A student said that a triangle with side lengths of 3 ft and 4 ft could have a third side with a length of 7 ft. Explain why the student is incorrect. What is a correct statement about the third side of the triangle?
By the Triangle Inequality Theorem, the length of the third side must be
▼
less than
greater than
enter your response here ft because the sum of two side lengths must be
▼
less than
greater than
the length of the third side. The third side must be less than
enter your response here ft but greater than
enter your response here ft
Answers
Answer:
Step-by-step explanation:
Greater than
less then
the length of third side
Related Questions
will the sampling distribution of x always be approximately normally distributed? Explain. Choose the correct answer below 0 ?. Yes, because the Central Limit Theorem states that the sampling distribution of x is always approximately normally distributed O B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough O C. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the population being sampled is normally distributed O D No, because the Central Limit Theorem states that the sampling d bution of x is approximately no aly distribui d only i the sa le sae is mere than 5% of the population.
Answers
B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
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The results of a paired-difference test are shown below to the right. d = 5.6
a. Construct and interpret a 99% confidence interval estimate for the paired difference Sd =0.25 in mean values.
b. Construct and interpret a 90% confidence interval estimate for the paired difference n=16 in mean values_ (Round to two decimal places as needed:) Choose the correct answer below:
OA This interval will contain the true population mean 90% of the time_
OB. There is a 90% chance that the true population mean is contained in the interval.
Oc: If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean: 0
D. Approximately 90% of the differences will be contained in the interval.
Answers
If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.
When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.
This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.
The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.
In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.
It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.
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Since 1975 the average fuel efficiency of U. S. Cars and light trucks (SUVS) has increased from 13. 5 to 25. 8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28. 1 mpg per vehicle. The porulation S. D is 4. 7 mpg. Estimate the mean gas mileage
Answers
We can be 95% confident that the true mean gas mileage for cars in the large community is at least 24.764 mpg.
To estimate the lower bound of the true mean gas mileage with a 95% confidence level, we can use the one-sample t-test with the formula
Lower bound = x - (tα/2 * (s/√n))
Where
x = sample mean = 25.25
tα/2 = t-value for the 95% confidence level with (n-1) degrees of freedom = 1.998 (from t-table or calculator)
s = population standard deviation = 4.99
n = sample size = 65
Substituting the values, we get
Lower bound = 25.25 - (1.998 * (4.99/√65)) ≈ 24.764
Therefore, we can estimate with 95% confidence that the true mean gas mileage is at least 24.764 mpg.
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--The given question is incomplete, the complete question is given
" Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%. A random sample of 65 cars from a large community got a mean mileage of 25.25 mpg per vehicle. The population standard deviation is 4.99 mpg. Estimate the lower bound true mean gas mileage with 95% confidence.
Round your answer to 3 decimal places."--
we get statistics of 2017-2018 average starting teacher salaries by state measured by nea. given that the salary of arkansas is 33323, the sample size is 3,600 and the standard deviation is 399.876. a. what is the margin of error for a 80% confidence interval in arkansas? symbolic expression b. if we want to get a 80% confidence interval with a small margin of error, say only 7%. how many people do you need to sample?
Answers
a) The margin of error for an 80% confidence interval in Arkansas is 0.1041
b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359
The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
n = 3600
standard deviation = 399.876
Confidence Interval = 80%
a) α = 0.20
The margin of error = Zα/2 (σ / √n)
Zα/2 = 1.4395 --- (From the tabular value)
The margin of Error = 1.4395 + 399.876 / √3600
Therefore, the Margin of Error = 8.1041
b) Margin of Error = 0.07 = 7%
α = 0.20
Critical Value = 1.2816
Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²
n = [(1.2816 * 399.876) / 0.07]²
n = 53599358.98
Therefore, Sample size, n = 53599359
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PLEASE ANSWER
One pump can fill a tank of water in 2 hours. A second tank can fill the same tank in 3 hours. If both pumps are used together, how long will it take to fill the tank? 5/6 hours 6/5 hours 3/2 hours 2/3 hours
Answers
Answer:
6/5 hours
Step-by-step explanation:
GIVEN :-
Lets say ,
Pump A takes 2 hours to fill the tank alonePump B takes 3 hours to fill the tank aloneTO FIND :-
Time taken by both pumps to fill the tank when used togetherPROCEDURE :-
In 2 hours , Pump A fills the whole tank.
