Answer:
step 1
Step-by-step explanation:
Alanna divided one side of the equation by 4 but multiplied the other side by 444. Alanna should have divided both sides of the equation by 4 to isolate c.
Alanna's mistake was dividing the equation by 12.4 instead of dividing both sides by 4.
Alanna made a mistake in the second step of solving the equation. The correct step should be as follows:
Step 1: 4c = 12
Step 2: Divide both sides by 4, not 4.4: (4c) / 4 = 12 / 4
Step 3: c = 3
So, the correct solution is c = 3, not c = 48 as Alanna calculated.
Alanna's mistake in solving the equation 4c = 12 occurred during the second step of the process. When attempting to isolate the variable "c," she divided both sides of the equation by 4, but her error lies in the value she used for this division. Instead of correctly dividing by 4, she mistakenly divided by 4.4.
The correct approach in this situation is to perform the same mathematical operation on both sides of the equation to maintain its balance. Dividing both sides by 4 allows us to isolate "c" and find its value. When we divide 12 by 4, we get 3, which is the correct solution to the equation.
In contrast, Alanna's incorrect division by 4.4 led her to the erroneous result of c = 48. This error likely arose from a simple calculation mistake. It's crucial to pay attention to each step of solving equations to avoid such errors, as they can significantly affect the final solution and lead to incorrect conclusions.
In summary, Alanna's mistake was dividing both sides of the equation by 4.4 instead of 4, resulting in the incorrect solution c = 48, when the correct solution is c = 3.
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In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 296 trials, the touch therapists were correct 143 times.
Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
Answer:
a 0.5
b 0.4831
c 0.4354 < P < 0.53008
Step-by-step explanation:
Given that :
Probability (P) of a head or a tail when a coin is being tossed or flipped = 1/2 = 0.5
Sample size (n) = 296
Selected sample (X) = 143
a) Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
The proportion of correct responses that would be expected if the touch therapists made random guesses is 0.5
b) Using Emily's sample results, what is the best point estimate of the therapists' success rate?
Point estimate [tex](p') = \frac{X}{n}[/tex]
= [tex](p') = \frac{143}{296}[/tex]
= 0.4831
c) Using Emily's sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.
The [tex]Z_c[/tex] for 90% is 1.645
Using the formula P" -E < P < P" + E
where E = margin of error : [tex]Z_c * \sqrt{\frac{P(1-P)}{n} }[/tex]
[tex]=1.645 * \sqrt{\frac{0.4831(0.5169)}{296} }[/tex]
[tex]=1.645 * \sqrt{\frac{0.2497}{296} }[/tex]
[tex]=1.645*0.029[/tex]
= 0.0477
∴ P" -E < P < P" + E
= 0.4831 - 0.0477 < P < 0.4831 + 0.0477
= 0.4354 < P < 0.53008
Answer:
The proportion of correct responses would be in between [tex](0.4345)<P<(0.53008)[/tex]
Step-by-step explanation:
Given information:
Sample size [tex](n)=296[/tex]
Selected sample [tex](x) =143[/tex]
Probability of head or tail will be 0.5 because a coin is tossed.
So the proportion of correct responses if the therapist made random decision will be 0.5.
Now with the help of sample result:
Point estimate:
[tex](p)'=x/n\\(p')=143/296\\(p')=0.4831[/tex]
Now, if we take confidence level of 90%
Then, [tex]Z=1.645[/tex]
As,
[tex](P"-E)<(P)<(P"+E)[/tex]
Where , E is the margin of error.
[tex]E=Z \times \sqrt \frac{P(1-P)}{n} \\E=1.654 \times \sqrt \frac{(0.4831 \times0.5169}{296} \\E=1.645\times 0.029\\E=0.0477[/tex]
Therefore:
[tex](P"-E)<(P)<(P"+E)[/tex]
[tex](0.4831-0.0477)<P<(0.4831+0.0477)\\(0.4345)<P<(0.53008)[/tex]
Hence, the proportion of correct responses would be in between [tex](0.4345)<P<(0.53008)[/tex].
