At the end of the passage, Javier says, "By the time you have a sip of
coffee, many hands have touched those coffee beans." By this,
Javier means to say that

John Doe was killed approximately 4.06 hours ago.

To determine the time of death for John Doe, we will use the given formula: [tex]T = T0 + (T1 - T0)(0.97)^t[/tex],[/tex]where T is the body temperature at time t, T0 is the air temperature (74°F), and T1 is the body temperature at the time of death (93°F).

We are trying to find the time (t) when John Doe's body temperature was 98.6°F (normal body temperature). So, we'll set T equal to 98.6°F and solve for t:

[tex]98.6 = 74 + (93 - 74)(0.97)^t[/tex]

To solve for t, follow these steps:

1. Subtract 74 from both sides:
[tex]24.6 = 19(0.97)^t[/tex]

2. Divide by 19:
[tex]1.2947 ≈ (0.97)^t[/tex]

3. Take the natural logarithm of both sides:
ln(1.2947) ≈ [tex]ln((0.97)^t)[/tex]

4. Apply the logarithm power rule:
ln(1.2947) ≈ t * ln(0.97)

5. Divide by ln(0.97):
t ≈ ln(1.2947) / ln(0.97)

6. Calculate t:
t ≈ 4.06

So, John Doe was killed approximately 4.06 hours ago.

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The  Surface area of Composed figure is 1,341 square feet.

First, Surface Area of Prism

= (9 + 9 + 9)15 + (9)(6)

= 27 x 15 + 54

= 405 + 54

= 459 square feet

Now, Surface area of Cuboid

= 2 (105 + 210+ 126)

= 2(441)

= 882 square feet

Thus, the Surface area of Composed figure

= 459 + 882

= 1,341 square feet

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In this scenario, we need to identify the null and alternative hypotheses. The null hypothesis represents the status quo or the current belief, while the alternative hypothesis represents the claim or what we want to test against the null hypothesis.

H0: The average time for Master's students to graduate is 4.9 years.
Ha: The average time for Master's students to graduate is less than 4.9 years (alternative hypothesis).

The null hypothesis (H₀) states that the average time it takes for students to graduate with a Master's degree is 4.9 years. The alternative hypothesis (Hₐ) represents the claim made by the dean, which is that Master's students at his university graduate earlier than 4.9 years.

So, the null and alternative hypotheses can be written as:

H₀: μ = 4.9
Hₐ: μ < 4.9

where μ represents the average time it takes for students to graduate with a Master's degree at the dean's university.

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The answer is (3) 0.

For the first integral, we have:

I = ∭W x^2 + y^2 dV

Using cylindrical coordinates, we have:

x = r cos(theta)

y = r sin(theta)

z = z

where 0 <= r <= 5, 0 <= theta <= 2pi, and -5 <= z <= 1.

Also, dV = r dz dr d(theta)

Substituting these into the integral, we have:

I = ∭W r^2 dV

= ∫(0 to 2pi) ∫(0 to 5) ∫(-5 to 1) r^2 (r dz dr d(theta)) dz dr d(theta)

= ∫(0 to 2pi) ∫(0 to 5) [(r^4/4)(1 - (-5))] dr d(theta)

= ∫(0 to 2pi) ∫(0 to 5) (13r^4/4) dr d(theta)

= ∫(0 to 2pi) [(13/20)r^5] from 0 to 5 d(theta)

= ∫(0 to 2pi) (13/20)(5^5) d(theta)

= (13/20)(3125)(2pi)

= 112pi

Therefore, the answer is (1) 112π.

For the second integral, we have:

I = ∭W y dV

Using cylindrical coordinates, we have:

x = r cos(theta)

y = r sin(theta)

z = z

where 2 <= r <= 4, 0 <= theta <= 2pi, and 0 <= z <= x+6.

Also, dV = r dz dr d(theta)

Substituting these into the integral, we have:

I = ∭W y dV

= ∫(0 to 2pi) ∫(2 to 4) ∫(0 to r cos(theta)+6) r sin(theta) (r dz dr d(theta)) dz dr d(theta)

= ∫(0 to 2pi) ∫(2 to 4) [(r^3 sin(theta)/3)(r cos(theta)+6)] dr d(theta)

= ∫(0 to 2pi) ∫(2 to 4) [(r^4/3) cos(theta) + 2r^3/3] sin(theta) dr d(theta)

= ∫(0 to 2pi) [(4^4/3 - 2^4/3)(cos(theta)/4) + 2(4^3/3 - 2^3/3)/3] sin(theta) d(theta)

= ∫(0 to 2pi) [(16/3)(cos(theta)/4) + (32/3)] sin(theta) d(theta)

= 0

Therefore, the answer is (3) 0.

