Cat Behavior A report stated that the average number of times a cat returns to its food bowl during the day is 34. Assuming the variable is normally distributed with a standard deviation of 3 , what is the probability that a cat would return to its dish between 32 and 37 times a day? Round the final answer to four decimal places and intermediate z-value calculations to 2 decimal places. P(32
Answers
The probability that a cat would return to its food bowl between 32 and 37 times a day is approximately 0.589.
To find the probability that a cat would return to its food bowl between 32 and 37 times a day, we need to calculate the z-scores corresponding to these values and then find the area under the normal curve between these z-scores. Given: Mean (μ) = 34; Standard Deviation (σ) = 3. Step 1: Calculate the z-scores. For the lower value, 32: z₁ = (32 - 34) / 3 . For the higher value, 37: z₂ = (37 - 34) / 3. Calculating the z-scores: z₁ = -2 / 3 ≈ -0.67; z₂ = 1. Step 2: Calculate the probabilities. Now we need to find the area under the normal curve between these z-scores. This represents the probability that a cat would return to its food bowl between 32 and 37 times a day. Using a standard normal distribution table or calculator, we find the cumulative probabilities associated with the z-scores: P(Z ≤ -0.67) ≈ 0.2514; P(Z ≤ 1) ≈ 0.8413.
Step 3: Calculate the desired probability. To find the probability between the two values, we subtract the lower probability from the higher probability: P(32 ≤ X ≤ 37) = P(Z ≤ 1) - P(Z ≤ -0.67); P(32 ≤ X ≤ 37) ≈ 0.8413 - 0.2514; P(32 ≤ X ≤ 37) ≈ 0.5899. Therefore, the probability that a cat would return to its food bowl between 32 and 37 times a day is approximately 0.589.
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Related Questions
assume there are 5 red balls, 6 blue balls, and 4 green balls. if the balls are removed from the box one at a time, in how many different orders can the balls be removed assuming two balls of the same type are indistinguishable?
Answers
The number of ways that we can remove the balls one at a time from the box is 1307674368000
Given,
The number of balls in a box;
5 red balls
6 blue balls
4 green balls
We have to find the number of ways the balls can removed from the box one at a time;
Here,
Order is indistinguishable, so combination can be followed;
Combination formula;
ⁿCr = n! / r1(n - r)!
Here,
Total number of balls in the box = 5 + 4 + 6 = 15 balls
Then.
¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000
That is,
We can remove the balls one at a time from the box in 1307674368000 ways.
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Log2 x = -5 Write into exponential equation
Answers
\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_2(x)=-5\implies 2^{-5}=x\)
Answer:
y=mx+b
Step-by-step explanation:
John took 600mg of a medicine. Each hour, the amount of medicine in his body decreases by about 25%. Which function represents the amount of medicine in johns body after x hours
A.f(x)=600(0.75)^x
B.f(x)=600-25x
C.f(x)=600(0.25)^x
D.f(x)=600-75x
Answers
Initially 600
Decrease so 1-.25=.75
Tonya's dog walking service charges a flat rate of $20 per month, plus $3 Per mile that each dog is walked. Beth does not charge a monthly fee for her dog walking service, but she charges five dollars per mile that each dog is walked.
pls helppp!
Answers
Answer:
A) 20+3m = 5m
Step-by-step explanation:
20+3m = 5m
20 = 2m
m = 10
after each girl has walked dogs for 10 miles, their amount they charge would be equal
Tonya would charge: 20+3(10) = 20+30 or $50
Beth would charge: 5(10) or $50
The population of a small town is increasing at the rate of 2% per year. The town historian records the population at the end of each year and tracks the growth using the function P.-P.(1+r)"where P, is the population when n = 0, P, is the population in n years and r is the rate of change. In 2010, the population was 6,000. If it continues to increase, what will be the population, to the nearesthundred, in 2020
Answers
What is the relationship between attending training and preferred source of ordering parts? which of these would be an appropriate Null Hypothesis?
1.
