Answer:
1.19% probability that fewer than 101 commuters drive to work alone
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]p = 0.75, n = 150[/tex]
[tex]\mu = E(X) = 150*0.75 = 112.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.75*0.25} = 5.3[/tex]
(a) What is the probability that fewer than 101 commuters drive to work alone
Using continuity corretion, this is [tex]P(X < 101-0.5) = P(X < 100.5)[/tex], which is the pvalue of Z when X = 100.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100.5 - 112.5}{5.3}[/tex]
[tex]Z = -2.26[/tex]
[tex]Z = -2.26[/tex] has a pvalue of 0.0119
1.19% probability that fewer than 101 commuters drive to work alone
The probability that fewer than 101 U.S. commuters drive to work alone, based on a 75% solo driving rate, is calculated using the binomial probability formula, resulting in the answer.
To solve this problem, we can use the binomial probability formula, as this is a binomial distribution (success/failure) with a known probability of success.
The formula for the probability mass function of a binomial distribution is:
[tex]\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k} \][/tex]
where:
-[tex]\( n \)[/tex] is the number of trials (sample size),
- [tex]\( k \)[/tex] is the number of successful outcomes,
- [tex]\( p \)[/tex]is the probability of success on a single trial.
In this case, [tex]\( n = 150 \)[/tex] (number of commuters),[tex]\( p = 0.75 \)[/tex] (probability of driving alone), and we want to find the probability that fewer than 101 commuters drive alone (\( k < 101 \)).
[tex]\[ P(X < 101) = P(X \leq 100) = \sum_{k=0}^{100} \binom{150}{k} \cdot 0.75^k \cdot (1 - 0.75)^{150 - k} \][/tex]
Now, we can use a calculator or statistical software to compute this probability. Keep in mind that the binomial coefficient[tex]\(\binom{n}{k}\)[/tex] is the number of ways to choose \(k\) successes from \(n\) trials and can be calculated as[tex]\(\frac{n!}{k! \cdot (n - k)!}\).[/tex]
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At the fair 4 employees were paid $8.75 an hour to work at a funnel cake stand. They worked 8 hours at regular pay then for 5 hours at overtime pay for extra $2.50 an hour.How much did each employee earn?
Answer:
$125.25
Step-by-step explanation:
8.75*h+11.25*e
h is hours regular pay and e is extra pay for overtime. Since its an extra $2.50 for overtime, add that to the regular pay. Put in the hours:
[tex]8.75*8+11.25*5[/tex]
Simplify by multiplying 8.75 by 8
[tex]70+11.25*5[/tex]
Simplify by multiplying 11.25 by 5
[tex]70+56.25[/tex]
Add
[tex]70+56.25=126.25[/tex]
Since it says how much did each earn, as in individually, leave it as it is (unless regular pay was $2.18 an hour, which would be a rip-off). I'm pretty sure including the number of employees was meant to throw you off.
Ms. Burke invested $23,000 in two accounts, one yielding 4% interest and the other yielding 10%. If she received a total of $1,280 in interest at the end of the year, how much did she invest in each account?
Answer:
$17,000 at 4%$6,000 at 10%Step-by-step explanation:
Let x represent the amount invested at 10%. Then 23000-x is the amount invested at 4%, and the total interest is ...
0.10x +0.04(23000-x) = 1280
0.06x = 360 . . . . . subtract 920, simplify
x = 6000 . . . . . . . . divide by the coefficient of x
Ms Burke invested $6000 at 10% and $17000 at 4%.
Two married couples have purchased theater tickets and are seated in a row consisting of just 4 seats. If they take their seats in a completely random order, what is the probability that at least one of the wives ends up sitting next to her husband? Hint: Use probability of a complement event. That is, P(A) = 1 − P(A′), where A′ is the complement of an event A.
Answer:
The answer is 0.75.
Step-by-step explanation:
To use probability of a complement event, we need to find the situation where none of the couples are sitting next to each other which can happen either two husbands are sitting in the seats 2 and 3 or two wives are sitting in the seats 2 and 3. Also in the first scenario, the wives would need to be sitting at the opposite ends to their husbands and vice versa for the second scenario.
So there are in total 4 scenarios where no couple is sitting next to each other.
