We have been given that a right circular cone has a height of 12.2 cm and a base with a circumference of 18.5 cm. We are asked to find the volume of the cone to nearest tenth.
We know that circumference of circle is equal to [tex]2\pi r[/tex].
[tex]2\pi r=18.5[/tex]
[tex]r=\frac{18.5}{2\pi}[/tex]
[tex]r=2.944366[/tex]
Now we will use volume of the cone formula to solve our given problem.
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
[tex]V=\frac{1}{3}\pi (2.944366)^2\cdot (12.2)[/tex]
[tex]V=\frac{1}{3}\pi (8.669291141956)\cdot (12.2)[/tex]
[tex]V=\frac{1}{3}\pi (105.7653519318632)[/tex]
[tex]V=\frac{1}{3}(332.2716526334804752)[/tex]
[tex]V=110.7572175[/tex]
Upon rounding to nearest tenth, we will get:
[tex]V\approx 110.8[/tex]
Therefore, the volume of the given cube would be approximately 110.8 cubic centimeter.
Final answer:
To find the volume of a right circular cone, the base radius is calculated from the circumference, and then the volume is determined using the cone volume formula V = (1/3)πr²h, with the final result being rounded to the nearest tenth. So, [tex]\( V \approx 110.415 \) cm^3[/tex].
Explanation:
To calculate the volume of a right circular cone, we first need to determine the radius of the base which can be found from the circumference. Since the formula for circumference is C = 2πr, where C is the circumference and r is the radius, we can solve for r. For a circumference of 18.5 cm, we have:
18.5 = 2πr => r = 18.5 / (2π)
Now that we have the radius, the volume of the cone can be found using the formula:
V = (1/3)πr²h
Plugging in the radius and height:
V = (1/3) * π * (18.5 / (2π))² * 12.2
After performing the calculation, we can round the result to the nearest tenth to find the volume in cubic centimeters.
Let's calculate it:
1. [tex]\( \frac{18.5}{2\pi} \) \approx \( \frac{18.5}{6.28319} \) \approx 2.942881[/tex]
2. Square the result: [tex]\( (2.942881)^2 \) \approx 8.66347[/tex]
3. Multiply by 12.2: [tex]\( 8.66347 \times 12.2 \)[/tex] ≈ 105.685554
4. Multiply by [tex]\( \frac{1}{3} \) and \( \pi \)[/tex]:
[tex]\( V = \frac{1}{3} \times \pi \times 105.685554 \)[/tex]
Now, let's calculate \( V \):
[tex]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx 110.415 \][/tex]
So, [tex]\( V \approx 110.415 \) cm^3[/tex].
A package has dimensions 10x10x6 inches mrs James wants to gift a wrap it for her grandson what is the total surface area to be wrapped?
Answer:
440 square inches
Step-by-step explanation:
10x10x2=200
10x6x4=240
240+200=440
Which formula should be used to find the circumference of a circle?
C =πd
C=2πd
C=πr C=π/d
NEED HELP ASAP !
Answer:
C = πd or 2πr
Step-by-step explanation:
2r equals d
2r = d
Kelly walks 4/5 of a mile each day. How many miles does Kelly walk after three days?
Answer:
Kelly walks 4/5 of a mile each day.
After 3 days, Kelly walks a distance: D = 3 x 4/5 = 12/5 = 2.4 miles
Hope this helps!
:)
Kelly walks 4/5 of a mile each day, and after three days, she would have walked 2 and 2/5 miles.
Kelly walks 4/5 of a mile each day. To find out how many miles Kelly walks after three days, we simply multiply the daily distance by three.
Calculation:
4/5 mile/day * 3 days = 12/5 miles
To convert 12/5 miles into a mixed number, we divide 12 by 5. The quotient is 2 with a remainder of 2, so Kelly walks 2 and 2/5 miles after three days.
How is a net useful when finding the surface area or prisms and pyramids?
Answer:oh yeah I remember that
Step-by-step explanation:
That’s tuff
A rectangular field is 0.3 kilometers long and 0.15 kilometers wide. What is the area of the field in square meters?
Final answer:
To find the area of the rectangular field in square meters, convert the dimensions from kilometers to meters and then multiply them together, resulting in 45,000 square meters.