There is a relationship between attending training and the preferred source of auto parts.
2.
There should be a relationship between attending training and the preferred source of auto parts.
3.
There is no relationship between attending training and the preferred source of auto parts.
4.
There will be no difference in the number of auto parts ordered.
Answers
The correct option is,
There is no relationship between attending training and the preferred source of auto parts.
What is Null Hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.
Null hypothesis always states that there is no significant difference between given observations. This also means that there is no such relationship between the two sets. That is, there is no effect of value in one set increases on value of another set will increase or decrease.
Hence the Null Hypothesis for given statement , "the relationship between attending training and preferred source of ordering parts " is :
H0 : There is no relationship between attending training and the preferred source of auto parts.
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Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
I do want to help, but i'm on school computer, and school computers BLOCK every image on brainly
Step-by-step explanation:
Answer:
y - 5x - 3
Step-by-step explanation:
Write expressions for the length and width of a rectangle that has an area equal to 3x^2-5x+2.
Answers
Answer:
B
Step-by-step explanation:
3x^2-5x+2
(3x-2)(x-1)=0
therefore
rectangle= L×B
L= (3x-2)(x-1)
a ballroom had a square dance floor. The area of the floor is 400 square feet. If the length of each side of the square increased by one foot, would its area be a rational number?
Answers
Answer:
Yes
Step-by-step explanation:
The area of a square is equal to the length squared.
So, the length of one side of the original floor is √400 which equals 20.
If you increase the length by 1, the area of the dance floor is 21 squared.
21 * 21 is certainly a rational number.
Answer:
Step-by-step explanation:
I think so, yes.
The area of a square is A = s*s where s is the length of the side
s^2 = 400
sqrt(s^2) = sqrt(400)
s = 20
If you increase each dimension by one foot you get 21 * 21 for the area of the new ballroom.
The result is rational. That's because the square root was rational when you found 20.
Area = 21 * 21 = 441 which is rational.
expand and simplify (x+1)(x+7)
Answers
Answer:
Factored?
x^2 + 8x +7
Step-by-step explanation:
x times x = x^2, with 7 times x = 7x and x times 1 = 1x. Add those two common terms together to get 8x. Then lastly 7 times 1 =7 so add that.
Simplify form of (x + 1)(x + 7) is equals to x² +8x +7.
What is simplification?
"Simplification in mathematics means to write the given expression in such a way that it is easy to understand."
According to the question,
Simplify the given equation by opening the brackets we get,
(x + 1)(x + 7)
= x² + 1x +7x +7
= x² + 8x + 7
Hence, simplify form of (x + 1)(x + 7) is equals to x² +8x +7.
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Describe the transformation of the parent
function f(x) = x².
f(x) = (x − 1)² +3
Answers
The transformation from the parent function is a translation by 1 unit right and 3 units up
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
f(x) = (x − 1)² + 3
First, we have the transformation to be:
From f(x) = x² to f(x) = (x − 1)²
This means the function is translated right by 1 unit
Next, we have:
From f(x) = (x − 1)² to f(x) = (x − 1)² + 3
This means the function is translated up by 3 units
Hence, the transformation is 1 unit right and 3 units up
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HELP IM ON A TIMER WILL GIVE BRAINLISTEST AND 5 STAR REVIEW
Answers
Answer:
Step-by-step explanation:
angle ACD is corresponding to the angle BCE, hence the line DE is congruent to line AB
the ratio of boys to girls in the class is 4:5. if there is a total of 27 students, how many more girls than boys are in the class?
Answers
Answer:
3 more girls than boys.
Step-by-step explanation:
Let's change 4:5 to 4x(boys) and 5x(girls).
Since there are 27 students, the equation would be:
4x+5x=27
Then, you simplify the equation:
9x=27
x=3
We are not finished yet!
Since there is 4x boys and 5x girls,
do 4 times 3 which gets you 12 boys
and 5 times 3 which gets you 15 girls.
15 girls minus 12 boys is 3 more girls than boys!