There are a total of 16 different ways that they can be seated so the probability of compelement is 16 - 4 = 12, which is 3/4 of the total, meaning that the probability of at least one of the wives sittting next to her husband is 0.75 or 75%.
I hope this answer helps.
A product with an annual demand of 1000 units has Co = $25.50 and Ch = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with μ=25 and σ=5. a.What is the recommended order quantity? b. What are the recorder point and safety stock if the firm desires at most a 2% probability of stockout on any given order cycle? c. If a manager sets the reorder point at 30, what is the probability of a stockout on any given order cycle? How many times would you expect a stockout during the year if the reorder point were used?
Answer:
a) Recommended order quantity = 79.84 = 80
b) recorder point = 35
Safety stock = 10
Safety stock cost = $0/year
ci) P(stock out/cycle) = 0.1587
cii) Number of stock outs/ year = 2
Step-by-step explanation:
The pictures attached show a clear explanation of all the processes.
Final answer:
To determine the recommended order quantity, use the EOQ formula. The reorder point and safety stock can be calculated using the normal distribution. If the reorder point is set at 30, the probability of a stockout and the expected number of stockouts can be calculated.
Explanation:
To determine the recommended order quantity, we need to consider the economic order quantity (EOQ) model. The EOQ formula is given by:
EOQ = √((2 * D * Co) / Ch)
Where:
D is the annual demand (1000 units)
Co is the ordering cost per order ($25.50)
Ch is the holding cost per unit ($8)
Plugging in the values, we get:
EOQ = √((2 * 1000 * 25.50) / 8) = 79.79 (rounded to 2 decimal places)
Therefore, the recommended order quantity is 80 units.
To calculate the reorder point, we need to consider the lead-time demand. Since the lead-time demand follows a normal probability distribution with μ=25 and σ=5, we can use the normal distribution to find the reorder point.
To calculate the recorder point and safety stock for a desired probability of stockout of 2%, we need to find the Z value corresponding to the desired probability. We can use the Z-score table or a calculator to find the Z value. For a 2% probability of stockout, the Z value is approximately -2.05 (rounded to 2 decimal places).
The reorder point is given by:
Reorder Point = μ + (Z * σ)
Where:
μ is the mean of the lead-time demand (25 units)
Z is the Z value (-2.05)
σ is the standard deviation of the lead-time demand (5 units)
Plugging in the values, we get:
Reorder Point = 25 + (-2.05 * 5) = 14.75 (rounded to 2 decimal places)
The safety stock is given by:
Safety Stock = Z * σ
Plugging in the values, we get:
Safety Stock = -2.05 * 5 = -10.25 (rounded to 2 decimal places)
Therefore, the recorder point is approximately 15 units (rounded to the nearest whole unit) and the safety stock is approximately 10 units (rounded to the nearest whole unit).
If the manager sets the reorder point at 30 units, we can use the normal distribution to find the probability of a stockout. The probability of a stockout can be calculated using the Z-score formula.
The Z value is calculated using the formula:
Z = (Reorder Point - μ) / σ
Where:
Reorder Point is the given reorder point (30 units)
μ is the mean of the lead-time demand (25 units)
σ is the standard deviation of the lead-time demand (5 units)
Plugging in the values, we get:
Z = (30 - 25) / 5 = 1 (rounded to 1 decimal place)
Looking up the Z value in the Z-score table, we find that the corresponding probability is approximately 0.8413. Therefore, the probability of a stockout on any given order cycle is approximately 0.1587 or 15.87% (rounded to 2 decimal places).
The number of times you would expect a stockout during the year can be estimated using the formula:
Number of Stockouts = (Annual Demand / EOQ) * (1 - Probability of Stockout)
Plugging in the values, we get:
Number of Stockouts = (1000 / 80) * (1 - 0.1587) = 10.69 (rounded to 2 decimal places)
Therefore, you would expect a stockout approximately 11 times during the year (rounded to the nearest whole number).
14) World Wide Insurance Company found that 53% of the residents of a city had homeowner’s insurance (H) with the company. Of these clients, 27% also had automobile insurance (A) with the company. If a resident is selected at random, find the probabil- ity that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company.
Answer:
The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 14% (P=0.1431).
