Roslyn is an engineer. She is designing a part for a new engine. The length of the part is 16 centimeters (cm), the width is 6 cm, and the height of the cone top is 5 cm, as shown.
Answers
\(\bold{\huge{\underline{ Solution }}}\)
Given :-The length of the part is 16 centimeters The part of new engine is composed of 1 cone, 1 cylinder and 1 hemisphere The width of the engine is 6 cmThe height of the cone is 5 cmTo Find :-We have to find the total volume of the part Let's Begin :-Let divide the part of engine into three parts as it is composed of 3 different figures.
We know that,
Volume of cone
\(\bold{=}{\bold{\dfrac{ 1}{3}}}{\bold{{\pi}r^{2}h}}\)
Here, we have,
The height of the cone is 5 cmThe diameter of the cone is 6 cmTherefore, Radius of the cone = 3 cmSubsitute the required values,
Volume of the first part that is cone
\(\sf{=}{\sf{\dfrac{ 1}{3}}}{\sf{ {\times}3.14{\times}(3)^{2}{\times}5}}\)
\(\sf{=}{\sf{\dfrac{ 1}{3}}}{\sf{ {\times}3.14{\times}9{\times}5}}\)
\(\sf{ = 3.14 {\times} 3 {\times} 5 }\)
\(\sf{ = 3.14 {\times} 15 }\)
\(\sf{ = 3.14 {\times} 15 }\)
\(\bold{ = 47.1 cm^{3} }\)
Thus, The volume of cone is 47.1 cm³ .
For second part Second part is composed of cylinderWe know that,
The volume of cylinder
\(\bold{ = {\pi}r^{2}h }\)
Here,
The diameter of the cylinder is 6 cmSo, Radius = 3 cmThe length of the cylinder = 16 - (Length of cone + Length of hemisphere) Length = 16 - 11 = 5 cmSubsitute the required values in the above formula,
Volume of the second part that is cylinder
\(\sf{ = 3.14{\times} (3)^{2}{\times} 5}\)
\(\sf{ = 3.14{\times} 9 {\times} 5}\)
\(\sf{ = 3.14{\times} 45 }\)
\(\bold{ = 141.3 cm^{3}}\)
Thus, The volume of the cylinder is 141.3 cm³
For third partThird part is composed of hemisphereWe know that,
Volume of hemisphere
\(\bold{=}{\bold{\dfrac{ 2}{3}}}{\sf{ {\pi}r}}\)
Here,
The diameter of the hemisphere is 6 cmSo, Radius = 3cmSubsitute the required values,
Volume of third part that is hemisphere
\(\sf{=}{\sf{\dfrac{ 2}{3}}}{\sf{{\times} 3.14 {\times}3}}\)
\(\sf{ = 2 {\times} 3.14 }\)
\(\bold{ = 6.28 cm^{3} }\)
Thus, The volume of the hemisphere is 6.28 cm³
Therefore,The total volume of the part
= Volume of cone + Volume of cylinder + Volume of hemisphere
\(\sf{ = 47.1 + 141.3 + 6.28 }\)
\(\sf{ = 188.4 + 6.28 }\)
\(\sf{ = 194.68 cm^{3} }\)
\(\bold{ = 194.7 cm^{3} }\)
Hence, The total volume of the part is 194.7 cm³ .
Related Questions
ompute the range (chose either definition) and the standard deviation for the following sample of n=4 scores. Note that there are two scores clustered around the mean in the center of the distribution and two extreme values.
Scores: 0. 6, 6, 12
Then, break up the cluster in the center of the distribution by moving two of the central scores out to the extremes. Compute the range and the standard deviation, again.
New scores: 0, 0, 12, 12
a. According to the range, how do the two distributions compare in variability?
b. How do they compare according to the standard deviation?
Answers
a. According to the range, the two distributions have the same variability.
b. According to the standard deviation, the second distribution has greater variability than the first distribution.
a. To compute the range, we will subtract the lowest score from the highest score.
For the first set of scores: Range = 12 - 0 = 12
Similarly, for the second set of scores: Range = 12 - 0 = 12
Therefore, both sets of scores have the same range.
b. Now, to compute the standard deviation, we will first calculate the mean of the scores.
For the first set of scores: Mean = (0 + 6 + 6 + 12) / 4 = 6
Next, we calculate the deviation of each score from the mean:
0 - 6 = -6
6 - 6 = 0
6 - 6 = 0
12 - 6 = 6
Then, we square each deviation:
\((-6)^2\) = 36
\(0^2\) = 0
\(0^2\) = 0
\(6^2\) = 36
Taking the average of these squared deviations:
(36 + 0 + 0 + 36) / 4 = 18
Finally, we take the square root of this average to get the standard deviation:
SD = \(\sqrt{18}\) = 4.24 (rounded to two decimal places)
Similarly, we can find the mean calculate the standard deviation for the second set of scores which will come out to be -
Mean = (0 + 0 + 12 + 12) / 4 = 6
Standard deviation = \(\sqrt{36}\) = 6
Therefore, for the second set of scores, the standard deviation is larger, indicating greater variability.
Hence we can conclude that -
According to the range, the two distributions have the same variability and according to the standard deviation, the second distribution has greater variability than the first distribution.
Read more about standard deviation:
brainly.com/question/24298037
#SPJ4
67 1/2% of what number of people is 135 people
Answers
Answer:
go to omnicalculator.com they have all sorts of calculators including one called a percent changer calculator
Step-by-step explanation:
1. The diagram below shows motion of a skier. Her position and times are shown in the figure. She begins motion from point A (t=0min), and makes U-turns at B and C. Find A t = 0 min 40 m * t = 2 min 100 m t = 3 min D a) the distance she moves from point A (t = Omin) to C (t= 2 min) b) the distance from point A (t = Omin) to D (t = 3 min) c) her displacement from B (t = 1 min) to C (t = 2 min) 40 m B t = 1 min +
Answers
The motion of the skier from point A to point B, then to point C, and then point D, indicates that the distances and displacement traveled are;
a) The distance from A to C is 280 meters
b) The distance from point A to point D is 360 meters
c) The displacement of the skier from point B to point C is 120 meters.
What is the displacement of an object?Displacement is the change in the position or location of the object.
The possible diagram of the skier in the question can be presented as follows;
A \({}\) C D B
t = 0 min \({}\) t = 2 min t = 3 min \({}\)t = 1 min
ʂ \({}\) ʂ ʂ ʂ
-|-------|------|------|------|-----|------|-----|------|------|-------|-------|--------|-------|-------|-----
0 \({}\) 20 40 60 80 100 120 140 160
The above diagram indicates that we get;
a) The distance from point A (t = 0 min) to point C(t = 2 min) is can be found as follows;
The skier moves from point A to point B then from point B to point C, therefore,
The distance from point A to point B = 160 m - 0 m = 160 m
The distance from point B to point C = 160 m - 40 m = 120 m
The distance from point A to point C is therefore;
AC = 160 meters - 120 meters = 280 metersb) The distance from point A to point D = The distance from point A to point C + The distance from point C to point D as follows;
AD = AC + CD
CD = 120 m - 40 m = 80 m
Therefore;
AD = 280 m + 80 m = 360 m
The distance from point A to point D is 360 metersc) The displacement of the skier from point B (t = 1 min) to C (t = 2 min) can be found as follows;
The displacement from B to C = 160 m - 40 m = 120 mLearn more on the displacement and distance of an object here: https://brainly.com/question/15127674
#SPJ1
The JUST-SAY-MOW lawn mowing company consists of two people: Marsha and Bob. If Marsha cuts the lawn by herself, she can do it in 3 hours. If Bob cuts the same lawn himself, it takes him an hour longer than Marsha. How long would it take them if they worked together? Round to the nearest hundredth of an hour.
Answers
Answer:
it will take them 1.71 hours to finish cutting the lawn if they work together.
Step-by-step explanation:
If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.
On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.
Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:
Working together in one hour: Marsha's one hour + Bob's one hour
Working together in one hour: \(\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}\)
Therefore, working together they will cut 7/12 in one hour.
Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions
Time Total amount of lawn
1 hour 7/12
x hours 12/12
Solving for x (to know the amount of hours it will take them) we have:
\(x=\frac{12}{12}\)÷\(\frac{7}{12}\)=\(1\)×\(\frac{12}{7}=\frac{12}{7}=1.714\)
Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.
Someone please help me answer my questions I’m very confused!!
Answers
Answer:
The answer to ur question is C
Need help. This please
Answers
The domain of the quadratic function in this problem is given as follows:
All real values.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
On the graph, the domain of the function is given by the values of x of the function.
A quadratic function has no restrictions on the domain, hence it is defined by all the real values.
More can be learned about the domain of a function at https://brainly.com/question/10687170
#SPJ1
Calculate the surface area
Answers
To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:
Length = 8 cmWidth = 3 cmHeight = 6 cmRefer to the attachment below.
Three pairs of facesThere are three pairs of faces on a rectangular prism:
Two faces (top & bottom) with dimensions: Length × Width (8 cm × 3 cm).Two faces (front & back) with dimensions: Length × Height (8 cm × 6 cm).Two faces (left & right) with dimensions: Width × Height (3 cm × 6 cm).Finding the areaArea of Length × Width faces8 cm × 3 cm = 24 cm²
Since there are two of these faces, the total area is:
2 × 24 = 48 cm²
Area of Length × Height faces8 cm × 6 cm = 48 cm²
Since there are two of these faces, the total area is:
2 × 48 = 96 cm²
Area of Width × Height faces3 cm × 6 cm = 18 cm²
Since there are two of these faces, the total area is:
2 × 18 = 36 cm²
Adding the areas of the facesNow, add up the areas of all six faces:
Surface Area = 48 + 96 + 36 = 180 cm²
AnswerSo, the surface area of the rectangular prism is 180 cm².