Hope this helps :)
If mr. douty goes to the store and purchases 5 equally priced items for a total of $172.45, how much did each item cost individually?
Answers
Answer:
$34.49
Step-by-step explanation:
To figure out this problem, you would need to divide the total price by the total amount of items you are buying
In this case it is...
172.45/5
=34.49
So the price of each item is approx. $34.49
if d=√4×9×16, find the value of d
Answers
Answer:
d = 288
Step-by-step explanation:
Answer:
d = 24
Step-by-step explanation:
hope this helps!!!
the probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. you have 2 such alarms in your home and they operate independently. Calculate the probability that both sound an alarm in the presence of smoke
Answers
The probability that both smoke alarms will sound an alarm in the presence of smoke is 0.64.
When two independent events occur, the probability of both events happening is calculated by multiplying their individual probabilities. In this case, the probability of one smoke alarm functioning properly and sounding an alarm in the presence of smoke is 0.8. Since the two smoke alarms operate independently, we can multiply the probability of one alarm functioning (0.8) by the probability of the other alarm functioning (also 0.8).
So, the probability of both smoke alarms sounding an alarm is 0.8 * 0.8 = 0.64. Therefore, there is a 64% chance that both alarms will function properly and sound an alarm in the presence of smoke.
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Suppose that a tire manufacturer believes that the lifetimes of its tires follow a normal distribution with mean 50,000 miles and standard deviation 5,000 miles.
1. Based on the empirical rule, about 95% of tires last for between what two values for miles?
2. How many standard deviations above the mean is a tire that lasts for 58,500 miles? Record your answer with two decimal places of accuracy. I
3. Determine the percentage of tires that last for more than 58,500 miles. Record your answer as a percentage with two decimal places of accuracy, but do not include the % symbol. (Here and below, you may use Table Z or the Normal Probability Calculator applet or Excel or another software tool.)
4. Determine the mileage for which only 25% of all tires last longer than that mileage. Record your answer to the nearest integer value.
5. Suppose the manufacturer wants to issue a money back guarantee for its tires that fail to achieve a certain number of miles. If they want 99% of the tires to last for longer than the guaranteed number of miles, how many miles should they guarantee? Record your answer to the nearest integer value.
Answers
1) About 95% of tires last between 40,000 miles and 60,000 miles.
2) A tire that lasts for 58,500 miles is (58500-50000)/5000=1.7 standard deviations above the mean.
3) the probability of a tire lasting for more than 58,500 miles is 0.0446. This is equivalent to 4.46%.
4) the manufacturer should guarantee a mileage of 37,850 miles to ensure that 99% of the tires last for longer than the guaranteed number of miles.
Explanation:
1.
About 95% of tires last for between what two values for miles?
According to empirical rule, about 95% of the data should fall within 2 standard deviations of the mean (assuming normal distribution).
Therefore, about 95% of the tires should last for between (50000 - 2*5000) = 40000 miles and (50000 + 2*5000) = 60000 miles.
Thus, about 95% of tires last between 40,000 miles and 60,000 miles.
2.
How many standard deviations above the mean is a tire that lasts for 58,500 miles? Record your answer with two decimal places of accuracy.
A tire that lasts for 58,500 miles is (58500-50000)/5000=1.7 standard deviations above the mean.
3.
Determine the percentage of tires that last for more than 58,500 miles.
The Z-score for a tire that lasts for more than 58,500 miles is (58500-50000)/5000 = 1.7.
Using a standard normal distribution table, the probability of a tire lasting for more than 58,500 miles is 0.0446.
This is equivalent to 4.46%.
4.
Determine the mileage for which only 25% of all tires last longer than that mileage. Record your answer to the nearest integer value.
The Z-score that corresponds to the 25th percentile is -0.67. Using the standard normal distribution table, we get:
0.25 = P(Z < -0.67)
Therefore, the mileage for which only 25% of all tires last longer than that mileage is (z × σ + μ) = (-0.67 × 5,000 + 50,000) = 46,650 miles.