Step-by-step explanation:
The probability of having homeowner’s insurance (H) with the company is P(H)=0.53.
The probability that, given that the resident has homeowner insurance with the company, also had a automobile insurance is P(A|H)=0.27.
We have to calculate P(A&H): probability of having automovile and homeowner:
[tex]P(A\&H)=P(H)*P(A|H)=0.53*0.27=0.1431[/tex]
Answer:
The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.
Step-by-step explanation:
We are given that:
53% of the residents had homeowner's insurance i.e. P(H) = 0.53
Of these people, 27% also had automobile insurance i.e. they had automobile insurance given that they had homeowner's insurance. So, P(A|H) = 0.27.
We need to find out the probability that the resident has both homeowner's and automobile insurance i.e. P(A and H) or P(A∩H). To compute P(A∩H) we will use the conditional probability formula:a
P(A|B) = P(A∩B)/P(B)
Here we have:
P(A|H) = P(A∩H)/P(H)
P(A∩H) = P(A|H) * P(H)
= 0.27 * 0.53
P(A∩H) = 0.143
The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.
Do flashcards help students retain the Chinese Language? Six randomly selected students are given a pretest, asked to study a set of flashcards once a day for a week and then given post test for their Chinese Language class. Is there evidence that flashcards can improve scores? Their data is below. What is the test statistic?(pretest – posttest)
Answer:
-1.64
Explanation:
Multiple Choice Answers that were not provided in the question:
a. 0.103 .
b. None of the above.
c. -4.16
d. -1.45
e. 2.86
f .-1.64
The provided data is as below:
Student 1 Student 2 Student 3 Student 4 Student 5 Student 6
Pre- test 80 76 76 50 48 67
Post- test 75 86 87 60 48 68
Further Explanation:
Student 1 Student 2 Student 3 Student 4 Student 5 Student 6
Pre- test 80 76 76 50 48 67
Post- test 75 86 87 60 48 68
Pretest-Postest 5 -10 -11 -10 0 -1
Calculating the mean of the difference (Pretest-postest) we get d bar = -4.5
Calculating the standard deviation of the difference (Pretest-postest) we get sd= 6.716.
Since sample score is under 30 and population standard deviation is unknown, we will use a tscore to find the standardized test statistic
t = dbar/(sd/√n) = -4.5/(6.716√6) = -1.642 ≈ -1.64
The test statistic is -1.64.
You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ = 60.8 H a : μ ≠ 60.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 8 with mean M = 66.9 and a standard deviation of S D = 10.7 . What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = -.1228 Incorrect The p-value is... less than (or equal to) α greater than α Correct This p-value leads to a decision to... reject the null accept the null fail to reject the null Incorrect
Answer:
Step-by-step explanation:
This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 60.8
For the alternative hypothesis,
µ ≠ 60.8
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8,
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 66.9
µ = population mean = 60.8
s = samples standard deviation = 10.7
t = (66.9 - 60.8)/(10.7/√8) = 1.61
We would determine the p value using the t test calculator. It becomes
p = 0.076
Since alpha, 0.01 < than the p value, 0.076, then we would fail to reject the null hypothesis. Therefore, At a 1 % level of significance, the sample data showed that there is no significant evidence that μ ≠ 60.8
Therefore, this p-value leads to a decision to accept the null hypothesis
solve the system equations -x-y=0 and 6x-5y=66 by combining the equations
Answer:
x,y(6.-6)
Step-by-step explanation:
{x=-y
6(-y)-5y=66
-6-5y=66
11y=66
y=6
-x-y=0
x=-y;
x=-6
6.6.1. Rao (page 368, 1973) considers a problem in the estimation of linkages in genetics. McLachlan and Krishnan (1997) also discuss this problem and we present their model. For our purposes, it can be described as a multinomial model with the four categories C1, C2, C3 , and C4 . For a sample of size n, let X = (X1, X2, X3 , X4 )′ denote the observed frequencies of the four categories. Hence, n = +4 i=1 Xi. The probability model is
Answer:
Step-by-step explanation:
find attached the solution
Write parametric equations of the line 9x + y = -1
a. X= 1, y = -9z+ 9
b. X= 1, y =--9
C. X= t_y= 9- 1
d. X= 1, y=-97- 1
The question is faulty written. I'll solve it assuming values for one variable and provide the answer to guide the student in their own question
Answer:
x=t
y=-1-9t
Step-by-step explanation:
Parametric Equations
Given an explicit relation between variables x and y, we can find expression for both of them in term of a third parameter t, such as
x=f(t)
y=g(t)
provided the main relation holds.
