Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7. 26cm and a standard deviation of 0. 43cm. Using the empirical rule, what percentage of the apples have diameters that are less than 8. 12cm?
Answers
Using the empirical rule states that for a bell-shaped distribution, approximately 95% of the apples have diameters that are less than 8.12cm.
68% of the data falls within 1 standard deviation of the mean, approximately 95% falls within 2 standard deviations of the mean, and approximately 99.7% falls within 3 standard deviations of the mean.
Here, we are given that the mean diameter of the apples is 7.26 cm and the standard deviation is 0.43 cm. We want to find the percentage of apples with diameters less than 8.12 cm, which is 0.86 cm greater than the mean.
To find the number of standard deviations that 8.12 cm is from the mean, we can use the formula z = (x - μ) / σ, where z is the number of standard deviations from the mean, x is the value we want to convert, μ is the mean, and σ is the standard deviation.
z = (8.12 - 7.26) / 0.43 = 1.99
This means that 8.12 cm is approximately 1.99 standard deviations above the mean. Using the empirical rule, we know that approximately 95% of the data falls within 2 standard deviations of the mean.
Since 1.99 is less than 2, we can estimate that the percentage of apples with diameters less than 8.12 cm is approximately 95%.
Therefore, we can estimate that approximately 95% of the apples have diameters that are less than 8.12cm.
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Related Questions
kylie works for a large nursery and is investigating whether to use a new brand of seeds. the new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. she will change over to this new brand unless the actual germination rate is less than what is advertised. kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. she finds that 70 of those seeds germinated. what are the null and alternative hypotheses for this hypothesis test?
Answers
The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93, Hₐ : p > 0.93.
What is Hypothesis ?A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
What is Null and Alternative Hypotheses?Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Let 'p' be the population proportion.
Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.
Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some difference,
Hence, the null and alternative hypotheses for this hypothesis test will be :- H₀ : p = 0.93
Hₐ : p > 0.93
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A line with a slope of 7 passes through the points (2,–8) and (4,z). What is the value of z?
Answers
Answer:
z : 6
Step-by-step explanation:
points: (2,-8) and (4, 6)
Sam is stacking cans of vegetables at the Store His shelf is 10 inches tall, 10 inches deep, and 50 inches wide The cans are 4 inches tall and each has a volume of 50 24 in³ How many cans will fit on the shelf?
Answers
Answer:
48
Step-by-step explanation:
You want to know the number of cans 4 inches tall with a volume of 50.24 in³ that will fit on a shelf with a height and depth of 10 inches and a length of 50 inches.
DiameterThe diameter of the can will be found from the volume formula:
V = (π/4)d²h
d = √(4V/(πh)) = √(4·50.24/(4·3.14)) = √16 = 4 . . . inches
The cans are 4 inches in diameter.
NumberThe number of cans that will fit in each dimension will be the integer part of the dimension divided by the size of the can in that dimension.
Height: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans high
Depth: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans deep
Length: (50 in/4 in/can) = 12.5 cans . . . . cans will fit 12 cans long
A total of 2 × 2 × 12 = 48 cans will fit on the shelf.
__
Additional comment
There will be 2 inches of empty space in each direction.
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Suppose there are two individuals in the society, and 4 possible allocations. The net benefit for each individual in each allocation is given below: (The two numbers in each of the following brackets indicate the net benefits for individual 1 and individual 2, respectively.)
Outcome A: (10,25)
Outcome B: (20,10)
Outcome C: (14,20)
Outcome D: (15,15)
Suppose it is impossible to make transfers between the two individuals.
____ are Pareto efficient outcomes.
a. A and C only
b. A,C, and D
c. A and B only
d. C and D only
e. A only
f. A,B,C, and D
Answers
only Outcome D is a Pareto efficient outcome. In this given scenario, "A and D" are Pareto efficient outcomes.What is Pareto efficiency? Pareto efficiency is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.
What are the given allocations and benefits of individuals? The net benefit for each individual in each allocation is given below: (The two numbers in each of the following brackets indicate the net benefits for individual 1 and individual 2, respectively.) Outcome A: (10, 25) Outcome B: (20, 10) Outcome C: (14, 20)Outcome D: (15, 15) Which of the outcomes are Pareto efficient?
Now, let's see which of the given outcomes are Pareto efficient: Outcome A: If we take Outcome A, then individual 1 gets 10 and individual 2 gets 25 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome B, then individual 1 gets 20 which is greater than 10 as his net benefit, and the net benefit for individual 2 would become 10 which is still greater than 25. Therefore, Outcome A isn't Pareto efficient. Outcome B: If we take Outcome B, then individual 1 gets 20 and individual 2 gets 10 as their net benefits.
