Ted and alan are in a race to double their money. ted feels he will win if he puts his $4,000 into a savings account offering 4.5% interest compounded annually. alan feels he will win because he intends to put his $1,000 into a savings account offering 6% interest compounded annually. using the rule of 72, startfraction 72 over r endfraction , who will win, and how many years will it take to double his money? alan will win. it will take 16 years. alan will win. it will take 12 years. ted will win. it will take 12 years. ted will win. it will take 16 years.

AB || CD and AC is oblique ;

So : Angle ( BAC ) = Angle ( DCA )

_________________________________

∆ ABC - ∆ ACD :

(1) AB = CD

(2) Angle ( BAC ) = Angle ( DCA )

(3) AC = AC

So According to (1) , (2) , (3) :

∆ ABC =~ ∆ ACD

Well, if two triangles are deposited, all their components are equal peer to peer.

So : AD = BC

Answer:

0.64

Step-by-step explanation:

Area of circle = π r ²

= π (4√2)²

= (4² X √2²) π

= 32π.

area of square = 8 X 8 = 64.

we want P(inside red square)

= 64/(32π)

= 0.64 to nearest one hundredth

For the two lines to be parallel, the value of n must be 3

When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.

The slope of each line is calculated as (y2-y1)/x2-x1

for line AB, the slope = (6n-n)/10-4 = 5n/6

for line CD, the slope= 8n-(-6)/9-(-3)=( 8n+6)/12

for AB and CD to be parallel,

5n/6 = (8n+6)/12

multiply both sides by 12

10n= 8n+6

collect like terms

10n-8n= 6

2n= 6

n= 6/2= 3

therefore for the value of n= 3 line CD and AB are parallel.

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Answer:

Q = 108°

R = 72°

Step-by-step explanation:

Quadrilateral means this is a four-sided shape. Parallelogram means that both sets of opposite side are parallel, so all the angles are either equal or add up to 180° (supplementary)

The order of the letters matters bc PQRS means that you go along an edge from P to Q, but you have to go thru the middle of the shape to get from P to R. So P and Q add up to 180°.

P + Q = 180°

72° + Q = 180°

Q = 108°

Opposite from each other, across the middle of the shape, P and R are equal.

P = R = 72°

Answer:

5x - 4

Step-by-step explanation:

4x - 2 + x - 2

simplify

5x - 4

hope this helps <3

The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

The missing image is attached below.

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The proportion for Clairemont is 0.09.

There are various methods to compute proportions in statistics. Here, the formula for proportion is defined as "a part, share, or number considered in comparative relation to a whole."

In this case, the frequency of people without health insurance in Clairemont is part of the whole population of individuals surveyed in Clairemont.

The calculation is as follows:
The proportion of uninsured in Clairemont = Frequency of uninsured in Clairemont / Total number of survey respondents in Clairemont

The frequency of uninsured individuals in Clairemont is 18, and the total number of survey respondents in Clairemont is 200. The proportion of uninsured individuals in Clairemont is:

Proportion of uninsured in Clairemont = 18 / 200 = 0.09

Therefore, the proportion of uninsured individuals in Clairemont is 0.09.

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Statisticians calculate the Consumer Price Index (CPI) by combining the 80,000 prices of individual products using a weighted average based on their relative importance or expenditure weights.

The Consumer Price Index is a measure of the average change over time in the prices paid by urban consumers for a basket of goods and services. To calculate the CPI, statisticians collect price data for a representative sample of approximately 80,000 individual products that are commonly purchased by urban consumers. These products cover a wide range of categories, including food, housing, transportation, healthcare, and more.

Each product's price is then multiplied by its respective expenditure weight, which represents the proportion of total consumer spending allocated to that product. These weights are determined through surveys and data analysis to reflect the typical spending patterns of urban consumers. The resulting values are then summed up to obtain a total expenditure amount.

To calculate the CPI, statisticians divide the total expenditure by a base period expenditure and multiply the result by 100. The base period is typically a reference point or benchmark year against which the price changes are measured. This process allows for tracking and comparing price changes in the basket of goods and services over time, providing insight into inflation and changes in the cost of living.

