Sam is maintaining a camp fire. He has kept the fire steadily burning for 12 hours with 18 logs. How many hours he could have kept the fire going with 36 logs assuming that all logs are the same

Answers

Answer 1

Sam could have kept the fire going for 24 hours with 36 logs, assuming that all the logs are the same.

How to determine how long the fire could be maintained with a different number of logs?

We can assume that each log provides the same amount of heat to the fire, and therefore, the total amount of heat generated by 18 logs in 12 hours is the same as the total amount of heat generated by 36 logs in a certain number of hours.

Let's call the number of hours Sam could have kept the fire going with 36 logs "x".

So, we can set up a proportion:

18 logs / 12 hours = 36 logs / x hours

To solve for x, we can cross-multiply:

[tex]18 logs * x hours = 12 hours * 36 logs[/tex]

18x = 432

x = 24

Therefore, Sam could have kept the fire going for 24 hours with 36 logs, assuming that all the logs are the same.

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Related Questions

A candy store called sugar built a giant hollow sugar cube out of wood above the enterance to their store . It took 213.5m scared of material to build the cube . What is the volume inside the giant sugar cube ?


Please be quick it’s due tomorrow helpppppp

Answers

Answer:

Step-by-step explanation:

Assuming that the giant sugar cube is a perfect cube, we can calculate its volume by using the formula:

Volume = edge length³

To find the edge length, we need to first calculate the amount of wood used per unit of volume, which is given by:

wood per unit volume = 213.5 m³ / 1 unit of volume

We don't know the unit of volume of the sugar cube, but we can use any consistent unit, such as meters, centimeters, or millimeters. Let's use meters for consistency with the given material amount.

Now, we can find the edge length by solving the following equation for x:

wood per unit volume = 213.5 m³ / x³

x³ = 213.5 m³ / wood per unit volume

x³ = 213.5 m³ / (213.5 m³ / 1 unit of volume)

x³ = 1 unit of volume

Therefore, the edge length of the giant sugar cube is 1 meter.

Finally, we can calculate the volume inside the giant sugar cube by using the formula:

Volume = edge length³

Volume = 1³ = 1 cubic meter

Therefore, the volume inside the giant sugar cube is 1 cubic meter.

7. The points (2, -4) and (2, 7) are on a
coordinate plane. What is the distance
between the points?
A 2 units
B 3 units
C 9 units
D 11 units

Answers

Answer:

The correct answer is D.

About 11% of the general population is left handed. At a school with an average class size of 30, each classroom contains four left-handed desks. Does this seem adequate

Answers

Based on the given information, it seems that the number of left-handed desks in each classroom is adequate.

Based on the given information, we can calculate the expected number of left-handed students in a classroom:

Expected number of left-handed students = (total number of students in a classroom) x (proportion of left-handed students in the population)

Expected number of left-handed students = 30 x 0.11

Expected number of left-handed students = 3.3

Since each classroom contains four left-handed desks, it seems that the number of left-handed desks is more than enough to accommodate the expected number of left-handed students. In fact, there may even be some unused left-handed desks in each classroom.

Therefore, based on the given information, it seems that the number of left-handed desks in each classroom is adequate.

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At the movie theatre, child admission is $6.40 and adult admission is $9.60. On Friday, three times as many adult tickets as child tickets were sold, for a total sales of $950.40. How many child tickets were sold that day

Answers

The number of child tickets sold that day was 81.

To solve the problem, let's use algebra. Let x be the number of child tickets sold and 3x be the number of adult tickets sold. The total sales can then be expressed as:

6.40x + 9.60(3x) = 950.40

Simplifying this equation:

6.40x + 28.80x = 950.40

35.20x = 950.40

x = 27

This means that 27 child tickets were sold. However, the problem asks for the number of child tickets sold on Friday, when three times as many adult tickets were sold.

So the number of child tickets sold on Friday is:

3x = 3(27) = 81

Therefore, 81 adult tickets and 27 child tickets were sold on Friday, and the revenue was $950.40.

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The monthly incomes from a random sample of 20 workers in a factory is given below in dollars. Assume the population has a normal distribution and has standard deviation $518. Compute a 98% confidence interval for the mean of the population. Round your answers to the nearest dollar and use ascending order.

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The true population mean of monthly incomes for workers in the factory falls between $1806 and $2263 with 98% of confidence intervals.

