The height and radius of the cone that will use the smallest amount of paper are h ≈ 2.45 cm and r ≈ 1.22 cm, respectively.
The minimum paper will be used when the surface area of the cone is minimized. Let the height and radius of the cone be h and r, respectively. Then, using the formula for the volume of a cone, we have:
V = (1/3)πr^2h = 33 cm^3
Solving for h, we get:
h = 99/(πr^2)
Next, we need to express the surface area of the cone in terms of r. The surface area is given by:
A = πr√(r^2 + h^2)
Substituting the expression for h obtained above, we have:
A = πr√(r^2 + (99/πr^2)^2)
To find the value of r that minimizes A, we take the derivative of A with respect to r and set it equal to zero:
dA/dr = π(2r√(r^2 + (99/πr^2)^2) + (r^2 + (99/πr^2)^2)^(-1/2)(2r(99/πr^3)))
Setting dA/dr = 0 and solving for r, we get:
r = (33/(2π))^(1/4) ≈ 1.22 cm
Substituting this value of r back into the equation for h, we obtain:
h ≈ 2.45 cm
Therefore, the height and radius of the cone that will use the smallest amount of paper are h ≈ 2.45 cm and r ≈ 1.22 cm, respectively.
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suppose that a soup recipe calls for two teaspoons of salt. how many milligrams of sodium is that? ?
Two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.
Given that a soup recipe calls for two teaspoons of salt. We need to find out how many milligrams of sodium is that?
1 teaspoon = 5.69 grams 1 gram = 1000 milligrams
2 teaspoons of salt = 2 * 5.69 grams = 11.38 grams of salt
11.38 grams of salt = 11.38 * 1000 milligrams = 11380 milligrams of salt
Now, we have to find out how much sodium (Na) is there in 11380 milligrams of salt. Sodium chloride is the chemical name for table salt (NaCl). So, the atomic mass of NaCl can be calculated as follows:
Na = 1Cl = 35.45
Atomic mass of NaCl = Na + Cl= 1 + 35.45= 36.45
So, 1 mole of NaCl = 36.45 grams 11380 milligrams of NaCl = 11380/1000 grams= 11.38/36.45 moles
Therefore, Moles of Na = 11.38/36.45 = 0.3121
mol Atomic mass of Na is 22.99 g/mol.
So, 1 mole of Na weighs = 0.3121 * 22.99= 7.16 grams
Therefore, 11380 milligrams of NaCl = 7.16 grams of Na. Hence, two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.
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BRAINLY AND 20 POINTS IF ANSWERED!!!!!! roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds
[ ] meters per second
1.4m/s is the rate that Roberto is walking. We know the formula for calculating the time i.e. t= d/r.
The term "distance" refers to how far we move. The rate is a measurement of our trip speed. Time is measured by how far we travel. The distance an object will travel over time and at a specific average rate is the subject of rate problems.
Given,
Distance = D
D= 1.4t
Rate= ?
Substituting the given values in the formula t= d/r
where,
t= time in seconds
d= distance
r= rate
We get,
t= 1.4t/r
t/1.4t= 1/r
t gets cancelled
so we have,
1/1.4= 1/r
r= 1.4m/s
Therefore, 1.4m/s is the rate at which Roberto is walking.
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The complete question is as follows:
Roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds.
What is the rate that Roberto's walking in meters per second?
Find the measure of the last angle of the triangle below.
28⁰
35°
Measure of last angle of triangle is 117°
Triangle PropertiesThe triangle's characteristics include:
All triangles have a total of 180 degrees in their angles.The length of the longest two sides of a triangle is greater than the length of the third side.The length of the third side of a triangle is shorter than the difference between its two sides.Angle Sum PropertyThe angle sum property states that the sum of a triangle's three interior angles is always 180 degrees.
Angle of Triangle are
28° and 35°
Let the third angle be x
According to angle sum property
28°+35°+x=180°
x=117°
Measure of last angle of triangle is 117°
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The complete question is;
Find the measure of the last angle of the triangle below.
28⁰
35°
Image is attached below.
Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(153, 14.5). z-score when x=108 is _____. The mean is 153. The z-score tell you that x=108 is _____ standard deviations to the left of the mean.
The z-score when x=108 is 3.1034. The z-score tells you that x=108 is 3.1034 standard deviations to the left of the mean.