5.
Suppose the manufacturer wants to issue a money-back guarantee for its tires that fail to achieve a certain number of miles. If they want 99% of the tires to last for longer than the guaranteed number of miles, how many miles should they guarantee?
Record your answer to the nearest integer value.
The Z-score that corresponds to the 1st percentile is -2.33.
Using the standard normal distribution table, we get:
0.01 = P(Z < -2.33)
Therefore, the manufacturer should guarantee a mileage of (z × σ + μ) = (-2.33 × 5,000 + 50,000) = 37,850 miles to ensure that 99% of the tires last for longer than the guaranteed number of miles.
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1. Based on the empirical rule, about 95% of tires last for between 40,000 and 60,000 miles.
2. The z-score for a tire that lasts for 58,500 miles is = 1.7 standard deviations above the mean.
3. The probability of a tire lasting more than 58,500 miles is = 0.0446 or 4.46%.
4. The mileage for which only 25% of all tires last longer than that mileage is = 46,650 miles.
5. the guaranteed number of miles is =37,850 miles.
1. The empirical rule for a normal distribution states that 68% of the values are within one standard deviation of the mean, 95% of the values are within two standard deviations of the mean, and 99.7% of the values are within three standard deviations of the mean.
Since the mean is 50,000 miles and the standard deviation is 5,000 miles, about 95% of tires last for between 40,000 and 60,000 miles.
Therefore, 40,000 and 60,000 are the two values.
2. The z-score formula is (x - µ) / σ,
where x = data value,
µ = mean,
σ = standard deviation.
Thus, the z-score for a tire that lasts for 58,500 miles is
= (58,500 - 50,000) / 5,000
= 1.7 standard deviations above the mean.
3. The percentage of tires that last for more than 58,500 miles can be found using a standard normal distribution table.
Using Table Z or the Normal Probability Calculator, we find that the probability of a z-score being less than 1.7 is 0.9554.
Therefore, the probability of a tire lasting more than 58,500 miles is
= 1 - 0.9554
= 0.0446 or 4.46%.
4. The mileage for which only 25% of all tires last longer than that mileage can be found using the inverse normal function.
Using Table Z or the Normal Probability Calculator, we find that the z-score for the 25th percentile is -0.67.
Thus, the mileage for which only 25% of all tires last longer than that mileage is = (z-score × standard deviation) + mean
= (-0.67 * 5,000) + 50,000
= 46,650 miles.
Rounded to the nearest integer, this is 46,650 miles.
5. Suppose the manufacturer wants to issue a money-back guarantee for its tires that fail to achieve a certain number of miles. If they want 99% of the tires to last for longer than the guaranteed number of miles.
The number of miles the manufacturer should guarantee can be found using the inverse normal function.
Since they want 99% of the tires to last longer than the guaranteed number of miles, they want the number of miles to be at the 1st percentile.
Using Table Z or the Normal Probability Calculator, we find that the z-score for the 1st percentile is -2.33.
Thus, the guaranteed number of miles is
= (z-score × standard deviation) + mean
= (-2.33 × 5,000) + 50,000
= 37,850 miles.
Rounded to the nearest integer, this is 37,850 miles.
Therefore, the manufacturer should guarantee 37,850 miles.
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Describe some mathematical approaches to aggregate
planning.
Answers
Mathematical approaches to aggregate planning involve using quantitative methods to determine the optimal production and resource allocation strategies over a specified planning horizon. These approaches utilize mathematical models to optimize various factors such as production costs, inventory levels, and customer demand.
One mathematical approach to aggregate planning is linear programming, which formulates the planning problem as a linear optimization model. Linear programming considers constraints such as capacity limits, labor availability, and demand variability to find the best allocation of resources and production levels. The objective is to minimize costs or maximize profit while meeting demand requirements.
Another approach is the use of mathematical forecasting techniques to predict future demand. Time series analysis, regression analysis, and other statistical methods can be employed to forecast demand patterns. These forecasts serve as inputs to mathematical models, such as inventory control models or production planning models, which determine the optimal production levels and inventory policies based on the anticipated demand.
