How much money has to be invested at 2.9% interest compounded
continuously to have $34,000 after 18 years?
A. $20,173.31
B. $20,211.34
C. $20,249.07
D. $20,186.02

The area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.

To find the area to the right of the z-score 0.41 under the standard normal curve, we need to calculate the cumulative probability or area under the curve from 0.41 to positive infinity.

Since the standard normal distribution is symmetric around the mean (z = 0), we can use the property that the area to the right of a z-score is equal to 1 minus the area to the left of that z-score.

From the given z-table, we can look up the area to the left of 0.41, which is 0.6591.

The area to the right of 0.41 is then:

Area = 1 - 0.6591

Area = 0.3409

Therefore, the area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.

This means that approximately 34.09% of the data falls to the right of the z-score 0.41 in a standard normal distribution.

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The temperature of 30° is within one standard deviation of the mean.

To determine which temperature is within one standard deviation of the mean, we need to consider the range that falls within one standard deviation above and below the mean.

Given that the mean temperature is 24° with a standard deviation of 4°, one standard deviation above the mean would be 24° + 4° = 28°, and one standard deviation below the mean would be 24° - 4° = 20°.

Looking at the temperatures in the chart, we can see that the temperature of 30° is within one standard deviation of the mean. It falls within the range of 28° (one standard deviation above the mean) and 20° (one standard deviation below the mean).

Therefore, the temperature of 30° is within one standard deviation of the mean.

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The correct answer is c) =, because the fraction four eighths is equal to the fraction two fourths.

To determine which symbol should go in the box to make the equation true, let's analyze the fractions given and compare their values.

The fraction "two fourths" can be simplified to "one-half" since both the numerator and denominator can be divided by 2. Therefore, "two fourths" is equal to "one-half."

Now, let's look at the fraction "four eighths." We can simplify this fraction by dividing both the numerator and denominator by 4, which gives us "one-half" as well. So, "four eighths" is also equal to "one-half."

Now, based on the given fractions, we have the equation:

(one-half) [BOX] (one-half)

We need to determine the correct symbol to fill in the box.

Looking at the values of the fractions, we see that both "two fourths" and "four eighths" are equivalent to "one-half." Therefore, the correct symbol to make the equation true is the equality symbol (=).

Hence, the correct answer is:

c) =, because the fraction four eighths is equal to the fraction two fourths.

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Answer:

h = 12 units

Step-by-step explanation:

The formula for the area of a parallelogram is given by:

A = bh, where

Thus, the base is 6 units.  We can find the height by dividing the area by 6:

A = bh

72 = 6h

72/6 = h

12 = h

Thus, the height of the parallelogram is 12 units.

The correct graph of the linear inequality 1/2x - 2y > -6 is the one where a solid straight line has a positive slope and goes through (negative 4, 2) and (4, 4), and everything below and to the right of the line is shaded.

Answer:

D. 1/2

Step-by-step explanation:

9^x - 1 = 2

9^x = 3

x = log{sub}9 (3)

x = 1/2 (9^(1/2)=3)

2 5 7 ÷ 4 5 6 3

- 2 5 7

1993

- 1 7 9 9

Answer:

194

Given the following diagram: We need to find the coordinates of triangle ABC, translate the triangle (-2, 5) and draw the new image on the grid above, and determine the amount each coordinate will move on the x-axis and y-axis during translation.

1. Coordinates of triangle ABC:A = (2, 6)B = (5, 8)C = (6, 3)2. Translation of triangle (-2, 5)The translation of a triangle can be done by adding or subtracting a constant value from the x-coordinates and y-coordinates of each vertex of the original triangle.

For example, if we want to translate a triangle by 3 units to the right and 2 units up, we would add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of the original triangle. Using this method, we can translate the triangle (-2, 5) as follows:

New coordinates of A = (2 + (-2), 6 + 5) = (0, 11)New coordinates of B = (5 + (-2), 8 + 5) = (3, 13)New coordinates of C = (6 + (-2), 3 + 5) = (4, 8)3. New image of triangle (-2, 5)The new image of the triangle (-2, 5) is shown in the following diagram:4. Amount each coordinate moves on x-axis During translation, each coordinate moves 2 units to the right (from -2 to 0).5. Amount each coordinate moves on y-axis During translation, each coordinate moves 6 units up (from 5 to 11).

Therefore, the coordinates of the translated triangle image are (0, 11), (3, 13), and (4, 8).

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Step-by-step explanation:

To find the difference in total revenue projected by the two models over the six-year period ending at t = 5, we need to calculate the revenue for each model from t = 0 to t = 5 and subtract the results.