Explanation:
To calculate the area of a rectangular field that is 0.3 kilometers long and 0.15 kilometers wide, use the following steps:
Convert the dimensions from kilometers to meters. Since there are 1,000 meters in a kilometer, the length in meters is 0.3 km × 1,000 = 300 meters and the width is 0.15 km × 1,000 = 150 meters.Multiply the length and width in meters to get the field's area in square meters. So the area is 300 m × 150 m = 45,000 square meters.Which equation represents an exponential function with an initial value of 500?
Answer:
the fourth one
Step-by-step explanation:
Answer:
Answer: f(x) = 500(2)^x
Step-by-step explanation:
Just took the test .
I=$54, P=$900, t=18 months
Answer:
about $982.20
Step-by-step explanation:
Formula = P(1+I)^T
T =18/12 because its in months not years, so 1.5 years
1+I = 1 + 54/900 or 1.03
P = 900
Plug those in and you get about 982.20
Answer:
4%
Step-by-step explanation:
For the simple interest rate,
I=P(i)t
54=900(i)(18/12)
i=54/900*(12/18)=4% annually
The per capita electric power consumption level in a recent year in Ecuador is normally distributed, with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilowatt-hours. Random samples of size 35 are drawn from this population. Find (a) the mean and (b) the standard deviation of the sampling distribution of sample means. Round the answer from part (b) to the third decimal place.
Answer:
a) 471.5 kilo-watt hours.
b) 31.76 kilo-watt hours
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.
For the population:
Mean 471.5 kilo-watt hours.
Standard deviation of 187.9 kilowatt-hours.
For the sample:
Sample size of 35, by the Central Limit Theorem:
a) Mean
471.5 kilo-watt hours.
b) Standard deviation
[tex]s = \frac{187.9}{\sqrt{35}} = 31.76[/tex]
31.76 kilo-watt hours
Final answer:
The mean of the sampling distribution of sample means is 471.5 kilo-watt hours, and the standard deviation (or standard error) of the sampling distribution, rounded to the third decimal place, is 31.749 kilo-watt hours.
Explanation:
The question concerns the concept of sampling distribution and its parameters, namely the mean and standard deviation, within the field of statistics. Given that the per capita electric power consumption level in Ecuador is normally distributed with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilo-watt hours, and considering samples of size 35, we are to find the mean and standard deviation of the sampling distribution of sample means.
(a) The mean of the sampling distribution of sample means is equal to the population mean. Therefore, the mean is:
471.5 kilo-watt hours
(b) The standard deviation of the sampling distribution of sample means, also known as the standard error (SE), is calculated using the following formula:
SE = σ / √n
where σ is the population standard deviation and n is the sample size. In this case:
SE = 187.9 / √35 ≈ 31.749 kilo-watt hours (rounded to the third decimal place)
Each student in a statistics class had a randomly assigned bag of candies and counted the number of each color (Blue, Red, Orange, Green, Brown, Yellow). The bags were all the same size. The investigators claimed to use a randomized block design, with Bag as the blocking factor. They counted the number of candies of each color in each bag. Their results are reproduced in the given ANOVA output. Complete parts (a) through (c).
Source Degrees Sum of Mean F-ratio P-value
of Freedom Squares Square
Bag 13 4.726 0.364 0.10 1.000
Color 6 350.679 70.136 18.72 <0.001
Error 65 243.488 3.746
Total 83 598.893
(a) Was this an observational or experimental study?
(b) What was the treatment? What factors were manipulated?
A. The factors were color and bag and the treatments were all possible combinations of those two factors.
B. The factors were bag and student and the treatments were all possible combinations of those two factors.
C. The factors were color and student and the treatments were all possible combinations of those two factors
D. There is no treatment. No factors were manipulated.
(c) What was the response variable?
Answer:
Step-by-step explanation:
Hello!
a)
An observational study is one where the investigator has no control or intervenes on it. He just defines the variable of interest and merely collects and documents the information. These types of studies are usually made as precursors to a more formal experimental study, to have an idea of what's to be expected from the population.