Simulation modeling is another mathematical approach where computer-based simulations are used to evaluate different scenarios and make decisions about production levels, inventory levels, and workforce scheduling. These models consider various factors like demand variability, production capacity, and resource availability to simulate the system's behavior and analyze the impact of different planning strategies.
Overall, mathematical approaches to aggregate planning provide a systematic and quantitative way to optimize production and resource allocation decisions, considering factors such as demand, capacity, costs, and constraints. These approaches help organizations make informed decisions to meet customer demand efficiently while minimizing costs and maximizing operational performance.
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______ has at least one solution, and an inconsistent system has no solution.
Answers
The statement "Consistent system of equations has at least one solution, and an inconsistent system has no solution" is true.
In the context of systems of linear equations, a consistent system refers to a system where there exists at least one solution that satisfies all the equations in the system. This means that the equations can be simultaneously satisfied by a set of values for the variables.
On the other hand, an inconsistent system refers to a system of equations that has no solution. This occurs when the equations are contradictory or cannot be satisfied simultaneously by any values for the variables.
Therefore, a consistent system guarantees the existence of at least one solution, while an inconsistent system does not have any solution.
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What is the equation 2n x 2m equal to?
Answers
Answer: 2n x 2m
Step-by-step explanation:
Since the variables are different, you cannot do anything.
PLS HELP ME WILL MARK BRAINLIEST TO BEST ANSWER!
Answers
Answer:
The length of the longer base is a. 33 in
Step-by-step explanation:
This is true because if the longer base is 3 more inches than 2 times the amount of the shorter base, all you have to do is 15 x 2 + 3 = 33 in
Hope it helps! =)
Answer: A or 33inches
Step-by-step explanation
First write expressions for the longer base
Longer base: 3 + 2x
Shorter base: x
then solve
If x = 15 then..
3 + 2x
3 + 2(15)
3 + 30
33
THE LONGER BASE IS 33 INCHES
Choose the smallest number. 3/18 10/3
Answers
Answer:
3/18
Step-by-step explanation:
3/18= 0.16
10/3= 3.33
Answer:
3/18
Step-by-step explanation:
3/18 , 10/3
Simplify it to the smallest size
3/18 , 10/3
1/6 , 10/3
1/6 = 3/18
What fraction is equal to 50% of 1/3
Answers
Answer:
1/6
Step-by-step explanation:
50% is 0.5 or 1/2 so you just multiply 1/3 by 1/2 to get 1/6
Answer:
your answer is 1/6
Step-by-step explanation:
1/3 of 50% so what you do is 1/3*50% which 50% in fraction form is 1/2
so you do this
\(\frac{1}{2}*\frac{1}{3}\)
and that equals 1/6
thats better
help asap! pls pls i will mark brailiest
Answers
Sisjsjjd
Answer:
B. r = 6 h = 5.
The Porters are moving because Mr. Porter got a new job. Until Mrs. Porter finds a job in the new city, the Porter family will live on Mr. Porter’s salary. In the new city, his gross pay is $7,500 per month. His deductions include the following:
Answers
Answer: 5000
Step-by-step explanation:
Solve inequality for x. 2x(2x-1)-5x<4x^2-x
Answers
The inequality of (2x1)2x5x4x can be solved by determining that x>0.
How does inequality work?In mathematics, a statement of the order connection between two integers equivalent algebraic expressions that is greater than, equal to or greater to, less than, or lower than or equal to is referred to as an inequality.
According to the given data:(2x−1)2x−5x<4x +2−x
To multiply 2x-1 by 2, use the distributive property.
(4x−2)x−5x<4x + 2 −x
multiplying 4x-2 to x using the distributive property.
4x + 2 −2x−5x<4x + 2 −x
-2x and -5x together provide 7x.
4x + 2 −7x<4x + 2 −x
Subtract 4x + 2 by both sides.
