Answers
According to the information, the surface area of the first prism is 795 cm², sencond prism is 843 in², and the cylinder is 3775.87 mm²
How to find the surface area of two triangular prims?To find the surface area of two triangular prisms, we need to add the surface area of each prism. We can use the formula we found in the previous question to calculate the surface area of each triangular prism:
Surface area of first triangular prism = 2(0.5 x base x height) + perimeter x height
where base is the width of the triangular face, height is the height of the triangular face, and perimeter is the sum of the lengths of the three sides of the triangular face.
In this case, the first triangular face has a base of 9 cm, a height of 16 cm, and a perimeter of (9+15+12)=36 cm. Therefore, the area of each triangular face is:
0.5 x 9 cm x 16 cm = 72 cm²
The rectangular faces have dimensions of 9 cm x 15 cm, 15 cm x 16 cm, and 9 cm x 16 cm. Therefore, the area of each rectangular face is:
9 cm x 15 cm = 135 cm²
15 cm x 16 cm = 240 cm²
9 cm x 16 cm = 144 cm²
The total surface area of the first triangular prism is:
2(72 cm²) + (135 cm² + 240 cm² + 144 cm²) = 795 cm²
Similarly, for the second triangular prism, we have:
Surface area of second triangular prism = 2(0.5 x base x height) + perimeter x height
where base is the width of the triangular face, height is the height of the triangular face, and perimeter is the sum of the lengths of the three sides of the triangular face.
In this case, the second triangular face has a base of 8 in, a height of 15 in, and a perimeter of (8+15+20)=43 in. Therefore, the area of each triangular face is:
0.5 x 8 in x 15 in = 60 in²
The rectangular faces have dimensions of 8 in x 21 in, 15 in x 21 in, and 8 in x 15 in. Therefore, the area of each rectangular face is:
8 in x 21 in = 168 in²
15 in x 21 in = 315 in²
8 in x 15 in = 120 in²
The total surface area of the second triangular prism is:
2(60 in²) + (168 in² + 315 in² + 120 in²) = 843 in²
Therefore, the surface area of two triangular prisms is:
795 cm² + 843 in² = 795 cm² + (843 in² x 6.452 cm²/in²) ≈ 5508 cm²
For the cylinder, we can use the formula we found in the previous question to calculate the surface area:
Surface area of cylinder = 2πr² + 2πrh
where r is the radius of the circular face, h is the height of the cylinder.
In this case, the radius is 14 mm and the height is 29 mm. Therefore, the surface area of the cylinder is:
2π(14 mm)² + 2π(14 mm)(29 mm) = 2π(14 mm)(43 mm) ≈ 3775.87 mm²
Therefore, the surface area of two triangular prisms and a cylinder is approximately:
5508 cm² + 3775.87 mm² = 5508 cm² + (3775.87 mm² x 0.01 m²/mm²) ≈ 5885.47 cm²
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Related Questions
a battery company makes 12-volt car batteries. after many years of product testing, the company knows that the average life of its battery is normally distributed, with a mean of 44 months and a standard deviation of 7 months. a button hyperlink to the salt program that reads: use salt. (a) if the company guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (round your answer to two decimal places.) % (b) if the company does not want to make refunds for more than 9% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Answers
a) The percentage of batteries the company expects to replace is:
0.1271 * 100% = 12.71%
b) The company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.
Step by step explain about both part of the question?(a) Let X be the random variable representing the life of a battery. We want to find the probability that a battery fails within 36 months after purchase, which is equivalent to finding P(X ≤ 36).
Using the normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:
Z = (X - μ) / σ = (36 - 44) / 7 = -1.14
Using a standard normal table or calculator, we find that the probability of a standard normal variable being less than or equal to -1.14 is 0.1271. Therefore, the percentage of batteries the company expects to replace is:
0.1271 * 100% = 12.71% (rounded to two decimal places)
(b) Let Y be the random variable representing the length of the guarantee period in months. We want to find the value of Y such that P(X ≤ Y) = 0.09, where X has the same normal distribution with mean μ = 44 months and standard deviation σ = 7 months.
Using the inverse normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:
Z = invNorm(0.09) = -1.34
where invNorm is the inverse normal function. Solving for Y, we have:
(Y - μ) / σ = Z
(Y - 44) / 7 = -1.34
Y - 44 = -1.34 * 7
Y ≈ 34.42
Therefore, the company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.