For R1:

R1 = 7.23 + 0.25t + 0.03t^2

Substituting t = 5:

R1(5) = 7.23 + 0.25(5) + 0.03(5^2)

R1(5) = 7.23 + 1.25 + 0.75

R1(5) = 9.23 + 0.75

R1(5) = 9.98 million dollars

For R2:

R2 = 7.23 + 0.1t + 0.01t^2

Substituting t = 5:

R2(5) = 7.23 + 0.1(5) + 0.01(5^2)

R2(5) = 7.23 + 0.5 + 0.25

R2(5) = 7.73 + 0.25

R2(5) = 7.98 million dollars

To find the difference, we subtract R2(5) from R1(5):

Difference = R1(5) - R2(5)

Difference = 9.98 - 7.98

Difference = 2 million dollars

Therefore, the model R1 projects 2 million dollars more in total revenue than R2 over the six-year period ending at t = 5.

The density of lead is 11,300 kg/[tex]m^3[/tex], which means that lead is a dense material with a significant mass per unit volume.

To find the density of lead, we can use the formula:

Density = Mass / Volume

Given that the mass of lead is 3,390 kg and the volume is 0.3 [tex]m^3[/tex], we can substitute these values into the formula:

Density = 3,390 kg / 0.3[tex]m^3[/tex]

To simplify the calculation, we divide the mass by the volume:

Density = 11,300 kg/[tex]m^3[/tex]

Therefore, the density of lead is 11,300 kg/[tex]m^3[/tex].

Density is a physical property of a substance that describes how much mass is packed into a given volume. In this case, the density of lead tells us that for every cubic meter of lead, there are 11,300 kilograms of mass.

It is important to note that the density of lead is a characteristic property and remains constant regardless of the size or shape of the sample. It is a useful parameter in various scientific and industrial applications.

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The question probable may be:

If 3,390 kg of lead occupy a volume of 0.3 m^3, find the density of lead.

a. Mean = 3

Standard deviation = 2

b. The z-scores for each score in the sample are: 1, -1.5, 0.5, 1, -1, -0.5, 0.5.

a. To compute the mean and standard deviation for the sample, we follow these steps:

Calculate the mean (average)

Mean = (sum of all scores) / (number of scores)

Mean = (5 + 0 + 4 + 5 + 1 + 2 + 4) / 7

Mean = 21 / 7

Mean = 3

The mean of the sample is 3.

Calculate the standard deviation

The formula for standard deviation for a sample is given by:

Standard deviation = sqrt((sum of squared differences from the mean) / (number of scores - 1))

First, calculate the squared differences from the mean for each score:

(5 - 3)^2 = 4

(0 - 3)^2 = 9

(4 - 3)^2 = 1

(5 - 3)^2 = 4

(1 - 3)^2 = 4

(2 - 3)^2 = 1

(4 - 3)^2 = 1

Next, sum up these squared differences:

4 + 9 + 1 + 4 + 4 + 1 + 1 = 24

Now, divide this sum by (number of scores - 1):

24 / (7 - 1) = 24 / 6 = 4

Finally, take the square root of this result:

Standard deviation = sqrt(4) = 2

The standard deviation of the sample is 2.

b. To find the z-score for each score in the sample, we use the formula:

z = (X - Mean) / Standard deviation

For each score, we substitute the values into the formula:

X = 5, z = (5 - 3) / 2 = 2 / 2 = 1

X = 0, z = (0 - 3) / 2 = -3 / 2 = -1.5

X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5

X = 5, z = (5 - 3) / 2 = 2 / 2 = 1

X = 1, z = (1 - 3) / 2 = -2 / 2 = -1

X = 2, z = (2 - 3) / 2 = -1 / 2 = -0.5

X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5

The z-scores for each score in the sample are:

z = 1, z = -1.5, z = 0.5, z = 1, z = -1, z = -0.5, z = 0.5

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The area of the figure is 114 square units.

To determine the area of the figure, we need to identify its shape.

From the given dimensions, it appears that we have three rectangular sections.

The first section has a length of 3 units and a width of 8 units, giving us an area of 3 [tex]\times[/tex] 8 = 24 square units.

The second section has a length of 3 units and a width of 9 units, resulting in an area of 3 [tex]\times[/tex] 9 = 27 square units

The third section has a length of 3 units and a width of 21 units, yielding an area of 3 [tex]\times[/tex] 21 = 63 square units.

To find the total area of the figure, we need to sum up the areas of the individual sections:

Total area = 24 + 27 + 63 = 114 square units.

Therefore, the area of the figure is 114 square units.

It's important to note that without a clear description or diagram of the figure, it's challenging to provide an accurate interpretation.

The given dimensions could represent various arrangements, and the resulting area would vary accordingly.

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Answer:

a) 50

Step-by-step explanation:

The variance will not change as all the observations are increased uniformly.