⇒ In 1 hour , Pump A will fill 1/2 part of tank. (By using Unitary method)
In 3 hours , Pump B fills the whole tank.
⇒ In 1 hour , Pump B will fill 1/3 part of tank. (By using Unitary method)
In 1 hour , when both pumps will be used together , they will fill =
(Part of tank filled by A in 1hr) + (Part of tank filled by B in 1hr)
⇒ \(\frac{1}{2} + \frac{1}{3}\)
\(=> \frac{5}{6}\) part of tank
5/6 part of tank will be filled by both the pumps in = 1 hour.
Using unitary method, multiplying both the sides with 6/5 -
⇒ 5/6 × 6/5 part of tank will be filled by both the pumps in = 1 × 6/5 hours
⇒ Total tank (or 1 whole tank) will be filled by both the pumps in = 6/5 hours
∴ Both the pumps will take 6/5 hour to fill the tank , when used together.
Find A ∩ B if A = {4, 7, 10, 13, 17} and B = {3, 5, 7, 9}. a.{3, 4, 5, 7, 9, 10, 13, 17} b.Ø c.{7}
Answers
Answer:
The answer is option CStep-by-step explanation:
A = {4, 7, 10, 13, 17}
B = {3, 5, 7, 9}
To find A ∩ B means to find the intersection of the two sets A and B
To find the intersection find the elements that occur in both sets.
That's for set A and B the elements that occur in both sets is only 7
So we have
A ∩ B = { 7 }Hope this helps you
a 60-year-old female is diagnosed with hyperkalemia. which symptom would most likely be observed?
Answers
Hyperkalemia is a medical condition that refers to an elevated level of potassium in the blood.
This condition can be caused by several factors, including kidney disease, certain medications, and hormone imbalances. Symptoms of hyperkalemia can range from mild to severe, depending on the level of potassium in the blood.
In a 60-year-old female diagnosed with hyperkalemia, the most likely symptom that would be observed is muscle weakness. This is because high levels of potassium can interfere with the normal functioning of muscles, leading to weakness, fatigue, and even paralysis in severe cases.
Other symptoms that may be observed in hyperkalemia include nausea, vomiting, irregular heartbeat, and numbness or tingling in the extremities. Treatment of hyperkalemia typically involves addressing the underlying cause of the condition, as well as managing symptoms through medication and lifestyle changes.
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suppose you have 2 coins, and you flip them at the same time different times. what is the expected number of times that both coins have come up tails?
Answers
The expected number of times that both coins have come up tails will be 0.5 or 50%.
The probability of both coins coming up tails on a single flip is 1/4, since each coin has a 1/2 probability of coming up tails and the events are independent. If we flip the coins n times, the number of times both coins come up tails is a binomial random variable with parameters n and 1/4.
The expected value of a binomial random variable is given by np, where p is the probability of success on a single trial. In this case, we have p = 1/4, so the expected number of times that both coins come up tails in n flips is n(1/4). Therefore, if we flip the coins twice simultaneously, the expected number of times that both coins come up tails is (2)*(1/4) = 0.5.
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The law of conservation of mass states that in a closed system, matter cannot be created or destroyed. This means that during a chemical reaction, the atoms of the reactants are rearranged to form the products.
In atomic models of simple reactions, the number of atoms found in the reactants should be the same as the number of atoms found in the products.
Note: In the image below, one dot equals one atom.
Using the image of the reaction of methane above, fill in the blanks below.
In the reaction of methane, the reactants have
?
total atoms. The law of conservation of mass states that during a reactions atoms are
?
. Therefore, the products of this reaction will have ?
atoms.