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a marketing organization claims that less than 15% of its employees are paid minimum wage. if a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? g
Answers
If a hypothesis test is performed and fails to reject the null hypothesis, it would mean that there is not enough evidence to support the claim that less than 15% of the marketing organization's employees are paid minimum wage.
Therefore, it would not be concluded that the claim is true. The null hypothesis assumes that the claim is false or that the percentage of employees paid minimum wage is not significantly different from 15%.
The failure to reject the null hypothesis means that the evidence does not contradict the null hypothesis, but it does not necessarily prove it to be true.
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_________are important to a systems analyst who must work with people at all organizational levels, balance conflicting needs of users, and communicate effectively.
Answers
Organizational skills
Organizational skills and the ability to communicate effectively are crucial for a systems analyst who needs to work with individuals at all levels of an organization, manage conflicting user needs, and ensure that information is communicated clearly and efficiently. Interpersonal skills are important to a systems analyst who must work with people at all organizational levels, balance conflicting needs of users, and communicate effectively. The knowledge and skills in leadership and strategic management are essential for the creation and achievement of an organizational vision and strategy. These skills include effective communication, decision-making, and the ability to evaluate and measure success, as well as a deep understanding of the organization and its environment. Leadership and strategic management play a crucial role in the success of any organization. A strong and effective leader with a well-developed understanding of strategic management is essential for the creation and achievement of an organizational vision and strategy.
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observe that for every value of that satisfies , the value of is constant. what does this tell you about the behavior of the graph of on this interval?
Answers
The graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.
If the value of is constant for every value that satisfies a certain condition, it means that the graph is a horizontal line on that interval. The behavior of the graph is constant or unchanging in terms of its vertical position.
When every value of x that satisfies a given condition results in a constant value of y, this tells us that the behavior of the graph of the function on this interval is horizontal. In other words, the graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.
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PLEASE HELP ASAP!!!!
Answers
Answer:
f
Step-by-step explanation:
thats the explanation
have a new hobby - a saltwater fish tank that will contain mostly live corals (called a reef tank). i am currently in the planning stage and am gathering knowledge to give me the best chance of success with my tank. as part of the planning stage, i reached out to 700 experienced central florida reefers (people who currently have a reef tank) and asked them to provide the following information: size of the tank (in gallons), type of lighting used (florescent, led, hybrid, or other), and how long (in years) they have been in the hobby. part of the analysis involves trying to estimate the proportion of all central florida reefers who use led lighting. a 95% confidence interval was constructed to be: (.755, .816). the sample proportion reported was .7855. was the sample size considered large in the construction of this confidence interval? group of answer choices no, since n is less than 30. yes, since n is at least 30. yes, since np and nq are both at least 15. no, since np and nq are not both at least 15.
Answers
This indicates that the sample size was large enough to construct a reasonably precise confidence interval.
Since n is at least 30" or "yes, since np and nq are both at least 15."
The sample size, we cannot definitively choose between these two options.
Information provided; the sample size is not explicitly stated.
Determine whether the sample size is considered large enough for the construction of a confidence interval based on the conditions for using a normal approximation to the binomial distribution.
One condition is that np and nq are both at least 15, where n is the sample size, p is the proportion of interest (in this case, the proportion of central Florida reefers who use LED lighting), and q is the complement of p (i.e., 1-p). This condition ensures that the distribution of the sample proportion is approximately normal.
Another condition is that the sample size is large enough that the standard error of the sample proportion (sqrt[pq/n]) is small enough to use a normal approximation.
This condition is not explicitly stated, but it is typically considered to be met when n is at least 30.
Since we do not know the sample size, we cannot directly determine whether the conditions are met.
That a 95% confidence interval was constructed with an interval estimate of (.755, .816) and a sample proportion of .7855.
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Which simulation is a representation of independent events?
Answers
The independent events are the ones in the third option, spinning the spiner twice.
Which simulation represents independent events?Two events are called independent if the outcome of the first event does not affect the outcome of the second event.
From the given options, the only two that are independent are spining the spinner two times.
For example in the case of the candy, when you pull one candy and eat it, you can't pull it again, so the outcomes for the second event are modified.
In the case of the spinner that does not happen, that is why the events are independent.
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In triangle LMN, angle N = 90 degrees. LM = 10, MN = 6, & LN = 8
What is tan of angle M?.