Z-score is used in statistics to compare a score to a normal distribution. The z-score is a measure of how far away from the mean a value is in standard deviation units.
To find the z-score when x = 108, we use the formula:
z = (x - μ) / σ
where x = 108, μ = 153, and σ = 14.5.
Substituting these values, we get:
z = (108 - 153) / 14.5 = -3.1034
So the z-score when x = 108 is -3.1034.
The z-score tells us how many standard deviations away from the mean a particular value is. In this case, since the z-score is negative, we know that x = 108 is to the left of the mean.
The absolute value of the z-score tells us how many standard deviations away from the mean the value is. In this case, the absolute value of the z-score is approximately 3.1034, which means that x = 108 is approximately 3.1034 standard deviations to the left of the mean.
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You roll a fair 666-sided die. What is \text{P(roll greater than 4})P(roll greater than 4)start text, P, left parenthesis, r, o, l, l, space, g, r, e, a, t, e, r, space, t, h, a, n, space, 4, end text, right parenthesis?
When a 666-sided fair die is rolled, then the probability of rolling greater than 4 is 0.9940 or 99.40%.
Given that the die is fair and has 666 sides. So, each face of the die will have a probability of 1/666, i.e.,
p(1) = p(2) = ... = p(666) = 1/666.
The probability of rolling greater than 4 is P(roll greater than 4), which is the sum of the probabilities of rolling a 5, 6, 7, 8, 9, ..., 666. So,
P(roll greater than 4) = p(5) + p(6) + p(7) + ... + p(666)
P(roll greater than 4) = (1/666) + (1/666) + (1/666) + ... + (1/666)
(There are 661 terms)P(roll greater than 4) = 661(1/666)
P(roll greater than 4) = 0.9940 (rounded to four decimal places)
Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.
Alternatively, the probability of rolling greater than 4 is
1 - P(roll less than or equal to 4)P(roll greater than 4)
= 1 - P(roll less than or equal to 4)P(roll greater than 4)
= 1 - (p(1) + p(2) + p(3) + p(4))P(roll greater than 4)
= 1 - (4/666)P(roll greater than 4)
= 1 - 0.0060P(roll greater than 4)
= 0.9940 (rounded to four decimal places)
Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.
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what is the surface area
Answer: 24
Step-by-step explanation:
Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units.
= 2[(2*2)+(2*2)+(2*2)]
= 2[4+4+4]
=2[12]
24
Your teacher prepares a large container full of colored
beads. She claims that 1/8 of the beads are red, 1/4 are
blue, and the remainder are yellow. Your class will take a
simple random sample of beads from the container to test the teacher's claim. The smallest number of beads you
can take so that the conditions for performing inference
are met is.
15
16
30
40
90
The smallest number of beads we can take so that the conditions for performing inference are met is 40.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probability of two complementary events A and B - A occurring or B occurring - adds up to 1.
According to the Question:
Given in the question,
Teacher prepares a large container filled with colored beads. She claims that 1/8 beads are red, 1/4are blue, and the rest are yellow. Your class will test the teacher's claim by randomly drawing a simple sample of beads from the container.
Quadrant Frequency
1 18
2 22
3 39
4 21
The proportions are 1/8 , 1/4 and 5/8
Here, the smallest probability is 1/8 , thus it would be used to compute the frequency.
Now,
The expected frequencies are calculated as:
E = np₁ = 15 (1/8) = 1.875
E = np₂ = 16(1/8) = 2
E = np₃ = 30(1/8) = 3.75
E = np₄ = 40(1/8) = 5
E = np₅ = 80(1/8) = 10
Here, conditions are fulfilling for 40 and 90 but the smallest sample size is contained by 40. Thus, the correct option is 40.
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Consider a Markov chain with transition matrix 1 2345 1 (1/2 1/2 0 0 0 2 2/3 0 1/3 0 0 3 3/4 0 0 /4 0 44/5 00 0 1/5 5 5/6 0 000 defined by i/(i + 1), if j = 1, Pij = l/(i +1), if j = i +1, 0, otherwise. (a) Does the chain have a stationary distribution? If yes, exhibit the distribution. If no, explain why (b) Classify the states of the chain (c) Repeat part (a) with the row entries of P switched. That is, let 1/(i +1), ifjsl. 0, otherwise
Considering the Markov chain with transition matrix, the chain does have stationary distribution which exhibits State 1 is transient and the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729).
