Marco is in elementary school. his father is 30 years older than marco, and his mother is 4 years younger than his father. the ages of marco, his mother, and his father are all prime numbers. what are their ages?
Answers
Marco's age is 3, his father's age is 33, and his mother's age is 29. All of these ages are prime numbers and fulfill the given conditions.
The ages of Marco, his father, and his mother are all prime numbers. To find their ages, let's start by assigning variables. Let Marco's age be represented by the variable M.
According to the information given, Marco's father is 30 years older than Marco. So, we can represent his father's age as M + 30.
It is also stated that Marco's mother is 4 years younger than his father. Therefore, we can represent his mother's age as M + 30 - 4, which simplifies to M + 26.
Since all the ages are prime numbers, we can try different values for M to find the prime numbers that satisfy the given conditions.
One possible solution could be:
- Marco is 3 years old (M = 3).
- Marco's father is 33 years old (M + 30 = 3 + 30 = 33).
- Marco's mother is 29 years old (M + 26 = 3 + 26 = 29).
In this case, Marco's age is 3, his father's age is 33, and his mother's age is 29. All of these ages are prime numbers and fulfill the given conditions.
It's important to note that there could be other combinations of prime numbers that satisfy the conditions, so this is just one example.
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Related Questions
I need help Pls help with both
Answers
Answer:
the first one is 84
Step-by-step explanation:
subtract 145-61 then you get 84for the missing angle.
Answer:
1. 84, 2. 7.31
Step-by-step explanation:
1. 145-61=84
2. 16x+4-3x+11=110
13x+15=110
13x=95
x=7.31
(a) After 1 hour there were g remaining. (Round to the nearest integer as needed.) (b) The half-life was at approximately hrs. (Round to one decimal place as needed.) grams per hour. (c) The sample was decaying at a rate of (Round to one decimal place as needed.) hrs. (d) The sample was decaying at the rate of 2 grams per hour after (Round to the nearest integer as needed.) Ау 9- A sample of radioactive material decays over time (measured in hours) with decay constant 3. The graph of the exponential function y=P(t), shown on the right, gives the number of grams remaining after t hours. (a)How much was remaining after 1 hour? (b)Approximate the half-life of the material. (c)How fast was the sample decaying after 5 hours? (d)When was the sample decaying at the rate of 2 grams per hour?
Answers
(a) To find the remaining grams after 1 hour, we use the formula y = P(t) with decay constant 3, and t = 1 hour. The formula for exponential decay is y = P(0)e^(-kt), where P(0) is the initial amount, k is the decay constant, and t is the time in hours. Plugging in the values, we have y = P(0)e^(-3*1). Since we only know the decay constant, we cannot determine the exact grams remaining. However, we can see that the amount of grams is decreasing exponentially.
(b) To approximate the half-life of the material, we use the formula P(t) = P(0)/2, since half-life is the time it takes for the amount to reduce by half. Using the decay formula, we have P(0)/2 = P(0)e^(-3t). Solving for t, we get t = ln(2)/3 ≈ 0.231 hours, rounded to one decimal place.
(c) To find how fast the sample was decaying after 5 hours, we can find the derivative of the decay formula with respect to time: dP(t)/dt = -3P(0)e^(-3t). Plugging in t = 5 hours, we get dP(5)/dt = -3P(0)e^(-3*5). Again, we cannot determine the exact rate without knowing the initial amount, but it is decaying at a rate proportional to e^(-15).
(d) To find when the sample was decaying at a rate of 2 grams per hour, we set the derivative equal to -2: -2 = -3P(0)e^(-3t). Simplifying, we get e^(-3t) = 2/3P(0). Solving for t, we get t = ln(2/3P(0))/(-3). Without knowing the initial amount, we cannot determine the exact time when the sample was decaying at 2 grams per hour.
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? what is the ans of the question
Answers
Answer:
a. 12x+22, b. x = 9
Step-by-step explanation:
a. The perimiter in terms of x is 2((4x+8)+(2x+3)) = 12x+22
b. 12x+22=136, 12x=108, x=9
a. 12x+22, b. x = 9
Step-by-step explanation:
a. The perimiter in terms of x is 2((4x+8)+(2x+3)) = 12x+22
b. 12x+22=136, 12x=108, x=9
Abc company’s budgeted sales for june, july, and august are 12,800, 16,800, and 14,800 units, respectively. abc requires 30% of the next month’s budgeted unit sales as finished goods inventory each month. budgeted ending finished goods inventory for may is 3,840 units. each unit that abc company produces uses 2 pounds of raw material. abc requires 25% of the next month’s budgeted production as raw material inventory each month.