Answers
Answer:
Step-by-step explanation:
First question mark
The reactants have 1 carbon atom, 4 hydrogen atoms, 4 oxygen atoms
Second question mark
The law of conservation of mass states that during a reactions atoms are conserved over time.
Third Question mark
1 carbon atom , 4 oxygen atoms, 4 hydrogen atoms, or in short number of atoms in the reactants equals number of atoms in the products.
How many triangles can be drawn given 2 sides and a non-included angle?
Answers
Triangles are singular because you can only ever draw one. A triangle can be created using two side lengths and the angle's measurement.
What is meant by Angle ?Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays known as the vertex is referred to as an angle's sides. Angles are often measured using one of two different units. The degree is the measurement unit that is most widely used. A straight angle is 90 degrees when a circle is divided into 360 equal degrees.To learn more about Angle refer to:
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PLEASE HELP!!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Based on the figure on the graph, match the described transformations with the transformed figures.
reflected across the x-axis
rotated 180° clockwise
translated 9 units to the
right and 2 units down
reflected across the y-axis
Answers
The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.
How to carry out transformation reflection?
From the given first image, we see that it is in the first quadrant but by the second image, we see that it is now mirrored along the horizontal axis. Thus, we can say that it is reflected across the x-axis.
After reflection, across the x-axis, we see that it was translated down by 2 units.
The last transformation is that we see it is now in quadrant 3 which means it was now reflected across the y-axis.
The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.
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All the 5th graders at Lincoln Elementary School will go on a field trip to the science museum. Counting all the children, teachers, and chaperones, there will be 147 people. Each bus holds 44 people.
Why must the answer be a whole number?
need anwser fast
Answers
The answer must be a whole number because for example how are you suppose to fit half a child on a bus that can hold 44 people when it already holds that amount.
It will always be a whole number because if there are several left over students they will be put in another bus with more empty seats.
Simplify 8 over negative 4 ÷ negative 3 over 9.
Answers
Answer:
1.33
because you have to divide
Develop a POQ solution and calculate total relevant costs for the data in the following table.
Period 1 2 3 4 5 6 7 8 9 10 11 12
Gross requirements 30 40 30 70 20 10 80 50
fill in the table and calculate total costs.
*Holding cost =$ 3.50 / unit/week; setup cost =$ 200 ; lead time =1 week; beginning inventory =40 . a lot-for-lot solution (enter your responses as whole numbers).
Answers
Using the information provided in the table, The total holding cost is $547.50, the total setup cost is $600 and the total cost is $1,147.50.
How to calculate the total costTo develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.
The missing values can be found on the attached table.
From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.
Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.
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She must determine height of the clock tower using a 1.5 m transit instrument (calculations are done 1.5 m above level ground) from a distance 100 m from the tower she found the angle of elevation to be 19 degrees. How high is the clock tower from 1 decimal place?
Answers
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's draw a diagram:
```
A - observer (1.5 m above ground)
B - base of the clock tower
C - top of the clock tower
D - intersection of AB and the horizontal ground
E - point on the ground directly below C
C
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B
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A
```
We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:
tan(ACD) = CE / AB
tan(19) = CE / 100
CE = 100 * tan(19)
CE ≈ 34.5 m (rounded to 1 decimal place)
Therefore, the height of the clock tower is approximately 34.5 m.
you are bored at a lunch meeting and decide to place a raisin in your glass of water. the raisin swells to twice its original size. relative to the water, the raisin must have been:
Answers
If the raisin swells to twice its original size, relative to the water, the raisin must have been hypertonic solution.