we have the equation
9x+y=-1
There are infinitely many forms to find parametric expressions for the variables, let's assume
x=t
Solving the equation for y
y=-1-9x=-1-9t
Thus the parametric equations are
x=t
y=-1-9t
The blacksmith had two identical iron wires, which were used for making two chains containing 80 and 100 links accordingly. Each of the links in the shorter chain was 5 grams heavier than that in the longer one. What was the weight of each chain ?
PLEASE HELP I NEED THIS NOW!!!
Answer:
2kg is the answer
ok well let's see it's 2000 grams
A manufacturer of brand A jeans has daily production costs of Upper C equals 0.3 x squared minus 114 x plus 11 comma 405, where C is the total cost (in dollars) and x is the number of jeans produced. How many jeans should be produced each day in order to minimize costs? What is the minimum daily cost?
Answer:
190 Jeans
Step-by-step explanation:
The daily production cost of the jeans manufacturer is given as:
[tex]C=0.3x^2-114x+11405[/tex]
To determine the number of Jeans,x that should be produced daily to minimize cost, C. We take the derivative of C and solve for its critical points.
[tex]C'=0.6x-114\\$When C'=0\\0.6x-114=0\\0.6x=114\\x=190[/tex]
Therefore, to minimize daily cost, 190 Jeans is the number of jeans that should be produced daily.
Find the volume of a cone with a diameter of 40cm and a height of 40 cm.
Answer:
[tex]v = \pi {r}^{2} \frac{h}{3} \\ \: \: \: \: = \pi \times 20 \frac{40}{3} \\ \: \: \: \: = 16755.16 {cm}^{3} [/tex]
hope this helps you
Paul plays a video game that is scored by round . In about 500 rounds his career average is 20 points per round with a standard deviation of 5 points per round . Suppose we take random samples of past 3 rounds and calculate the mean number of points scored in each sample . What is the mean and sd of sampling distribibution
Answer:
The mean of the sampling distribution is 20 and the standard deviation is 2.89.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Mean 20, standard deviation of 5.
Sampling distribution:
3 rounds
Mean = 20
[tex]s = \frac{5}{\sqrt{3}} = 2.89[/tex]
The mean of the sampling distribution is 20 and the standard deviation is 2.89.
Final answer:
The mean of Paul's sampling distribution is 20 points per round, and the standard deviation is approximately 2.89 points per round, calculated using the formula for the standard error of the mean.
Explanation:
The scenario involves a sampling distribution of the mean scores over random samples of 3 rounds from Paul's video game scores. To calculate the mean and standard deviation (sd) of the sampling distribution, we use the following formulas:
The mean of the sampling distribution (μX) is equal to the population mean (μ), which is 20 points per round.The standard deviation of the sampling distribution (σX), also known as the standard error, is equal to the population standard deviation (σ) divided by the square root of the sample size (n), so σX = σ/√n. In this case, it would be 5/√3, approximately 2.89 points per round.Therefore, the mean of the sampling distribution is 20, and the standard deviation is approximately 2.89.
A circle has a radius of square root 98 units and is centered at (5.9, 6.7). Write the equation of this circle. Please help!
Given:
Given that the radius of the circle is √98 units.
The circle is centered at the point (5.9, 6.7)
We need to determine the equation of the circle.
Equation of the circle:
The general form of the equation of the circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is the center and r is the radius of the circle.
Substituting the center point (h,k) = (5.9, 6.7) and r = √98, we get;
[tex](x-5.9)^2+(y-6.7)^2=(\sqrt{98})^2[/tex]
Simplifying, we get;
[tex](x-5.9)^2+(y-6.7)^2=98[/tex]
Thus, the equation of the circle is [tex](x-5.9)^2+(y-6.7)^2=98[/tex]
the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]
We know that the equation of circle is given by the formula:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
here h and k are the x and y coordinates of the center of circle and r is the radius. It is given to us that:
Radius = √98 units
Center at (5.9, 6.7)
Putting values into the equation we get:
[tex](x - 5.9)^2 + (y - 6.7)^2 = (\sqrt{98})^2\\\\ (x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]
Therefore, the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]
An "x-bar" control chart is developed for recording the mean value of a quality characteristic by use of a sample size of three. The control chart has control limits (LCL and UCL) of 1.000 and 1.020 pounds, respectively. If a new sample of three items has weights of 1.023, 0.999, and 1.025 pounds, what can we say about the lot (batch) it came from?