Answers
In a right triangle, tangent of one of non-right angles is equal to ratio of the length of opposite side to the length of adjacent side. The tangent of angle M is 5/3.
In this case, we want to find tangent of angle M.
Let's label the sides of triangle opposite, adjacent, and hypotenuse, as follows:
Opposite: side LM, which is opposite to angle M.
Adjacent: side MN, which is adjacent to angle M.
Hypotenuse: side LN, which is the longest side and opposite to the right angle N.
Using the Pythagorean theorem, we can find the length of the hypotenuse LN:
[tex]LN^2 = LM^2 + MN^2 \\LN^2 = 10^2 + 6^2\\LN^2 = 100 + 36\\LN^2 = 136LN = sqrt(136) = 2*sqrt(34)[/tex]
Now, we can use the tangent formula:
tan(M) = opposite/adjacent = LM/MN
tan(M) = 10/6 = 5/3
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question 1: how many style a shades can be loaded into a 40-foot container? question 2: how many style b shades can be loaded into a 40-foot container?
Answers
The total number of Style B shades that can be loaded into the container is 3,840 Style B shades in total.
A 40-foot container can hold 3,840 Style B shades.
A 40-foot container typically has a volume of 67.7 cubic meters (2,390 cubic feet), but without knowing the size and packing configuration of the shades, it's impossible to determine how many of each type can fit into the container.
Once you provide the dimensions and packing requirements for Style A and Style B shades, I can help you calculate how many of each type can be loaded into a 40-foot container.
Assuming that each carton of Style B shades has the same dimensions and that there is no wasted space within the container, we can calculate the number of cartons that can be loaded into a 40-foot container as follows:
First, we need to determine the total number of cartons that can fit in the container:
8 cartons in width x 40 cartons in length x 2 cartons in height = 640 cartons in total
Next, we need to determine the number of Style B shades in each carton:
6 shades x carton
Therefore, the total number of Style B shades that can be loaded into the container is:
640 cartons x 6 shades per carton = 3,840 Style B shades in total.
So a 40-foot container can hold 3,840 Style B shades.
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Question: How many Style B shades can be loaded into a 40-foot container? There are 6 shades x carton which could be shipped nested, with the squared foot on the bottom. According to the container dimensions, it's possible to put 8 cartons in width, 40 cartons in length and 2 cartons in height.
Find the three trigonometric ratios. If needed, reduce fractions.
Answers
[tex]\sin(X )=\cfrac{\stackrel{opposite}{36}}{\underset{hypotenuse}{45}}\implies \sin(X )=\cfrac{4}{5} \\\\\\ \cos(X )=\cfrac{\stackrel{adjacent}{27}}{\underset{hypotenuse}{45}}\implies \cos(X)=\cfrac{3}{5} \\\\\\ \tan(X )=\cfrac{\stackrel{opposite}{36}}{\underset{adjacent}{27}}\implies \tan(X)=\cfrac{4}{3}[/tex]
suppose a scientist designs an experiment to test a hypothesis. which of the following is true? 1 point if the experimenter does the test correctly, the hypothesis will be proven correct. a good experiment is one that produces the most data. an experiment should always be done in a professional science lab, using lab equipment. the results of the experiment might support the hypothesis, or might not.
Answers
The results of the experiment might support the hypothesis, or might not.
The correct statement is that the results of the experiment might support the hypothesis, or might not. It is important to design a well-controlled experiment that tests the hypothesis in a rigorous and systematic way. The goal is not to prove the hypothesis correct, but rather to gather evidence that either supports or contradicts the hypothesis. It is also important to conduct the experiment in a suitable environment with appropriate equipment and procedures to ensure accurate and reliable results.
Your question focuses on understanding the relationship between a hypothesis, an experiment, and the possible outcomes.
An experiment is designed to test a hypothesis, which is an educated guess or prediction about a phenomenon. When conducting an experiment, the results might either support the hypothesis or contradict it, leading to further investigation and refinement of the hypothesis. A well-designed experiment should be able to provide valuable data and insights, regardless of the outcome.
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The statement that is true is:
"The results of the experiment might support the hypothesis or might not."
A scientist designs an experiment to test a hypothesis.
In such a scenario, it is important to note that the outcome of the experiment cannot be predicted with certainty.