A response that is hypertonic refers to one that has a larger osmotic strain than another arrangement. In the end, a hypertonic arrangement is one in which the concentration of solute particles outside of a layer is greater than that inside.An arrangement that has a higher solute fixation than another arrangement is said to be hypertonic.The inside of a red platelet compared with the solute concentration of fresh water serve as illustrations of a hypertonic arrangement.When two arrangements come into contact, the solute or dissolvable moves until the arrangements reach harmony and are isotonic with one another.To know more about hypertonic check the below link:
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5(-2x-1)-5x+2=27
Solve for x
Answers
Answer:
x = -2
Step-by-step explanation:
5(-2x - 1) = -10x -5
-10x -5 - 5x + 2 = 27
-15x -3 = 27
+3 +3
-15x = 30
x = -2
x= -2
Step-by-step explanation:
-10x-5-5x+2=27
-15x-3=27
-15x=27+3
-15x=30
x=-2
Question is attached
Answers
A2=ar^2=1•3^2=9
A3=ar^3=1•3^3=27
Option D} none of the above
Answer:
D) None of the above------------------------------------
Let the numbers be:
1, x, y, z, 81Geometric means give us:
y² = 1*81 ⇒ y = 9Then:
y² = xz ⇒ xz = 81Given options give us:
A) 3*21 = 63 ≠ 81;B) 3*18 = 54 ≠ 81;C) Same as option A (must be a typo);Since all the above options are false, the answer is option D.
expand and simplify 5(2x+1)-2(3x-6)
Answers
Answer:
4x + 17
Step-by-step explanation:
10x+5-2(3x-6)
10x + 5-6x+12
you need to construct a fence around an area of 1600ft2 . what are the dimensions of the rectangular pen to minimize the amount of material needed?
Answers
The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.
What is the meaning of minimum dimension?The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.
With regard to the above problem,
let us say L is the lenght of the rectangle and W is the width
Based on the formula for the area of a rectangle,
L x W = 1600ft
To minimize the perimeter, of the rectangle, we must assume that:
L = W
that is L² = 1600
If we applied square root to both sides of the equation, we'd have
L = 40
Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.
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Solve for x.
5x +13
x = [?]
X+23.
Answers
Answer:
5/2
Step-by-step explanation:
15%of 250
Pls give and step by step
Answers
Answer:
Step-by-step explanation:
15% = 15/100 = .15
250 x .15 = 37.5
Answer:
37.5
Step-by-step explanation:
15%of 250 will be
15/100×250 = 75/2 = 37.5
A study is done to determine the attitudes of male university students towards careers. The researcher interviews 100 of the male students enrolled in a first-year course at the university. What is the sample in this situation?
all university students
male university students
the male students taking this course
the 100 male students interviewed
Answers
Answer:
I need the answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed
a writer wrote 10,010 words for his book on the first day of writing. he wrote 9,760 words on the second day, 9,510 words on the third day, and continued this way in an arithmetic sequence. write an explicit rule showing the equation for the number of words the writer would write on the 14th day, and solve.
Answers
Answer:
rule: an = 10010 -250(n -1)day 14: 6760 wordsStep-by-step explanation:
The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.
Formula for Arithmetic SequenceThe explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...
\(a_n=a_1+d(n-1)\)
ApplicationFor first term a₁ = 10010 and common difference d = -250, the explicit rule is ...
\(a_n=10010-250(n-1)\)
On day 14, n=14, and the number of words written is ...
\(a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760\)
The writer would write 6760 words on the 14th day.
What property states this equation
1 · a² = a²
Answers
Answer: a/2 + a/2
What property states this equation
Step-by-step explanation:
(1over5^2(3+2+5)^2=
i need helllllllllllllllllp pleaaaaaaassssseee
Answers
Answer:
2500
Step-by-step explanation:
5^2(3+2+5)^2
5^2(10)^2
25(100)
=2500
factored 6x2 – 31x - 30
Answers
Answer:
942
Step-by-step explanation:
I used the clculater
Problem 6
Let Tn be the nth triangular number, Qn be the nth square number and
Pn be the nth pentagonal number.
(a) Show that 3Pn = T3n-1.
(b) Show that Pn - Qn = Tn-1 and hence that P3n - 3Pn = Q3n.
Answers
It has been shown that \(3P_{n} =T_{3n-1}\), \(3P_{n} =T_{3n-1}\) and hence \(3P_{n} =T_{3n-1}\).