In summary, statisticians calculate the Consumer Price Index by combining the prices of 80,000 individual products using a weighted average based on their expenditure weights, representing the relative importance of each product in urban consumers' spending patterns. This method allows for measuring and monitoring changes in the overall price level and cost of living.

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The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.

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ANSWER:

STEP-BY-STEP EXPLANATION:

Answer:

  2120 ft³

Step-by-step explanation:

You want the volume of a hexagonal pyramid with side length 12 ft and height 17 ft.

The area of the base is given by the formula ...

  A = (3/2)√3·s² . . . . where s is the side length

  A = (3/2)√3·(12 ft)² = 216√3 ft²

The volume of a pyramid is given by the formula ...

  V = 1/3Bh

where B is the area of the base, and h is the height.

The volume of this pyramid is ...

  V = 1/3(216√3 ft²)(17 ft) ≈ 2120 ft³

The volume of the solid is about 2120 cubic feet.

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Answer:

x/-4 - 5 = -8

x/-4 = -8 + 5

x/-4 = -3

x = -3 x -4

x = 12

Hi, there.

____

» Add 5 to both sides.

\(\boldsymbol{\dfrac{x}{-4}=-3}\)

» Multiply both sides by -4.

\(\boldsymbol{x=12}\)

Hope the answer - and explanation - made sense,

happy studying!!

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer:

the two factors are (x + 1 ) , (x - 5)

Step-by-step explanation:

The factors of the quadratic equation x² - 4x - 5 is (x + 1) (x - 5)

A quadratic equation is an algebraic expression whose power is raised to the second degree. The solution of a quadratic equation usually leads to a pair of two factors.

From the given question, we are going to look for two numbers:

Thus, the expansion of the quadratic equation will lead to the following factors:

= (x + 1) (x - 5)

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If there is an odd number of values, the median is the middle value.

If there is an even number of values, the median is the average of the two middle values.

For the box plot for Rob's data, the median is 80°C.

For Ann's data, the median is 82°C.

Water boils at lower temperatures as elevation increases.

Rob and Ann live in different cities.

They both boil the same amount of water in the same size pan and repeat the experiment the same number of times.

Each records the water temperature just as the water starts to boil.

They use box plots to display their data.

The median of the data is the middle value.

In order to find the median, we must first place the values in order from least to greatest.

If there is an even number of values, the median is the average of the two middle values.

A box plot is a type of chart often used in statistical analysis.

It displays the range, median, and quartiles of a data set as well as any potential outliers.

The box extends from the lower quartile to the upper quartile.

The median is represented by a vertical line inside the box.

The whiskers extend from the box to show the range of the data.

The median is the middle value in a set of data.

In order to find the median, we must first arrange the data in order from least to greatest.

If there is an odd number of values, the median is the middle value.

If there is an even number of values, the median is the average of the two middle values.

For the box plot for Rob's data, the median is 80°C.

For Ann's data, the median is 82°C.

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Answer:

Graph the line using the slope and y-intercept, or two points.

Step-by-step explanation:

The variables can be represented as x and y for the two books.

y=3x+4

x+y=72

Use substitution or elimination to solve the problem. I would personally go with substitution, but its all personal preference.

When we differentiate the function y = f(x) with respect to x, we obtain dy/dx = 10x - 6. The differential of the function is then expressed as dy = (10x - 6)dx.

Let's go through the steps in more detail:

Start with the equation y = f(x).

To find the differential, we differentiate both sides of the equation with respect to x, which gives us dy/dx on the left side and d/dx (5x^2 - 6x) on the right side.

Applying the power rule of differentiation, the derivative of 5x^2 with respect to x is 10x. The derivative of -6x with respect to x is -6.

Combining these derivatives, we get dy/dx = 10x - 6.

The differential of the function is represented as dy = (10x - 6)dx, where dx represents a small change in the x-value and dy represents the corresponding small change in the y-value.

In summary, when we differentiate the function y = f(x) with respect to x, we obtain dy/dx = 10x - 6. The differential of the function is then expressed as dy = (10x - 6)dx.