(a) Yes, the chain has a stationary distribution. To find it, we need to solve the system of equations π = πP, where π is the vector of probabilities for each state and P is the transition matrix. This gives us:
π_{1} = π(1/2)
π_{2} = π(1/3) + π(2/2)
π_{3}= π(2/4) + π(3/2)
π_{4} = π(3/5) + π(4/2)
π_{5}= π4/5
We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.
Solving this system of equations, we get:
π_{1} = 10/97
π_{2} = 30/97
π_{3}= 40/97
π_{4} = 14/97
π_{5}= 3/97
So the stationary distribution is (10/97, 30/97, 40/97, 14/97, 3/97).
(b) State 1 is transient, and all other states are recurrent.
(c) Yes, the chain still has a stationary distribution. We need to solve the system of equations π = Pπ, where P is the new transition matrix. This gives us:
π_{1} = π(1/2)
π_{2} = π(1/3) + π(2/2)
π_{3}= π(2/4) + π(3/2)
π_{4} = π(3/5) + π(4/2)
π_{5}= π4/5
We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.
Solving this system of equations, we get:
π_{1} = 2/9
π_{2} = 4/9
π_{3} = 8/27
π_{4} = 16/81
π_{5} = 32/729
So the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729)
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In order to make the same amount of money, they would have to each sell ______ bicycles. They would both make $______.
In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500
How many bicycle would they sell to make the same amount of money?To find the number of bicycles they would need to sell to make the same amount of money,
We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:
250 + 50x = 400 + 20x
30x = 150
x = 5
So they would need to sell 5 bicycles to make the same amount of money.
How much would they make for selling that amountTo find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.
Let's use Jim's equation:
250 + 50(5) = 500
So they would make $500 for selling 5 bicycles.
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tomas has $1,000 to spend on a vacation. his plane ticket costs $348.25. if he stays 5.5 days at his destination, how much can he spend each day? write an inequality and then solve.
Tomas can spend at most $118.50 each day. The inequality equation is 5.5x ≤ 651.75.
Tomas has $1,000 to spend on a vacation. His plane ticket costs $348.25. If he stays 5.5 days at his destination, how much can he spend each day? Write an inequality and then solve.
Let x be the amount that Tomas can spend each day. Since Tomas has to pay for the plane ticket, he will have $1,000 − $348.25 = $651.75 left to spend on the rest of the vacation.
Then, since he is staying for 5.5 days, the total amount he can spend would be 5.5x dollars. The inequality that represents the problem is as follows:
5.5x ≤ 651.75
To solve for x, divide both sides by 5.5
5.5x/5.5 ≤ 651.75/5.5x ≤ 118.5
Therefore, Tomas can spend at most $118.50 each day.
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Answer:
The answer to this solution is 118.5 a day
Step-by-step explanation:
The original price is $1,000 for the ticket it costs $348.25 and Tomas is staying for 5.5 days so dividing 651.75 by 5.5 is the ANSWER 118.5
Determine if the ordered pair (-2, -4) is a solution for equation 2y - 3x = -2.
Answer:
Step-by-step explanation:
2(-4) - 3(-2) = -2
-8 + 6 = -2
-2 = -2
A triangle has one side that measures 1 1/2 inches and another side that measures 2 1/4 inches. The angle between these sides measures 60°. Draw the triangle in the space below. Label the given side lengths and angle measure on the figure. Is it possible to draw a different triangle with those measurements
the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
What is triangle?A triangle is a polygon with three sides, three vertices, and three angles. The sum of the interior angles of a triangle is always 180 degrees, and the longest side of a triangle is opposite to the largest angle, and the shortest side is opposite to the smallest angle. Triangles can be classified according to their side lengths and angles. For example, an equilateral triangle has three equal sides and three equal angles of 60 degrees each, while an isosceles triangle has two equal sides and two equal angles. A scalene triangle has no equal sides or angles. Triangles are important in geometry and have many applications in mathematics and other fields, such as architecture, engineering, physics, and computer graphics.
by the question.
Draw a straight-line segment and label it as the given side that measures 1 1/2 inches.
From one endpoint of the first line segment, draw another line segment that forms a 60° angle with the first line segment. Label this second line segment as the given side that measures 2 1/4 inches.
Draw a third line segment that connects the endpoints of the first two-line segments. This will complete the triangle.
To label the triangle, label the given side that measures 1 1/2 inches with the corresponding length measurement, and label the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
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the product of 2 rational numbers is 16/3.If one of the rational number is -26/3,find the other rational number
Answer:
- [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
let n be the other rational number , then
- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]
[a number × its reciprocal = 1 ]
multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]
n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex] ( cancel the 3 on numerator/ denominator )
n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]
In one year 120 students enrolled at a community college. This was 3/5 of the number of students accepted. How many of those accepted did not enroll
The number of students who did not enroll in the college given that only 3/5th of the total students accepted the admission is equal to 80 students.
Let us consider that the total number of students who enrolled for the process is equal to x. Since it is given that three-fifth of the total students who enrolled positively are equal to 120, this means that 3/5*x = 120.
Thus value of x can be calculated by cross multiplication as follows:
3/5*x = 120
x = 120 * 5/3 = 200
Now, since two third of the students didn't respond/ enroll, then this number can be calculated as the difference between the total numbers who joined and the number of students who accepted the enrollment process.
Number of students who accepted but did not enroll = 200 - 120 = 80
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the car that Andrew used to UWC has a fuel consumption rate of 0,0052k /100km.The cost of petrol for the month of January is R11,90 /litre. calculate the cost of petrol for the trip to UWC.
The cost of petrol for the trip to UWC is R1.2384.
What is cost?In general, cost refers to the amount of resources (usually money) that must be expended to produce or acquire something. It can be thought of as the value of the resources that are given up in order to obtain something else.
According to the given information:To calculate the cost of petrol for the trip to UWC, we need to know the distance traveled and the amount of fuel consumed.
Let's assume that the distance from Andrew's home to UWC is 20 kilometers (km). Then, the amount of fuel consumed for the trip is:
[tex]Fuel consumed = (0.0052 k/100 km) * 20 km = 0.00104 k[/tex]
where k stands for liters of petrol.
To convert the amount of fuel consumed to liters, we need to multiply by 100, since the fuel consumption rate is given in liters per 100 km:
[tex]Fuel consumed = 0.00104 k * 100 = 0.104 liters\\Fuel consumed = 0.00104 k * 100 = 0.104 liters[/tex]
Now we can calculate the cost of petrol for the trip:
[tex]Cost of petrol = (0.104 liters) * (R11.90/liter) = R1.2384[/tex]
Therefore, the cost of petrol for the trip to UWC is R1.2384.
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find the inverse of the function
F(x) = x² + 2x₁ [-1, 00]
The local hardware store has blue buckets that hold 2 gallons of water and white buckets that hold 5 gallons of water. You bought 7 buckets that can hold 26 gallons of water. How many buckets of each color were purchased?
Answer:
So 3 blue buckets and 4 white buckets were purchased
Step-by-step explanation:
We can solve this by algebra
Let B = number of blue buckets bought
Let W = number of white buckets bought
Total buckets bought:
B + W = 7 (1)
Each blue bucket can hold 2 gallons of water
So B blue buckets can hold 2B gallons of water
Each white bucket can hold 5 gallons of water
So W white buckets can hold 5W gallons of water
Totally they can hold
2B + 5W gallons
We are given that they both can hold 26 gallons of water
So our second equation is
2B + 5W = 26 (2)
By eliminating one of the variable terms we can solve for the other variable term
Let's eliminate the term for variable B
Multiply equation (1) by 2
(1) x 2 ==> 2(B + W) = 2(7)
2B + 2W = 14 (3)
Subtract (3) from (2); B terms are same so they cancel out
(2) - (3):
2B + 5W = 26 [tex]\bold{-}[/tex]
2B + 2W = 14
---------------------
0 + 3W = 12
------------------------
3W = 12
W = 12/3
W = 4
Substitute W= 4 in equation 1
B + W = 7
=> B + 4 = 7
B = 3
So 3 blue buckets and 4 white buckets were purchased
Jim orders prints from a website. The site charges him $6. 95 a month and $0. 04 for each print he orders.