An experimental study or experiment is one where the investigator intervenes by defining the variable of interest and artificially manipulates the study factor. It is also one of its characteristics the randomization of cases or subjects in groups (two or more, depending on what is the hypothesis of study).
In this example, the investigators used a randomized block design with "Bag" as the blocking factor and assigned the bags randomly to the students of the statistic class.
The researchers manipulated all confounding factors in this experiment leaving only "the number of candies per color per bag" as the only random variable. This is an experimental study.
b)
This is an ANOVA with two factors, "Bag" and "Colour" and the treatments are all possible combinations between these two factors.
Correct Option A.
c) The response variable is the "number of candies per color per bag"
Colors: Blue, Red, Orange, Green, Brown and Yellow.
I hope you have a nice day!
Select the correct answer.
Which value of x makes the equation true?
x + 7 = -9
A. -16
B. -2
C. 2
D. 16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
The given equation is x+7=-9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
x+7=-9
Transpose 7 to RHS of the equation, we get
x=-9-7
=-16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
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f(1) = -16
f(n) = f(n-1) · (-1/2)
f(3) =
Answer:
-4
Step-by-step explanation:
Use the given value of f(1) to find f(2):
f(2) = f(1) · (-1/2) = (-16)(-1/2) = 8
Now, we can find f(3) using f(2):
f(3) = f(2) · (-1/2) = (8)(-1/2)
f(3) = -4
Factor the expressions.
x2 + 25x + 24 =
Answer:
(x +1)(x +24)
Step-by-step explanation:
Factors of 24 that have a sum of 25 are 1 and 24. These are the constants you need in the binomial factors:
x^2 +25x +24 = (x +1)(x +24)
How many possible outcomes exist when Louisa spins the spinner below twice? A spinner with 8 equal sections labeled 1 through 8. 8 10 16 64
Answer:
64
Step-by-step explanation:
The spinner has 8 equal sections numbered from 1 to 8
Each time she spinns the spinner has 8 possible outcomes.
To know the number of possible results when spinning two times, you must multiply the possible results for the first spin (8 possible outcomes) by the possible results for the second spin (also 8 possible outcomes).
And because each spin has the same number of outcomes:
[tex]8*8=64[/tex]
the answer is that there are 64 possible outcomes
Answer:
64
Step-by-step explanation:
Jasmine has 3 and 3/8 pound of Turkey meat she is making 1/3 pound Turkey burgers does Jasmine have enough meat to make 12 Turkey burgers
Answer:
No
Step-by-step explanation:
To answer this you have to divide 3 and 3/8 by 1/3. The easiest way to do this without a calculator is to do this separately. First divide 3 by 1/3. When dividing fractions, the second number is flipped upside down and the two numbers are multiplied. From 3 pounds, Jasmine will be able to make nine 1/3 pound burgers.
3 ÷ 1/3 = 3 × 3/1 = 9
Next, divide 3/8 by 1/3. From 3/8 pounds, Jasmine will be able to make 1 1/8 burgers
3/8 ÷ 1/3 = 3/8 × 3/1 = 9/8 = 1 1/8
Add the two numbers together.
9 + 1 1/8 = 10 1/8
This is less than 12.
To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Jasmine has 3 and 3/8 pounds of turkey meat
Amount in pounds needed to make 1 burger = 1/3 pound
Number of burgers in 3 3/8 ⇒
(3 3/8)/(1/3) = 10 1/8
For making 12 Turkey burgers ⇒
Amount of meat required = 12 × 1/3 = 4 pounds
Hence "To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers".
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An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question.
Do you regularly recycle plastic bottles?
Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816)
How many students were in the sample selected by the environmental science teacher?
Answer:
60 students
Step-by-step explanation:
The confidence interval of a proportion is given by:
[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]
Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.
If the confidence interval is from 0.584 to 0.816, then:
[tex]p=\frac{0.584+0.816}{2}=0.7 \\0.816-0.584=2*(1.96*\sqrt{\frac{p*(1-p)}{n}}) \\0.116=1.96*\sqrt{\frac{0.7*(1-0.7)}{n}}\\n=16.8966^2*(0.7*0.3)\\n=60\ students[/tex]
60 students were in the sample.