Answer:
0.0879 or 8.79 % is the process capability of the batch and the batch doesn't meet the control limits.
Step-by-step explanation:
mean of three readings=(1.023+0.999+1.025)/3= 1.0157
standard deviation=√((1.023-1.0157)² + (0.999-1.0157)²+ (1.025-1.0157)²)/3)
= 0.0163
Process Capability= min((USL-mean)/3SD, (Mean-LSL)/3SD)
(USL-mean)/3SD= (1.02-1.0157)/(3×0.0163)= 0.0879
(Mean-LSL)/3SD)= (1.0157-1.00)/(3×0.0163)= 0.321
Process capability=(0.0879,0.321)
0.0879 or 8.79 % is the process capability
The x-bar control chart and other statistical tools are used to assess whether product weights are within acceptable limits, thereby determining if quality standards are met and if equipment recalibration might be necessary.
Explanation:The question involves evaluating if a batch of products (in this case, potentially cereal boxes, soda servings, lifting weights, apples, or lettuce) meets certain quality control standards, specifically relevant to the weights and measurements being within predefined control limits or tolerances. Using an x-bar control chart and statistical methods like hypothesis testing or calculating percent uncertainty, quality control specialists can determine whether a product's quality characteristic, such as weight, is within acceptable ranges, thereby assessing if equipment recalibration is needed or if a batch complies with quality standards.
For instance, if a new sample of items has weights that fall outside of the established control limits on the x-bar control chart, it would suggest that there may be an issue with the process control, indicating potential problems with the lot from which the sample was taken.
Concerning the exercises provided: In the case of the cereal boxes with a standard deviation higher than the acceptable limit, it suggests that recalibration might be needed. For the Class A apples, a hypothesis test at the specified significance levels would help determine compliance with weight tolerance. Calculating the percent uncertainty of a bag's weight informs us about the relative size of the uncertainty in measurements.
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−6y+13+9y=8y−3 How many solutions are there? A. No solutions
B. One solution
C. Infinite solutions
Answer:
B. One solution
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
-6y + 13 + 9y = 8y - 3
Step 2: Solve for y
Combine like terms: 13 + 3y = 8y - 3[Addition Property of Equality] Add 3 on both sides: 16 + 3y = 8y[Subtraction Property of Equality] Subtract 3y on both sides: 16 = 5yRewrite: 5y = 16[Division Property of Equality] Divide 5 on both sides: y = 16/5∴ We can see by solving the equation, we get 1 solution only.
The linear equation has one solution after simplifying and isolating the variable y, which results in y = 16/5.
Explanation:When solving the given linear equation −6y + 13 + 9y = 8y − 3, the first step is to simplify and collect like terms. Begin by combining the terms with y on the left side: 3y + 13 = 8y − 3. Next, move the terms with y to one side by subtracting 3y from both sides: 13 = 5y − 3. Lastly, isolate y by adding 3 to both sides and then dividing by 5: y = rac{16}{5}. Since we have successfully isolated y and found a specific value for it, the equation has one solution.
A rectangular prism has a volume of 120 square feet a height of 15 feet and a width of 4 feet find the length
Volume = length x width x height
120 = 15 x 4 x length
Simplify:
120 = 60 x length
Divide both sides by 60:
Length = 2 feet
Formula for the volume of a rectangular prism: V = length x width x height
120 = l x 4 x 15
120 = l x 60
l = 2
The length of the rectangular prism is 2 feet.
Hope this helps!! :)
If f(-3) = -8, then f(x)= 3x +
Answer:
f(x)= 3x + 1
Step-by-step explanation:
Let's set the unknown variable as b, since it's a linear equation.
Using the point given (-3, -8), we can find b by plugging in the known numbers and solving.