Given: \(T_{n}\) is the nth triangular number. \(Q_{n}\) is the nth square number. \(P_{n}\) is the nth pentagonal number.
To show:
\(3P_{n} =T_{3n-1}\) \(P_{n} -Q_{n} =T_{n-1}\) and hence \(P_{3n} -3P_{n} =Q_{3n}\)Triangular numbers are numbers formed by addition of consecutive natural numbers starting from 1. Square numbers are numbers formed by squaring natural numbers. Pentagonal numbers are numbers formed by distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex.
The formula for each of them is given by:
\(T_{n}=\frac{n(n+1)}{2}\)
\(Q_{n}=n^{2}\)
\(P_{n}=\frac{3n^{2}-n}{2}\)
(a).
Now, put \(n=3n-1\) in \(T_{n}=\frac{n(n+1)}{2}\) to get,
\(T_{3n-1}=\frac{(3n-1)(3n)}{2}\)
\(T_{3n-1}=3\frac{n(3n-1)}{2}\)
\(T_{3n-1}=3\frac{3n^{2}-n}{2}\)
Put \(P_{n}=\frac{3n^{2}-n}{2}\) in \(T_{3n-1}=3\frac{3n^{2}-n}{2}\) to get,
\(T_{3n-1}=3P_{n}\)
So, \(3P_{n}=T_{3n-1}\)
(b).
Now,
\(P_{n}-Q_{n}=\frac{3n^{2}-n}{2}-n^{2}\)
\(P_{n}-Q_{n}=\frac{3n^{2}-n-2n^{2}}{2}\)
\(P_{n}-Q_{n}=\frac{n^{2}-n}{2}\)
Put \(n=n-1\) in \(T_{n}=\frac{n(n+1)}{2}\) to get,
\(T_{n-1}=\frac{(n-1)(n-1+1)}{2}\)
\(T_{n-1}=\frac{(n-1)n}{2}\)
\(T_{n-1}=\frac{n^{2}-n}{2}\)
Comparing \(P_{n}-Q_{n}=\frac{n^{2}-n}{2}\) and \(T_{n-1}=\frac{n^{2}-n}{2}\), we get,
\(P_{n}-Q_{n}=T_{n-1}\)
Now, put \(n=3n\) in \(P_{n}-Q_{n}=T_{n-1}\) to get,
\(P_{3n}-Q_{3n}=T_{3n-1}\)
As shown in part (a), \(T_{3n-1}=3P_{n}\)
Put \(T_{3n-1}=3P_{n}\) in \(P_{3n}-Q_{3n}=T_{3n-1}\) to get,
\(P_{3n}-Q_{3n}=3P_{n}\)
\(P_{3n}-3P_{n}=Q_{3n}\)
So, \(P_{n}-Q_{n}=T_{n-1}\) and hence \(P_{3n}-3P_{n}=Q_{3n}\)
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The product of 4x and 0 is:
4x
4
0
Answers
Answer: 0
Step-by-step explanation:
Simply the answer is 0 because anything multiplied by 0 will result in 0
4x(0) = 0
Express the formula d=rt in terms of the time,t. Use your formula to find the time when the distance is 40 and the rate is 8.
Answers
The expression for d=rt in terms of the time is t = d/r; t = 5.
What is time? Time can be defined as a continuous and ongoing sequence of events that occur consecutively from the past to the present to the future. Time is used to measure, measure or compare the duration of events or the intervals between them, and even the sequence of events. Time is a useful concept that we use in our daily life. We have to watch when we cook, play, study, go to school, meet someone, etc. So knowing the right time is very important. Time is usually the answer to when an event happens or happened. The concept of time determines when a certain event occurs, has occurred or will occur. Time is a measurable quantity and is also infinite. The time is calculated in seconds, minutes, hours, days, months and years.Therefore,
In the equation d=rt
t = d/r
when distance is 40 and the rate is 8
t = d/r
Replace d with 40 and rate with 8
t = 40/8
t = 5
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