But the allocation isn't Pareto efficient because if we take Outcome C, then individual 1 gets 14 which is less than 20 as his net benefit, and the net benefit for individual 2 would become 20 which is greater than 10. Therefore, Outcome B isn't Pareto efficient.Outcome C: If we take Outcome C, then individual 1 gets 14 and individual 2 gets 20 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome A, then individual 1 gets 10 which is less than 14 as his net benefit, and the net benefit for individual 2 would become 25 which is greater than 20. Therefore, Outcome C isn't Pareto efficient.
Outcome D: If we take Outcome D, then individual 1 gets 15 and individual 2 gets 15 as their net benefits. The allocation is Pareto efficient because there is no other allocation where one individual will be better off without harming the other individual.Therefore, only Outcome D is a Pareto efficient outcome.
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if f(x)=3x-4 and g(x)=9x^2-16, find f o g and g o f
Answers
Given that f(x)=3x-4 and g(x)=9x^2-16.
The value of f o g can be obtained as follows:
\(\begin{gathered} f\circ g=f(g(x)) \\ =f(9x^2-16) \\ =3(9x^2-16)-4 \\ =27x^2-48-4 \\ =27x^2-52 \end{gathered}\)The value of g o f can be obtained as follows:
\(\begin{gathered} g\circ f=g(f(x)) \\ =9(3x-4)^2-16 \\ =9(9x^2-24x+16)-16 \\ =81x^2-216x+144-16 \\ =81x^2-216x+128 \end{gathered}\)What ratio is equivalent to 96 : 108
Answers
Answer:
8/9
Step-by-step explanation:
both numbers are multiples of 9
Answer:
8:9 uwu
Step-by-step explanation:
Hope this helps everyone
In how many ways can you select two people from a group of 15 if the order of selection is not important?
Answers
Answer:
105 ways
Step-by-step explanation:
Because the order of selection does not matter, we know that we will be using a combination instead of a permutation.
₁₅C₂ = 15! / (2! * 13!)
= 15 * 14 * ... * 2 * 1 / 2 * 1 * 13 * 12 * ... * 2 * 1
= 15 * 14 / 2 * 1 (The 13! cancels out)
= 105
Answer:
105 ways, because the order of selection does not matter, we know that we will be using a combination instead of a permutation.
find the area of the following regions. the region inside the lemniscate r^2=42cos20 and outside the circle r=sqrt(21)
Answers
The area of region inside lemniscate is 23.73 square units.
To find the area of the region inside the lemniscate and outside the circle, we first need to sketch the graphs of both equations.
The polar graph of the lemniscate is given by r^2 = 42 cos(2θ), which has a central point and two loops that intersect at the origin.
The polar graph of the circle is given by r = √21, which has a center at the origin and a radius of √21.
To find the area of the region inside the lemniscate and outside the circle, we need to subtract the area of the circle from the area of the lemniscate.
Using the polar area formula, we can find the area of the lemniscate and circle as follows:
Area of lemniscate = (1/2) ∫(π/4)0 [√(42cos(2θ))]^2 dθ + (1/2) ∫(5π/4) (3π/4) [√(42cos(2θ))]^2 dθ
= (1/2) ∫(π/4)0 42cos(2θ) dθ + (1/2) ∫(5π/4) (3π/4) 42cos(2θ) dθ
= 21 [sin(2θ)]|(π/4)0 + 21 [sin(2θ)]|(3π/4)(5π/4)
= 21 [sin(π/2) - sin(0) + sin(5π/2) - sin(3π/2)]
= 84 square units
Area of circle = π(√21)^2 = 21π square units
Therefore, the area of the region inside the lemniscate and outside the circle is:
Area = Area of lemniscate - Area of circle
= 84 - 21π
≈ 23.73 square units
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Scott works on cars. He charges a $75 repair fee plus $10 per hour. If Dave was charged $100 by Scott to work on his car, then 1) write an equation that represents the hours, h, Scott worked on his car. How many hours did Scott work on Dave's car?
Answers
Answer:
equation: y= 10x + 75
Hours (x)= 2.5 hours
Step-by-step explanation:
y= 10x + 75
100 = 10x + 75
-75 -75
25 = 10x
/10 /10
x = 2.5
Answer:
1). Inequality: 10h + 75 = 100.