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We can estimate that the underlying normal distribution from which the data was generated has a mean of 3 and a standard deviation of 1.

To estimate the mean and standard deviation of the underlying normal distribution from the given data using the probability plot method, we need to first create a probability plot of the data.

After creating the probability plot, we can visually inspect it to see if the data points fall on a straight line. If the data points fall on a straight line, then we can assume that the data is normally distributed. We can then use the slope of the line to estimate the standard deviation and the intercept of the line to estimate the mean.

Using the given data, we can create a probability plot as follows:

- First, we need to order the data from smallest to largest:
-3.58 -1.83 0.27 1.23 1.25 1.36 2.33 2.49 2.88 3.04 3.19 3.67 3.73 4.33 4.38 4.72 4.99 5.40 5.52 7.42

- Next, we need to calculate the percentiles for each data point:
0.5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 99.5%

- We can then plot the percentiles on the y-axis and the ordered data on the x-axis.

After creating the probability plot, we can see that the data points fall approximately on a straight line. This suggests that the data is normally distributed. We can then estimate the mean and standard deviation of the underlying normal distribution as follows:

- The slope of the line is approximately 1, which suggests that the standard deviation of the underlying normal distribution is approximately 1.
- The intercept of the line is approximately 3, which suggests that the mean of the underlying normal distribution is approximately 3.

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For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96. The statement is false.

The statement is incorrect. For a one-tailed test with a 0.05 level of significance, the critical z statistic is indeed 1.645. However, the critical t statistic value depends on the degrees of freedom (df), which is not provided in the statement. The 1.96 value mentioned is actually the critical z statistic for a two-tailed test with a 0.05 level of significance.

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Answer: I would say B srry if I'm  wrong

Step-by-step explanation:

To find the volume of the prism, we need to multiply the area of the base by the height. The base of the prism is made up of 6 cubes arranged in a rectangle, so its area is:

Base area = length x width Length = 2 cubes = 1 foot Width = 3 cubes = 1.5 feet Base area = 1 x 1.5 = 1.5 square feet

The height of the prism is also equal to one cube, which is 1/2 feet.

Therefore, the volume of the prism can be calculated as follows:

Volume = Base area x Height Volume = (1.5 square feet) x (0.5 feet) Volume = 0.75 cubic feet

Answer:

Step-by-step explanation:

first, you have to find the interest.

formula: Principal × Rate × Time ÷ 100

Principal - $1500

Rate - 5%

Time - 5 yrs

I=PRT÷100

= $1500 × 5% × 5yrs ÷ 100

= 1500 × 5 × 5÷ 100

= 37500 ÷ 100

= $ 375

That's the interest.

Amount = Principal + Interest

              = $ 1500 + $375

               =$ 1875

That's the total amount you'll have to pay back.

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e[tex].^{(-0.08(t-5)^2)}[/tex]  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e[tex].^{(-0.08u^2)}[/tex]  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e[tex].^{(-0.08u^2)}[/tex] du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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The graphical representation that would be most appropriate for the data, given the number of different breakfast cereals sold, is,

B. Histogram, because there is a large set of data.

Since, We know that;

Histograms are used for large sets of data because they provide a visual representation of the distribution of the data. They are particularly useful for understanding the distribution of continuous variables, such as measurements or time series data.

One of the main advantages of histograms is that they allow for easy comparison of large sets of data. The use of bars to represent the data makes it easy to see the overall shape of the distribution and identify patterns or outliers. Additionally, histograms can be used to compare multiple sets of data at once, allowing for easy comparison of different groups or changes over time.

Another advantage of histograms is that they can be used to identify the underlying probability distribution of a dataset, which is useful for statistical analysis and modeling.

This is why, given the fact that the data contains information from 1, 000 different cereals, a histogram is best to show this as the data is large.

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Answer:

g = 13/4 or 3.25

Step-by-step explanation:

Step 1:  First we can distribute the 2 on the right-hand side (rhs) of the equation:

[tex]\frac{2*5-2*g}{3}\\\\ \frac{10-2g}{3}[/tex]

Step 2:  We can also rewrite this fraction since we have two inverse operations, namely multiplication and division:

[tex]\frac{10}{3}+\frac{-2g}{3}\\ \\ \frac{10}{3}-\frac{2g}{3}\\ \\ \frac{10}{3}-\frac{2}{3}g[/tex]

Step 3:  We can convert both sides into whole numbers by multiplying both sides by the least common denominator (lcd), which is essentially the lowest multiple shared by the denominators 6 and 3.

The lowest multiple shared by the two numbers is 6 as 6*1 = 6 and 3*2 = 6

Thus, we multiply both sides by 6:

left-hand side (lhs)

[tex]\frac{7}{6}*\frac{6}{1}\\ \\ \frac{42}{6}\\ \\ 7[/tex]

right-hand side (rhs)

[tex](\frac{10}{3}-\frac{2}{3}g)*\frac{6}{1}\\ \\ (\frac{10}{3}*\frac{6}{1})+(-\frac{2}{3}g*\frac{6}{1})\\ \\ \frac{60}{3}-\frac{12}{3}g\\ \\ 20-4g[/tex]

Since we have simplified both sides, we can now solve for g:

[tex](7=20-4g)-20\\(-13=-4g)/-4\\13/4=g\\3.25=g[/tex]

You can keep the mixed number or use the decimal answer as both are the same answer in different forms.

For such a problem, it can be helpful to check by plugging in 3.25 for g in the equation

[tex]\frac{7}{6}=\frac{2(5-3.25)}{3}\\ \\ \frac{7}{6}=\frac{2(1.75)}{3}\\ \\ \frac{7}{6}=\frac{3.5}{3}\\\\ 1.167=1.167[/tex]

If line passes through points (0,3) and (-3,0), then the slope calculated by Martin as "3" is incorrect because the correct slope is 1.

The "Slope" of a line is defined as measure of its steepness or inclination, and it describes how much the line rises or falls over a given distance in the horizontal direction.

To find the slope of a line passing through two points (x₁, y₁) and (x₂, y₂), we use the slope formula ⇒ slope = (y₂ - y₁) / (x₂ - x₁),

In this case, the two points are (0, 3) and (-3, 0). Substituting the coordinates in formula, we get:

⇒ slope = (0 - 3)/(-3 - 0),

⇒ Slope = -3/-3,

⇒ Slope = 1,

Therefore, the correct slope of the line passing through the points (0, 3) and (-3, 0) is 1, not 3 as Martin incorrectly said.

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The given question is incomplete, the complete question is

The line in the graph passes through the points (0,3) and (-3,0), Martin incorrectly said that the slope of this line is "3" . What is the correct slope?

C. The more reliable survey would be: Tamira's survey is more reliable than Denise's survey, and approximately 1,500 residents of the town would likely be in favor of the construction of a new baseball stadium.

Tаmirа's survеy is mоre reliаble bеcаusе shе survеyed rеsidеnts frоm diffеrеnt sectiоns оf thе town, whiсh is а mоre representаtive sаmple оf thе entire populаtiоn. Denise's survеy, оn thе othеr hаnd, wаs cоnducted аt а bаsebаll gаme, whiсh might hаve introduced а biаs towаrds people who аre mоre likеly to bе in fаvor оf thе new stаdium.

Bаsed оn Tаmirа's survеy, 30 out оf 150 rеsidеnts (20%) аre in fаvor оf thе cоnstructiоn.

If we extrаpolаte this percentаge to thе entire populаtiоn оf 7,500 rеsidеnts, we cаn estimаte thаt аpproximаtely 1,500 rеsidеnts (20% оf 7,500) would likеly bе in fаvor оf thе new bаsebаll stаdium.

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Three different applications of linked list are mentioned here.

1. The most appropriate variation of a linked list for searching a list for a key and returning the keys of the two elements that come before it and the keys of the two elements that come after it would be a doubly linked list. A doubly linked list allows for bi-directional traversal, which means that it is easy to move forward and backward through the list. This makes it easy to locate the element with the key you are searching for and also retrieve the keys of the two elements that come before and after it.