-8 = -3 (3) + b
-8 = -9 + b
b = 1
If you want, you can check it by forming the complete equation and plugging in -3.
f(x)= 3x + 1
f(-3) = -9 + 1
f(-3) = -8 = -8
I hope this helped!
A metal rod is being carried down a corridor which is 7 feet wide.At the end of the corridor there is a right-angle turn (to the right) into a wider corridor whichis 8 feet wide. What is the length of the longest metal rod which can be carried horizontallyaround the right-angle turn
Answer:
Length of the longest metal rod which can be carried horizontally around the right-angle turn is 21.21ft
Step-by-step explanation:
Length of the longest metal rod which can be carried horizontally around the right-angle turn, can be determined at the point at where the distance between one end of rod and the 7feet corridor is same as the distance between other end of the rod and the 8feet corridor. How do I mean.
The length of longest metal rod will be determined when distance between the one end of rod and the 7feet corridor and the distance between other end of the rod and the 8feet corridor are both 15ft (7ft + 8ft).
See attachment for illustration.
Therefore using Pythagoras theorem we can find the length of longest metal rod that can be carried horizontally around the right angle turn
See illustration in attachment
i.e
Hyp² = opp²+adj²
Hyp = √(15²+15²)
Hyp = √450
Hyp = 21.21ft
Find the cubic unit make sure to put cubic units after your answer
Answer:
24 cubic units
Step-by-step explanation:
4 times 2 times 3 equals 24
Csc^2 u -cos u sec u=cot^2 u
Step-by-step explanation:
csc²u − cos u sec u
csc²u − 1
cot²u
About 8 million tons of plastic waste enters the world’s oceans every year. Write a y = mx equation to show this
Answer: [tex]y=8x[/tex]
Step-by-step explanation:
For this exercise it is important to remember that the equation of a line that passes through the origin (this is located at the point [tex](0,0)[/tex]), has the following form:
[tex]y=mx[/tex]
Where "m" is the slope of the line.
In this case, according to the information given in the exercise, you know that 8 million tons of plastic waste enters the world’s oceans every year, apprdoximately.
Then, let the independent variable "x" represents the number of years.
Analizing the data given, you can identify that the slope of that line is the following:
[tex]m=8[/tex]
So, knowing the value of "m", you can subsitute them into the equation [tex]y=mx[/tex], in order to get the equation that shows that situation.
This is:
[tex]y=8x[/tex]
Choose the graph of the function. g(x)=2.5x
Answer:
the graph that matches the function is
Step-by-step explanation:
What is the simplification if (x+2)(x+7)
The supervisor of a production line wants to check if the average time to assemble an electronic component is different from 14 minutes. Assume that the population of assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes. How would you calculate the p-value for the hypothesis test
Answer:
The p-value for the hypothesis test is 0.0042.
Step-by-step explanation:
We are given that the supervisor of a production line wants to check if the average time to assemble an electronic component is different from 14 minutes.
Assume that the population of assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes.
Let [tex]\mu[/tex] = average time to assemble an electronic component.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 14 minutes {means that the average time to assemble an electronic component is equal to 14 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 14 minutes {means that the average time to assemble an electronic component is different from 14 minutes}
The test statistics that will 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)
where, [tex]\bar X[/tex] = sample average time for completion = 11.6 minutes
[tex]\sigma[/tex] = population standard deviation = 3.4 minutes
n = sample of components = 14
So, test statistics = [tex]\frac{11.6-14}{\frac{3.4}{\sqrt{14} } }[/tex]
= -2.64
Now, P-value of the hypothesis test is given by the following formula;
P-value = P(Z < -2.64) = 1 - P(Z [tex]\leq[/tex] 2.64)
= 1 - 0.99585 = 0.0042
Hence, the p-value for the hypothesis test is 0.0042.
The p-value for the hypothesis test is approximately 0.0082
To calculate the p-value for the hypothesis test, follow these steps:
1. State the null and alternative hypotheses:
- Null hypothesis (\(H_0\)): The average assembly time is 14 minutes. \( \mu = 14 \)
- Alternative hypothesis (\(H_1\)): The average assembly time is different from 14 minutes. \( \mu \ne 14 \)
2. Determine the test statistic:
Since the population standard deviation (\(\sigma\)) is known, use the \( z \)-test for the mean. The test statistic is calculated using the formula:
[tex]\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \][/tex]
where:
- \(\bar{x}\) is the sample mean,
- \(\mu\) is the population mean under the null hypothesis,
- \(\sigma\) is the population standard deviation,
- \(n\) is the sample size.