Final answer:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher used a random sample and calculated a 95 percent confidence interval. Using the formula for the confidence interval for proportions, we can determine that the teacher selected approximately 223 students for the survey.
Explanation:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher selected a random sample of students and surveyed them one at a time, asking them if they regularly recycle plastic bottles. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816).
To find out how many students were in the sample selected by the teacher, we need to use the formula for the confidence interval for proportions:
n = (Z^2 * p * (1-p)) / (E^2)
Where:
n is the sample size,
Z is the Z-score corresponding to the desired level of confidence (in this case, 95 percent),
p is the estimated proportion of students who recycle plastic bottles (we can use the midpoint of the confidence interval, which is (0.584 + 0.816) / 2 = 0.7),
E is the margin of error (in this case, half the width of the confidence interval, which is (0.816 - 0.584) / 2 = 0.116).
Plugging in the values, we get:
n = (1.96^2 * 0.7 * (1-0.7)) / (0.116^2)
n = 2.992 / 0.013456
n ≈ 222.38
Since the sample size must be a whole number, we round up to the nearest whole number.
Therefore, the teacher selected approximately 223 students for the survey.
Which exponential expressions are equivalent to the one below? Check all
that apply.
(5x9)^12
Answer:D
Step-by-step explanation:
(5x9)^12
5^12 x 9^12
Labor statistics indicate that 77% of all U.S. cashiers and servers are women. A random sample of cashiers and servers in a particular metropolitan area found that 112 of 150 cashiers and 150 of 200 servers were women. At the 0.05 level of significance, is there sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population? What is the test statistic? Round to 2 decimal places.
Final Answer:
The test statistic for the difference in proportions between the metropolitan area and the U.S. population is approximately ( -0.11 ). Since this value does not exceed the critical value of [tex]\( \pm 1.96 \)[/tex] at the 0.05 significance level, there is insufficient evidence to conclude a significant difference. Therefore, we fail to reject the null hypothesis.
Step-by-step explanation:
To determine whether there is sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population, we can perform a hypothesis test for the difference in proportions.
Let:
[tex]\( p_1 \)[/tex] be the proportion of women in the metropolitan area.
[tex]\( p_2 \)[/tex] be the proportion of women in the larger U.S. population.
The null hypothesis [tex](\( H_0 \))[/tex] is that there is no difference between the proportions, and the alternative hypothesis [tex](\( H_1 \))[/tex] is that there is a significant difference.
The formula for the test statistic for the difference in proportions ( z ) is given by:
[tex]\[ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{p(1-p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} \][/tex]
Where:
[tex]\( \hat{p}_1 \)[/tex] and [tex]\( \hat{p}_2 \)[/tex] are the sample proportions of women in the metropolitan area and the U.S. population, respectively.
( p ) is the combined sample proportion.
[tex]\( n_1 \)[/tex] and [tex]\( n_2 \)[/tex] are the sample sizes for the metropolitan area and the U.S. population, respectively.
First, let's calculate [tex]\( \hat{p}_1 \)[/tex], [tex]\( \hat{p}_2 \)[/tex], ( p ), and then plug them into the formula to find the test statistic.
[tex]\[ \hat{p}_1 = \frac{112}{150} = 0.7467 \][/tex]
[tex]\[ \hat{p}_2 = \frac{150}{200} = 0.75 \][/tex]
[tex]\[ p = \frac{112 + 150}{150 + 200} = \frac{262}{350} = 0.7486 \][/tex]
Now, we can calculate the test statistic:
[tex]\[ z = \frac{(0.7467 - 0.75)}{\sqrt{0.7486(1-0.7486)\left(\frac{1}{150} + \frac{1}{200}\right)}} \][/tex]
Calculate the values and round the test statistic to two decimal places. If the absolute value of the test statistic is greater than the critical value for a two-tailed test at the 0.05 significance level, we reject the null hypothesis.
Note: The critical value for a two-tailed test at the 0.05 significance level is approximately [tex]\( \pm 1.96 \)[/tex].
a. The number 86,362,575 rounded to the nearest hundred is
Answer:
86362600
Step-by-step explanation:
We want to round to the hundreds place
We look at the 7 in the tens place. Since it is 5 or greater we round up
86,362,575 round to 86362600
Answer:
86,362,600
Step-by-step explanation
If Zoe paints the visible outside faces of her shed, what is the total surface area that she paints? Alternative Text A. 48 ft2 B. 64 ft2 C. 96 ft2 D. 112 ft2
The total surface area that she paints will be 96 square feet. Thus, the correct option is C.