Proof:

Variance formula:

[tex]s^{2} = \frac{\sum x_i^{2} }{n} -\frac{(\sum x_i)^{2} }{n^{2} }[/tex]

When the obervations are inc by 20,

[tex]s_1^{2} = \frac{\sum (x_i + 20)^{2} }{n} -\frac{(\sum (x_i + 20))^{2} }{n^{2} }\\\\=\frac{\sum(x_i^{2} + 2*20*x_i + 20^{2} )}{n} - \frac{(\sum x_i +20n)^{2} }{n^{2} } \\\\=\frac{\sum x_i^{2} + 40\sum x_i + 20^{2}n }{n} - \frac{(\sum x_i)^{2} +2*20n\sum x_i + 20^{2} n^{2} }{n^{2} } \\\\= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} } +\frac{40\sum x_i}{n} + 20^{2} - \frac{40\sum x_i}{n} - 20^{2}\\\\s_1^{2}= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} }\\\\=s^{2}[/tex]

Therefore variance doesn't change

Answer:

The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

Step-by-step explanation:

What is defined as the normal distribution?

A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.

A histogram inside a normal distribution curve is sometimes used to design the curve.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

z = z- score, taken fro table

Mean μ = 110

Standard deviation σ = 15

Sample mean x.

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

The person's expenditure is $1,755. (30 words)

To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.

Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)

In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.  

Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.

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I can't really see the graph clearly but I think that the x-intercepts should be (-16/7, 0) and (32/7, 0).

Answer:

x-intercepts:  -2, 4

Step-by-step explanation:

The given graph shows a parabola that opens downwards.

The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. From inspection of the given graph, we can see that the parabola crosses the y-axis when y = 8. Therefore, the y-intercept is (0, 8).

The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0. From inspection of the given graph, we can see that the parabola crosses the x-axis when x = -2 and x = 4. Therefore, the x-intercepts are (-2, 0) and (4, 0).

Answer:

0

Step-by-step explanation:

theres only 2 people each district

The equation of the conic section in conic form is (x - 1) = (y + 6)²/4.

To write the equation of the conic section in conic form, we can complete the square to transform the equation into its standard form. Let's start with the given equation:

y² - 4x + 12y + 32 = 0

Rearranging the terms, we have:

y² + 12y - 4x + 32 = 0

To complete the square for the y-terms, we add and subtract the square of half the coefficient of y (which is 6 in this case):

y² + 12y + 36 - 36 - 4x + 32 = 0

Simplifying this, we get:

(y + 6)² - 4x + 4 = 0

Now, rearranging the terms, we have:

(y + 6)² = 4x - 4

Dividing both sides of the equation by 4, we get:

(y + 6)²/4 = x - 1

Finally, we can write the equation in conic form:

(x - 1) = (y + 6)²/4

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The Probable question may be:
Which type of conic section is defined by the equation y²-4x+12y + 32 = 0?

This is an equation of a parabola

Write the equation of this conic section in conic form:

Answer:

(x + 13)(x - 7) = 69

x² + 6x - 91 = 69

x² + 6x - 160 = 0

(x + 16)(x - 10) = 0

x = 10, so the area of the original square is 100 m².

Answer:

11? I'm so sorry if it's incorrect. I apologize.

The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.

The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.

The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.

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Answer:

Proving that the limit of the equation 10 - 2x as x approaches -3 is 16 involves using the definition of a limit.

Here's how you would approach it:

Let epsilon be a small positive number. We want to find a value of delta such that if x is within a distance of delta from -3, then 10 - 2x is within a distance of epsilon from 16.

So, we start with:

|10 - 2x - 16| < epsilon

Simplifying,

|-2x - 6| < epsilon

And using the reverse triangle inequality,

|2x + 6| > ||2x| - |6||

Now, we can choose a value for delta such that if x is within delta of -3, then |2x + 6| is within delta + 6 of |-6| = 6.

So,

||2x| - |6|| < epsilon

and therefore:

|2x - 6| < epsilon

Choosing delta = epsilon/2, we can prove that:

0 < |x + 3| < delta -> |2x - 6| < epsilon

Therefore, we have proved that the limit of 10 - 2x as x approaches -3 is 16 using the definition of a limit.