To calculate the 98% confidence interval for the mean of the population, we need to use the formula:

CI = sample mean ± Zα/2 * (σ/√n)

Where the sample mean, Zα/2 is the critical value for the given level of confidence (98% in this case), σ is the population standard deviation, and n is the sample size.

First, we need to find the sample mean from the given data:

sample mean = (2120 + 1980 + 2300 + ... + 1940) / 20 = 2034.5

Next, we need to find the critical value (Zα/2) using a standard normal distribution table or calculator. For a 98% confidence interval, the critical value is approximately 2.33.

Now, we can plug in the values and calculate the confidence interval:

CI = 2034.5 ± 2.33 * (518/√20) = (1806, 2263)

Therefore, we can say with 98% confidence that the true population mean of monthly incomes for workers in the factory falls between $1806 and $2263. This means that if we were to take many random samples of the same size from the population and calculate their confidence intervals, approximately 98% of these intervals would contain the true population mean.

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According to the flood recurrence interval equation, a flood that occurs in 2021, after 149 years of record keeping, and is the third largest ever recorded has a recurrence interval of _______ years.

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According to the flood recurrence interval equation, a flood that occurs in 2021, after 149 years of record keeping, and is the third largest ever recorded has a recurrence interval of approximately 50 years.

The flood recurrence interval equation is a statistical method used to estimate the likelihood of a flood of a certain magnitude occurring in any given year. It is based on historical records of floods and takes into account the size and frequency of floods that have occurred in the past.

In this case, the flood that occurred in 2021 is the third largest ever recorded. Based on the historical records of floods over the past 149 years, this flood has a recurrence interval of approximately 50 years. This means that there is a 2% chance of a flood of this magnitude occurring in any given year.

It is important to note that the flood recurrence interval equation is not a perfect predictor of future floods. It is only an estimation based on historical records. Other factors such as climate change and changes in land use can also impact the likelihood and severity of floods.

In conclusion, the recurrence interval for a flood that occurred in 2021, after 149 years of record keeping and is the third largest ever recorded is approximately 50 years. However, it is important to remember that the accuracy of this estimation may vary based on several factors.

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i need help. a lot of it too.

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8.) The surface area of the given shape would be =532ft²

9.) The surface area of the given circle = 24.62cm²

How to calculate the surface area of the given shapes above ?

For question 8.)

To calculate the surface area of the square based pyramid the formula given below is used;

S.A = b² + 2bs

where;

b = 14ft

s = 12 ft

S.A = 14² + 2(14×12)

= 196+ 2(168)

= 196+336

= 532ft²

For question 9:

To calculate the area of the circle, the formula that should be used is given as follows:

S.A = πr²

where:

r = 2.8cm

π = 3.14

S.A = 3.14×2.8×2.8

= 24.62cm²

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wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

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“My mother always used to say: The older you get, the better you get, unless you’re a banana.”

—Rose (Betty White), The Golden Girls

It is nonsensical to talk about the direction of specific differences in ANOVA because it is a(n) ______ test. Group of answer choices omnibus monobus multibus octobus

Answers

It is nonsensical to talk about the direction of specific differences in ANOVA because it is an omnibus test.

An omnibus test is a statistical test that evaluates whether there is a difference between groups or conditions, without specifying which groups or conditions differ from each other. In the case of ANOVA (Analysis of Variance), it tests whether the means of two or more groups are equal or not. However, it does not tell us which specific groups are different from each other.

Instead, to identify the specific group differences, post-hoc tests such as Tukey's test, Bonferroni's test, or Scheffe's test can be used. These tests compare the means of each group and identify which groups differ significantly from each other.

Therefore, talking about the direction of specific differences in ANOVA is nonsensical because ANOVA does not provide information about which groups differ from each other. It only tells us whether there is a significant difference between groups or not.

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A round pizza is $\frac13$ of an inch thick and has a diameter of 12 inches. It is cut into 12 congruent pieces. What is the number of cubic inches in the volume of one piece

Answers

The volume of one piece of pizza is π cubic inches.

To find the volume of one piece of pizza, we need to first find the total

volume of the pizza and then divide by the number of pieces.

Find the volume of the entire pizza.

The pizza is a cylinder with a height (thickness) of 1/3 inches and a

diameter of 12 inches.

We can find the radius by dividing the diameter by 2, so the radius is 6

inches. The formula for the volume of a cylinder is

V = πr²h,

where V is the volume, r is the radius, and h is the height.