Enter an equation that can be used to find the number of prints, P, Jim ordered last month if the website charged
him $17. 79. Enter your response in the first response box
Enter the number of prints Jim ordered last month. Enter your response in the second response box,
Number of prints Jim ordered last month is 271
Let's assume Jim ordered "P" prints last month. The cost of ordering "P" prints would be the sum of the monthly charge and the cost of each print, which is given by the equation:
Cost = Monthly Charge + (Cost per Print x Number of Prints)
Substitute the values in the equation
$17.79 = $6.95 + ($0.04 x P)
Simplifying the equation, we get:
$10.84 = $0.04 x P
Dividing both sides by $0.04, we get:
P = $10.84 / $0.04
Divide the numbers
P = 271
Therefore, Jim ordered 271 prints last month.
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numeric prefixes are used to name select one compounds. they are not used for select one compounds, but the charges must select one .
Greek number prefixes are employed in the naming of molecular (covalent) substances.
Greek number prefixes are employed in the naming of molecular (covalent) substances. Prefixes are always combined in order of size (left-to-right in the table below). For instance, "heptadecatetracta" (7 + 10 + 400) would be the prefix for the number 417.
We utilise prefixes (mono-, di-, tri-, etc.) at the beginning of each element in molecular compounds to denote the element's subscript, but we only use the prefix mono- for the compound's second element.
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A regular hexagon has side lengths of 2x and has a perimeter that is equal to an isosceles triangle with legs of x + 4 and a base that is 3 less than one of the legs. Write and solve equation to find the length of one side of the hexagon.
According to the formula, the length of one side of the hexagon is 21/4 or 5.25 units.
What is the perimeter of the regular hexagon?
Let's call the length of one side of the regular hexagon "s". Since a hexagon has six sides, the perimeter of the hexagon is 6s.
According to the problem, this is equal to the perimeter of an isosceles triangle with legs of x+4 and a base that is 3 less than one of the legs.
The perimeter of the isosceles triangle is given by:
perimeter = 2(x+4) + (x+1)
where (x+1) is the length of the base (which is 3 less than one of the legs).
Setting the perimeters equal, we get:
6s = 2(x+4) + (x+1)
6s = 3x + 9
s = (3/2)x + (3/4)
We also know that the side lengths of the hexagon are 2x. Substituting this into the equation for "s", we get:
2x = (3/2)x + (3/4)
x = 3
Therefore, the length of one side of the hexagon is:
s = (3/2)x + (3/4) = (3/2)(3) + (3/4) = 9/2 + 3/4 = 21/4
So the length of one side of the hexagon is 21/4 or 5.25 units.
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Please help. Need answer ASAP!
Answer: 11
Step-by-step explanation:
Turn it into an improper fraction so 8 from 8 1/4 to 33/4
Then just divide by 3/4
This will give you 11
Write the first four terms of the sequence defined by a n = 5
{5, if n=1
a n -1 -5, if n>1
Answer:
The sequence is defined as follows:
a1 = 5
an = an-1 - 5, for n > 1
Using this definition, we can find the first four terms of the sequence as follows:
a1 = 5
a2 = a1 - 5 = 5 - 5 = 0
a3 = a2 - 5 = 0 - 5 = -5
a4 = a3 - 5 = -5 - 5 = -10
Therefore, the first four terms of the sequence are: 5, 0, -5, -10.
Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2
XZ +Y2
Answer: 37.85
Step-by-step explanation:
Substitute: 3.2x0.2+6.1^2
Calculate the product or quotient: 0.64+6.1^2
Calculate the power: 0.64+37.21
Calculate the sum or difference: 37.85
Answer: 37.85
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what percentage of the area under the normal curve falls between ±2 standard deviations?
Approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.
How the 95.44% of the area under the normal curve falls between ±2 standard deviations?To find the percentage of the area under the normal curve that falls between ±2 standard deviations, we need to follow the following steps:
We need to know the mean (μ) and standard deviation (σ) of the normal distribution in question. If we assume a standard normal distribution (i.e., a normal distribution with mean of 0 and standard deviation of 1), then we can use a z-score table to find the percentage of area under the curve.
Calculate the z-scores for ±2 standard deviationsThe z-score formula is:
z = (x - μ) / σ
For ±2 standard deviations, the values of x are μ ± 2σ. Therefore, the z-scores are:
z = (μ + 2σ - μ) / σ = 2
z = (μ - 2σ - μ) / σ = -2
Use a z-score table to find the percentage of area under the curveA z-score table gives the percentage of area under the standard normal curve that falls to the left of a given z-score. Since the normal distribution is symmetric, the percentage of area to the right of a negative z-score is the same as the percentage of area to the left of the corresponding positive z-score.