Answers
The budgeted ending raw material inventory for May is 2,560 pounds, calculated by taking 25% of the next month's budgeted production (12,800 units) multiplied by 2 pounds per unit.
To solve this problem, we need to calculate the budgeted production and raw material inventory for June, July, and August.
For June:Budgeted production = 12,800 units + 30% * 16,800 units = 17,440 units
Raw material inventory = 25% * 17,440 units * 2 pounds = 8,720 pounds
For July:Budgeted production = 16,800 units + 30% * 14,800 units = 20,840 units
Raw material inventory = 25% * 20,840 units * 2 pounds = 10,420 pounds
For August:Budgeted production = 14,800 units + 30% * 20,840 units = 20,632 units
Raw material inventory = 25% * 20,632 units * 2 pounds = 10,316 pounds
To find the budgeted ending finished goods inventory for June, we need to subtract the budgeted sales for June from the budgeted production for June and add the budgeted ending finished goods inventory for May:
Budgeted ending finished goods inventory for June = 17,440 units - 12,800 units + 3,840 units = 8,480 units
Similarly, we can find the budgeted ending finished goods inventory for July and August:
Budgeted ending finished goods inventory for July = 20,840 units - 16,800 units + 8,480 units = 12,520 units
Budgeted ending finished goods inventory for August = 20,632 units - 14,800 units + 12,520 units = 18,352 units
Therefore, the budgeted ending finished goods inventory for June, July, and August are 8,480 units, 12,520 units, and 18,352 units, respectively. The budgeted raw material inventory for June, July, and August are 8,720 pounds, 10,420 pounds, and 10,316 pounds, respectively.
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Vehicle Car A is now passing a truck that is 90 feet long. Vehicle A is traveling 40 mph (or 60 feet per second) and
Bis traveling 30 mph (or 45 feet per second), Vehicle A will begin the passing maneuver 4 seconds behind the truck
allow the truck driver to see him. Vehicle A will return to his lane when he is 60 feet ahead of truck e.
a.
Vehicle A must travel 240 feet further than truck B to complete this maneuver (calculation below
second following distance - 4 x 60 feet per second 240
feet
Length of truckB- 90 feet
Distance between truck B & vehicle A after vehicle A passes the truck and
returns to his lane 120 feet
Total = 120
feet
b.
Car A is traveling 60 feet per second faster than truck B.
Car A is traveling 60 fps. Truck B is traveling 45 fps.
.
Car A will need 14
seconds to safely pass truck B and return to the right lane.
Divide total feet (answer a) by answer b.
How does vehicle A determine when it is safe to return to the right lane after passing the truck?
ehicle A sees that the truck is at least a car length away
Explain how using headlights during the daytime Increases safety during passing maneuvers.
hts increase the visibility of your vehicle and passing vehicle.
Answers
Answer:
120
Step-by-step explanation:
HELPP I LOST MY BRAINCELLS WHILE TRYING TO WORK IT OUT ILL BE BRAINLISTING WHOEVER HAS A GO!
Answers
Omg is that you on your profile?? you're so pretty!!
Answer:
1. a and be
2. 7
3. 8
4. An expression is a number, a variable, or a combination of numbers and variables and operation symbol whereas n equation is made up of two expressions connected by an equal sign.
Which values are areas of cross sections that are parallel to a face of this right rectangular prism?
480 square units
120 square units
80 square units
24 square units
Answers
The value is 24 square units is parallel to the face of the right rectangular prism.
We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.
So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:
A = 6 × 4
A = 24
Thus, the value is 24 square units is parallel to the face of the right rectangular prism.
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A = 6 × 4
A = 24
Thus, the value is 24 square units is parallel to the face of the right rectangular prism.
2. How many 3 -digit even numbers can be formed from the digits 1,2,3,4,5,6 if the digits can be repeated?
Answers
Step-by-step explanation:
First digit : 6 choices
Second digit: 6 choices
Third digit: 3 choices ( 2, 4 or 6 to be an even number)
6 x 6 x 3 = 108 possibles
HELP ASAP! Its due in 10 minutes!!! NO FILES!!