What is the area of the rectangle?Let W be the rectangle's width and L its length. The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be given as,
Area of the rectangle = L × W square units
Given that:
Length, L = 12 ft
Width, W = 8 ft
The area of the rectangle is given as,
A = 12 x 8
A = 96 square feet
Thus, the correct option is C.
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The missing diagram is given below.
Sketch the region of integration and evaluate the following integral. ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper R StartFraction 1 Over 3 plus StartRoot x squared plus y squared EndRoot EndFraction dA , RequalsStartSet (r comma theta ): 0 less than or equals r less than or equals 2 comma StartFraction pi Over 2 EndFraction less than or equals theta less than or equals StartFraction 3 pi Over 2 EndFraction EndSet
Answer:
[tex]\frac{10\pi}{3}[/tex]
Step-by-step explanation:
According to the information of the problem we have to compute the following integral.
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA[/tex]
Where the region of integration is
[tex]R = \Big\{ (r,\theta) : 0 \leq r \leq 2 , \,\,\,\, \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \Big\}[/tex]
If you plot, that is just a circle between [tex]\pi/2[/tex] and [tex]3\pi/2[/tex], which is just half of the circle on the negative part of the plane.
When you switch coordinates
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA = {\displaystyle \int\limits_{0}^{2} \int\limits_{\pi/2}^{3\pi/2}} \bigg(\frac{1}{3} + r \bigg)r \, d\theta\, dr = \frac{10\pi}{3}[/tex]
Which of the following is the inverse of y = 12 Superscript x? y = log Subscript one-twelfth Baseline x y = log Subscript 12 Baseline StartFraction 1 Over x EndFraction y = log Subscript x Baseline 12 y = log Subscript 12 Baseline
The inverse of the function is logx/log12
The inverse of a functionGiven the function expressed as:
y = 12^x
To find the inverse, switch the variables to have:
x = 12^y
Take the log of both sides
logx = y log 12
y = logx/log12
Hence the inverse of the function is logx/log12
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You are in charge of buying office supplies for your business. Your workers use red and black pens. Red pens cost $5 per box and black pens cost $3 per box. You need at least 10 boxes of pens. You want no more than 7 boxes of black pens and no more than 6 boxes of red pens. You want to minimize the cost to your business.
The objective function for this situation is C = 5x + 3y. What (x, y) pair minimizes cost?
image
(6, 7)
(0, 7)
(3, 7)
(6, 4)
Answer:
C. (3, 7)
Step-by-step explanation:
plug all the numbers into all of the coordinates and (3, 7) is the lowest number :) pls rate 5 stars and thank me
The option of buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business, based on the objective function C = 5x + 3y and the given constraints of at least 10 boxes in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
Explanation:To minimize the cost of buying office supplies, particularly red and black pens, we need to use the given objective function C = 5x + 3y where x represents the number of boxes of red pens and y represents the number of boxes of black pens. We have the following constraints: at least 10 boxes of pens in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
By applying these constraints, we can determine the combinations of x and y that meet the criteria:
x + y ≥ 10 (at least 10 boxes of pens)x ≤ 6 (no more than 6 boxes of red pens)y ≤ 7 (no more than 7 boxes of black pens)Looking at the choices provided, (6, 4) meets all our constraints, and when plugged into the objective function:
C = 5(6) + 3(4) = 30 + 12 = $42
This results in the lowest cost when compared to the other presented options. Therefore, buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business.
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WHO IS GREAT AT MATH!!! PLEASEE HELPP MEE IN MATH WITH THIS PROBLEM PLEASEEE!!!! I need assistance!!! WILL BE MARKING BRAINLIEST FOR A REWARD BECAUSE PEOPLE PUT RANDOM ANSWERS TO JUST GET THE POINTS BUT ANYWAY PLEASEEEE PLEASEEE PLEASEE HELPP MEEEE!!!!!!!!!
