Cone a and cone b both have a height of 5 in. The volume of cone a is 20.9cubic in, the volume of cone b is 4 times the volume of cone a, about how many times longwr is the diameter of cone b than the diameter of cone a?
Answers
Answer: two times
Step-by-step explanation:
Given
height of cone A and B \(h_a=h_b=5\ in.\)
The volume of cone A \(V_a=20.9\ in.^3\)
The volume of cone B is 4 times of cone A
the volume of a cone is \(\frac{1}{3}\pi r^2h\)
The volume of cone A
\(V_a=\dfrac{1}{3}\pi r_a^2h_a=20.9\quad \ldots(i)\)
The volume of cone B
\(V_b=\dfrac{1}{3}\pi r_b^2h_b=4\times 20.9\quad \ldots(ii)\)
divide (i) and (ii) we get
\(\Rightarrow \dfrac{r_a^2}{r_b^2}=\dfrac{1}{4}\\\Rightarrow \dfrac{r_a}{r_b}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}\\\Rightarrow \dfrac{d_a}{d_b}=\dfrac{1}{2}\\\Rightarrow d_b=2d_a\)
thus, diameter of cone B is twice the diameter of A
Related Questions
What is the simplified value of the exponential expression 16 Superscript one-fourth?
2
4
Answers
Answer:
\(2\)
Step-by-step explanation:
\( {16}^{ \frac{1}{4} } \: is \: the \: same \: as \\ \\ \sqrt[4]{16} = \sqrt[4]{ {4}^{2} } \)
Note we broke down the 16 into 4 squared*. This is because 4 squared is the same as 16. The four and the two would cancel each other leaving:
\( \sqrt[2]{4} \;\\ or \\ \: \sqrt [2]{{2}^{2}} \)
Like before the two and the two would cancel each other out leaving:
\(2\)
Answer:
C. 2
Step-by-step explanation:
edge
find TX if RX=16 and if RX is ⅓ of TX
Answers
Answer:
48
Step-by-step explanation:
16 x 3
how do you know if the graph is a function or nonfunction
Answers
The most important aspect to have into account for a graph to be a function is that the function has a domain, and this domain has only an image in the range.
If we pass a vertical line through the function, we can check that the line will pass through this graph in only one point.
In this way, we can say that for each element of the domain, we have only one element in the range. Then, graphically, we have:
Therefore, we can say that this graph is a function.
X = 9 y = 4 is a solution of the linear equation (a) 2x+y=17 (b) x+y=17 (c) x+2y=17 (d) 3x-2y=17
Answers
Answer:
(c) is correct.
Step-by-step explanation:
(c) 9 + 2(4) = 9 + 8 = 17
Match the expressions to their verbal descriptions. Assume that all variables represent integer values and that none are equal to each other. m(2mn) - 6m m + 3n2 771 7mn m(-8m) -3mn2 m+ 3(m - 11)2 the difference between mand a factor depending on m the product of mand a multiple of m the product of mand a factor not depending on m the sum of mand a term depending on m
Answers
The expression for the sum of m and a term depending on m will be m + 3(m - 11)².
How to depict the expressions?The product of m and a multiple of m will be m(-8m).
A product of m and a factor not depending on m will be -3mn²
The difference between n and a factor depending on m will be:
m(2mn) - 6m.m - 7mnLearn more about expressions on:
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Sylvie needs $110 for a concert ticket. She already has $16 and she can earn the rest by working 10 hours at her job. If h represents her hourly earnings, which of the following equations can be solved to find Sylvie’s hourly earnings? Select all that apply
A 110 - 16 = 10h
B 110 = 16h + 10
C 16 = 110 - h
D 110 = 16 + 10h
E 110 + 16 = 10h
Answers
Answer:
Option A and D
Hope this helps!
Answer:
D
Step-by-step explanation:
16 +10h = 110 is the equation because it uses 10h to represent the hourly wages and you need $110. Therefore, with the starting $16, if you use the hourly $10 rate you can come to your answer using the equation.
the sum of two sumbers is 3 more than four times the firsst number. their difference is 10 less than twice the second number. find each of the numbers
Answers
The two numbers are 7/6 and 5 when the sum of two numbers is 3 more than four times the first number.
Let's call the two numbers x and y, where x is the first number and y is the second number.
The problem gives us two equations that relate the two numbers:
\(x + y = 3 + 4x\\y - x = 2y - 10\)
We can substitute the expression for y from equation 1 into equation 2:
\(y - x = 2(3 + 4x) - 10\)
Expanding the right side and simplifying, we get:
\(y - x = 6 + 8x - 10\\y - x = 8x - 4\)
Adding x to both sides:
\(y = 9x - 4\)
Substituting this expression for y into equation 1:
\(x + (9x - 4) = 3 + 4x\)
Expanding and simplifying the right side:
\(10x - 4 = 3 + 4x\)
Subtracting 4x from both sides:
\(6x - 4 = 3\)
Adding 4 to both sides:
\(6x = 7\)
Dividing both sides by 6:
\(x = 7/6\)
Substituting this value of x back into the expression for y:
\(y = 9x - 4 = 9 * (7/6) - 4 = 63/6 - 4 = 9 - 4 = 5\)
So the two numbers are 7/6 and 5.