2). Scott worked on his car for 2.5 hours.
Show Work:
Finding out The Inequality -
Sign: = (Equal Sign)
Variable: h (h for hours)
Coefficient: $10 per hour
Constant: $75 repair fee
Total: $100 was charged
Inequality: 10h +75 = 100
Figuring out the Inequality
10h +75 = 100
-75 - 75
0 25
10/10 = 1 25/10 = 2.5
h = 2.5
Explain:
With the Inequality I made with the Key concepts of the Word problem, I Started to answer the Question. First, I Subtracted 75 from 100 and 75, so I can see the Amount of Money Dave owes Scott without the Repair fee. 75 - 75 = 0, so I crossed it out, and 100 - 75 = 25. Then I bought the 10h down, so I could Divide it so I can get the Variable and the Answer together. So Because 10 was being Multiplied to the Variable h, I Had to do the opposite, so I divided 10÷10, and 25÷10. 10÷10 = 1, so I crossed it out, and 25÷10 = 2.5. So Scott worked on Dave's car for 2 and a half hours.
(23 pts) Let X and Y have joint density f XY (x,y)=24xy f XY (x,y)=\ matrix 24xy&x>=0,y>=0,x+y<=1\\ 0&otherwise matrix
Find the marginal density of X / Y
(1)
Answers
To find the marginal density of X/Y, we need to integrate the joint density function fXY(x, y) over the range of Y. By performing the integration, we obtain the marginal density of X/Y as a function of X. The resulting marginal density provides information about the distribution of the ratio X/Y.
The marginal density of X/Y can be obtained by integrating the joint density function fXY(x, y) over the range of Y. In this case, the joint density function is given by:
fXY(x, y) =
24xy if x >= 0, y >= 0, and x + y <= 1
0 otherwise
To find the marginal density of X/Y, we integrate fXY(x, y) with respect to y, while keeping x as a constant. The integration limits for y can be determined based on the given conditions x >= 0, y >= 0, and x + y <= 1. Since y must be non-negative, the lower limit of integration is 0. The upper limit of integration can be determined by the constraint x + y <= 1, which implies y <= 1 - x.
Integrating fXY(x, y) over the range of y, we obtain the marginal density of X/Y as follows:
fX/Y(x) = ∫[0 to (1 - x)] 24xy dy
Evaluating the integral, we have:
fX/Y(x) = 24x * ∫[0 to (1 - x)] y dy
= 24x * [(y^2)/2] evaluated from 0 to (1 - x)
= 12x * (1 - x)^2
The resulting marginal density fX/Y(x) represents the distribution of the ratio X/Y. It provides information about the likelihood of different values of X/Y occurring. The shape of the distribution can be further analyzed to understand the characteristics of the random variable X/Y.
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The graph shown below suggests:
A. a negative correlation.
B. no correlation
C. a weak correlation.
D. a positive correlation.
Answers
Answer:
B. no correlation
Step-by-step explanation:
Where in the cell does chromatin (DNA) found? A. endoplasmic reticulum B. Golgi bodies c. Mitochondria
Answers
A
Correct me if I’m wrong
A bunch of ballons contains many different colors. red 17 purple 11 orange 3 green 1 yellow 2 What is the probability that a randomly selected balloon will be red? Write your answer as a fraction or whole number.
Answers
Answer: 1/2
Step-by-step explanation:
Number of red balloons = 17
Number of purple balloons = 11
Number of orange balloons = 3
Number of green balloons = 1
Number of yellow balloons = 2
Total number of balloons = 34
The probability that a randomly selected balloon will be red will be:
= Number of red balloons/Total number of balloons
= 17/34
= 1/2
please answer fast and explain your answer.
Answers
Answer:
the sale price of the flip flops after tax is $12.87.