The scientific method involves formulating a hypothesis, designing an experiment to test the hypothesis,
collecting and analyzing data and drawing conclusions.
The hypothesis is an educated guess that can be tested through experimentation.
It is important to remember that a hypothesis can never be proven to be 100% correct, only supported or refuted by the evidence obtained through experimentation.
It is not accurate to say that if the experimenter does the test correctly, the hypothesis will be proven correct.
This is because there are many variables that can affect the outcome of the experiment, and it is impossible to control all of them.
Additionally, a good experiment is not necessarily one that produces the most data.
A good experiment is one that is well-designed, carefully controlled, and yields reliable results.
The use of lab equipment is also not a requirement for conducting experiments.
While it is often necessary for certain types of experiments, many experiments can be conducted with simple materials and equipment.
Ultimately, the results of the experiment might support the hypothesis, or might not. If the results support the hypothesis, it can be considered a step towards validating the hypothesis.
The results do not support the hypothesis, it does not necessarily mean that the hypothesis is incorrect.
It could mean that the experiment was flawed, or that the hypothesis needs to be revised based on the new information obtained from the experiment.
Designing and conducting experiments is an important part of the scientific method.
Guarantee that an experiment will yield the desired results, a well-designed and carefully controlled experiment can provide valuable information that can help scientists understand the natural world.
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unit 8 homework 4 numbers 11 and 13
Answers
Step-by-step explanation:
how could you solve 10., if you cannot solve 11. ? they are using the same thing : law of sine.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides, and A, B, C being the corresponding opposite angles.
11.
x/sin(90) = 13/sin(70)
as sin(90) = 1
x = 13/sin(70) = 13.83431104...
13.
remember, the sum of all angles in a triangle is always 180°.
angle JLM = 180 - 90 - 51 = 39°
angle LJK = 180 - 90 - 72 = 18°
14/sin(39) = JL/sin(51)
JL = 14×sin(51)/sin(39)
JL/sin(90) = JL = 14×sin(51)/sin(39) = KL/sin(18)
KL = 14×sin(51)×sin(18)/sin(39) = 5.342458907...
find the surface area of a cylinder with a radius of 2 feet and height of 8 feet
Answers
So, the surface area of a cylinder with a radius of 2 feet and height of 8 feet is:
- Area of top and bottom circles: 2 x pi x r^2 = 2 x pi x (2 ft)^2 = 8 x pi ft^2
- Area of curved lateral surface: 2 x pi x r x h = 2 x pi x (2 ft) x (8 ft) = 32 x pi ft^2
Adding these areas together gives us the total surface area:
8 x pi ft^2 + 32 x pi ft^2 = 40 x pi ft^2
Therefore, the surface area of the cylinder is 40 x pi square feet, or approximately 125.66 square feet.
If each book is 5$ and I have 133$ then how many books can I buy?
Answers
Answer:
26
Step-by-step explanation:
You just divide 133 and 5 and you get 26.6
Answer:
26
Step-by-step explanation:
[tex]\frac{133}{5}[/tex] = 26.6
You cannot buy part of a book, so you can buy 26 books
26 x 5 = 130. You will have $3.00 left over.
Helping in the name of Jesus.
A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.
First Randomization
Group A Group B
13.6 9.2
12.1 8.2
15.9 11.5
11.2 13.8
9.7 14.6
Second Randomization
Group A Group B
8.2 12.1
13.8 14.6
15.9 13.6
9.2 11.2
9.7 11.5
Third Randomization
Group A Group B
8.2 12.1
9.7 13.8
11.5 13.6
14.6 11.2
15.9 9.2
For each table, calculate the mean weight for each group,
x
A
¯
and
x
B
¯
, and find the difference of the mean of group A and the mean of group B (
x
A
¯
−
x
B
¯
).
After the first randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
After the second randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
After the third randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
Answers
Therefore, the mean weight for each group in the three randomizations are:
First Randomization:
Group A: 12.5
Group B: 11.46
Second Randomization:
Group A: 11.56
Group B: 12.4
Third Randomization:
Group A: 12.18
Group B: 12.18
What is mean?The mean, also known as the average, is a measure of central tendency in statistics. It is found by adding up all the values in a data set and dividing by the number of values in the set. The mean is sensitive to extreme values, or outliers, in the data set, and can be influenced by them. It is one of the most commonly used measures of central tendency, along with the median and mode.
Here,
First Randomization:
Group A: (13.6 + 12.1 + 15.9 + 11.2 + 9.7) / 5 = 12.5
Group B: (9.2 + 8.2 + 11.5 + 13.8 + 14.6) / 5 = 11.46
Second Randomization:
Group A: (8.2 + 13.8 + 15.9 + 9.2 + 9.7) / 5 = 11.56
Group B: (12.1 + 14.6 + 13.6 + 11.2 + 11.5) / 5 = 12.4
Third Randomization:
Group A: (8.2 + 9.7 + 11.5 + 14.6 + 15.9) / 5 = 12.18
Group B: (12.1 + 13.8 + 13.6 + 11.2 + 9.2) / 5 = 12.18
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Answer:
LOOK BELOW FOR ANSWER !!
Step-by-step explanation:
After the first randomization,
A is 12.5
B is 11.46
and A-B is 1.04
After the second randomization,
A is 11.36
B is 12.6
A and B is -1.24
After the third randomization,
A is 11.98
B is 11.98
A and B is 1
.
how many atheletes in total were acccused of using performance-enhancing drugs? of these, how many were using and how many were not? what percentage of those accused of using were falsely accused?
Answers
There have been numerous cases of athletes being accused of using performance-enhancing drugs, and the numbers may vary depending on the sport, country, and time period in question.
Additionally, determining how many athletes were using or not using performance-enhancing drugs would require specific information on individual cases.
Regarding the percentage of athletes falsely accused of using performance-enhancing drugs, it is difficult to determine an accurate figure without examining each case in detail. False accusations may occur due to various reasons, such as flawed testing procedures or contaminated supplements, and the percentage of false accusations may vary depending on the situation.
If you have a specific case or sport in mind, I can try to provide you with more information on that topic.
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the equations y = a and x = a are perpendicular true or false
Answers
Answer: True
Step-by-step explanation:
trust
Answer:
I believe they are true
Step-by-step explanation:
the auto parts department of an automotive dealership sends out a mean of 6.9 special orders daily. what is the probability that, for any day, the number of special orders sent out will be exactly 5 ? round your answer to four decimal places.
Answers
The answer to this question is 0.1754
URGENT PLEASE ANSWER 100 POINTS
Using the functions below, analyze the change in the key features from f(x) to g(x).
Answers
If X has the hypergeometric distribution, what is the minimum value that X can take?
N – K
N
K
n
0
Answers
If X has the hypergeometric distribution, the minimum value that X can take is option (e) 0
The hypergeometric distribution models the probability of getting a certain number of successes in a fixed-size sample drawn without replacement from a finite population containing a known number of successes and failures.
The minimum value that X can take depends on the specific parameters of the distribution.
If the population size is N, the number of successes in the population is K, and the sample size is n, then the minimum value that X can take is max(0, n - (N - K)).
This is because the sample can contain at most n items, and if all of them are failures (i.e., none of them are successes), then X would be 0. On the other hand, if there are fewer than n failures in the population, then the sample can contain at most n - (N - K) successes. If n - (N - K) is negative, then there are more successes than failures in the population, and X can take any value between 0 and n, inclusive.
Therefore, the correct option is (e) 0
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In 2008, the price of a gallon of unleaded gasoline was $4. 2. In 1990, it was only $1. 37 per gallon. What is the increase expressed as a percent change? Round to the nearest percent.
A. 66%
B. 393%
C. 193%
D. 134%
please i need help'
. ?
Answers
The percent increase in the price of a gallon of unleaded gasoline from 1990 to 2008 is 206.56%
To find the percent change from 1990 to 2008, we first need to calculate the actual change in price
Actual Change = 2008 Price - 1990 Price
Actual Change = $4.20 - $1.37
Subtract the numbers
Actual Change = $2.83
Next, we need to calculate the percent change as a ratio of the actual change to the original price in 1990
Percent Change = (Actual Change / 1990 Price) x 100%
Substitute the values in the equation
Percent Change = ($2.83 / $1.37) x 100%
Do the arithmetic operations
Percent Change = 206.56%
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The given question is incomplete, the complete question is:
In 2008, the price of a gallon of unleaded gasoline was $4. 2. In 1990, it was only $1. 37 per gallon. What is the increase expressed as a percent change? Round to the nearest percent.