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The dimensions of a triangle are represented by the functions shown. Which function represents the area of the triangle, ? h(x) = 12x2 + 6x h(x) = 12x2 – 6x h(x) = 24x2 – 12x h(x) = 12x – 6
Answers
Answer:
h(x) = 12x – 6
Step-by-step explanation:
To know which is the function that represents the area of a triangle, you take into account the degree of the given polynomials.
If the degree is 2, the graph of the function is a parabola.
If the degree is 1, the graph of the function is a line.
By comparing all functions you can conclude that only the last option (h(x)=12-x-6) is convenient to construct a triangle. The y-intersect of the function is at y=-6, the slope is positive and the x-intersect is x=1/2. This forms a triangle in the fourth quadrant of the coordinate system.
Answer:
B. g(x) = 12x2 – 6x
Step-by-step explanation:
correct on edge 2020
Please answer this in two minutes
Answers
Answer:
w=80
Step-by-step explanation:
The Exterior Angle Theorem states: The exterior angle formed by an extended sign of the triangle is the sum of the two angles in the triangle that it is not directly next to.
In this case, the exterior angle is w+44.
The interior angles we can use are w and w-36.
We can set up an equation:
w+44=w+w-36
Combine like terms.
w+44=2w-36
Add 36 to both sides.
w+80=2w
Subtract w from both sides.
w=80
Business Math I need help with fraction word problems.
Answers
Answer:
which kind?
Step-by-step explanation:
how do you simplify a x b x 7
Answers
Answer:
7ab
Explanation:ab=axb
So it's easy!!
The answer will be 7ab(always remember the whole number should come first)
A And B will join together cuz multiply sign
And seven also gets multiplied so
7AB is the answer
While at a store, Jared decided to buy some
shirts for $3.29 each and a jacket for $19.50.
Jared's purchase was a total of $35.95. Write an
equation to find how many shirts Jared bought.
3.29s + 19.50 = [?]
Answers
Answer:
5
Step-by-step explanation:
35.95 - 19.50 = 16.45 ÷ 3.29 = 5
Calculating brilliance in epidemiology Context. What follows is a data table showing the development of brilliance among a small class of PHE 450 students. NOTE: Student #8 came in as an existing case of brilliance and did not develop brilliance as a result of exposure to PHE 450. Student WK 1 WK 2 WK 3 WK 4 WK 5 WK6 WK 7 WK 8 WK 9 WK 10 CASE CASE CASE CASE DROP 1 2 3 4 5 6 7 8 9 10 11 12 CASE CASE CASE DROP CASE DROP ASSIGNMENT Referring to the data above, please answer the following questions What is the point prevalence of brilliance at the end of Week 1? What is the point prevalence of brilliance at the end of Week 2? • What is the point prevalence of brilliance at the end of Week 3? • Using person-weeks as your denominator, what is the incidence of brilliance over the course of the 10-week course?
Answers
The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.
The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.
The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.
Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%
In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:
The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.
The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.
The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.
The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation
Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.
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Asap!! step by step pls! After a new firm starts in business, it finds that it’s rate of profit (in hundreds of dollars) after t years of operations is given by P’(t)=3t^2+10t+6. Find the profit in year 4 of the operation.
Answers
Answer:
$ 7800
Step-by-step explanation:
P'(t) = 3t² + 10t + 6
\(P(t) = \int\limits^a_b {P'(t)} \, dt\)
For the 4th year, the limits are [3,4]
\(P(t) = \int\limits^4_3 {3t^2 + 10t + 6} \, dt\\\\= [\frac{3t^3}{3} + \frac{10t^2}{2} + 6t]^{^4}__{3}\\\\\)
\(=[\frac{3(4)^3}{3} + \frac{10(4)^2}{2} + 6(4)]-[\frac{3(3)^3}{3} + \frac{10(3)^2}{2} + 6(3)]\\\\=[\frac{3(64)}{3} + \frac{10(16)}{2} + 24]-[\frac{3(27)}{3} + \frac{10(9)}{2} + 18]\\\\= [64 + 5(16) + 24]-[27+5(9) + 18]\\\\= 168-90\\\\= 78\)
= $ 7800
This type of research is intended to be carried out by any professional, in any type of school, to investigate a problem. The findings are limited in their generalizability. a. Historical research. b. Survey research. c. Action research. d. Ethnographic study.