Step-by-step explanation:
To calculate the sale price of the flip flops after tax, we need to consider both the discount and the sales tax. Here's how we can calculate it:Calculate the discounted price:
The flip flops cost $15, and there is a 20% discount. To find the discounted price, we subtract the discount amount from the original price:
Discounted price = $15 - (20% of $15)
To calculate the discount amount, we multiply the original price by the discount percentage (expressed as a decimal):
Discount amount = 20% of $15 = 0.20 * $15Discounted price = $15 - (0.20 * $15)Calculate the sale price after tax:
After applying the discount, we need to calculate the sales tax on the discounted price. To do this, we add the sales tax amount to the discounted price:
Sale price after tax = Discounted price + (7.25% of Discounted price)
To calculate the sales tax amount, we multiply the discounted price by the sales tax percentage (expressed as a decimal):
Sales tax amount = 7.25% of Discounted price = 0.0725 * Discounted priceSale price after tax = Discounted price + (0.0725 * Discounted price)Now, let's substitute the values and calculate:Discounted price = $15 - (0.20 * $15) = $15 - ($3) = $12Sale price after tax = $12 + (0.0725 * $12) = $12 + $0.87 = $12.87
the value of the expression\[(2^{1004} 5^{1005})^2-(2^{1004}-5^{1005})^2\]is $k\cdot10^{1004}$ for some positive integer $k$. what is $k$?
Answers
The value of K is 20
The LHS (Left Hand Side) reduces to 2 x 10^1005
2 x 10^1005 =k x 10^1004
k =[2 x10^1005] / [10^1004] = 2 x 10
k =20
A positive integer is defined as a whole number greater than zero. All counting numbers are included in the set of positive integers.
Positive numbers include: 1, 2, 88, 800, 9000, and so on. Positive numbers are whole numbers with the symbol (+) in front of the numerical value. Most of the time, the plus sign is simply represented without the symbol. Positive numbers outnumber negative numbers and zero. On the number line, positive numbers are represented to the right of zero
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whats the equation of the line that goes through the points (6,8) and (-2,3)
Answers
Answer:
y = 5/8x + 17/4
Step-by-step explanation:
y2 - y1 / x2 - x1
3 - 8 / -2 - 6
5/8
y = 5/8x + b
3 = 5/8(-2) + b
3 = -5/4 + b
17/4 = b
Find an equation in point-slope form for the line having the slope m =1/3 and containing the point (-3,- 6).
Answers
consider the results of a poll where 48% of 331 americans who decide to not go to college do so because they cannot afford it. calculate a 90% confidence interval for the proportion of americans who decide to not go to college because they cannot afford it.
Answers
The 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it can be calculated using a statistical formula. The formula for a confidence interval is: CI = p ± zsqrt((p(1-p))/n)
Where CI is the confidence interval, p is the proportion of interest (in this case, 0.48 or 48%), and z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.645 for 90% confidence), sqrt is the square root function, and n is the sample size (in this case, 331).
Plugging in the values, we get:
CI = 0.48 ± 1.645sqrt((0.48(1-0.48))/331)
CI = 0.48 ± 0.062
Thus, the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is (0.418, 0.542). This means that we can be 90% confident that the true proportion of Americans who decide not to go to college because they cannot afford it falls between 41.8% and 54.2%.
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3. The area A of a triangle varies jointly as the base b and the altitude h of the triangle. If the area
of a triangle is 70 cm2 when the base is 14 cm and the altitude is 10 cm, find the area if the base is
8 cm and the altitude is 12 cm.
Answers
Answer:
48cm²
Step-by-step explanation:
If the area A of a triangle varies jointly as the base b and the altitude h of the triangle, this is expressed as;
A = kbh
k is the constant of proportionality
If A = 70cm², b = 14cm and h = 10cm
Substitute
70 = k(14)(10)
70 = 140k
k = 70/140
k = 0.5
To get the area if base is 8 cm and the altitude is 12 cm;
A = 0.5*8*12
A = 48cm²
Hence the required area is 48cm²
A potter is designing a large ceramic planter to grow herbs in. He wants to spin it on his potter’s wheel and fire it in his kiln. Before he begins, he needs to determine the dimensions of his pot so that he knows it will have enough volume to hold a bag of potting soil. The potter has drawn a 2-D view of the planter. Assume the base of the pot has a radius of 7 inches in all directions.
Answers
The volume of the pot is = 731.2 cubic inches.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured.
The space occupied within an object's borders in three dimensions is referred to as its volume.
It is sometimes referred to as the object's capacity.
Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.
Since the forms of various three-dimensional objects vary, so do their volumes.
According to our answer-
volume of a pot is = πr²h + 2πr³
22/7 * 698/3
731.2 cubic inches
Hence, The volume of the pot is = 731.2 cubic inches.
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x³- 16x write factorize
Answers
Answer:
x(x+4)(x−4)
Step-by-step explanation:
Factor x3−16x
x3−16x
=x(x+4)(x−4)
Answer:
x³-16x
x(x²-4²)
x(x+4)(x-4) is your answer
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BIG IDEAS MATH
0
The triangle shown is an equilateral triangle. What is the perimeter of the triangle?