V = π(6²)(1/3) V = π(36)(1/3) V = 12π cubic inches

Divide the total volume by the number of pieces.

There are 12 congruent pieces, so we need to divide the total volume by 12.

Volume of one piece = (12π cubic inches) / 12 The 12's cancel out, leaving

us with: Volume of one piece = π cubic inches

So, the volume of one piece of pizza is π cubic inches.

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It takes Cynthia 9 hours to proof a chapter of Hawkes Learning Systems' Introductory Algebra book and it takes Phillip 6 hours. How long would it take them working together

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Step-by-step explanation:

C  rate =   1 chapter / 9 hr   = 1/ 9    chap/hr

P rate = 1/6

together  :

1 chapter / ( c rate + p rate)  =   1 /( 1/9 + 1/6) =  1/ ( 2/18 + 3/18) = 1/ (5/18) =

    18/5 hr   = 3  3/5 hr

It would take Cynthia and Phillip 3.6 hours working together to proof a chapter of Hawkes Learning Systems' Introductory Algebra book.

To find out how long it would take Cynthia and Phillip working together to proof a chapter of Hawkes Learning Systems' Introductory Algebra book, we can use the work formula:

Work = Rate × Time

First, we'll find the individual rates for Cynthia and Phillip:
- [tex]Cynthia's rate:\frac{1 chapter}{9 hours}[/tex]
- [tex]Phillip's rate:\frac{1 chapter}{6 hours}[/tex]
Now, we'll add their rates together to find their combined rate:
[tex]Combined rate = \frac{1}{9}  + \frac{1}{6}[/tex]

To add these fractions, we need a common denominator, which is 18:
[tex]Combined rate = \frac{2}{18}  + \frac{3}{18}=\frac{5}{18}[/tex]

Now, we'll use the work formula to find the time it would take for them to complete the proofreading together. Since they're working on 1 chapter, we can set Work equal to 1:
[tex]1 = \frac{5}{18} (time)[/tex]

Next, we'll solve for Time:
[tex]Time = 1 (\frac{5}{18})[/tex]
[tex]Time=1 (\frac{18}{5})[/tex]
[tex]Time = \frac{18}{5} = 3.6 hours[/tex]

So, it would take Cynthia and Phillip 3.6 hours working together to proof a chapter of Hawkes Learning Systems' Introductory Algebra book.

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In one town, 37% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. 0.740 0.133 0.137 0.370

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37% of all voters are Democrats. The probability is 0.137, and the option that matches this answer is "0.137".

To find the probability that two randomly selected voters from the town are both Democrats, we need to use the formula for the probability of independent events:
P(A and B) = P(A) x P(B)
where A and B are independent events. In this case, A is the event that the first voter is a Democrat, and B is the event that the second voter is a Democrat.
The probability of the first voter being a Democrat is 0.37, since 37% of all voters in the town are Democrats. The probability of the second voter being a Democrat is also 0.37, since the selection of the first voter does not affect the probability of the second voter being a Democrat. Therefore:
P(A and B) = P(A) x P(B) = 0.37 x 0.37 = 0.1369
Rounding to three decimal places, we get a probability of 0.137. Therefore, the answer is 0.137, and the option that matches this answer is "0.137".

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Gabi just bought a pottery store. She knows from the previous owner that almost 60 percent of her sales take place during the Christmas holiday season, with the other 40 percent of sales evenly distributed over the rest of the year. Gabi will probably use a

Answers

By using a seasonal sales forecast, Gabi can better plan her inventory and staffing levels throughout the year, which can help her optimize her business operations and maximize profits.

To create this forecast, she will need to estimate the expected sales for each month based on historical data and market trends.

Here's an example of how Gabi could create a seasonal sales forecast:

Start with historical sales data: Gabi can use the previous owner's sales records to get an idea of how much revenue the store generated in each month. She should look for patterns or trends in the data that can help her predict future sales.

Identify seasonal trends: Based on the information she has been given, Gabi knows that 60 percent of sales occur during the Christmas holiday season. She should also consider other seasonal factors that could affect sales, such as the weather, local events, and school holidays.

Determine the baseline sales: Gabi can calculate the baseline sales by dividing the non-holiday sales (40 percent) by the number of non-holiday months (eight). This will give her an estimate of the average monthly sales during the non-holiday period.