Answer:
x=32, y=36, and z=25
Step-by-step explanation:
There are only two sums the equations can all add up to, 67 degrees and 113 degrees. I know that to the equation with x is equal to 67 degrees.
2x+3=67
2x=64 (subtract 3)
x=32 (divide by 2)
Now to find the measurement of the other angle, we subtract 180 and 67 since the measurement of a line is 180 degrees.
180-67=113
The equations of y and z are both equal to 113.
3y+5=113 4z+13=113
3y=108 (subtract 5) 4z=100 (subtract 13)
y=36 (divide by 3) z=25 (divide by 4)
Product A requires 9 minutes of milling, 7 minutes for inspection, and 6 minutes of drilling per unit; product B requires 10 minutes of milling, 5 minutes for inspection, and 8 minutes of drilling per unit; product C requires 7 minutes of milling, 3 minutes for inspection, and 15 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $2.0 per unit to profit, product B contributes $2.3 per unit, and product C contributes $4.0 per unit. a. How many constraints are there in the Linear Programming Formulation of this problem
Answer:
The Linear programming problem has 3 constraints :- Milling time, Inspection time, Drilling time constraints.
Step-by-step explanation:
Product A : 9 minutes milling, 7 minutes inspection, 6 minutes drilling Product B : 10 minutes milling, 5 minutes inspection, 8 minutes drilling Product C : 7 minutes milling, 3 minutes inspection, 15 minutes drilling
Total milling time available = 20 hours = (20 x 60) i.e 1200 minutes Total inspection time available = 15 hours = (15 x 60) i.e 900 minutes Total drilling time available = 24 hours = (24 x 60) i.e 1440 minutes
Let QA, QB, QC be quantities of product A, B, C respectively
Milling time constraint : 9QA + 10QB + 7QC = 1200 Inspection time constraint : 7QA + 5QB + 3QC = 900Drilling time constraint : 6QA + 8QB + 15QC = 1440Find the probability selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles when (a) you replace the first marble before drawing the second, and (b) you do not replace the first marble. Then, compare the probabilities. Round your answers to four decimal places.
Step-by-step explanation:
There are a total of 16 marbles, 8 of which are green.
(a) The probability the first marble is green is 8/16.
The marble is replaced, so there are still a total of 15 marbles, 8 of which are green. The probability the second marble is green is 8/16.
The probability of both events is (8/16) (8/16) = 1/4 = 0.2500.
(b) The probability the first marble is green is 8/16.
The marble is not replaced, so there are now a total of 15 marbles, 7 of which are green. The probability the second marble is green is 7/15.
The probability of both events is (8/16) (7/15) = 7/30 = 0.2333.
Final answer:
The probability of selecting a green marble, then another green marble from a bag of marbles is 0.25 when the first marble is replaced and 0.2333 when the first marble is not replaced.
Explanation:
To find the probability of selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles, we need to consider two scenarios: (a) replacing the first marble before drawing the second, and (b) not replacing the first marble.
a) If the first marble is replaced before drawing the second, the probability of selecting a green marble on the first draw is 8/16, and the probability of selecting a green marble on the second draw is also 8/16. We can multiply these probabilities together to get the overall probability: 8/16 × 8/16 = 16/64 = 0.25.
b) If the first marble is not replaced, the probability of selecting a green marble on the first draw is 8/16. However, since the first marble is not replaced, there are only 15 marbles left in the bag for the second draw, with 7 green marbles remaining. The probability of selecting a green marble on the second draw is 7/15. We can multiply these probabilities together to get the overall probability: 8/16 × 7/15 = 56/240 = 0.2333 (rounded to four decimal places).
Comparing the probabilities, we can see that the probability in scenario (a) when the first marble is replaced is higher than the probability in scenario (b) when the first marble is not replaced.
A manufacturing company is ready to introduce a new product with a national sales campaign. After extensive test marketing, the market research department estimates that sales (in millions of dollars) will increase at the monthly rate of S'(t) = 10 - 10e-0.2t for 0 ≤ t ≤ 24, t months after the national campaign has started. What will the total sales be five months after the beginning of the campaign if we assume zero sales at the beginning of the campaign? (Round the answer to the nearest million.)