Using a z-score table, we find that the percentage of area under the standard normal curve that falls to the left of z = 2 is 0.9772, or 97.72%. Therefore, the percentage of area under the curve that falls between ±2 standard deviations is:
97.72% - (100% - 97.72%) = 95.44%
This means that approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.
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To train for a race, Rosmaria runs 1.5 hours longer each week than she did the previous week. In the first week, Rosmaria ran 3
hours. How much time will Rosmaria spend running if she trains for 12 weeks?
first to answer with good explanation gets brainlest
In linear equation, 54 hours time will Rosmaria spend running if she trains for 12 week.
What is a linear equation in math?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Rosmaria runs 1.5 hours.
In the first week, Rosmaria ran 3 hours.
Rosmaria spend running if she trains for 12 weeks = 12 * 1.5 * 3
= 54
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She begins at sea level, which is an elevation of 0 feet.
She descends for 50 seconds at a speed of 5 feet per second.
She then ascends for 54 seconds at a speed of 4.4 feet per second.
Answer:
The diver descends:
50 seconds x 5 feet/second = 250 feet
The diver ascends:
54 seconds x 4.4 feet/second = 237.6 feet
Therefore, the total change in elevation is:
250 feet (descent) - 237.6 feet (ascent) = 12.4 feet
So, the diver's final elevation is:
0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet
Therefore, the diver ends up 12.4 feet below sea level.
Answer:
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Step-by-step explanation:
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the time it takes for a statistics professor to grade an exam is normally distributed with a mean of 9.7 minutes and a standard deviation of 1.9 minutes. there are 50 students in the professor's class. what is the probability that more than 8 hours are needed to grade all of the exams? (report your answer to 4 decimal places.)
The probability that more than 8 hours are needed to grade all of the exams is about 52%
What is the probability of a standard normal distribution?The probability of a standard normal distribution is the area under the curve of the normal distribution function within a specified interval.
Let X represent the random variable to grade an exam, and let Y represent the total time to grade all exams
The number of students = 50
Therefore;
Y = 50·X
The properties of the normal distribution indicates that we get;
E(Y) = E(50·X) = 50·E(X) = 50 × 9.7 = 485
Var(Y) = Var(50·X) = 50²·Var(X) = 50² × 1.92² = 9025
The standard deviation, SD(Y) = √(Var(Y)) = √(9025) = 95
The probability that more than 8 hours are needed can be found using the z-score of the normal distribution as follows;
8 hours = 480 minutes
Z = (480 - 485)/95 ≈ -0.0526
The probability obtained from a standard normal table, is therefore;
P(Z > -0.0526) = 1 - 0.48006 ≈ 0.52
The probability that more than 8 hours are needed to grade all students is therefore about 0.52 or 52%
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Alfonso wants to purchase a pool membership for the summer. He has no more than y dollars to
spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.
Answer:
Let A represent the cost of purchasing a pool membership from the Aquatics Club and let S represent the cost of purchasing a pool membership from the Swimming Hole. Then, we can write the following system of inequalities:
A ≤ y
A = 75 + 20x
S ≤ y
S = 15 + 65x
The first two inequalities represent the cost of purchasing a membership from the Aquatics Club, while the last two represent the cost of purchasing a membership from the Swimming Hole. The inequalities ensure that the cost of purchasing a membership from either company does not exceed Alfonso's budget of y dollars.
please help fast I am baffled
The expression for the number of non-adult sizes is s - 19.
What are expressions?A value or amount is represented by an expression, which is a collection of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. Calculations, complicated mathematical equations, and issues in a variety of disciplines, including science, engineering, economics, and statistics, may all be solved using expressions. Functions that depict a connection between variables, such as sin(x) and log(x), can also be included in expressions. Expressions are frequently employed to simulate real-world circumstances and provide predictions based on mathematical analysis.
Given that the total number od sweatshirts = s.
The number of non-adult sweatshirts can be calculated by:
Number of non-adult sizes = Total number of sweatshirts sold - Number of adult sizes
= s - 19
Hence, the expression for the number of non-adult sizes is s - 19.
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What is the circumference of the circle with a radius of 5.5 meters? Approximate using π = 3.14.
6.45 meters
34.54 meters
38.47 meters
199.66 meters