Answers
Answer:
d. 204
Step-by-step explanation:
Each triangle is 1/2 bh
base is 10x8
each side is 10x5
all that equals 204 inches squared
Find the slope of a graph with an y intercept of (4,2) and a y intercept of ( 1,3)
Answers
Answer:
-1/3
Step-by-step explanation:
formula is y2-y1/x2-x1 -> 3-2/1-4 -> 1/-3 -> -1/3
land's bend sells a wide variety of outdoor equipment and clothing. the company sells both through mail order and via the internet. random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. a random sample of 9 sales receipts for mail-order sales results in a mean sale amount of $72.10 with a standard deviation of $27.75 . a random sample of 13 sales receipts for internet sales results in a mean sale amount of $79.00 with a standard deviation of $25.75 . using this data, find the 95% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. assume that the population variances are not equal and that the two populations are normally distributed. step 1 of 3 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
Answers
we are 95% confident that the true mean difference between the amount of mail-order purchases and the amount of internet purchases lies between -$23.09 and $9.29.
Step 1: Find the critical value that should be used in constructing the confidence interval.
Since the sample sizes are small (n1=9, n2=13), we will use the t-distribution for the interval estimate. The degrees of freedom is calculated using the formula:
df = [(s1^2/n1 + s2^2/n2)^2] / [((s1^2/n1)^2)/(n1 - 1) + ((s2^2/n2)^2)/(n2 - 1)]
Plugging in the values gives:
df = [(27.75^2/9 + 25.75^2/13)^2] / [((27.75^2/9)^2)/(9 - 1) + ((25.75^2/13)^2)/(13 - 1)] ≈ 17.447
Using a t-table with 17 degrees of freedom and a confidence level of 95%, we find the critical value to be 2.110.
Step 2: Calculate the point estimate of the difference between the means.
The point estimate of the difference between the means is:
1x - x2 = $72.10 - $79.00 = -$6.90
Step 3: Calculate the confidence interval.
The formula for the confidence interval for the difference between two population means is:
(1x - x2) ± tα/2 * sqrt[s1^2/n1 + s2^2/n2]
Plugging in the values gives:
(-$6.90) ± 2.110 * sqrt[27.75^2/9 + 25.75^2/13] ≈ (-$23.09, $9.29)
Therefore, we are 95% confident that the true mean difference between the amount of mail-order purchases and the amount of internet purchases lies between -$23.09 and $9.29.
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The data set below is a random sample of the heights (in meters) of women belonging to a certain ethnic subgroup. Assume the population is normally distributed. 1.38 1.47 1.47 1.53 1.61 1.60 a) Find the mean and standard deviation of the data. (Give your answers to three decimal places.) Answers: mean - standard deviation b) Conduct a hypothesis test at the 0.10 significance level to test the claim that the population mean is less than 1.56. The critical region runs from to Answers: The value of the test statistic is The correct conclusion is At the 0.1 significance level, the sample data support the claim that the population mean is less than 1.56. At the 0.1 significance level, there is not sufficient sample evidence to support the claim that the population mean is less than 1.56. At the 0.1 significance level, there is sufficient sample evidence to reject the claim that the population mean is less than 1.56. At the 0.1 significance level, there is not sufficient sample evidence to reject the claim that the population mean is less than 1.56.
Answers
a) The mean is 1.515 and the standard deviation is 0.089. b) At the 0.1 significance level, there is sufficient sample evidence to reject the claim that the population means is less than 1.56. The correct conclusion is option C.
a) Mean: To calculate the mean, you need to add up all the values and divide by the total number of values.
μ = ΣX / n = 1.38 + 1.47 + 1.47 + 1.53 + 1.61 + 1.60 / 6= 1.515
Standard Deviation: It can be calculated as follows;
σ = √[Σ(X - μ)² / N]= √[(1.38 - 1.515)² + (1.47 - 1.515)² + (1.47 - 1.515)² + (1.53 - 1.515)² + (1.61 - 1.515)² + (1.60 - 1.515)² / 6]
= √[0.0442 / 6]
= 0.089
b) Null Hypothesis: H₀: μ ≥ 1.56
Alternative Hypothesis: H₁: μ < 1.56
Level of Significance: α = 0.10
This is a one-tailed test with the critical region to the left.
Test Statistic: Since the sample size is small (n < 30), we use a t-distribution.t = (x - μ) / (s / √n)
Where: x = Sample Mean
μ = Population Mean
S = Sample Standard Deviation
n = Sample Sizet = (1.515 - 1.56) / (0.089 / √6)
= -1.92
Critical Region: The critical value can be found using a t-table or a calculator with a t-distribution function. The critical value with 5 degrees of freedom at a 0.10 level of significance is -1.812.