5-2x
-4x+9
Answers
3
equilateral so 5-2x=-4x+9
x=2
5-2×2=1
the trainangle is equilateral and has three sides
1+1+1=3
Seattle star blends whole bean coffee worth $3. 00 per pound to get 25 pounds of a coffee blend worth $3. 50 per pound. How many pounds of both blends does she use?
Answers
Seattle start blends uses zero pound of the $3 per pound blend and 25 pounds of $3.5 per pound blend.
In order to solve this we setup a linear equation. We assume the $3 per pound blend used to be x. So, the $3.5 per pound blend used will be equal to (25 - x) .
Now, from the information given we setup equation as
(3.00/pound * x pounds) + (3.50/pound * (25 - x) pounds) = 3.50/pound × 25 pounds
On Solving for x, we get:
3.00/pound * x pounds + 3.50/pound * 25 pounds - 3.50/pound * x pounds = 3.50/pound * 25 pounds
3.00/pound * x pounds - 3.50/pound * x pounds = 0
0.50/pound * x pounds = 0
x = 0
So, the $3 per pound blend is equal to zero while the $3.5 per pound blend is equal to (25 - x) = 25.
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Solve:2/3 - 4x +7-2= -9.x +5/6
x = -3/2
x = -2/3
X=2/3
X=3/2
Answers
Answer:
2/3-4x+7-2=-9.x+5/6
2/3+7/1-2/1-5/6=-9.x+4x
12+126-36-15/18=-5x
87/18=-5x
29/6=-5x
29/6÷5=-5x÷5
29/6*1/5=-5x÷5
29/30=-x
-29/30=x
-0.9667=x
10. 8, 12, 14
Notas
Acute
Right
Obtuse
Answers
Saul's Corner Market sells large candy bars for $2 each. A bag of pretzels is $3. On Tuesday, the store sold twice
as many candy bars as Monday but the same number of pretzels. On Wednesday, the store sold the same
number of candy bars as Monday but only half the amount of pretzels. On Thursday, the store sold three times
as much as they sold on Tuesday. On Friday, the store sold 12 fewer candy bars and 5 more bags of pretzels
compared to Wednesday.
Let c represent the number of candy bars sold and p represent the number of pretzels sold on Monday. Write
an expression for each day to show the amount of money that the store brought in from candy bars and
pretzels.
1. Monday
2. Tuesday
3. Wednesday
4. Thursday
5. Friday
6. Monday through Friday
Answers
Answer:
Step-by-step explanation:
Monday: c and p
Tuesday: 2c+p
Wednesday: 2c+p/2
Thursday: 6c+3p/2
Friday: (2c-12)+(p/2+5)
Adding them all up, you get, for Monday-Friday: (13c-12)+(9p/2+5)
I'm not sure how to explain this to you though, you just follow the directions they gave, to multiply and subtract.
Hope this is helpful!
PLEASE HELP ME ANSWER THESE 2 QUESTIONS!! I beg you
Answers
Answer:
mgmgmmbmb
Step-by-step explanation:
40404
44
4
5
5
(2/3) ⋅ (5/9)
i just need the answer.
Answers
Answer:
10/27
Step-by-step explanation:
A scientist pours two liquids into a flask and swirls the flask to combine the liquids. The scientist then places the flask on a laboratory workbench. After a few seconds, the liquids separate into two layers. How are the contents of the flask classified?
Answers
when both are mixed and left to settle, they separate into two layers with oil on top and water underneath.
When a scientist pours two liquids into a flask and swirls the flask to combine the liquids, and then places the flask on a laboratory workbench, after a few seconds, the liquids separate into two layers.
This phenomenon is possible if the two liquids are immiscible.
The contents of the flask can be classified as immiscible liquids.
Immiscible liquids are liquids that do not mix to form a homogenous solution.
They separate into distinct layers instead. When two immiscible liquids are mixed together and then left to settle, they create a two-layer system, with one layer on top of the other.
In general, two liquids are said to be immiscible if the free energy change in mixing them is positive or if the entropy change in mixing them is negative.
A practical example of immiscible liquids is oil and water.
They are unable to mix with each other since oil is nonpolar while water is polar.
As a result, when both are mixed and left to settle, they separate into two layers with oil on top and water underneath.
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PLZZ HELP ASAP
Order these numbers from least to greatest
Answers
Answer:
1.4722, 2.901, 2.9, 2.91
Step-by-step explanation: