A cone is 10 inches tall and has a radius of 3 inches. What is the cone's volume?
O 31.4 cubic inches
0 94.2 cubic inches
282.6 cubic inches
O 847.8 cubic inches
Answer:
B) 94.2 in³
Step-by-step explanation:
V = (πr²h)/3
= 9π(10)/3 = 90π/3 = 30π ≈ 94.25
Find the measure of each angle indicated.
940
94
58
77
127
please help me help help help
xy+xb+ya+ab = 32
x(y+b) + a(y+b) = 32
(x+a) (y+b) = 32
4.(y+b) = 32
(y+b) =32/4
(y+b) = 8
OPTION C
Simplify:
a.5³×5‐²×5⁴.
b.a⁴×a‐²×x³.
c.(x⁵)²×(y⁵)³
__________
(x³)³×(y²)²
Answer:
a. 125 * 0.04 * 625 = 5 * 625 = 3125
b. a^2 * x^3
c. x^10 * x^ y^15
Last one: x^9 * y^4
Step-by-step explanation:
Because yes.
Write the next 3 terms in the sequence.
108, -432, 1728, -6912, ...
Answer:
27,648
-110,592
442,368
Step-by-step explanation:
each term is multiplied by -4
2-X is a uniform random variable over the interval of [-11]. What is the PDF of Y = |X|-1?
The PDF of Y = |X|-1 is 1/2 for y in [-1, 0] and 0 otherwise. This is because the range of Y is [-1, 0], and the probability of X taking on any value in this range is equal.
The PDF of Y = |X|-1 can be found using the transformation technique. We know that the PDF of X is 1/2 for x in [-11, 11]. We can transform this to the PDF of Y by using the following formula: f_Y(y) = f_X(|y|) * |dX/dY|, where f_Y is the PDF of Y, f_X is the PDF of X, and |dX/dY| is the Jacobian of the transformation. In this case, the Jacobian is equal to 1, so the PDF of Y is simply: f_Y(y) = f_X(|y|). The PDF of X is 1/2 for x in [-11, 11], so the PDF of Y is 1/2 for y in [-1, 0].
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Marc is building a rectangular wooden frame for his canvas. If the canvas is 7 feet long by 5 feet wide, what is the perimeter of the canvas?
Answer:
24 feet
Step-by-step explanation:
Use the perimeter formula, P = 2l + 2w, where l is the length and w is the width.
Plug in the values, and solve:
P = 2l + 2w
P = 2(7) + 2(5)
P = 14 + 10
P = 24
So, the perimeter of the canvas is 24 feet
Find the probability of getting any triple-digit number where all the digits are the same in a lottery game that consists of selecting a three-digit number.
Thus, the probability is 1/100 or 0.01, which means there is a 1% chance of getting a triple-digit number with all the same digits in this lottery game.
To calculate the probability of getting a triple-digit number where all digits are the same in a lottery game that consists of selecting a three-digit number, you should first determine the number of favorable outcomes and the total possible outcomes.
There are 9 favorable outcomes, as the triple-digit numbers with the same digits are: 111, 222, 333, 444, 555, 666, 777, 888, and 999. Note that we don't include 000 since it's not a triple-digit number.
Now, let's find the total possible outcomes. In a three-digit number, there are 10 possible digits (0-9) for each of the three positions. However, the first position cannot be 0, as that would not be a triple-digit number.
So, there are 9 possible digits for the first position and 10 for the other two. The total possible outcomes are 9 x 10 x 10, which equals 900.
Finally, to find the probability of getting a triple-digit number with all the same digits, divide the number of favorable outcomes by the total possible outcomes:
Probability = Favorable Outcomes / Total Possible Outcomes
Probability = 9 / 900
The probability is 1/100 or 0.01, which means there is a 1% chance of getting a triple-digit number with all the same digits in this lottery game.
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The continuous random variable V has a probability density function given by: 6 f(v) = for 3 ≤ ≤7,0 otherwise. 24 What is the expected value of V? Number
The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.
The PDF of V is defined as:
f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.
The expected value of V, denoted as E(V), can be calculated as:
E(V) = ∫v * f(v) dv
To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.
E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.
E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].
E(V) = (0.25) * [(49 / 2) - (9 / 2)].
E(V) = (0.25) * (40 / 2).
E(V) = (0.25) * 20.
E(V) = 5.
Therefore, the expected value of the continuous random variable V is 5.
The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
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Using technology, calculate the weighted mean of the rors for each portfolio. based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst? portfolio 3, portfolio 1, portfolio 2 portfolio 2, portfolio 3, portfolio 1 portfolio 1, portfolio 2, portfolio 3 portfolio 3, portfolio 2, portfolio 1
Option B is the correct choice.
Based on the findings, the following list compares the portfolios' overall performances, ranking them from best to worst:
Portfolios 2, 3, and 1, respectively.
The weighted average ROR is calculated by adding the rates of return on the portfolio's assets and the percentage of the portfolio that is invested in each investment.
For Portfolio 1:
Total Investment= $700 + $2575 + $220 + $1000 + $1430 = $5925
Therefore, total investment = $5,925
Weighted Average ROR= (-3.8% * $700) / $5925 + (2.1% * $2575) / $5925 + (11.3% * $220) / $5925 + (5.8% * $1000) / $5925 + (1.6% * $1430) / $5925
WAROR = (-0.0045) + 0.0091 + 0.0042 + 0.0098 + 0.0039 = 0.0225
Therefore, the Weighted Average ROR= 2.25% (third)
For Portfolio 2:
Total Investment = $1250 + $1700 + $1515 + $1345 + $1,675 = $7485
Therefore, Total Investment = $7,485
Weighted Average ROR = (-3.8% * $1250) / $7485 + (2.1% * $1700) / $7485 + (11.3% * $1515) / $7485 + (5.8% * $1345) / $7485 + (1.6% * $1,675) / $7485
= (-0.0063) + 0.0048 + 0.0229 + 0.0104 + 0.0036 = 0.0354
Therefore, the Weighted Average ROR = 3.54% (first)
For Portfolio 3:
Total Investment = $1025 + $500 + $790 + $250 + $2500 = $5065
Therefore, Total Investment = $5,065
Weighted Average ROR = (-3.8% * $1025) / $5065 + (2.1% * $500) / $5065 + (11.3% * $790) / $5065 + (5.8% * $250) / $5065 + (1.6% * $2,500) / $5065
= (-0.0077) + 0.0021 + 0.0176 + 0.0029 + 0.0079 = 0.0228
Therefore, Weighted Average ROR = 2.28% (second)
Therefore, the correct order of portfolios based on the performance from best to worst will be:
Portfolio 2, Portfolio 3, and Portfolio 1. (Option B)
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COMPLETE QUESTION:
ROR Portfolio 1 Portfolio 2 Portfolio 3 −3.8% $700 $1,250 $1,025 2.1% $2,575 $1,700 $500 11.3% $220 $1,515 $790 5.8% $1,000 $1,345 $250 1.6% $1,430 $1,675 $2,500 Using technology, calculate the weighted average of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?
A) Portfolio 1, Portfolio 3, Portfolio 2
B) Portfolio 2, Portfolio 3, Portfolio 1
C) Portfolio 1, Portfolio 2, Portfolio 3
D) Portfolio 3, Portfolio 2, Portfolio 1
the hourly pay rate of employees at a local resort follows a reasonably normal distribution with mean $14.41. if 77% of employees make less than $16.11, what is the standard deviation of the distribution of hourly rate?
Therefore, the standard deviation of the distribution of hourly pay rates is approximately $2.24.
What is mean?In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is also called the arithmetic mean or the average. The mean is a useful summary statistic that can give you an idea of the typical or central value of a data set. However, it can be affected by extreme values, or outliers, that are much higher or lower than the other values in the data set. In such cases, other measures of central tendency, such as the median or mode, may be more appropriate.
Here,
Let X be the hourly pay rate of employees at the resort. We know that X follows a normal distribution with mean μ = $14.41. Let σ be the standard deviation of X.
To find σ, we need to use the fact that 77% of employees make less than $16.11. We can standardize the value $16.11 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, and z is the standard normal variable with mean 0 and standard deviation 1.
Since we want to find the standard deviation σ, we can rearrange the formula to get:
σ = (x - μ) / z
We know that 77% of employees make less than $16.11, so we can find the corresponding z-score using a standard normal table or calculator:
P(X < $16.11) = P(Z < (16.11 - 14.41) / σ) = 0.77
Solving for the z-score, we get:
Z = 0.76
Plugging in the values we know, we can solve for σ:
σ = (16.11 - 14.41) / 0.76
σ ≈ $2.24
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Let an = 5n/4n + 1 Determine whether {an) is convergent. convergent divergent
To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.
First, let's rewrite the expression for the nth term of the sequence:
an = 5n / (4n + 1)
As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:
an ≈ n / (4n + 1)
Now, we can consider the limit of the sequence as n approaches infinity:
lim(n→∞) n / (4n + 1)
To evaluate this limit, we can divide both the numerator and denominator by n:
lim(n→∞) (1 / 4 + 1/n)
As n approaches infinity, the term 1/n approaches zero, leaving us with:
lim(n→∞) 1 / 4 = 1/4
Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.
In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.
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a cake was cut into 20 equal pieces. daniel ate 3 pieces. what percent of the cake did daniel eat
Answer:15%
Step-by-step explanation:
3 cylinders have a height of 8 cm cylinder one has a radius of 1 cm cylinder 2 has the radius of 2 cm cylinder 3 has a radius of 3 cm find the volume of each cylinder
The volume of the cylinder 1 = 25.12 cubic centimeters.
The volume of the cylinder 2 = 100.48 cubic centimeters.
The volume of the cylinder 3 = 226.08 cubic centimeters.
What is a cylinder?A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.
Given:
3 cylinders have a height of 8 cm cylinder one has a radius of 1 cm cylinder 2 has the radius of 2 cm cylinder 3 has a radius of 3 cm.
The volume of the cylinder 1,
= πr²h
= (3.14)(1)(8)
= 25.12 cubic centimeters.
The volume of the cylinder 2,
= πr²h
= (3.14)(4)(8)
= 100.48 cubic centimeters.
The volume of the cylinder 3,
= πr²h
= (3.14)(9)(8)
= 226.08 cubic centimeters.
Therefore, the volume of each cylinder is given above.
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A veterinarian knows that the supplement glucosamine is beneficial for dogs’ joints. He wants to determine if a supplement with both glucosamine and chondroitin would be more beneficial than glucosamine alone for dogs’ joint health. The veterinarian asks the owners of dogs with known joint issues if they would be willing to have their dog participate in his study, and 32 owners agree to the study. The veterinarian also knows that breed and age may affect the results of the experiment.
Which of the following designs would be most appropriate for this experiment?
A) Completely randomized design: Randomly assign the treatments to the dogs.
B) Matched pairs design: Block the dogs based on breed. Then, within each block, pair the dogs based on age. Randomly assign the treatments to each dog in the pairs.
C) Randomized block design: Block the dogs based on breed. Then, randomly assign half of the dogs in each block to receive glucosamine only and the other half to receive glucosamine with chondroitin.
D) Observational study: The veterinarian should randomly select patient records. Then, use the joint health of dogs that use glucosamine only and those that use glucosamine with chondroitin.
The correct option: A) Completely randomized design: Randomly assign the treatments to the dogs.
How does randomized design work?"Any randomized design is regarded as a form of experiment that is assigned to various treatments by carrying out various experiments on various groups.
The answer to the query is
A veterinarian performs an experiment to see if glucosamine on its own or glucosamine + chondroitin is more useful.By randomly splitting the canines into 2 groups of sixteen each, a veterinarian experimented on 32 dogs. 16 dogs receive glucosamine therapy, and the remaining 16 receive glucosamine and chondroitin therapy.Each dog's health is assessed and compared after six months.Therefore, we get to the conclusion that the treatment given to the dogs at random is the best course of action.
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A tower made of wooden blocks measures114 feet high. Then a block is added that increases the height of the tower by 8 inches.
What is the final height of the block tower?
Responses
9 1\4 in.
10 in.
18 in.
23 in.
There are six boys to every five girls in an introductory geology course. If there are 374 students enrolled in the course, how many are boys
there are approximately 34 boys in the introductory geology course.
To determine the number of boys in the introductory geology course, we need to calculate the ratio of boys to girls and use the total number of students enrolled.
The given ratio states that there are six boys for every five girls. This can be expressed as 6 boys : 5 girls.
Let's assume the number of boys in the course is represented by B and the number of girls is represented by G.
According to the given information, we can set up the following equation:
6 boys / 5 girls = B / G.
Since the total number of students enrolled in the course is 374, we can write another equation:
B + G = 374.
To solve these equations simultaneously, we can use the concept of proportion.
From the first equation, we can rewrite it as:
6G = 5B.
Now we can substitute this expression into the second equation:
B + G = 374
5B + 6B = 374
11B = 374
B = 374 / 11
B ≈ 34.
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How can get better at geogrwphy
Answer:
study DUHHHH
Step-by-step explanation:
Which function is the inverse of f(x) = 2x + 3?
Answer:
m=2
Step-by-step explanation:
Use rounding to estimate the product. 4three-fourths • 7Start Fraction 2 over 17 End Fraction A. about 28 B. about 32 C. about 35 D. about 40
Answer:
I think the answer is D
Step-by-step explanation:
Solve the following three equations
Answer:
2 sq rt 33
Step-by-step explanation:
1st step: subtract one, each side
(radical 2/3)r = 22
2nd step: set up a proportion
(radical 2/3)r = 22
3rd step: cross-multiply
radical 2*r = 66
4th step: solve for 'r'
r = 66 / radical 2
5th step: rationalize the denominator
multiply numerator and denominator by radical 2
6th step: simplify
(66\(\sqrt{2}\)) / 2 = 33 \(\sqrt{2}\)
Two tankers contain 580 liters and 680 liters of petrol. find the maximum capacity of the container which can measure the petrol of either tanker in exact number of times. ____ litters
The maximum capacity of the container that can measure the petrol in either tanker in exact numbers of times is 100 liters.
To find the maximum capacity of the container that can measure the petrol in both tankers in exact numbers of times, we need to find the greatest common divisor (GCD) of the two volumes. The GCD will represent the maximum number of times the container can measure both tankers.
First, let's find the GCD of 580 liters and 680 liters. We can use the Euclidean algorithm to do this.
Step 1: Divide the larger number (680) by the smaller number (580):
680 ÷ 580 = 1 with a remainder of 100.
Step 2: Now, divide the smaller number (580) by the remainder (100):
580 ÷ 100 = 5 with no remainder.
Step 3: Repeat the previous step with the remainder (100) and the new remainder (0):
100 ÷ 0 = undefined.
Since we obtained a remainder of 0, we stop here. The GCD of 580 liters and 680 liters is the last non-zero remainder, which is 100 liters.
Therefore, the maximum capacity of the container that can measure the petrol in either tanker in exact numbers of times is 100 liters.
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Vax + Consider the limit lim where a, b, c, and d are positive real numbers. Show that L'Hôpital's ・300 ſex+d Role fails for this limit. Find the limit using another method.
To evaluate the limit (ax^b)/(cx^d) as x approaches infinity that are use L'Hôpital's Rule if b ≠ d, divide both numerator and denominator by x^d if b = d and a/c ≠ 1 and if b = d and a/c = 1, simplify by dividing both numerator and denominator by x^d.
To evaluate the limit lim as x approaches infinity for the expression (a*x^b)/(c*x^d), we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (a*b*x^(b-1))/(c*d*x^(d-1)). Simplifying this expression, we get (a*b)/(c*d)*x^(b-d). As x approaches infinity, this expression goes to infinity if b > d, goes to zero if b < d, and approaches a nonzero constant if b = d.However, L'Hôpital's Rule fails for this limit if b = d and the ratio a/c is not equal to 1. In this case, taking the derivative of the numerator and denominator separately gives (a*b*x^(b-1))/(c*d*x^(d-1)) = (a*b)/(c*d)*x^(b-d-1), which still has an indeterminate form of 0/0 as x approaches infinity. Thus, we cannot use L'Hôpital's Rule to evaluate this limit.Instead, we can simplify the expression by dividing both the numerator and denominator by x^d. This gives us (a*x^(b-d))/(c), which approaches infinity as x approaches infinity if b > d, approaches zero if b < d, and approaches a nonzero constant if b = d. Thus, we have found that the limit of the original expression is equal to the limit of (a*x^(b-d))/(c), which can be evaluated without using L'Hôpital's Rule.Learn More About L'Hôpital's Rule: https://brainly.com/question/28170672
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Connor is a 400m runner His median time is
Answer: 57.8
Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8
Please help I will give brainliest.
Answer:
3 Rd one
Step-by-step explanation:
donee....!!✓give me the branliest
help me solve this with explanation
Answer:
x = 19
<6 = 109
<7 = 109
Step-by-step explanation:
Angles 6 and 7 are vertical angles so they are equal
7x -24 = 5x+14
Subtract 5x from each side
7x-5x -24 = 5x-5x+14
2x-24 = 14
Add 24 to each side
2x-24 +24 = 14+24
2x = 38
Divide by 2
2x/2 = 38/2
x = 19
<6 = 7x -24 = 7*19 -24 = 109
<7 = 5(19)+14 = 109
Two ropes support a lantern that weighs 50 n. if you measure the tension in each rope and add those two scalar values together, is that sum less than, equal to, or more than 50 n? 1.
The sum of the tension in each rope will be equal to 50 N.
When an object is in equilibrium, the sum of the forces acting on it is zero. In this case, the lantern is in equilibrium as it is not accelerating vertically.
If we consider the tension in each rope, they act in opposite directions and have equal magnitudes. Let's denote the tension in one rope as T1 and the tension in the other rope as T2.
Since the lantern is not accelerating vertically, the sum of the vertical forces must be zero. Therefore, the sum of the tension in each rope (T1 + T2) must be equal to the weight of the lantern, which is 50 N.
T1 + T2 = 50 N
The sum of the tension in each rope will be equal to 50 N, which is the weight of the lantern.
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Let u = ln x and v = lny. Write In(x²y^5) in terms of u and v.
The value of the given logarithm ln(x²y⁵) in terms of u and v will be 2u + 5v thus option (D) is correct.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
As per the given expressions,
u = ln x and v = ln y
Take anti-log as
x = \(e^{u}\) and y = \(e^{v}\)
Thus, x² = \(e^{2u}\) and y⁵ = \(e^{5v}\).
Multiply both as
x²y⁵ = \(e^{2u}\)\(e^{5v}\)
Take logarithms on both sides,
ln(x²y⁵) = ln( \(e^{2u}\)\(e^{5v}\))
By log property that ln(A x B) = lnA + lnB
ln(x²y⁵) = ln (\(e^{2u}\)) + ln(\(e^{5v}\))
ln(x²y⁵) = 2u ln e + 5v ln e
ln(x²y⁵) = 2u + 5v
Hence "In terms of u and v, the value of the given logarithm ln(x²y⁵) will be 2u + 5v.".
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In the triangle below, with right angle ZL, suppose that mM=(5x+15)° and m N= (4x+3)⁰.
Find the degree measure of each angle in the triangle.
N
(4x + 3)°
15x+15)
Please help I’m super stressed and crying I need this
On solving the provided question, we can say that by using the triangle, ∠LNM=35° and ∠NML=55°
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
∠LNM=(4x+3)°
∠NML=(5x+15)°
∠NLM=90°
Since, its right angle triangle, sum of all angle is 180°
∠LNM+∠NML+∠NLM=180°
(4x+3)+(5x+15)+90=180°
9x+18=90°
9x=72
x=8
Hence,
∠LNM=(4x+3)°=4*8+3=35°
∠NML=(5x+15)°=5*8+15=55°
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See photo to answer!
The length of AB of the triangle is 13 units.
How to find the side of a triangle?The side AB of the triangle can be found using cosine law,
Therefore,
c² = a² + b² - 2ab cos C
c² = 7² + 8² - 2 × 7 × 8 cos 120
c² = 49 + 64 - 112 cos 120
c²= 113 - (-56)
c² = 113 + 56
c² = 169
c = √169
c = 13 units
Therefore, the value of AB is 13 units
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