Step-by-step explanation:

brainliest Pls

Answer:

B , D , A

Step-by-step explanation:

(4x³ - 4 + 7x) - (2x³ - x - 8)

distribute the first parenthesis by 1 and the second by - 1

= 4x³ - 4 + 7x - 2x³ + x + 8 ← collect like terms

= 2x³ + 8x + 4 ← equivalent to expression B

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

(- 3x² + [tex]x^{4}[/tex] + x) + (2[tex]x^{4}[/tex] - 7 + 4x) ← remove parenthesis

= - 3x² + [tex]x^{4}[/tex] + x + 2[tex]x^{4}[/tex] - 7 + 4x ← collect like terms

= 3[tex]x^{4}[/tex] - 3x² + 5x - 7 ← equivalent to expression D

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

(x² - 2x)(2x + 3)

each term in the second factor is multiplied by each term in the first factor, that is

x²(2x + 3) - 2x(2x + 3) ← distribute parenthesis

= 2x³ + 3x² - 4x² - 6x ← collect like terms

= 2x³ - x² - 6x ← equivalent to expression A

Answer:

Incomplete Question

Answer:

y = x + 12

Step-by-step explanation:

y = -x² + x + 12

y intercept form is, y = mx + c

where m = -b / a

the general quadratic equation is,

y = ax² + bx + c

thus, according to the question

m = -1 / -1 = 1

constant, c = 12

thus, the intercept form of the equation would be,

y = x + 12

X = 4√6 because the tangent of 35 degrees is equal to X/8 in the first right triangle and 12/X in the second right triangle.

We have two right triangles with an angle of 35 degrees and side lengths of 8 units and 12 units.

To explain why X = 12, we can use the trigonometric ratio of tangent (tan). In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In the first right triangle, the side opposite to the angle of 35 degrees is X, and the adjacent side is 8 units. So, we have:

tan(35 degrees) = X / 8

Similarly, in the second right triangle, the side opposite to the angle of 35 degrees is 12 units, and the adjacent side is X. So, we have:

tan(35 degrees) = 12 / X

Since the tangent of an angle is the same regardless of the orientation of the triangle, we can equate the two ratios:

X / 8 = 12 / X

To solve for X, we can cross-multiply:

X^2 = 8 * 12

X^2 = 96

Taking the square root of both sides, we get:

X = √96

Simplifying, we have:

X = 4√6

Therefore, X is equal to 4 times the square root of 6.

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To solve for x in the equation v2 = v0^2 + 2ax, we can rearrange the equation to isolate x:

x = (v2 - v0^2) / (2a)

In this equation, v2 represents the final velocity, v0 is the initial velocity, a is the acceleration, and x is the displacement. By substituting the given values of v2, v0, and a into the equation, we can calculate the value of x.

The equation v2 = v0^2 + 2ax is derived from the kinematic equation that relates displacement, velocity, acceleration, and time. By isolating x, we can determine the displacement.

The equation represents the final velocity (v2) as the sum of the square of the initial velocity (v0^2) and the product of twice the acceleration (2a) and displacement (x).

To solve for x, we subtract v0^2 from v2 to obtain (v2 - v0^2), and then divide this difference by 2a. This yields the value of x, which represents the displacement.

By substituting the provided values of v2, v0, and a, we can evaluate the expression and calculate the value of x. This equation is commonly used in physics and mechanics to determine the displacement of an object given its initial and final velocities and acceleration.

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The asymptotic distribution of the estimator S(X₁, ..., Xₙ) is a standard normal distribution, denoted as N(0, 1).

To find the asymptotic distribution of the estimator S(X₁, ..., Xₙ), we can use the Central Limit Theorem (CLT). However, we need some additional assumptions to apply the CLT, such as the finite variance of the random variables.

Given that E(Xᵢ^k) = αₖ for all k, we can assume that the random variables Xᵢ have a finite variance. Let's denote the variance of Xᵢ as Var(Xᵢ) = σ².

First, let's simplify the estimator S(X₁, ..., Xₙ):

S(X₁, ..., Xₙ) = 1 / (1/n ∑ᵢ (Xᵢ - c)²)

Notice that the numerator is a constant and doesn't affect the asymptotic distribution. So, we can focus on analyzing the denominator.

Let's calculate the expected value and variance of the denominator:

E[1/n ∑ᵢ (Xᵢ - c)²] = 1/n ∑ᵢ E[(Xᵢ - c)²] = 1/n ∑ᵢ (Var(Xᵢ) + E[Xᵢ]² - 2cE[Xᵢ] + c²)

= 1/n (nσ² + α₁ - 2cα₁ + c²) (using the fact that E[Xᵢ] = α₁ for all i)

Var[1/n ∑ᵢ (Xᵢ - c)²] = 1/n² ∑ᵢ Var[(Xᵢ - c)²] = 1/n² ∑ᵢ (Var(Xᵢ - c)²) = 1/n² ∑ᵢ (Var(Xᵢ))

= 1/n² (nσ²) = σ²/n

Now, let's apply the CLT. According to the CLT, if we have a sequence of independent and identically distributed random variables with a finite mean (μ) and a finite variance (σ²), the sample mean (in this case, our denominator) converges in distribution to a standard normal distribution as the sample size approaches infinity.

Therefore, as n approaches infinity, the asymptotic distribution of S(X₁, ..., Xₙ) will follow a standard normal distribution.

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Answer:

ok t means some thing but zero and seven should be solved