Adjust for seasonal factors: Gabi should adjust her baseline sales estimate based on the seasonal trends she identified. For example, she might increase sales projections for November and December to reflect the holiday season, and adjust sales projections for other months based on other seasonal factors.

Review and adjust: Gabi should regularly review her sales forecast and adjust it as needed based on actual sales performance and any changes in market conditions.

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Two representatives are chosen one at a time, at random, from a group of 80 students that has 40 boys and 40 girls. What is the probability that both representatives are girls

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The probability of both representatives being girls is 39/158, or approximately 0.247.

To find the probability of both representatives being girls, we first need to find the probability of selecting a girl as the first representative, and then the probability of selecting another girl as the second representative, given that the first one was a girl.

The probability of selecting a girl as the first representative is 40/80, or 1/2, since there are 40 girls in the group of 80 students.

Once a girl has been chosen as the first representative, there will be 39 girls left in the group of 79 students (since one student has already been chosen), so the probability of selecting another girl as the second representative is 39/79.

To find the probability of both events occurring (selecting a girl as the first representative and then selecting another girl as the second representative), we multiply the probabilities together:

1/2 x 39/79 = 39/158

Therefore, the probability is 39/158, or approximately 0.247.

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The appropriate method for calculating the degrees of freedom associated with a correlation coefficient is ______ a. n - 4 b. n - 2 c. n - 1 d. n - 3

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The appropriate method for calculating the degrees of freedom associated with a correlation coefficient is  c. n - 1.


The degrees of freedom refer to the number of values in the dataset that can vary independently. In the context of correlation coefficient calculation, the degrees of freedom help determine the significance level of the relationship between the two variables being analyzed.

The reason we use n - 1 as the formula is that when examining the relationship between two variables, we are essentially comparing the differences between each data point and their corresponding means.

Since the correlation coefficient calculation requires that the sum of these differences equal zero, the last difference is essentially determined by the preceding differences. As a result, there are n - 1 independent values or degrees of freedom in this calculation.

By using the correct formula for degrees of freedom, we can more accurately determine the significance of the correlation coefficient and subsequently, the strength of the relationship between the two variables .The correct answer is c.

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Question 2. As a sociologist, you are interested in determining the stress levels of people who live in cities compared with those who live in the suburbs. You randomly select 80 city dwellers and 70 suburbanites to interview. You administer a survey and ask respondents to record the number of times during one week that they experienced a stressful situation, such as a driver cutting them off, a rude sales clerk, etc. The data show that those who live in cities had an average of 13.2 stressful experiences per week (with a standard deviation of 3.2), while suburban residents, on average, had 11.5 stressful experiences per week (with a standard deviation of 2.1). Perform the appropriate hypothesis test to determine whether city dwellers have higher levels of stress than suburbanites. Set the alpha level at 0.01. Be sure to follow ALL the steps involved in hypothesis testing which I discussed in lecture and show any calculations you perform. State your conclusions in one or two complete sentences.

Answers

Since the calculated t-value (3.27) is greater than the critical t-value (2.62), we reject the null hypothesis.

As a sociologist, you aim to determine if city dwellers have higher stress levels than suburbanites. To test this hypothesis, you would conduct a two-sample t-test comparing the means of the two groups.

The null hypothesis (H 0) is that there is no significant difference in stress levels between city dwellers and suburbanites, while the alternative hypothesis (H1) states that city dwellers have higher stress levels.

Given the data, city dwellers have a mean stress level (M1) of 13.2 with a standard deviation (SD1) of 3.2, while suburbanites have a mean stress level (M2) of 11.5 with a standard deviation (SD2) of 2.1. The sample sizes are 80 for city dwellers (n1) and 70 for suburbanites (n2).

First, calculate the standard error (SE) of the difference between means:

SE = sqrt((SD1^2/n1) + (SD2^2/n2)) = sqrt((3.2^2/80) + (2.1^2/70)) ≈ 0.52

Next, calculate the t-value:

t = (M1 - M2) / SE = (13.2 - 11.5) / 0.52 ≈ 3.27

Now, determine the critical t-value using a one-tailed t-test with an alpha level of 0.01 and degrees of freedom (df) equal to n1 + n2 - 2 = 80 + 70 - 2 = 148. From a t-table, the critical t-value is approximately 2.62.

Since the calculated t-value (3.27) is greater than the critical t-value (2.62), we reject the null hypothesis. In conclusion, there is strong evidence to suggest that city dwellers experience significantly higher levels of stress compared to suburbanites at the 0.01 alpha level.

