 100

percentage = 0.7156 x 100

percentage = 71.56%

Therefore, percentage of 322 out of 450 is approximately 71.56%.

A percentage is a way to express a number as a fraction of 100. It is often denoted using the "%" symbol.

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Answer: 81

Step-by-step explanation: If you add all of the numbers, then you end up getting 81.35 and 81.35 estimated to the nearest whole number is 81 because that's the closest whole number to 81.35.

Answer:5

Step-by-step explanation:

25 miles divided by 5 days equal the 5 miles

5 times 5 =25

Answer:

The total distance is 129

Step-by-step explanation:

In order to answer this question you will need to find 2 distances and then add them to each other.

Begin at -29.  How far will you have to move to the right 29 in order to get to 0?

Now how far will you have to more to get from 0 to 100?

Draw an open number line to help you.

_____________________________________________________

-29                                           0                                                   100

Your first distance is 29.  Your second distance is 100.

The total distance is 129.

Answer:

x = ±\(\sqrt{7}\) - 5

Step-by-step explanation:

x^2 - 10x = -18

x^2 - 10x + 18 = 0

(x + 5)^2 - 5^2 + 18 = 0

(x + 5)^2 - 7 = 0

(x + 5)^2  = 7

\(\sqrt{(x + 5)^2}\) \(=\) ±\(\sqrt{7}\)

x = ±\(\sqrt{7}\) - 5

1

Function notation is a helpful way to represent a relationship between x and y.

Function Notation

Function notation is often expressed as f(x) = x. This is said as "f of x equals x." The "f(x)" presents the y-value. While f(x) is the most common, any letter can be used. In this case, h is used instead of f. In function notation, you have h(x) set equal to some function. The variable inside the parentheses is the independent variable of the function.

Additionally, if a constant is in the parentheses, then the function should be solved for that constant. This means to find h(2), we should plug 2 in for x and solve.

Solving the Function

To solve this, we need to plug 2 in.

Then, simplify and solve.

This means that given the function, h(2) is equal to 1.

Answer:

The first option

Step-by-step explanation:

The percent probability that a person likes blue pens is approximately 18.75%.

In a survey of 400 people, an estimated 175 people would say they like pencils or black pens.

To find the percent probability that a person likes blue pens, we need to calculate the proportion of people who like blue pens out of the total number of people surveyed.

Given that the number of people who like blue pens is 75 and the total number of people surveyed is 400, we can calculate the percent probability as follows:

P(blue pens) = (Number of people who like blue pens / Total number of people surveyed) * 100

P(blue pens) = (75 / 400) * 100

P(blue pens) ≈ 18.75%

To estimate the number of people who would say they like pencils or black pens in a survey of 400 people, we need to add the number of people who like pencils and the number of people who like black pens.

Number of people who like pencils or black pens = Number of people who like pencils + Number of people who like black pens

Number of people who like pencils or black pens = 63 + 112

Number of people who like pencils or black pens = 175

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after 14 years, there will be approximately 1.97g of the radioactive substance remaining.

To solve this problem, we can use the concept of exponential decay for radioactive substances. The decay of a radioactive substance can be modeled by the equation:

N(t) = N₀ * e^(-kt),

where N(t) is the amount of substance at time t, N₀ is the initial amount of substance, e is the base of the natural logarithm, k is the decay constant, and t is the time elapsed.

In this case, we are given that the initial amount N₀ is 10g and the amount after 9 years N(9) is 5g. We can use this information to find the value of k.

5 = 10 * e^(-9k).

Divide both sides of the equation by 10:

0.5 = e^(-9k).

Take the natural logarithm of both sides:

ln(0.5) = -9k.

Solve for k:

k = ln(0.5) / -9.

Now that we have the value of k, we can use it to find the amount of substance after 14 years, N(14):

N(14) = N₀ * e^(-kt).

N(14) = 10 * e^(-ln(0.5) / -9 * 14).

N(14) = 10 * e^(14 * ln(0.5) / 9).

N(14) ≈ 10 * 0.197 = 1.97.

Therefore, after 14 years, there will be approximately 1.97g of the radioactive substance remaining.

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From first to third base, it is 3 3/8 inches in length. 3 3/8 inches, or 127 feet, separate first base from third base.

First- and third-base lines' intersection is the starting point for all measurements taken from home base. An real square with 90-foot sides is what a baseball "diamond" looks like.

How far must the catcher throw from home plate if a runner attempts to steal second base in order to declare the runner "out"? Explain why more runners attempt to steal second base than third base given this information. but 127 feet to second and third base is established. 3 3/8 inches, or 127 feet, separate first base from third base.

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Answer: area =45   perimeter=28

Step-by-step explanation:    height is 9, length is 5   5x9 =45

9+9+5+5= 28

Answer:

3 tan theta=root 3

tan theta=root 3/3

tan theta=0.57

Step-by-step explanation:

The expression that is equivalent to the area of the metal sheet required to make this square-shaped traffic sign is 22,500.

We are given a square-shaped traffic sign and we are to find the expression that is equivalent to the area of the metal sheet required to make this traffic sign.