A gray whale swims 161 kilometers in 24 hours. The equation below can be used to find the rate (r), in kilometers per hour (kph), at which the gray whale swims. Rounded to the nearest tenth, what is the rate at which the gray whale swims?
Answers
The rate at which the gray whale swims is 6.7 kilometers per hour.
What is the equation that relates the distance, rate, and time?
The equation that relates the distance, rate, and time is distance = rate × time
This equation can be used to calculate any one of the three variables if the other two are known.
For example, if you know the rate at which an object is moving and the time it has been moving, you can use this equation to find the distance it has traveled. Or, if you know the distance traveled and the time it took to travel that distance, you can use this equation to find the average rate of travel.
We are given that the distance traveled by the gray whale is 161 kilometers in 24 hours. Therefore, we can use the equation to find the rate at which the gray whale swims,
rate = distance / time = 161 km / 24 h ≈ 6.7 kph
Rounding to the nearest tenth, the rate at which the gray whale swims is approximately 6.7 kilometers per hour.
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Jada swims 4 laps, which is 2/5
of the number of laps she plans to swim.
How many laps does Jada plan to swim? Use x
for the number of laps Jada plans to swim.
Equation:
Solution:
Answers
Let x be the number of laps Jada plans to swim.
According to the problem, 4 laps is 2/5 of the number of laps she plans to swim, so we can write:
4 = 2/5 * x
To solve for x, we can first multiply both sides by the reciprocal of 2/5, which is 5/2:
4 * 5/2 = x
Simplifying the left side:
10 = x
Therefore, Jada plans to swim 10 laps.
A can contains
15/16 pounds of vegetables. One serving of these vegetables weights
pound.
What is the total number of servings of vegetables in the can?
Answers
As portion of the vegetables weights 1/4 pound and totals **15/16 pounds , the can has **3 and 3/4 servings** of veggies.
What does pound and weight mean?A pound is a unit of weight or mass measurement. The Latin word "libra," which means "weight" or "balance," denotes a measurement system employed in ancient Rome and which is equivalent to around 12 ounces.
Mass is the quantity of matter in a thing, whereas weight is the force of gravity acting on the object
Each portion of the vegetables weights 1/4 pound and totals **15/16 pounds** in the can. We must divide the can's overall weight by the weight of one serving to determine how many servings of veggies are included therein.
We thus have:
'''The can weighs 15/16 pounds in total.
Weight of one serving is one-fourth of a pound.
We divide the entire weight of the can by the weight of one serving to get how many servings are in it:
``` (15/16) ÷ (1/4) = (15/16) × (4/1)
= 60/16 = 3 3/4 ```
As a result, the can has **3 and 3/4 servings** of veggies.
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Verify Associative property: 2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5..
Please help tomorrow is my final exam
Answers
We verified that the associative property of addition holds for the given expression below
Verifying the Associative propertyLet's verify the associative property of addition for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
We can simplify both sides of the equation by finding a common denominator for the fractions:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 20/20, we get:
40/60 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5
Multiplying 3/4 by 15/15, we get:
40/60 + 45/60 + 1/5 = (2/3 + 3/4) + 1/5
Combining the first two terms on the left-hand side, we get:
85/60 + 1/5 = (2/3 + 3/4) + 1/5
Simplifying the fraction 85/60, we get:
17/12 + 1/5 = (2/3 + 3/4) + 1/5
Multiplying 2/3 by 4/4, we get:
17/12 + 1/5 = (8/12 + 9/12) + 1/5
Combining the fractions in the parentheses, we get:
17/12 + 1/5 = 17/12 + 1/5
Since both sides of the equation are equal, we have verified that the associative property of addition holds for the given expression:
2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5.
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A bus is traveling at a speed of 15m/s2. The driver approaches the same traffic light in another traffic lane. He does not brake and continues at the same speed. Write an equation for the distance the bus travels in time (t) (Hint: At a constant speed, the acceleration is 0m/s2)
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This equation tells us that the distance the bus travels is directly proportional to the time it travels at a constant speed of 15m/s.
What is speed?
Speed is the method of measuring how quickly an object moves from one place to another. It is a scalar quantity that expresses the rate of change of distance over time. In other words, it is the distance traveled per unit of time.
If the bus is traveling at a constant speed of 15m/s, then its acceleration is 0m/s². Therefore, we can use the formula for distance traveled at constant speed:
distance = speed × time
In this case, the speed of the bus is 15m/s, so the equation for the distance the bus travels in time (t) is:
distance = 15t
This equation tells us that the distance the bus travels is directly proportional to the time it travels at a constant speed of 15m/s.
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Write the equation, domain, and range of the graphs.
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The equation of the function on the graph is y = ∛(x-3).
Calculating the equation, domain, and range of the graphThe graph is a cubic function shifted 3 units right
The function y = ∛(x-3) represents the cube root function shifted 3 units to the right.
So, the equation of the function is y = ∛(x-3).
The domain of the function is all real numbers since we can take the cube root of any real number.
The range of the function is also all real numbers because for any real number x, there is a real number y such that y = ∛(x-3).
Also, the function is defined for all values since taking the cube root of any number is a real number.
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Answers is what I need! Thankkksss
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The possible dimensions of the plot are:
Length = 9.2 meters, width = 25.6 meters
Length = 25.6 meters, width = 9.2 meters
What is quadratic equation?
It's a second-degree quadratic equation which is an algebraic equation in x.
Let the length of the rectangular plot be L meters and the width be W meters. Then the perimeter of the plot is:
P = 2L + W
Since there are only three sides to the fence, we can set the perimeter equal to the length of the fencing:
2L + W = 44
Solving for W, we get:
W = 44 - 2L
The area of the plot is given as 210 square meters:
L * W = 210
Substituting for W, we get:
L * (44 - 2L) = 210
Simplifying and rearranging, we get a quadratic equation:
2L² - 22L + 105 = 0
Using the quadratic formula, we can solve for L:
L = (22 ± √(22² - 4(2)(105))) / (2(2))
L = (22 ± 2√34) / 4
L = 11/2 ± √34/2
We discard the negative solution, so:
L = 11/2 + √34/2 ≈ 9.2 meters
Now we can use the equation W = 44 - 2L to find the corresponding width:
W = 44 - 2(9.2) = 25.6 meters
Therefore, the possible dimensions of the plot are:
Length = 9.2 meters, width = 25.6 meters
Length = 25.6 meters, width = 9.2 meters
Note that both sets of dimensions result in the same area of 210 square meters.
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assuming we are testing a hypothesis using the one-way anova test with more than 2 independent normally distributed populations, how can the f-statistic be calculated?
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One measure we use to determine the F-statistics is the ratio of the variability within and across groups when we are doing the one way-ANOVA test.
We are interested in discovering whether there are significant differences between the means of the populations when doing a one-way ANOVA test on more than two independent normally distributed populations. A test statistic used to reach this conclusion is the F-statistic.
The ratio of the variability of the between group and within group is the a tool that we use to find the F-statistics.
F is equal to (SSB/k-1) / (SSW/N-k)
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the $5\times 5$ grid shown contains a collection of squares with sizes from $1\times 1$ to $5\times 5$. how many of these squares contain the black center square?
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the total number of squares that contain the black center square is[tex]$1 + 4 + 9 + 16 + 1 = \boxed{31}$.[/tex]
To solve this problem, we need to count the number of squares of each size that contain the black center square.
There is only one square of size[tex]$5\times 5$[/tex], which is the entire grid and obviously contains the black center square.
For squares of size[tex]$4\times 4$[/tex], there are [tex]$4$[/tex]possible squares that contain the black center square (one for each corner).
For squares of size[tex]$3\times 3$,[/tex] there are 9 possible squares that contain the black center square (one for each position that the center square could occupy, and then each of those squares could be oriented in three different ways).
For squares of size $2\times 2$, there are $16$ possible squares that contain the black center square (one for each pair of adjacent squares).
For squares of size [tex]$1\times 1$[/tex], there is only one possible square that contains the black center square (the center square itself).
Therefore, the total number of squares that contain the black center square is[tex]$1 + 4 + 9 + 16 + 1 = \boxed{31}$.[/tex]
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There are 11 squares containing the black center square in the 5x5 grid.
To find the number of squares that contain the black center square, we'll consider the sizes of the squares and their positions in the 5x5 grid.
The black center square is a 1x1 square itself, so that's 1 square.
For 2 x 2 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
For 3x3 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle). So, that's 1 square.
4. For 4x4 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
5. For 5x5 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle).
So, that's 1 square.
Now, we'll add up the number of squares we found in each step:
1 + 4 + 1 + 4 + 1 = 11.
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