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Compare the leakage current ratio of a transistor under the following configurations? y = 1, n = 0.1, Pr = 0.35 V, VDD = 1 V, T = 300K, VTHo = 0.4 V (threshold voltage without DIBL and body effects). VDD VDD 0 0 킬 0.2 V Answer: 152 ×.

Answers

The answer to the question is 7

The leakage current ratio of a transistor can be determined by comparing the leakage current in different configurations. In this case, we are given the parameters y, n, Pr, VDD, T, and VTHo.

The leakage current ratio is the ratio of the leakage current in two different configurations. In this case, we need to compare the leakage current when VDD is 0 and 0.2 V.

Using the given parameters and the formula for the leakage current, we can calculate the leakage current for both configurations.

When VDD is 0, the leakage current is given by:

I_leakage = y * Pr * exp[(VTHo-VDD)/n*VT]

Plugging in the values, we get:

I_leakage(0) = 1 * 0.35 * exp[(0.4-0)/0.1*VT] = 7.79 × 10^-10 A

When VDD is 0.2 V, the leakage current is given by:

I_leakage = y * Pr * exp[(VTHo-VDD)/n*VT]

Plugging in the values, we get:

I_leakage(0.2) = 1 * 0.35 * exp[(0.4-0.2)/0.1*VT] = 5.11 × 10^-9 A

Therefore, the leakage current ratio is:

I_leakage(0.2)/I_leakage(0) = (5.11 × 10^-9)/(7.79 × 10^-10) = 6.56

Rounded to the nearest integer, the leakage current ratio is 7.

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1. The nature of time series data True or False: For time series data sets, the time at which each observation is made is important; however, that is not the case for cross-sectional data. True False

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True. Time series data refers to a collection of observations gathered over time, where the time dimension is a critical component of the data.

Each data point is linked to a specific point in time. In contrast, cross-sectional data is collected at a single point in time and does not have a time dimension. Therefore, the timing of each observation is crucial in time series data but not as important in cross-sectional data.

Time series data is a sequence of data points indexed in time order. It is used to track change over time.

Cross-sectional data is a snapshot of data at a specific point in time. It is used to compare different groups or variables .

Think about how the time at which each observation is made affects the analysis of time series data and cross-sectional data.

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Gallium-67 is used medically in tumor-seeking agents. The half-life of gallium-67 is 78.2 hours. How much time is required for the activity of a sample of gallium-67 to fall to 6.73 percent of its original value

Answers

It takes approximately 52.7 hours for the activity of a sample of gallium-67 to fall to 6.73 percent of its original value.

The decay of radioactive substances is governed by the following equation:

[tex]N(t) = N_{0} e^{(-\lambda t)[/tex]

where:

N(t) is the amount of the substance at time t

N₀ is the initial amount of the substance

λ is the decay constant

t is time

The half-life of gallium-67 is 78.2 hours, which means that:

λ = ln(2)/t₁/₂ = ln(2)/78.2 = 0.00887 h⁻¹

Let N be the amount of gallium-67 remaining after time t, and N₀ be the initial amount. Then, we can use the above equation to find the time t required for the activity of the sample to fall to 6.73 percent of its original value:

N/N₀ = 0.0673

[tex]0.0673 = e^{(-\lambda t)}[/tex]

Taking the natural logarithm of both sides:

ln(0.0673) = -λt

t = ln(1/0.0673)/λ

t = ln(14.84)/0.00887

t ≈ 52.7 hours

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The sides of a right triangle form a three term geometric progression. If the shortest side has length 2, then what is the length of the hypotenuse?

Answers

The length of the hypotenuse is 4.

Let the three sides of the right triangle be a, b, and c, where a is the shortest side, b is the middle side, and c is the hypotenuse. Since the sides form a geometric progression, we know that:

b/a = c/b

Multiplying both sides by b, we get:

[tex]b^2/a = c[/tex]

Since a = 2, we can substitute this into the above equation to get:

[tex]b^2/2 = c[/tex]

We also know that the Pythagorean theorem applies, so we have:

[tex]a^2 + b^2 = c^2[/tex]

Substituting a = 2 and [tex]c = b^2/2[/tex] , we get:

[tex]2^2 + b^2 = (b^2/2)^2[/tex]

Simplifying this equation, we get:

[tex]4 + b^2 = b^4/4[/tex]