Conclusion: Since the test statistic (-1.92) is less than the critical value (-1.812), we reject the null hypothesis. This means that there is sufficient sample evidence to support the claim that the population mean is less than 1.56. Hence, the correct option is C.
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Expand and simplify (x - 6)(x + 2)
Answers
Answer: x^2-4x-12
Step-by-step explanation:
(x-6)(x+2)
-Use the FOIL Method (First Outer Inner Last)
x(x)=x^2
x(2)=2x
x(-6)=-6x
(-6)(2)=-12
-6x+2x=-4x
x^2-4x-12
During the early morning hours, customers arrive at a branch post office at an average rate of 69 per hour (Poisson), while clerks can provide services at a rate of 23 per hour. If clerk cost is $29.76 per hour and customer waiting time represents a cost of $32 per hour, how many clerks can be justified on a cost basis a. 7 b. 5 C. 8 d. 6 e. 4
Answers
Based on the given information, a total of 7 clerks can be justified on a cost basis for the branch post office during the early morning hours.it is based on average.
The average customer arrival rate at the branch post office is given as 69 per hour, which follows a Poisson distribution. The clerks, on the other hand, can provide services at a rate of 23 per hour. To determine the number of clerks that can be justified on a cost basis, we need to consider the balance between customer arrival and service rates.
The formula for calculating the number of clerks can be derived using queuing theory. In this case, the formula is:
Number of Clerks = (Customer Arrival Rate / Clerk Service Rate) + 1
Plugging in the given values, we have:
Number of Clerks = (69 / 23) + 1 = 4 + 1 = 5
However, the cost analysis also needs to be considered. Each clerk costs $29.76 per hour, and customer waiting time represents a cost of $32 per hour. To minimize the overall cost, it is necessary to reduce the waiting time. Increasing the number of clerks reduces the waiting time and, consequently, the cost associated with it.
Considering the cost analysis, it is evident that having more clerks is beneficial. Therefore, to justify the cost and minimize waiting time, 7 clerks can be employed at the branch post office during the early morning hours.
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Evaluate the expression for b = 5
3b + 10
Answers
Answer:
3b = 3 x 5
3 x 5 + 10 = 15 + 10 = 25
Evaluate the expression when x = -6
x^2 + 5x - 3
Answers
substitute the value of the variable into the equation and simplify.
the answer is 3.
On Saturday, Luke recorded the temperature on his outside thermometer three times. When he woke up, the temperature read 79°F. By noon, the temperature had risen 15°F. When Luke went to bed, it had dropped 12°F from his last reading at noon. What was the difference in temperature when Luke went to bed compared to when he woke up?\
Answers
Answer: 82 was the temperature at bedtime, 13 degree difference
Step-by-step explanation:
79 + 15 - 12
82, 13 difference
Find the x - intercept of the graph of the equation
1) x + y = 9
2) 3x + y = 15
3) 2x + 3y = 12
4) x - y = 4
5) 4y - x = 18
6) 3y - 7x = 35
7) x - y = -1
8) 2x + 5y =14
9) 9x - 4y = 10
Help plz!!
Answers
Answer:
ugh should i drop out
Step-by-step explanation:
The answer to this question is 13x + 5y = 48. <3
a faulty watch gains 10 seconds an hour if it is correctly set to 8 p.m. one evening what time will it show when the correct time is 8 p.m. the following evening
Answers
The watch gains 4 min till 8:00 PM in the next evening and show 8:04 pm the next evening.
What does it gain?Considering that,
A broken watch adds ten seconds per hour.
Find the number of hours between 8:00 PM this evening and 8:00 PM the following evening.
There are 24 hours in a day.
number of seconds the defective watch gained.
1 hour equals 10 seconds
24 hours ÷ by 10
24 * 10 is 240 seconds.
Now figure out how many minutes your defective watch has gained.
60 s = 1 minute
240 sec = 240/60
= 4 min
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Missing parts;
A faulty watch gains 10 seconds an hour. If it is set correctly at 8:00 pm one evening, what time will it show when the correct time is 8:00 pm the following evening
The distribution of ph levels for all community swimming pools in a large county is approximately normal with mean 7. 5 and standard deviation 0. 2. According to swimming pool studies, the safest ph levels for water in swimming pools are between 7. 2 and 7. 8. (a) one community swimming pool in the county will be selected at random. What is the probability that the selected pool has a ph level that is not considered safe?.