Final answer:
The total sales five months after the beginning of the campaign is approximately 72 million dollars.
Explanation:
To find the total sales five months after the beginning of the campaign, we need to calculate the definite integral of the sales rate function from t=0 to t=5. The sales rate function can be expressed as S'(t) = 10 - 10e^(-0.2t).
First, let's find the antiderivative of the sales rate function. The antiderivative of 10 is 10t, and the antiderivative of -10e^(-0.2t) is 50e^(-0.2t). Therefore, the indefinite integral of S'(t) is S(t) = 10t - 50e^(-0.2t) + C, where C is the constant of integration.
Next, we evaluate the definite integral over the interval t=0 to t=5. Substituting the upper and lower limits into the antiderivative, we get S(5) - S(0) = (10(5) - 50e^(-0.2(5))) - (10(0) - 50e^(-0.2(0))) = (50 - 50e^(-1)) - (0 - 50e^0) = 50 - 50e^(-1) + 50 = 100 - 50e^(-1) million dollars.
Rounding the answer to the nearest million, the total sales five months after the beginning of the campaign is approximately 72 million dollars.
The average speed of a baseball line drive is 83 miles per hour. Josiah practiced a new technique to improve his hitting speed. His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour. Part A: State the correct hypotheses Josiah is trying to prove the new technique is an improvement over the old technique. (4 points) Part B: Identify the correct test and check the appropriate conditions. (6 points)
Answer:
We conclude that the new technique is not an improvement over the old technique at 5% level of significance.
Step-by-step explanation:
We are given that the average speed of a baseball line drive is 83 miles per hour.
His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour.
Let [tex]\mu[/tex] = true average speed using the new technique.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 83 miles per hour {means that the new technique is not an improvement over the old technique}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 83 miles per hour {means that the new technique is an improvement over the old technique}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed using the new technique = 84.2 mph
s = sample standard deviation = 4.7 mph
n = sample of hits = 42
So, the test statistics = [tex]\frac{84.2-83}{\frac{4.7}{\sqrt{42} } }[/tex] ~ [tex]t_4_1[/tex]
= 1.655
The value of t test statistics is 1.655.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of 1.6832 at 41 degree of freedom for right-tailed test.
Since our test statistic is less than the critical value of t as 1.655 < 1.6832, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the new technique is not an improvement over the old technique.
A mountain climber starts a climb at an elevation of 453 feet above sea level. At his first rest stop he has climbed 162 feet, and by his second rest stop he has climbed another 207 feet. It's getting late in the day, so the climber starts his way down. If the climber descends 285 feet, how much does he need to ascend or descend to return to the original starting point?
A) ascend 84 feet
B) ascend 78 feet
Eliminate
C) descend 84 feet
D) descend 78 feet
Answer:
C) Descend 84 feet
Step-by-step explanation:
162+207=369
369-285=84ft above starting point, this means that he must descend 84 feet to reach the starting point.
write a number with two decimal places, that is bigger than 4 wholes and 1/5 but smaller than 4.25
Answer :
11.45
step-by-step explantion :
4.25=17/4
when we add 41/5 and 17/4, we get
41×4+17×5/4×5
164+65/20
229/20
11.45 Ans
:
A survey of 76 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.55 minutes. The population standard deviation was 12 minutes. Construct a 95% confidence interval for the average time that a commercial flight of under 2 hours is late. What is the point estimate? What does the interval tell about whether the average flight is late?
Answer:
The best point of estimate for the true mean is:
[tex]\hat \mu = \bar X = 2.55[/tex]
[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]
[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]
Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.
Step-by-step explanation:
Information given
[tex]\bar X=2.55[/tex] represent the sample mean for the late time for a flight
[tex]\mu[/tex] population mean
[tex]\sigma=12[/tex] represent the population deviation
n=76 represent the sample size
Confidence interval
The best point of estimate for the true mean is:
[tex]\hat \mu = \bar X = 2.55[/tex]
The confidence interval for the true mean is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level given is 0.95 or 95%, th significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got [tex]z_{\alpha/2}=1.96[/tex]
Replacing we got:
[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]
[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]
Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.