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Answer:

Step-by-step explanation:

product of 6 and 7= 6×7= 42

product of 6 and 7 square root 128= 42✓128

42✓128= 42✓64×2= 42×8✓2

42×8√2 = 336√2

therefore, the product of 6 and 7 square root 128 in simplest radical form is 336✓2

Answer:

-3.75

Step-by-step explanation:

Answer:

4a: 1

4b: 6, -6

Step-by-step explanation:

4a. (3 - 5)= -2; (9 - 6)=3

(-2 + 3) = 1

4b. We aren't told which cards Jesse pick up, only that they didn't affect his total points. Therefore, the two cards have the same number, but opposite signs. We coluld pick any teo an an example: 6 and -6, or 4 and -4, etc. They don't affect his score since they ccancel each other with a result of zero.

The simplified form of the given fraction is, 2/3.

What is greatest common factor?

The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.

Consider, the given fraction \(\frac{48}{72}\)

The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

So, from above the greatest common factor of 48 and 72 is 24.

Therefore,

\(\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}\)

Therefore, the simplified form of the given fraction is, 2/3.

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The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.

False.

It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.

It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.

In other words, the probability of the intersection and the probability of the union are subsets of one another.

The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.

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Answer:

The drama club bought 35 t-shirt

Step-by-step explanation:

Let

t-shirt = x

Sweatshirt = y

Total cost = $795

They purchase 20 more tshirts than sweatshirts

x = y + 20

The equation is:

12x + 25y = 795

12(y + 20) + 25y = 795

12y + 240 + 25y = 795

37y = 795 - 240

37y = 555

y = 15

Substitute y = 15 into

x = y + 20

x = 15 + 20

x = 35

t-shirt = 35

Sweatshirt = 15

The drama club bought 35 t-shirt

Answer:

the answer is C

Step-by-step explanation:

Based on the given algorithm, we can analyze the recurrence relation for the running time of the algorithm on inputs of arrays of n elements.

Let's denote the running time of the algorithm for an input of size n as t(n).

For n = 1, the algorithm computes f(g) for a single entry in the array, which costs a constant time, let's say C1. Therefore, we have:

t (1) = C1

For larger values of n, the algorithm splits the array into two subarrays of size 2n/3 each and runs recursively on each subarray. This step incurs a running time of t(2n/3) for each subarray.

Additionally, the algorithm performs the computation g(x, y) on the resulting ordered set of two integers, which costs a constant time, let's say C2.

Considering these factors, we can write the recurrence relation for the running time as:

t(n) = 2t(2n/3) + C2

Therefore, the correct option among the given recurrence relations that seems to fit the running time of the algorithm is:

c. t(1) = C, and t(n) = 2t(2n/3) + C2, for some positive constants C, C2

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The range and the standard deviation of the data set is 7.7 and 2.78, respectively.

The range of a data set is the difference between the largest and smallest values in the data set. In this case, the largest value is 10.1 and the smallest value is 2.4. Therefore, the range is 10.1 - 2.4 = 7.7.

The standard deviation of a data set is a measure of the spread of the data set. To calculate the standard deviation, we first need to calculate the mean of the data set.

The mean is the sum of the data values divided by the number of data values. In this case, the mean is (8.2 + 10.1 + 2.6 + 4.8 + 2.4 + 5.6 + 7.0 + 3.3) / 8 = 5.5

Next, we need to calculate the variance of the data set. The variance is the average of the squared differences between each data value and the mean. In this case, the variance is [(8.2 - 5.5)² + (10.1 - 5.5)² + (2.6 - 5.5)² + (4.8 - 5.5)² + (2.4 - 5.5)² + (5.6 - 5.5)² + (7.0 - 5.5)² + (3.3 - 5.5)²] / 8 = 7.7229

Finally, we take the square root of the variance to get the standard deviation. In this case, the standard deviation is √7.7229 = 2.78

Therefore, the range of the data set is 7.7 and the standard deviation is 2.78.

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Solution:

w(x) = 2(x + 2) + 5

w(x) = 2x + 4 + 5

w(x) = 2x + 9

Best of Luck!