2. The most appropriate variation of a linked list for creating a sorted list from a text file containing integer elements, one per line, sorted from smallest to largest would be a sorted linked list. A sorted linked list is a type of singly linked list that maintains its elements in a sorted order. As each element is added to the list, it is placed in its correct position to maintain the sorted order of the list.

3. The most appropriate variation of a linked list for a list that is short and frequently becomes empty, and is optimal for inserting an element into the empty list and deleting the last element from the list would be a circular linked list with header and trailer nodes. A circular linked list with header and trailer nodes is a type of singly linked list that has a special header node at the beginning of the list and a special trailer node at the end of the list. This type of linked list is optimal for inserting an element into an empty list because it is easy to update the header and trailer nodes to point to the new element. It is also easy to delete the last element from the list by updating the trailer node to point to the second-to-last element. Additionally, since this type of linked list is circular, it is easy to traverse the list repeatedly without having to worry about reaching the end of the list.

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Three different applications of linked list are mentioned here.

1. The most appropriate variation of a linked list for searching a list for a key and returning the keys of the two elements that come before it and the keys of the two elements that come after it would be a doubly linked list. A doubly linked list allows for bi-directional traversal, which means that it is easy to move forward and backward through the list. This makes it easy to locate the element with the key you are searching for and also retrieve the keys of the two elements that come before and after it.

2. The most appropriate variation of a linked list for creating a sorted list from a text file containing integer elements, one per line, sorted from smallest to largest would be a sorted linked list. A sorted linked list is a type of singly linked list that maintains its elements in a sorted order. As each element is added to the list, it is placed in its correct position to maintain the sorted order of the list.

3. The most appropriate variation of a linked list for a list that is short and frequently becomes empty, and is optimal for inserting an element into the empty list and deleting the last element from the list would be a circular linked list with header and trailer nodes. A circular linked list with header and trailer nodes is a type of singly linked list that has a special header node at the beginning of the list and a special trailer node at the end of the list. This type of linked list is optimal for inserting an element into an empty list because it is easy to update the header and trailer nodes to point to the new element. It is also easy to delete the last element from the list by updating the trailer node to point to the second-to-last element. Additionally, since this type of linked list is circular, it is easy to traverse the list repeatedly without having to worry about reaching the end of the list.

Based on the given information, I assume that you have a dataset and you are required to identify an appropriate transformed model for it. There are different types of transformations that can be applied to data such as logarithmic, square root, power, etc. The choice of the transformation depends on the nature of the data and the research question being addressed.

To identify an appropriate transformed model, you can start by examining the distribution of the response variable. If the distribution is skewed or has heavy tails, a transformation may be necessary to normalize the data. One way to assess the distribution is by creating a histogram or a density plot of the response variable.

Once you have identified an appropriate transformation, you can fit the transformed model to the data using regression analysis. The regression model will include the transformed response variable and one or more predictor variables.

After fitting the model, it is important to conduct the usual tests of model adequacy to ensure that the model is appropriate for the data. These tests include examining the residuals for normality, checking for homoscedasticity (i.e., equal variances), and testing for outliers and influential observations.

In summary, identifying an appropriate transformed model involves examining the distribution of the response variable and choosing a transformation that normalizes the data. Once the model is fitted, the usual tests of model adequacy should be conducted to ensure that the model is appropriate for the data.

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True. The mathematical equations that describe simple harmonic motion (SHM) involve sine and cosine functions. For example, if the block is released at a distance from its equilibrium position, its displacement x varies with time t according to the equation x = a cos(ωt), where ω is the angular frequency of the motion.

True. Due to the periodic properties of Simple Harmonic Motion (SHM), the mathematical equations that describe this motion involve sine and cosine functions. If the block is released at a distance A from its equilibrium position, its displacement x varies with time t according to the equation:

x(t) = A * cos(ωt + φ)

where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. Both sine and cosine functions are used to describe the displacement, velocity, and acceleration of an object in SHM because of their periodic nature.

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Therefore, there are 4 vertices in this graph.

Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.

We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.

If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:

3v + 2 * 4 = 20

3v = 12

v = 4

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Using a table or calculator, we find that the area between z = -1.67 and z = -0.33 is approximately 0.3121 or 31.21%. Therefore, approximately 31.21% of plants in this region are between 10 and 14 inches tall.

we will use the concepts of standard, percentage, and deviation. We know that the mean height (µ) of plants is 15 inches and the standard deviation (σ) is 3 inches. We want to find the percentage of plants with heights between 10 and 14 inches.