Answers
The probability that the selected pool has a ph level not considered safe is approximately 0.22 (or 22%). This can be calculated using the cumulative probability of a normal distribution with a mean of 7.5 and a standard deviation of 0.2.
1. Calculate the z-score for the lower limit of 7.2: (7.2 - 7.5) / 0.2 = -1.5
2. Calculate the z-score for the upper limit of 7.8: (7.8 - 7.5) / 0.2 = 1.5
3. Calculate the cumulative probability of the lower limit: P(-1.5) = 0.0668
4. Calculate the cumulative probability of the upper limit: P(1.5) = 0.9332
5. Calculate the probability that the selected pool has a ph level not considered safe: P(not safe) = 1 - (P(1.5) - P(-1.5)) = 0.22
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Can you help me with number 50 and how the answer is that?
Answers
Answer:
Transitive Property of Congruence
Explanation:
Here, we want to get the congruence law used
From what we have, given 3 set of angles with 1 one of the angles equal to the two others, it mean that the other two are equal to one another
Thus, we can see that there is a linkage between the values as a result of one of the angles being equal to the other two
The name of the congruence property that represents this is the transitive property of congruence
We can use it to infer or get the value of a third angle or use to define the equality of two angles given a third one in which the first two are equal to
Evaluate the following expression. 6^-1
Answers
Lesley mixed 1 ounces of green paint with 4 ounce of purple paint. She decided to create 20
ounces of the same mixture. How many ounces of green paint does Lesley need for the new
mixture?
Answers
Answer:
4 oz
Step-by-step explanation:
1:4 is the ratio for this. in total, this makes 5 oz of paint. multipy 5 by 4 to get 20 oz. multiply the 1 oz of green paint by 4 as well.
May I please receive help
Answers
y+77=180
y=103
Now we know vertical angles are congruent do we can set the equation to find X as
6x-113=103
6x=216
x=36
The 9th grade class was surveyed about their plans after high school graduation. The table describes the results.
Plans to live at home Plans to live on their own Row Totals
Plans to attend college 55%. 10% 65%
Plans not to attend college 20% 15% 35%
Column Totals 75% 25% 100%
Part A: Find the conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home. (3 points)
Part B: Is there an association between not attending college and living on their own? (3 points)
Answers
a) The conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home is of: 0.5714 = 57.14%.
b) There is a negative association between not attending college and living on their own.
How to obtain a relative frequency?The relative frequency of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For the conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home, in item a, the outcomes are given as follows:
Desired outcomes: 20% that plans to live at home and not attend college.Total outcomes: 35% that plan to live at home.Hence the relative frequency is of:
p = 0.2/0.35 = 0.5714 = 57.14%.
Among people who plan to live on their own, the relative frequency of people who plan to attend college is of:
0.55/0.65 = 0.846 = 84.6%.
Hence there is a negative association between not attending college and living on their own, as people who live on their own are significantly more likely to attend college then people who do not live on their own.
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Will upvote correct answers that show steps.
For the following expressions, indicate the input ranges (or conditions) when there may be significant errors in evaluation. Provide algebraically equivalent terms that would reduce or avoid error.
a. √x + (1/x) - √x - (1/x)
b. 1 - sin x
Answers
a. The input range where there may be significant errors in evaluation is when x is very large or very small.
b. The input range where there may be significant errors in evaluation is when x is very close to multiples of π.
For a, In these cases, significant figures may be lost in the subtraction of two nearly equal numbers (√x and -√x, and 1/x and -1/x). To avoid this error, we can simplify the expression to 0.
√x + (1/x) - √x - (1/x) = 0For b, This is because the sine function has a maximum error of 1 in the vicinity of these points, which can cause cancellation errors in the subtraction of 1 and sin x. To avoid this error, we can use the identity:
1 - sin x = (1 - sin x)(1 + sin x)/(1 + sin x) = (cos² x)/(1 + sin x)This expression avoids subtraction and reduces error using the more stable cosine function.
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compute the critical value za/2 that corresponds to a 83% level of confidence
Answers
The critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.
To find the critical value zₐ/₂, we need to determine the value that leaves an area of (1 - α)/2 in the tails of the standard normal distribution. In this case, α is the complement of the confidence level, which is 1 - 0.83 = 0.17. Dividing this value by 2 gives us 0.17/2 = 0.085.