A square-shaped traffic sign has 4 equal sides. Let each side measure 150 centimeters.

Therefore, the area of the square-shaped traffic sign is given by: Area = side²

Substitute the value of the side as given in the question= (150)²= 22,500

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\(y = \frac{28}{5} \)

Answer:

\(y=5.6\) or \(y=28/5\)

Step-by-step explanation:

4/5 = y/7

⇒ Cross multiply:

4 × 7 = 5 × y

⇒ Multiply 4 × 7 & 5 × y:

\(28=5y\)

⇒ Solve the formed equation:

\(28=5y\)

⇒ Move all the terms containing y to the right side and the other values to the left side:

⇒ Add '-5y' to each side of the equation:

\(28+-5y=5y+-5y\)

⇒ Combine like terms: \(5y+-5y=0\)

\(28+-5y=0\)

⇒ Add '-28' to each side of the equation:

\(28+-28+-5y=0+-28\)

⇒ Combine like terms: \(28+-28=0\)

\(0+-5y=0+-28\)

\(-5y=0+-28\)

⇒ Combine like terms: \(0+-28=-28\)

\(-5y=-28\)

⇒ Divide each side by '-5':

\(y=5.6\) or \(y=28/5\)

hope this helps :)

Answer:

a) 4

b) 8

Step-by-step expla nation:

a) 3.2 ÷ 0.8 = 4

b) 7.5 + 0.5 = 8

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer:

a

Step-by-step explanation:

Answer:C.

Step-by-step explanation:

The plain language for the probability of the event "A or B" is "A or B" is the event that the person chosen is overweight or obese.

Probability is a term to describe the chance of some event can occur. The probability is often written as percentages or proportions.

p(A) is the probability of event A can occur in this case this the probability of the chosen child is obese which is 0.41 according to the national center for health statistics.

p(B) is the probability of event B can occur in this case this the probability of the chosen child is overweight but not obese which is 0.33 according to the national center for health statistics.

The plain language for the event "A or B" is event A or event B can occur, so the "A or B" is the event that the person chosen is overweight or obese.

Your question is incomplete, but most probably your full question was

Although the rules of probability are just basic facts about percentages or proportions, we need to be able to use the language of events and their probabilities. Choose an American kid (between 8 and 12) at random. Define two events:

A = the person chosen is obese

B = the person chosen is overweight, but not obese

According to the national center for health statistical,

P(A) = 0.41and P(B) = 0.33.

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Answer:

Step-by-step explanation:

Prime factors of 2100 are:

The single-digit divisors are:

-----------------------------------------------------------------

Another solution is you divide 2100 by all numbers 1 through 9 and list those divisible:

So all the numbers from 1 to 7

When a rational number is expressed as a decimal, the maximum length of the repeating section in the decimal representation is equal to the number of distinct prime factors in the denominator.

For example,

If we consider the fraction 1/7, the decimal representation is 0.142857142857..., and the repeating section has a length of 6 digits. This is because the denominator 7 is a prime number, and there is only one distinct prime factor.

Similarly, for the fraction 1/6, the decimal representation is 0.1666..., and the repeating section has a length of 1 digit. The denominator 6 has two distinct prime factors (2 and 3), but since the prime factor 2 is repeated, it contributes to a repeating section of length 1.

In general, if a rational number can be expressed in the form p/q, where p and q are coprime integers (they have no common factors other than 1), and q has prime factors p1^a1 * p2^a2 * p3^a3 * ..., then the maximum length of the repeating section in the decimal representation is equal to the number of distinct prime factors, which is a1 + a2 + a3 + ...

It's important to note that not all rational numbers have repeating decimal representations. For example, the fraction 1/2 can be expressed as the terminating decimal 0.5.

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

adjacent

Step-by-step explanation:

It is the leg that touches the 18 degree angle

A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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Answer:

42 Eggs

Step-by-step explanation:

6×7=42

6 eggs every day for 7 days, gives us 42 eggs at the end of the week

Hope this Helps!

Answer:

(-5, -7)

Step-by-step explanation:

To rotate a point (x,y) by 180 degrees about the origin, we can multiply its coordinates by the matrix:

-1  0

0 -1

So, to rotate the triangle JKL by 180 degrees about the origin, we can apply this transformation to each of its vertices. We have:

J(3,1)  ->  J^`(−3,−1)

K(7,−5) ->  K^`(−7,5)

L(5,7)  ->  L^`(−5,−7)

Therefore, the coordinates of the vertex L^(`) after the triangle is rotated by 180 degrees clockwise about the origin are (-5, -7).

To solve this problem, we can use algebraic equations. Let's say that the number of weeks it takes for Ted and Carly to have the same account balance is "w".

Ted's account balance after "w" weeks can be represented by:

300 + 4w

Carly's account balance after "w" weeks can be represented by:

16w

We want to find out when their account balances will be equal, so we can set these two equations equal to each other:

300 + 4w = 16w

Simplifying this equation, we get:

300 = 12w

Dividing both sides by 12, we get:

25 = w

Therefore, it will take 25 weeks for Ted and Carly to have the same account balance.