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Which two values are greater then 3/5
Answer:
4/5 and 1
Step-by-step explanation:
4/5 is greater then 3/5 and 5/5=1 whole which is greater than 3/5, 4/5 and 1 is greater than 3/5 and 1 1/5, 1 2/5 so on and so on it could go forever but 4/5, and 1 is the only ones that our after 3/5 so those are the two greatest ones in this quistion.
Hope this helps.
The two values are 4 by 5 and 1
The following information should be considered:
4 by 5 is greater then 3 by 5 and 5 by 5 = 1 whole which is more than 3 by 5, 4 by 5 and 1 is greater than 3 by 5 and 1 1 by 5.However 4 by 5, and 1 is the only ones that after 3 by 5 so those are the two greatest ones in this given question.Learn more:
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How many different ways can a string of 23 pearls be strung
Answer:
22
Step-by-step explanation:
It can be strung 22 ways!!
Answer:
22!
Step-by-step explanation:
The circular permutation formula requires n-1. So the answer is 22!
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. The appropriate hypotheses to determine if the manufacturer's claim appears reasonable are
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W
Step-by-step explanation:
We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.
They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Let [tex]\mu[/tex] = mean power consumption of microwave ovens.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W
Here, null hypothesis states that the mean power consumption of microwave ovens is no more than 250 W.
On the other hand, alternate hypothesis sates that the mean power consumption of microwave ovens is more than 250 W.
The test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.
Find the circumference of each circle. Use your calculator's value of 1. Round your answer to
the nearest tenth for
[tex]area = 50.3 in^{2} [/tex]
Answer:
25.1
Step-by-step explanation:
area = pi x r x r
r x r = 50.3 / pi = 16.0109
r = 4.00137
circumference = pi x 2 x r = pi x 2 x 4.00137 = 25.141
Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which confidence interval would you expect to have greater precision (a smaller width) for estimating the population mean?
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - α)% confidence interval for population mean μ is:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
n₁ = 25
n₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Width for n = 64:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Thus, the sample consisting of 64 data values would give a greater precision
Answer:
Confidence Interval with sample size 25 = Broader, less precision; Confidence Interval with sample size 64 = Narrower, more precision
Step-by-step explanation:
Confidence Interval is the range around sample statistic, which contains the actual population parameter. Confidence level is the percentage probability, with which the population parameter is expected to be in confidence interval.
When sample size increases : the margin of error, ie sampling error between population parameter & sample statistic decreases. The reduced margin of error increases the level of confidence & precision in confidence interval range. So, the confidence interval range becomes narrower.
Hence, confidence interval becomes narrower & has more precision, when sample size increases from sample number = 25 to sample number = 64.
Myriad Solutions, Inc., issued 10% bonds, dated January 1, with a face amount of $320 million on January 1, 2013 for $283,294,720. The bonds mature on December 31, 2022 (10 years). For bonds of similar risk and maturity the market yield is 12%. Interest is paid semiannually on June 30 and December 31.
a. What would be the net amount of the liability Myriad would report in its balance sheet at December 31, 2018? 2.
b. What would be the amount related to the bonds that Myriad would report in its income statement for the year ended December 31, 2018?
c. What would be the amount(s) related to the bonds that Myriad would report in its statement of cash flows for the year ended December 31, 2018?
Answer:
a. $ 285,349,947
b. $ 34,055,227
c. $ 283,294,720 and $ 32,000,000
Step-by-step explanation:
We have the following data as of Jan. 1, 2013:
Cash 283,294,720
Discount on Bonds Payable 36,705,280
Bonds Payable 320,000,000
Now for the date of June 30, 2013, we do the following calculations:
320,000,000 x 10% x 2 = $ 16,000,000 cash payment
interest expense:
283,294,720 carrying value x 6% market rate = 16,997,683
to calculate depreciation:
16,997,683 - 16,000,000 = $ 997,683 discount amortization
Now for the new carrying value of bonds, we do the following:
283,294,720 + 997,683 = 284,292,403
As of Dec. 31, 2013, we have to:
320,000,000 x 10% x 2 = $ 16,000,000 cash payment
interest expense:
284,292,403 carrying value x 6% market rate = 17,057,544
to calculate depreciation:
17,057,544 - 16,000,000 = $ 1,057,544 discount amortization
Now for the new carrying value of bonds, we do the following:
284,292,403 + 1,057,544 = 285,349,947
Answering the questions:
a. The bonds would be listed at their current carrying value, $ 285,349,947
b. Interest Expense : 16,997,683 + 17,057,544 = $ 34,055,227
c. The $ 283,294,720 cash received from the sale of bonds would be added to cash flows under financing activities. The $ 32,000,000 in interest payments would be subtracted from cash flows under operating activities.
The net amount of liability, amount in income statement, and cash outflows related to Myriad Solutions, Inc.’s bonds are all calculated based on semiannual interest payments and the amortization of the discount over the life of the bonds. The carrying value of the bonds increases each year, and the interest expense and cash payments are reported in the financial statements.
Explanation:To determine the net amount of the liability Myriad Solutions, Inc. would report in its balance sheet at December 31, 2018, we need to calculate the carrying value of the bonds five years after issuance. Assuming the bonds were issued at a discount because the market rate of 12% was higher than the coupon rate of 10%, the discount is being amortized over the life of the bonds. This means the liability in the balance sheet is increasing every year until it reaches the face value at maturity.
The amount related to the bonds that Myriad would report in its income statement for the year ended December 31, 2018, includes the interest expense. Since the interest is paid semiannually, there would be two interest payments in 2018. Each payment would be a portion of the annual 10% coupon rate on the face value of $320 million, adjusted for any amortization of the bond discount over the reporting period.
For the statement of cash flows for the year ended December 31, 2018, Myriad would report the actual cash paid out as interest payments on the bonds. This would total the semiannual payments made on June 30 and December 31, which would be 10% of the $320 million face value divided by two, reflecting that interest is paid semiannually.
This week Emma earned ten more than half the number of dollars she earned last week a babysitting. If this week she earned 100 dollars how much did she earn last week
Answer:180
Step-by-step explanation:
100 - 10 is 90
90 x 2 is 180
I did a reverse calculation you can also check this is correct by knowing that half of 180 is 90 and 100 dollars is 10 more than 90 dollars.
For 16 and 17, use the dot plot of the number
of cars sold at a car dealership per week
during the first half of the year.
8
121 16
Cars Sold
20 24
2
16. Find the mean, median, and range.
Mean =
Median
Range -
Answer:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.
i hope i helped a bit
Step-by-step explanation:
Quiana has 7 times more text messages from Yolanda than from Pierre. Quiana has 56 text messages from Yolanda. Which equation can be used to find how many text messages Quiana has from Pierre, p?
Answer:
Quiana has 8 text messages from Pierre.
Step-by-step explanation:
This question can be solved using a rule of three.
Quiana has 7 times more text messages from Yolanda than from Pierre.
This means that for each message that she receives from Pierre, she receives 7 from Yolanda.
She received 56 from Yolanda.
So
7 messages from Yolanda - 1 messages from Pierre
56 messages from Yolanda - x messages from Pierre
[tex]7x = 56[/tex]
[tex]x = \frac{56}{7}[/tex]
[tex]x = 8[/tex]
Quiana has 8 text messages from Pierre.
Quiana has 8 text messages from Pierre.
To find how many text messages Quiana has from Pierre, represented as p, given that Quiana has 7 times more text messages from Yolanda than from Pierre, and she received 56 text messages from Yolanda, we can set up the following equation:
p × 7 = 56
To solve for p, we divide both sides of the equation by 7:
p = 56 ÷ 7
p = 8
So, Quiana has 8 text messages from Pierre.
Point A is (-7, 5) and point M is at (0, 4)
Point M is the midpoint of point A and Point B
What are the coordinates of point B
Answer: (7,3)
Step-by-step explanation:
The coordinates of point B(7, 3).
What is Section Formula?The formula below gives the coordinates of the point A(x, y), which internally splits the line segment between the points P([tex]x_1[/tex], [tex]y_1[/tex]) and Q([tex]x_2[/tex], [tex]y_2[/tex]) in the ratio [tex]m_1[/tex]: [tex]m_2[/tex],
A (x, y) = [tex]((m_1 x_2 + m_2 x_1) / ( m_1 + m_2), \;\; (m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]
Given:
Point A is (-7, 5) and point M is at (0, 4).
and, Point M is the midpoint of point A and Point B.
A (x, y) = [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]
So, x= [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]
0 = ( 1 x [tex]x_2[/tex] + 1 x (-7)) / (1 + 1)
0 = [tex]x_2[/tex] - 7
[tex]x_2[/tex] =7
and, y= [tex](m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]
4= ( 1 x [tex]y_2[/tex] + 1 x 5)/ 2
8 = [tex]y_2[/tex] + 5
[tex]y_2[/tex] = 3
Hence, the coordinates of B(7, 3).
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Find the perimeters of the following shapes
Answer:
a.) 26.2
Step-by-step explanation:
b.)13.8
hope this helps
Answer:
A) 26.2
B) 13.8
Step-by-step explanation:
Perimeter is just adding
-2x-8y= -32 slope intercept form
Answer:
y = -1/4x +4
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
-2x-8y = -32
Add 2x to each side
-2x+2x-8y =2x -32
-8y = 2x-32
Divide each side by -8
-8y/-8 = 2x/-8 -32/-8
y = -1/4x +4
Ayudaaaa porfavorrrrrrrr
The length of the 'top' vector is sqrt(3^2 + 3^2) = 3sqrt2
The length of the 'bottom' vector is sqrt(4^2 + 1^2) = sqrt17
Suppose the students construct a 95% confidence interval for the true weight of their rocks. Whose interval do you expect to be more precise (narrower)? (i) The student who weighed the rock 20 times. (ii) The student who weighed the rock 5 times. (iii) Both intervals would be equally precise.
Answer:
(i) The student who weighed the rock 20 times.
Step-by-step explanation:
The margin of error of a confidence interval is:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
From the equation above, the larger the size of the sample, the lower the margin is, that is, the narrower the interval is.
In this question:
A student weighed the rock 20 times and other the 5. From above, the one who weighed the rock 20 times will have the more precise interval.
So the correct answer is:
(i) The student who weighed the rock 20 times.
SOMEONE PLEASE HELP
The table lists the types of blocks found in a box of toys. Find P
Answer: P= 0.174
Step-by-step explanation:
Using the principle of probability, the probability of obtaining a green and round block from the toy box would be 0.174
P(green and round) can be interpreted as P(GREEN n ROUND)
From the table given :
P(green and round) = 4Total number of blocks in the toy = 23Recall :
Probability = required outcome / Total possible outcomesHence, P(green and round) = 4/23 = 0.1739 = 0.174
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Q1: A group of 50 biomedical students recorded their pulses rates by counting the number of beats for 60 seconds. (15)
80
48
88
70
84
82
66
84
82
64
44
72
90
70
86
104
58
84
72
60
90
108
62
52
72
86
66
104
78
82
96
54
68
76
72
88
102
74
68
74
78
66
72
90
62
100
92
84
76
72
(a) Construct frequency distribution.
(b) Compute mode, median and mean of the frequency distribution.
(c) The lower and upper quartile of the frequency distribution.
Answer:
The answers are in the explanation.
Step-by-step explanation:
a)
X1 -Absolute frecuency -cumulative absolute frequency -Relative frecuency
44 1 1 0.021
48 1 2 0.021
52 1 3 0.021
54 1 4 0.021
58 1 5 0.021
60 1 6 0.021
62 2 7 0.042
64 1 8 0.021
66 3 12 0.063
68 2 14 0.042
70 2 16 0.042
72 6 22 0.126
74 2 24 0.042
76 2 26 0.042
78 2 28 0.042
80 1 29 0.021
82 3 32 0.063
84 4 36 0.084
86 2 38 0.042
88 2 40 0.042
90 3 43 0.063
92 1 44 0.021
96 1 45 0.021
100 1 46 0.021
102 1 47 0.021
104 2 49 0.042
108 1 50 0.021
Total: 50 50 1
b) Mean: is the number average = 3806/48 = 78.12 Median: is the number or average number of half = 76 Mode: Is the number that appears most frequently = 72c) Lower quartile: 67Upper quartile: 84Thelma served five pieces of a pie. The pie was cut into eighths. What fraction of the pie did she serve? Write a multiplication equation using a unit fraction to represent the information
Answer:
Pi (π) is one of the most important and fascinating numbers in mathematics. Roughly 3.14, it is a constant that is used to calculate the circumference of a circle from that circle's radius or diameter.[1] It is also an irrational number, which means that it can be calculated to an infinite number of decimal places without ever slipping into a repeating pattern.[2] This makes it difficult, but not impossible, to calculate precisely.
Step-by-step explanation:
Pi (π) is one of the most important and fascinating numbers in mathematics. Roughly 3.14, it is a constant that is used to calculate the circumference of a circle from that circle's radius or diameter.[1] It is also an irrational number, which means that it can be calculated to an infinite number of decimal places without ever slipping into a repeating pattern.[2] This makes it difficult, but not impossible, to calculate precisely.
consider the function f(x)= x^2 and the function g(x) shown below. how will the graph of g(x) differ from the graph of f(x)
g(x) = 4×f(x) = 4x^2
Answer:
f(x) = x^2
g(x) = 4*x^2
=> For a value of x, the g(x) is 4 times larger than f(x).
=> g(x) is the stretched version of f(x) with stretched ratio = 4).
=> Option D is correct
Hope this helps!
:)
Answer:
D
Step-by-step explanation:
The multiple "4" is the stretch factor. The stretch is parallel to y-axis, which is a vertical stretch
Multiply 71 by 8 and then add 379
Answer: 947
Step-by-step explanation:
71 x 8 = 568
568 + 379 = 947
Answer = 947
Answer:
947
Step-by-step explanation
multiply 71 and 8 then add 379
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let AAA be the event that the six-sided die is an even number and BBB be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions. What is P(A)P(A)P, (, A, ), the probability that the six-sided die is an even num
Answer:
0.5
Step-by-step explanation:
The sample space of a fair six-sided die and a fair four-sided die rolled simultaneously is given below:
[tex](1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\[/tex]
where in each pair (x,y), x represents the four-sided die and y represents the six sided die.
Total Number of Possible Outcomes =24
Event A is the event that the six-sided die is an even number.
n(A)=12
Therefore, the probability that the six-sided die is an even number:
P(A)=12/24=0.5
Two solution of salt water contain 0.03% and 0.23 salt respectively. A lab technician
wants to make 1 liter of Solution which contains
0.18% salt. How much of each solution should
She use?
Amount of 0.3% solution-milliliter
Amount of 0.23% solution - Milliliter
Answer:
750 mL of 0.23% solution250 mL of 0.03% solutionStep-by-step explanation:
Let x represent the quantity (in liters) of the higher percentage solution, the 0.23% solution. Then 1-x will be the quantity of 0.03% solution. The amount of salt in the mix is ...
0.23%·x +0.03%·(1 -x) = 0.18%·1
Multiply by 100% and subtract 3:
20x = 15
x = 15/20 = 0.75 . . . . liters of 0.23% solution
1-x = 1-0.75 = 0.25 . . liters of 0.03% solution
The lab tech needs 750 mL of 0.23% solution and 250 mL of 0.03% solution.
Evaluate -8 -3+8+ (-3).
Answer:-6
Step-by-step explanation:
-8-3+8+(-3)
-8-3+8-3
Rearranging we get
8-8-3-3
0-6=-6
The correct answer is:
[tex]-8 - 3 + 8 + (-3) = -6.[/tex]
1. Start with -8.
2. Subtract 3: [tex]-8 - 3 = -11[/tex].
3. Add 8: [tex]-11 + 8 = -3.[/tex]
4. Subtract 3: [tex]-3 - 3 = -6[/tex].
Complete correct question:
Evaluate [tex]-8 -3+8+ (-3)[/tex].
Sarah enjoys reading books as a hobby. Complete the rate chart below to find how many pages Sarah reads in a certain number of hours. Time (in hours) 3 6 9 12 15 Number of Pages Read 120 240 360 480 ? A. 780 B. 520 C. 600 D. 578
Answer: C. 600
Step-by-step explanation:
Sarah reads at a pace of 120 pages per 3 hours.
All we have to do is add 120 pages to the 480 pages.
480+120=600
PLZ HELP FAST WILL MARK BRAINLIEST
The box plots show the number of hours that Mr. Yan’s biology class spent studying for a test. It also shows the number of hours Mrs. Gonzalez’s class spent studying for a geography test. Mr. Yan’s Class 2 box plots. The number line goes from 0 to 10. For Mister Yan's class, the whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4. For Misses Gonzalez's Class, the whiskers range from 1 to 9, and the box ranges from 4 to 7. A line divides the box at 5.5. Mrs. Gonzalez’s Class Four students compared the data in the box plots. Nadine Kendrick Tahara Dean The medians are the same because both sets of data have the same minimum and maximum values. Mr. Yan’s class has a greater median because the box in that box plot is larger. Mrs. Gonzalez’s class has a greater median because the line inside that box is located at a greater value. The medians are both 7 because the upper quartile for the sets of data is 7. Which student is correct?
Nadine
Kendrick
Tahara
Dean
The correct student is Dean.
To determine which student is correct, let's analyze the information given in the box plots for both classes:
For Mr. Yan's class, the box plot shows:
- Minimum value (lower whisker): 1
- Maximum value (upper whisker): 9
- Lower quartile (Q1): 2
- Median (Q2): 4
- Upper quartile (Q3): 7
- Interquartile range (IQR): Q3 - Q1 = 7 - 2 = 5
For Mrs. Gonzalez's class, the box plot shows:
- Minimum value (lower whisker): 1
- Maximum value (upper whisker): 9
- Lower quartile (Q1): 4
- Median (Q2): 5.5
- Upper quartile (Q3): 7
- Interquartile range (IQR): Q3 - Q1 = 7 - 4 = 3
Now let's evaluate each student's statement:
- Nadine: The medians are the same because both sets of data have the same minimum and maximum values. This statement is incorrect because the medians are different. Mr. Yan's class has a median of 4, while Mrs. Gonzalez's class has a median of 5.5.
- Kendrick: Mr. Yana's class has a greater median because the box in that box plot is larger. This statement is incorrect because the size of the box does not determine the median. The median is the value that divides the data into two equal halves, and it is indicated by the line inside the box.
- Tahara: Mrs. Gonzalez's class has a greater median because the line inside that box is located at a greater value. This statement is correct. The median for Mrs. Gonzalez's class is 5.5, which is greater than the median for Mr. Yan's class, which is 4.
- Dean: The medians are both 7 because the upper quartile for the sets of data is 7. This statement is incorrect because the median is not determined by the upper quartile but by the value that separates the higher half from the lower half of a data sample.
Therefore, the only correct statement is made by Tahara, who correctly identifies that Mrs. Gonzalez's class has a greater median because the line inside the box is located at a greater value (5.5) compared to Mr. Yan's class (4).
On a coordinate plane, a line goes through (negative 8, 10), (0, 0), and (8, negative 10). What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)? 4x – 5y = 5 5x + 4y = 37 4x + 5y = 5 5x – 4y = 8
Answer:
4x-5y =5
Step-by-step explanation:
First we need to find the slope of the line
m = (y2-y1)/(x2-x1)
= (0-10)/(0- -8)
= -10/(0+8)
-10/8
-5/4
We want a line with a perpendicular slope
That line will have a negative reciprocal slope
-1 (-5/4)
4/5
We have the slope and a point
y= mx+b is the slope intercept form of a line
y = 4/5x+b
Substitute the point into the equation
3 = 4/5(5)+b
3 =4+b
b = -1
The equation of the line is y = 4/5x-1
Multiply each side by 5 to get rid of the fractions
5y = 4x -5
Subtract 4x from each side
-4x+5y = -5
Multiply each side by -1
4x-5y =5
Answer:
4x - 5y = 5
Step-by-step explanation:
Slope of the given line:
(-10-0)/(8-0)
-10/8
-5/4
Slope of the Perpendicular line
4/5
y = ⅘x + c
3 = (4/5)(5) + c
3 = 4 + c
c = -1
y = (4/5)x - 1
5y = 4x - 5
4x - 5y = 5
If the volume of the pyramid shown is 216 inches cubed, what is the area of its base?
A rectangular pyramid with a height of 6 inches.
12 inches squared
36 inches squared
72 inches squared
108 inches squared
Answer:
D.) 108 in.2
Step-by-step explanation:
Use the equations you know to help you figure this out. It may not be easy, but for you to understand, you need to learn how to do it. If you want work, try it out.. Not to be rude...
Answer:
D) 108 inches squared.
Step-by-step explanation:
When you have the height of a pyramid, you must find the area of the base. Then multiply the base and height. When you find the product, divide this by three. There's your answer.
If sally walked 1/2 mile in 1/4 hour, how fast was she walking measured in miles per hour
2 mile per hour
Step-by-step explanation:
I use the equation :
[tex] \frac{ \frac{1}{2} }{ \frac{1}{4} } = \frac{x}{1} \\ x = \frac{ \frac{1}{2} \times 1}{ \frac{1}{4} } \\ x = \frac{ \frac{1}{2} }{ \frac{1}{4} } \\ x = \frac{1}{2} \times \frac{4}{2} \\ x = \frac{4}{2} \\ x = 2 \: mile[/tex]
So, she walked 2 mile per hour
Hope it helpful and useful :)
6x-2(x+1)>0 a. X>2 b. X<2 c. X>1/2 d. X<1/2
Answer:
c. x>1/2
Step-by-step explanation:
Distribute the -2 to eliminate parentheses:
6x -2x -2 > 0
4x -2 > 0 . . . . . . combine terms
Now, you can divide by 4:
x -2/4 > 0
and add 1/2
x > 1/2 . . . . . matches choice C
Answer:
[tex]x > \frac{1}{2} [/tex]
Suppose that prices of a certain model of a new home are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Answer:
68% of buyers paid between $147,700 and $152,300.
Step-by-step explanation:
We are given that prices of a certain model of a new home are normally distributed with a mean of $150,000.
Use the 68-95-99.7 rule to find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Let X = prices of a certain model of a new home
SO, X ~ Normal([tex]\mu=150,000 ,\sigma=2,300[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean price = $150,000
[tex]\sigma[/tex] = standard deviation = $2,300
Now, according to 68-95-99.7 rule;
Around 68% of the values in a normal distribution lies between [tex]\mu-\sigma[/tex] and [tex]\mu-\sigma[/tex].
Around 95% of the values occur between [tex]\mu-2\sigma[/tex] and [tex]\mu+2\sigma[/tex] .
Around 99.7% of the values occur between [tex]\mu-3\sigma[/tex] and [tex]\mu+3\sigma[/tex].
So, firstly we will find the z scores for both the values given;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{147,700-150,000}{2,300}[/tex] = -1
Z = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{152,300-150,000}{2,300}[/tex] = 1
This indicates that we are in the category of between [tex]\mu-\sigma[/tex] and [tex]\mu-\sigma[/tex].
SO, this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.
Approximately 95% of the buyers paid between $147,700 and $152,300.
Explanation:To find the percentage of buyers who paid between $147,700 and $152,300, we can use the 68-95-99.7 rule for normal distributions. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
The mean of the prices is $150,000 and the standard deviation is $2,300. The difference between $147,700 and $152,300 is $4,600, which is 2 standard deviations away from the mean. Therefore, we can expect approximately 95% of buyers to have paid between $147,700 and $152,300.
So, approximately 95% of the buyers paid between $147,700 and $152,300.
Learn more about Percentage of buyers here:https://brainly.com/question/30811283
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