Step 1: Calculate the z-scores for 10 and 14 inches.
z = (X - µ) / σ

For X = 10 inches:
z1 = (10 - 15) / 3 = -5/3 ≈ -1.67

For X = 14 inches:
z2 = (14 - 15) / 3 = -1/3 ≈ -0.33

Step 2: Find the percentage of plants corresponding to these z-scores using a z-table or calculator.
P(-1.67 < Z < -0.33) = P(Z < -0.33) - P(Z < -1.67)

Using a z-table or calculator, we find:
P(Z < -0.33) ≈ 0.3707
P(Z < -1.67) ≈ 0.0475

Step 3: Calculate the percentage of plants between 10 and 14 inches.
Percentage = (0.3707 - 0.0475) * 100% ≈ 32.32%

Next, we look up the area between these two z-scores in a standard normal distribution table. This area represents the percentage of plants in the region between 10 and 14 inches tall.

As for the bonus, I'm unable to plot a graph here, but you can use graphing software to plot a normal distribution curve with a mean of 15 and a standard deviation of 3. Shade the area between 10 and 14 inches to represent the percentage of plants in this range.

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It would take (6π/5) seconds to bend a straight wire into a circle of radius 6 using a machine that bends wire at a rate of 10 unit(s) of curvature per second.

To calculate the time it takes to bend a straight wire into a circle of radius 6 using a machine that bends wire at a rate of 10 unit(s) of curvature per second, we need to find the length of the wire and then divide it by the rate of curvature.

The circumference of a circle with a radius of 6 is 2πr = 2π(6) = 12π. Therefore, the length of the wire that needs to be bent is 2πr = 12π.

Now we can calculate the time it takes to bend the wire by dividing the length by the rate of curvature:

Time = length of wire / rate of curvature = (12π units) / (10 units/second)

Simplifying, we get:

Time = (6π/5) seconds

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Using the relative frequency we can estimate that 1355 people will preffer mustard.

To find this estimation, we need to find the relative frequency of people that preffers mustard.

To get this, take the quotient between the people that preffers mustard (27) and the total number of people surveyed (150)

It gives:

F = 27/150

Now multiply the total number of people in the game by that number:

N = 7,525*27/150 = 1354.5

Rounding we get 1355

So the correct option is the first one.

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Answer:

B

Step-by-step explanation: its 3,010. EZ

The area between z=-1.3 and z=1.4 under the standard normal curve is approximately 0.8224.

To find the area of the indicated region under the standard normal curve, we need to use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find the area to the left of z=-1.3, which is 0.0968. We can also find the area to the left of z=1.4, which is 0.9192.

To find the area between z=-1.3 and z=1.4, we subtract the area to the left of z=-1.3 from the area to the left of z=1.4:

0.9192 - 0.0968 = 0.8224

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The length of the base of the triangular base is 4 feet.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The formula for the volume of a triangular prism is:

V = (1/2)bh x h

where b is the base of the triangular base, h is the height of the triangular base, and h is the height of the prism.

Substituting the given values, we get:

72 = (1/2)(x) x 3 x 12

Simplifying, we get:

72 = 18x

Dividing both sides by 18, we get:

x = 4

Therefore,

The length of the base of the triangular base is 4 feet.

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Answer:

The length, x, of the base of the triangular base of the prism is 4 ft.

Step-by-step explanation:

The volume of a regular prism can be found by multiplying the area of its base by its height.

[tex]\boxed{\textsf{Volume of a regular prism}=\textsf{Base area} \times\textsf{height}}[/tex]

The base of a triangular prism is a triangle.

The area of a triangle is half the product of its base and height.