Given:
[tex]\(\bar{x} = 11.6\) minutes,\\ \(\mu = 14\) minutes,\\ \(\sigma = 3.4\) minutes,\\ \(n = 14\).[/tex]
Plug these values into the formula:
[tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} \][/tex]
3. Calculate the value of the test statistic:
[tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} = \frac{-2.4}{3.4 / \sqrt{14}} \approx \frac{-2.4}{0.9087} \approx -2.64 \][/tex]
4. Find the p-value:
The p-value for a two-tailed test is calculated by finding the probability that the test statistic is at least as extreme as the observed value, under the null hypothesis.
[tex]\[ p\text{-value} = 2 \times P(Z \leq z) \][/tex]
Since we have a \( z \)-score of -2.64, we look up the cumulative probability for \( Z = -2.64 \) in the standard normal distribution table or use a calculator to find:
[tex]\[ P(Z \leq -2.64) \approx 0.0041 \][/tex]
Therefore:
[tex]\[ p\text{-value} = 2 \times 0.0041 = 0.0082 \][/tex]
5. Interpret the results:
Compare the p-value to the significance level (\(\alpha\)) to make a decision. Typically, \(\alpha\) is set at 0.05. If the p-value is less than \(\alpha\), we reject the null hypothesis.
In this case:
[tex]\[ p\text{-value} = 0.0082 \][/tex]
Since \(0.0082 < 0.05\), we reject the null hypothesis. There is significant evidence to suggest that the average assembly time is different from 14 minutes.
So, the p-value for the hypothesis test is approximately 0.0082.
What shapes have all sides that are different lengths
Answer:
Scalene Triangles
Step-by-step explanation:
Isosceles triangles have one pair of equivalent edges, and equilateral triangles of course have all equivalent edges, it would obviously be the scalene triangles.
I am joyous to assist you at any time.
how many cups are equal to 34 pint
By using multiplication, there are 68 cups is equal to 34 pints.
Given that,
Change the number 34 pint into cups.
Used the concept of measurement unit,
A measurement unit is a standard quality used to express a physical quantity. Also, it refers to the comparison between the unknown quantity with the known quantity.
Since we know that;
1 pint = 2 cups
Hence, we get;
34 pint = 34 x 2 cups
= 68 cups
Therefore, the number of cups in 34 pints is 68.
To learn more about multiplication visit:
brainly.com/question/10873737
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The sun shines at a 60° angle to the ground. How long is the shadow cast
by a 20 ft tall flagpole?
Answer:
11.55 ft
Step-by-step explanation:
tan 60° = 20 / x
x = 20 / tan 60° = 20 / √3 = 11.55
The length of the shadow will be 11.55 ft. It is found by the help of the tangent formula of trigonometry.
What is the depression angle?Angle of depression is the angle formed by the horizontal and the place where your head came to a halt.
You keep your gaze level with the ground. When you need to keep an eye on anything, though, you raise your head and lower your gaze.
The given data in the problem is;
Angle of depression = 60°
Length of the shadow(x) = ?
Height of flagpole = 20 ft
From trigonometry formula of tanΘ is;
[tex]\rm tan \theta = \frac{P}{B} \\\\ tan60^0=\frac{20}{x} \\\\ x= \frac{20}{tan60^0} \\\\ x= \frac{20}{\sqrt{3} } \\\\ x=11.55 \ ft[/tex]
Hence, the length of the shadow will be 11.55 ft.
To learn more about the depression angle, refer to the link;
https://brainly.com/question/13514202
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What is the answer of 7/8 x 1/2 equals
Answer:
[tex]\frac{7}{16}[/tex]
Step-by-step explanation:
[tex]\frac{7}{8}[/tex]×[tex]\frac{1}{2}[/tex]
Multiply straight forward:
So 7 and 1. 8 and 2.
7x1=7
8x2=16
[tex]\frac{7}{16}[/tex]