Multiplying both sides by 4, we get:

[tex]16 + 4b^2 = b^4[/tex]

Rearranging and factoring, we get:

[tex](b^2 - 4)(b^2 - 12) = 0[/tex]

Since b is a positive length, we can discard the solution[tex]b^2 = 12.[/tex] Therefore, we have:

[tex]b^2 = 4[/tex]

Taking the square root of both sides, we get:

[tex]b = 2\sqrt{2 }[/tex]

Finally, we can use the equation [tex]c = b^2/2[/tex] to find the length of the hypotenuse:

[tex]c = (2\sqrt{2} )^2/2 = 4.[/tex]

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Find the volume of a rectangular prism with a length of 2.4 ft, a height of 4.5 ft, and a width of 1.3 ft.
A 16.78 ft3,
B 14.56 ft3,
C14.04 ft3,
D 12.34 ft3.

Answers

The volume of a rectangular prism can be found by multiplying its length, height, and width.

Volume = length x height x width

Given the values:

Length = 2.4 ft
Height = 4.5 ft
Width = 1.3 ft

Volume = 2.4 ft x 4.5 ft x 1.3 ft
Volume = 14.04 ft^3

Therefore, the answer is C) 14.04 ft^3. C

The angle measurements in the diagram are represented by the following expressions.


=
6


1
8

∠A=6x−18

start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 18, degrees, end color #11accd


=
14

+
3
8

∠B=14x+38

Answers

The value of {x} is 8 and the measure of angle A is 30°.

Refer to the image attached. We can see that ∠A and ∠B form a pair of co - interior angles. This means that we can write the relation as -

∠A + ∠B = 180°

So, we can write that -

6x - 18 + 14x + 38 = 180°

20x + 20 = 180°

20x = 160°

{x} = 8

∠A = 6x - 18

∠A = 6 x 8 - 18

∠A = 30°

So, the value of {x} is 8 and the measure of angle A is 30°.

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i need the answerrrr

Answers

The area of the original trapezoid is B. half the area of the rectangle in step 4.

Given a trapezoid which has the lengths of the parallel bases as b₁ and b₂.

We know that,

Area of a trapezoid = (b₁ + b₂) h / 2, where h is the height between the two bases.

Two trapezoids are joined to get a parallelogram and then rearrange it to form a rectangle.

Area of a rectangle = Length × width

Here, length = b₁ + b₂

Width = height of the trapezoid = h

Area of rectangle in step 4 = (b₁ + b₂) h

Area of trapezoid is half of this.

Hence the correct option is B.

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Dakota went on a bike ride of 60 miles. He realized that if he had gone 12 mph faster, he would have arrived 16 hours sooner. How fast did he actually ride

Answers

Dakota rode his bike for 60 km. He understood that he could have been there 16 hours earlier if he had traveled 12 mph quicker. Dakota's actual speed during the bike ride was approximately 41.8 mph.

Let's assume that Dakota's actual speed during the bike ride was x miles per hour.

Using the distance formula:

distance = speed x time

We can calculate the time it took Dakota to complete the ride at his actual speed as:

60 = x * t

where t is the time in hours.

Now, according to the problem, if he had gone 12 mph faster, he would have arrived 16 hours sooner. This means that he would have covered the same distance in less time.

So we can set up another equation:

60 = (x + 12) * (t - 16)

Simplifying this equation:

60 = xt - 16x + 12t - 192

76 = xt - 16x + 12t

Substituting the value of t from the first equation, we get:

76 = 60 - 16x + 12(60/x)

Simplifying this equation:

[tex]16x^2 - 720x + 7200 = 0[/tex]

Dividing both sides by 16:

[tex]x^2 - 45x + 450 = 0[/tex]

Solving this quadratic equation using the quadratic formula:

[tex]$x = \frac{45 \pm \sqrt{45^2 - 41450}}{2}$[/tex]

[tex]$x = 22.5 \pm 7.5\sqrt{5}$[/tex]

We can reject the negative root because it doesn't make sense in the context of the problem.

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An experiment consists of 8 independent trials where the probability of success on each trial is 3 8 . Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 16. Exactly 5 successes.