Given that b = x and h = 3, the area of the triangular base of the prism is:

[tex]\begin{aligned}\textsf{Area of triangular base}&=\dfrac{1}{2} bh\\\\&=\dfrac{1}{2} \cdot x \cdot 3\\\\&=\dfrac{3}{2}x\; \sf ft^2\end{aligned}[/tex]

To find the value of x, substitute the given volume, v = 72 ft³, the given height, h = 12 ft, and the found area of the base into the formula for volume, and solve for x:

[tex]\begin{aligned}\textsf{Volume}&=\textsf{Base area} \cdot \textsf{Length}\\\\\implies 72&=\dfrac{3}{2}x \cdot 12\\\\72&=\dfrac{36}{2}x \\\\2 \cdot 72&=2 \cdot \dfrac{36}{2}x \\\\144&=36x\\\\\dfrac{144}{36}&=\dfrac{36x}{36}\\\\4&=x\end{aligned}[/tex]

Therefore, the value of x is 4 feet.

Answer:

​

Answer: x>1

Step-by-step explanation:

9x-3>6

move the 3 over so: 9x>6+3, 9x>9

divide both sides by 9: (9x)/9>9/9, x>1

and bam, that's your answer x>1

The total amount of money in the purse was approximately 23 ducats. A man finds a purse with an unknown number of ducats in it. After he spends 1/4, 1/5, and 1/6 of the amount, 9 ducats remain. To find the initial amount in the purse, let's represent it as "x".

He spent (1/4)x, (1/5)x, and (1/6)x. The sum of these fractions plus the remaining 9 ducats equals the total amount:

(1/4)x + (1/5)x + (1/6)x + 9 = x

To solve this equation, first find a common denominator for the fractions, which is 60. Rewrite the equation with the common denominator:

(15/60)x + (12/60)x + (10/60)x + 9 = x

Combine the fractions:

(37/60)x + 9 = x

Now, isolate x on one side of the equation:

9 = (23/60)x

To find x, divide both sides by (23/60):

x = 9 / (23/60)

x = 9 * (60/23)

x = 540/23

Since x represents the number of ducats, it should be a whole number. So, we round it to the nearest whole number:

x ≈ 23

Therefore, there were approximately 23 ducats in the purse initially.

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Answer:

Step-by-step explanation: 85% of college students prefer to shop on line, while they have access to internet 90% of the day.]

So by process of elimination, response 1 and 2 is speaking of better deals and students time which wasn't discussed in the scenario.  

Therefore, response 3 coincides with the convenience of the preferred reasoning for shopping online and response 4 falls into the internet access college students have 90% of the day.

So choices 3 and 4

Answer:

23/28

Step-by-step explanation:

1/4 + 4/7

make them have same denominator of 28

7/28 + 16/28

=23/28

Answer:

23/28

Step-by-step explanation:

Hope this helps! Pls give brainliest!

The height of the right triangular prism whose surface are is 480 square inches is equal to 9 inches.

Total surface area of the right prism = 480 square inches

Surface area of a right triangular prism is,

S = 2B + Ph

where S is the surface area,

B is the area of the triangular base,

P is the perimeter of the base,

and h is the height of the prism.

First, area of the triangular base.

Use the formula for the area of a triangle,

B = (1/2)bh

where b is the base of the triangle

and h is the height of the triangle.

⇒ B = (1/2) × 8 × 15

⇒ B = 60 in²

Since the base is a right triangle,

Use the Pythagorean theorem to find the length of the third side,

c² = 8² + 15²

⇒ c² = 64 + 225

⇒ c² = 289

⇒ c = 17

Perimeter of the base is,

⇒ P = 8 + 15 + 17

⇒ P = 40 inches

Surface area of right prism = 480

⇒ 2B +Ph = 480

⇒ 2×60 + 40h = 480

⇒40h = 480 - 120

⇒ h = 360 /40

⇒ h = 9 inches.

Therefore, the height of the right prism is equal to 9inches.

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Step-by-step explanation:

Area of ENTIRE (360 degrees) circle = pi r^2 = 144 pi  cm^2

  you want 60 degrees of this out of the 360 degrees

         60 / 360   *   144 pi = 1/6 * 144 pi =    24 pi cm^2  <=====exact answer

The Explanation for product of powers rule works and multiply exponents when raising a power to a power is shown below.

1. We know,

When the terms with the same base are multiplied, the powers are added.

So, 7² x 7³

Here the base is same (7) and multiplication applied here then the powers get added.

So, [tex]7^{2+3[/tex]

= [tex]7^5[/tex]

2. Now, According to the power to the power rule, when a base is raised to a higher power, the two powers are multiplied while the base stays the same.

So, (7²)³

= [tex]7^{2 .3}[/tex]

= [tex]7^6[/tex]

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