Answers
The type of research described in the scenario is "survey research." The correct answer is B.
Survey research is a method that allows professionals from any field to investigate a problem in any type of school or setting. It involves collecting data from a sample of individuals or groups through surveys or questionnaires.
While survey research provides valuable insights into the specific problem being studied, its findings are often limited in their generalizability. This means that the conclusions drawn from the survey may not be applicable to a larger population or different contexts. The sample surveyed may not represent the entire population accurately, leading to potential biases or limitations in generalizing the results.
Other research methods, such as historical research, action research, or ethnographic study, may also be used in different contexts. However, survey research is specifically characterized by its broad applicability to various professionals and settings, as well as the limitations in generalizing its findings. The correct answer is B.
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create the regression model for fuel economy using horsepower, quarter mile time, and rear axle ratio as predictors. include interaction terms for horsepower and quarter mile time; horsepower and rear axle ratio. write the prediction model equation using outputs obtained from your r script.
Answers
The prediction model equation is constructed using outputs from an R script.
We are creating a regression model to accurately predict fuel economy using horsepower, quarter mile time, and rear axle ratio as predictors. We will include interaction terms for horsepower and quarter mile time, as well as for horsepower and rear axle ratio.
The prediction model equation is written below, based on the outputs obtained from the R script:
Fuel Economy = β0 + β1*Horsepower + β2*Quarter Mile Time + β3*Rear Axle Ratio + β4*Horsepower*Quarter Mile Time + β5*Horsepower*Rear Axle Ratio
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Personnel tests are designed to test a job​ applicant's cognitive​ and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last​ year, the distribution of scores was approximately normal with mean 77 and standard deviation 7.5 . a. A particular employer requires job candidates to score at least 82 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 82 ​?
Answers
Approximately 25.14% of the test scores during the past year exceeded 82 on the dexterity test. Based on the given information, we can use the normal distribution to estimate the percentage of test scores that exceeded 82 on the dexterity test.
To find the percentage of test scores that exceeded 82, we need to calculate the area under the normal distribution curve to the right of 82. This area represents the proportion of scores that are greater than 82.
First, we need to standardize the score of 82 using the formula z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. Substituting the given values, we get z = (82 - 77) / 7.5 = 0.67.
Next, we need to find the cumulative probability corresponding to this z-score. We can look up this value in a standard normal distribution table or use a calculator. The cumulative probability for a z-score of 0.67 is approximately 0.7486.
Since we want to find the percentage of scores that exceeded 82, we subtract the cumulative probability from 1 (since the cumulative probability represents the area to the left of the z-score). So, 1 - 0.7486 = 0.2514.
Therefore, approximately 25.14% of the test scores during the past year exceeded 82 on the dexterity test.
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Imagine a 3-dimensional box in the shape of a rectangular prism with side lengths are A (length), B (width), and C (height). What is the length of the longest stick that can fit in this box in terms of the variables A, B, and C? Assume this stick is perfectly straight and has an extremely small diameter (this stick is basically a line).
Answers
The longest stick that can fit in the box is the diagonal line that goes from one corner of the box to the opposite corner.
What is diagonal line?A diagonal line is a straight line that slants or slopes in any direction. It is used to connect two points which are not on the same level, or to create a shape that would not be possible with a straight line. Diagonal lines are often used in art and design to add interest, movement, and texture.
This line is of length √A2 + B2 + C2.
This is because the diagonal line of a rectangular prism of side lengths A, B, and C is given by the Pythagorean theorem, √A2 + B2 + C2.
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For each pair of points, find the slope of the line that passes through the points.(5,4) and (0,1)(3,7) and (-2,2)
Answers
Consider that the slope of a line passing through two given points, is given by the formula,
\(m=\frac{y_2-y_1}{x_2-x_1}\)So the slope of line passing through the points (5,4) and (0,1) is calculated as,
\(\begin{gathered} m=\frac{1-4}{0-5} \\ m=\frac{-3}{-5} \\ m=\frac{3}{5} \end{gathered}\)Thus, the slope of straight lines passing through (5,4) and (0,1) is 3/5 .
Similarly, the slope of line passing through the points (3,7) and (-2,2) is calculated as,
\(\begin{gathered} m=\frac{2-7}{-2-3} \\ m=\frac{-5}{-5} \\ m=1 \end{gathered}\)Thus, the slope of line passing through the points (3,7) and (-2,2) is 1 .
Mrs. DeMarco wants to estimate the length of her porch so she knows how much paint to buy. What is the best benchmark for her to use? A her fingertip B a license plate C a baseball bat D how far she could walk in 20 minutes
Answers
Need help it’s URGENT!
Answers
Answer:
either b or c
Step-by-step explanation:
i think
A recipe calls for 5 teaspoons of honey for every 2 cups of sugar. Tracy has only 3 teaspoons of honey left. How much sugar should she use to appropriately adjust the recipe?
Answers
Answer:
If a recipe calls for 5 teaspoons of honey for every 2 cups of sugar, then the ratio of honey to sugar is 5:2. Since Tracy has only 3 teaspoons of honey left, she should use (3/5)*2 = 6/5 = 1.2 cups of sugar to appropriately adjust the recipe.
Step-by-step explanation:
A project has an initial cost of $30 million.The project is expected to generate a cash flow of $2.85 million at the end of the first year.All the subsequent cash flows will grow at a constant growth rate of 3.85% forever in future.If the appropriate discount rate of the project is 11%,what is the profitability index of the project? a.1.917 b.1.328 c.1.387 d.1.114 ortcehov e. None of the above
Answers
Profitability index is 1.387. Thus, the correct option is (c) 1.387.
The formula for calculating the profitability index is:
P.I = PV of Future Cash Flows / Initial Investment
Where,
P.I is the profitability index
PV is the present value of future cash flows
The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.
The present value of cash flows can be calculated using the formula:
PV = CF / (1 + r)ⁿ
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
n is the number of periods
For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.
Substituting the values, we get:
PV = 2.85 / (1 + 0.11)¹ = $2.56 million
To calculate the present value of all future cash flows, we can use the formula:
PV = CF / (r - g)
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
g is the constant growth rate
For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.
Substituting the values, we get:
PV = 2.85 / (0.11 - 0.0385) = $39.90 million
The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.
PV of future cash flows = $39.90 million + $2.56 million = $42.46 million
Profitability index (P.I) = PV of future cash flows / Initial investment
= 42.46 / 30
= 1.387
Therefore, the correct option is (c) 1.387.
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What is the answer to this problem?
Answers
Answer:
x + 10
Step-by-step explanation:
It says 10 MORE than a number.
SO that's + 10
The numbr is x so:
x + 10
Answer
x + 10
Step-by-step explanation:
The question asking "more than" implies that you need to add, and x represents your unknown number.
in how many ways can $8$ people sit around a round table if $3$ of the people -- pierre, rosa, and thomas -- all want to sit together? (two seatings are considered the same if one is a rotation of the other.)
Answers
The number of ways in which we can make a sitting arrangements to meet the requirement is 1440.
= 5!⋅4⋅3
= 120⋅12
= 1440
Combinations are ways to choose things from a collection where the order of the choices is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen which is nCr.
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I NEED HELP!!!!!!! PLEASE!!!!!
Answers
Answer: a
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
Hey There!
In a parallelogram opposite angles are equal to each other
the first step in this problem is to find the value of angle D and angle B
To do so we set up an equation
6x+6=10x-30
step 1 add 30 to each side
-30+30 cancels out
6+30=36
now we have
6x+36=10x
step 2 subtract 6x from each side
10x-6x=4x
6x-6x cancels out
now we have 4x=36
step 3 divide each side by 4
4/4 cancels out
36/4=9
so x=9
now we plug in the values of x
9x10=90
90-30=60
angle C and angle B are supplements meaning that they add up to equal 180
so in order to find angle C we subtract the given angle (60) from 180
180-60=120
so angle C=120
1. The first four terms of a geometric progression are 3, -1, 1/3, -1/9
Find the sum to infinity.
Answers
The sum to infinity of the sequence is -2.25
How to determine the sum to infinityFrom the question, we have the following parameters that can be used in our computation:
3, -1, 1/3, -1/9
Using the above as a guide, we have the following:
First term, a -3
Common ratio, r = -1/3
The sum to infinity is then calculated as
Sum = a/1 - r
So, we have
Sum = -3/(1 + 1/3)
Evaluate
Sum = -2.25
Hence, the sum is -2.25
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Convert: 3120 millimeters= centimeters
Answers
Explanation:
The question is
Convert
\(3120mm\text{ }to\text{ }cm\)Concept:
To do this, we will use the conversion below
\(1mm=0.1cm\)Hence,
Uidn the conversion rate, we will have trha
\(\begin{gathered} 1mm=0.1cm \\ 3120mm=x \\ cross\text{ multipl, we will have} \\ x=3120\times0.1 \\ x=312cm \end{gathered}\)Hence,
The final amswer is
\(312\text{ }centimeters\)Resa wanted to find out what percentage of her daily Vitamin C she gets from one carrot.
Answers
Answer:
See the picture.
Step-by-step explanation:
Can someone help please
Answers
Answer:
sorry i dont know
Step-by-step explanation:
Answer:
Sorry for the long wait i was taking my cumulative exam for precal and it took a bit but i hope im correct. My brain is fried and dont know if i even came close.