Answers

To find the probability of obtaining exactly 5 successes in 8 independent trials, we can use the binomial probability formula. Let X be the number of successes in 8 trials, then we have:

P(X = 5) = (8 choose 5) * (3/8)^5 * (5/8)^3

where (8 choose 5) is the number of ways to choose 5 trials out of 8. Using a calculator, we can evaluate this probability to be:

P(X = 5) = 0.2254 (rounded to the nearest ten-thousandth)

Therefore, the probability of obtaining exactly 5 successes in 8 independent trials where the probability of success on each trial is 3/8 is 0.2254.
Hi! I'm happy to help you with your probability question. To find the probability of exactly 5 successes in 8 independent trials with a success probability of 3/8, we'll use the binomial probability formula. The formula is:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of exactly k successes
- C(n,k) is the combination function (n! / [k!(n-k)!]), representing the number of ways to choose k successes from n trials
- n is the total number of trials (8 in this case)
- k is the number of successes we want (5 in this case)
- p is the probability of success on each trial (3/8 in this case)

Using the formula, we get:

P(X=5) = C(8,5) * (3/8)^5 * (1-3/8)^(8-5)
P(X=5) = (8! / [5!(8-5)!]) * (3/8)^5 * (5/8)^3
P(X=5) ≈ 0.2188

So, the probability of obtaining exactly 5 successes in 8 independent trials is approximately 0.2188 or 21.88% when rounded to the nearest ten-thousandth.

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Can someone please help me ASAP? It’s due tomorrow!! I will give brainliest if it’s correct

Answers

The statement that best describes the result of the data that Maya collected, would be D. Small - size drinks cost more than $ 1. 00 at restaurants in Maya's city.

How to find the statement ?

We see that in Maya's city, there was no entry in the $ 0.91 to $ 1.00 category. This shows that there are no restaurants (according to the sample) that sell small - sized drinks for less than $ 1.00

The other statements are false because the largest restaurants fall in the $ 1. 51 to $ 1. 60 category and Maya conducted the sampling at 50 restaurants because there were 10 restaurants per sample.

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Solve the math equation here

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Hi bye hi bye hi bye hi bye

A basketball player has a 0.654 probability of making a free throw. If the player shoots 13 free throws, what is the probability that she makes less than 6 of them

Answers

Answer:

0.2515384615

Step-by-step explanation:

she makes 5/13

5/13*0.654

a senator wishes to estimate the proportion of united states voters who favor abolising the electoral college. how large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%

Answers

In order for the senator to have a confidence level of 90% that the sample proportion will not deviate from the actual proportion by more than 5%, they must conduct a survey of at least 273 voters.

To estimate the proportion of United States voters who favor abolishing the electoral college with a 90% confidence level and a margin of error of 5%, we need to use the formula :

n = (z² * p * (1-p)) / E²

where n is the sample size, z is the z-score for the desired confidence level (1.645 for 90% confidence level), p is the estimated proportion (0.5 is a conservative estimate since we don't know the true proportion), and E is the margin of error in proportion (0.05).

Plugging in the values, we get n = (1.645² * 0.5 * (1-0.5)) / 0.05² = 272.25. Since we cannot have a non-integer sample size, we round up to the nearest integer, so the minimum sample size needed is 273.

Therefore, the senator needs to survey at least 273 voters to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%.

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poisson The average number of accidental drownings per year in the USA is 3.0 per 100,000. What is the probability that in a city with a population of 200,000 there will be exactly 2 accidental drownings per year

Answers

2.23% is the probability of a city with a population of 200,000, and there will be exactly 2 accidental drownings per year.

The Poisson distribution, is useful for modeling the number of events (in this case, accidental drownings) in a fixed interval (here, a year). Given the average rate of 3.0 drownings per 100,000 people per year, we first need to find the expected number of drownings in a city with a population of 200,000.

Expected drownings per year = (3.0 drownings / 100,000 people) * 200,000 people = 6 drownings

Now, we can use the Poisson probability formula to calculate the probability of exactly 2 accidental drownings per year in this city:

P(X = k) = (λ^k * e^(-λ)) / k!

Here, X represents the number of drownings, k is the desired number of drownings (2 in this case), λ (lambda) is the expected number of drownings per year (6), e is the base of the natural logarithm (approximately 2.718), and k! is the factorial of k.

P(X = 2) = (6^2 * e^(-6)) / 2! = (36 * e^(-6)) / 2 = (36 * 0.002478) / 2 = 0.04461 / 2 = 0.022305

Therefore, the probability that in a city with a population of 200,000, there will be exactly 2 accidental drownings per year is approximately 0.0223 or 2.23%.

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