To find the z-value that corresponds to an area of 0.085 in the tails of the standard normal distribution, we can use a standard normal distribution table or a statistical calculator. The corresponding z-value is approximately 1.381.
Therefore, the critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.
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a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 425 gram setting. it is believed that the machine is underfilling the bags. a 18 bag sample had a mean of 416 grams with a standard deviation of 19 . assume the population is normally distributed. a level of significance of 0.01 will be used. find the p-value of the test statistic. you may write the p-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answers
A significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
Based on the information provided, the manufacturer of chocolate chips is interested in determining if there is a deviation from the expected value of 425 grams for the bag filling machine. They have collected a sample of 18 bags and calculated a mean of 416 grams with a standard deviation of 19. Assuming a normal distribution, they would like to determine the p-value of the test statistic with a significance level of 0.01.
To do this, they would conduct a one-sample t-test using the formula:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the population mean (expected value), s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
t = (416 - 425) / (19 / √18) = -2.21
Using a t-distribution table or calculator with 17 degrees of freedom (n-1), we can find the p-value associated with a t-score of -2.21 and a one-tailed test (since we are interested in whether the bags are underfilled). The p-value is approximately 0.0212, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis and conclude that the bags are likely being underfilled by the bag filling machine at the 425-gram setting.
In summary, the p-value of the test statistic is approximately 0.0212, indicating a significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
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A significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
Based on the information provided, the manufacturer of chocolate chips is interested in determining if there is a deviation from the expected value of 425 grams for the bag filling machine. They have collected a sample of 18 bags and calculated a mean of 416 grams with a standard deviation of 19. Assuming a normal distribution, they would like to determine the p-value of the test statistic with a significance level of 0.01.
To do this, they would conduct a one-sample t-test using the formula:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the population mean (expected value), s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
t = (416 - 425) / (19 / √18) = -2.21
Using a t-distribution table or calculator with 17 degrees of freedom (n-1), we can find the p-value associated with a t-score of -2.21 and a one-tailed test (since we are interested in whether the bags are underfilled). The p-value is approximately 0.0212, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis and conclude that the bags are likely being underfilled by the bag filling machine at the 425-gram setting.
In summary, the p-value of the test statistic is approximately 0.0212, indicating a significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
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After completing the fraction division 5 divided by five-thirds, Miko used the multiplication shown to check her work. 3 times five-thirds = StartFraction 3 Over 1 EndFraction times five-thirds = StartFraction 15 Over 3 EndFraction or 5 Which is the most accurate description of Miko's work? Miko found the correct quotient and checked her work using multiplication correctly. Miko found the correct quotient but checked her work using multiplication incorrectly. Miko found an incorrect quotient but checked her work using multiplication correctly. Miko found an incorrect quotient and checked her work using multiplication incorrectly.
Answers
Answer:
Miko found an incorrect quotient and checked her work using multiplication incorrectly.
Step-by-step explanation:
The given expression is
\(\dfrac{5}{\dfrac{5}{3}}\)
Applying the reciprocal rule we get
\(5\times \dfrac{3}{5}=5\)
What Miko did was
\(3\times \dfrac{5}{3}=\dfrac{3}{1}\times\dfrac{5}{3}=\dfrac{15}{3}\ \text{or}\ 5\)
So, Miko took the wrong values of the quotients and applied multiplication incorrectly.
Hence, Miko found an incorrect quotient and checked her work using multiplication incorrectly.
1) Louis is dilating triangle ABC at right. He
multiplied each x-coordinate and y-coordinate of
triangle ABC by -2.
a. What are the new coordinates of the points?
Answers
To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:
New x-coordinate = -2 * old x-coordinate
New y-coordinate = -2 * old y-coordinate
Let's apply these formulas to each point in triangle ABC:
Point A: (-3, 4)
New x-coordinate of A = -2 * (-3) = 6
New y-coordinate of A = -2 * 4 = -8
New coordinates of A: (6, -8)
Point B: (1, 1)
New x-coordinate of B = -2 * 1 = -2
New y-coordinate of B = -2 * 1 = -2
New coordinates of B: (-2, -2)
Point C: (5, -2)
New x-coordinate of C = -2 * 5 = -10
New y-coordinate of C = -2 * (-2) = 4
New coordinates of C: (-10, 4)
Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:
A: (6, -8)
B: (-2, -2)
C: (-10, 4)