4x + 2 −7x−4x + 2 <−x
Combine 4x + 2 and −4x + 2 to obtain 0.
−7x<−x To both sides, add x.
−7x+x<0
7x and x together yield 6x.
−6x<0
The product is 0 if any of the two numbers in it is greater than 0 and the other is 0 as well. 6 > 0, indicating that x would have to be greater than 0.
x>0
The Inequality of (2x−1)2x−5x<4x is x>0
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in a company, 95% of the workers are women. if 115 people work for thr company who aren't women, how many workers are there in all?
Answers
There are 2300 workers in all in the company.
Let the number of all workers in company be = 100x
95% workers are female then (100-95) = 5% of workers are not female.
So, the number of workers who are not female = 5x
According to the condition, the suitable equation is
5x = 115
x = 115/5
x = 23
So, the total number of workers in the company is = 100*23 = 2300.
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Find the height a 17-foot ladder can reach on the side of a building when it
hits the ground at a 65° angle.
A. 7.2 ft
B. 15.4 ft
C. 36.5 ft
D. 48 ft
E 224 ft
SHOW EXPLANATION
Answers
Answer:
B. 15.4 ft
Step-by-step explanation:
this answer, without any formulas used, can be answered correctly and logically.
answer c, d and e are eliminated as the opposite side cant be greater than the hypotenuse.
now we have to find which is correct between a and b
the answer will be 'B' as the value of sine of an angle keeps increasing as the angle itself increases. thus, giving a bigger value of the opposite side (required height). as 15.4 ft.
mathematically,
sin65° = x/17
17 × sin65° = x
where x is height of the side of the building.
when the correlation between two variables begins as a direct correlation, then becomes an indirect correlation, or vice versa, what relationship exists?
Answers
The relationship between two variables that begins as a direct correlation and then becomes an indirect correlation, or vice versa, is known as a nonlinear correlation.
A nonlinear correlation is when the relationship between two variables is not linear - that is, the correlation between them does not increase or decrease proportionately as one variable increases or decreases. Nonlinear correlations are important in research as they can suggest that a phenomenon is more complex than a linear correlation would indicate.
For example, if two variables have a direct linear correlation, then a small increase in one variable would result in a predictable increase in the other. However, with a nonlinear correlation, a small increase in one variable may result in a much larger or much smaller increase in the other. This suggests that other factors, not captured in the linear correlation, are influencing the relationship between the two variables.
Nonlinear correlations can be positive (the two variables increase or decrease together), negative (one variable increases as the other decreases, or vice versa), or both. Depending on the circumstances, the type of nonlinear correlation can have important implications for the research question being studied.
It is important to note that nonlinear correlations may be caused by a variety of factors, including chance, measurement errors, or the presence of an extraneous variable that has not been accounted for. As such, they should always be further investigated and not taken as an absolute conclusion.
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Debora deposits $5000 into a savings account. The bank promises to provide an annual interest rate of 5%, compounded yearly. Assuming that Debora keeps the money in her bank account and does not withdraw any funds, calculate the value of her investment after 10 years
Answers
After 10 years, Debora's investment of $5000 in the savings account with a 5% annual interest rate, compounded yearly, will grow to approximately $6,633.16.
To calculate the value of Debora's investment after 10 years, we can use the formula for compound interest:
\(A = P(1 + r/n)^(nt)\)
Where:
A is the final amount (the value of the investment after the given time period)
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, Debora deposits $5000 into the savings account with an annual interest rate of 5%, compounded yearly. Plugging in the values into the formula:
\(A = 5000(1 + 0.05/1)^(1*10)\)
Simplifying the calculation:
\(A = 5000(1.05)^10\)
Using a calculator or computing the value iteratively, we find:
A ≈ 5000 * 1.628895
A ≈ 6,633.16
Therefore, after 10 years, Debora's investment of $5000 in the savings account will grow to approximately $6,633.16. This means that the investment will accumulate approximately $1,633.16 in interest over the 10-year period, given the 5% annual interest rate compounded yearly.
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