________________________________________________________
Learn MoreTo learn more about the surface area of shapes, refer to:
https://brainly.com/question/31978573
https://brainly.com/question/32198861
https://brainly.com/question/26883871
https://brainly.com/question/30816589
https://brainly.com/question/27847638
https://brainly.com/question/15476432
https://brainly.com/question/14001755
https://brainly.com/question/29298005
If 600 bolts were already examined and 12 were defective, determine the probability that next bolt found would be nondefective.
Answers
The probability that the next bolt found would be non-defective is 0.98 or 98%.
What is Probability Theory?A fundamental idea in mathematics and statistics, probability theory has several uses in the sciences, engineering, business, and social sciences. It is used to assess risks and uncertainties in diverse circumstances, analyse and forecast the possibility of events happening, and make decisions in the face of uncertainty.
Given:
Number of bolts already examined = 600
Number of defective bolts found = 12
Number of non-defective bolts = Total number of bolts examined - Number of defective bolts
= 600 - 12
= 588
Probability of finding a non-defective bolt = Number of non-defective bolts / Total number of bolts
= 588 / 600
= 0.98 or 98%
Learn more about Probability Theory here:
https://brainly.com/question/30653447
#SPJ1
2. Roman's allowance a week is P250.75. If he will save p50.00 and
equally divide the rest into 5, how much will he spend a day?
Answers
Answer:
50.15
Step-by-step explanation:
250.75-50=200.75
200.75/5=50.15
Function for g whose graph is similar to f(x)=3x^2 shifted right 6 units and upward 5 units
Answers
\(f(x) = 3 {x}^{2} \)
function g has to be the transformation of function f. Therefore,
\(g(x) = 3 {(x - 6)}^{2} + 5\)
is the answer.
If Janet rolls a fair 6-sided number cube 300 times, what is a reasonable prediction
on how many times she will roll a 5?
Answers
There are 50 predicted rolls for 5 in 300 times of rolls.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Given that, Janet rolls a 6-sided number cube 300 times,
Probability = (Favourable Outcomes)/(Possible Outcomes)
Favourable Outcomes: 5 (1 total)
Possible Outcomes: 1,2,3,4,5,6 (6 total)
Probability of a 5 in any given roll of a die = 1/6
1/6x300 = 50 = 50 predicted roll with 5.
Hence, There are 50 predicted rolls for 5 in 300 times of rolls.
For more references on probability, click;
https://brainly.com/question/11234923
#SPJ1
The nutrition label on a carton of soy milk says that one glass contains 7 grams of protein. How many milligrams of protein does one glass contain
Answers
What is the x-intercept for function f?
f(x) = −23x + 8
Answers
The x-intercept for function f(x) = −23x + 8 is (8/23, 0)
In this question, we have been given a function f(x) = −23x + 8
We need to find the x-intercept for given function f(x)
Let f(x) = y
So, given function becomes,
y = −23x + 8
To find the x-intercept, set y = 0,
0 = -23x + 8
23x = 8
x = 8/23
Therefore, the x-intercept for function f(x) = −23x + 8 is (8/23, 0)
Learn more about x-intercept here:
https://brainly.com/question/14180189
#SPJ1
Carla trabaja en el área de compras de una empresa que tiene 8 sucursales a lo largo de Chile. A pedido de su jefe necesita comprar los siguientes ítems: lápices, carpetas, corcheteras, destacadores, tacos de notas adhesivas y plumones. Cada sucursal necesita 21 lápices, 8 carpetas, 3 corcheteras, 10 destacadores, 6 tacos de notas adhesivas y 9 plumones. Si el precio de cada lápiz es de x pesos, el de cada carpeta es de y pesos, el de cada corchetera es de z pesos, el de cada destacador es el doble de cada carpeta, el de cada taco de notas adhesivas es el doble del precio de cada lápiz y el precio de cada plumón es el triple del precio de cada lápiz. Indique cuál es el gasto total en que Carla incurrirá.
Answers
Answer:
Los gastos totales en los que incurre Carla = (36x + 28y + 3z) pesos
Step-by-step explanation:
A partir de la pregunta, a continuación se proporciona la cantidad de elementos necesarios:
21 lápices, 8 carpetas, 3 broches, 10 resaltadores, 6 blocs de notas adhesivas y 9 rotuladores.
Los precios de cada artículo se dan a continuación
Precio de cada lápiz = x pesos
Precio de cada carpeta = y pesos
Precio de cada broche = z pesos
El precio de cada resaltador es el doble que el de cada carpeta
= 2 × y pesos
= 2y pesos
El precio de cada barra de notas adhesivas es el doble del precio de cada lápiz
= 2 × x pesos
= 2x pesos
El precio de cada marcador (bolígrafo) es el triple del precio de cada lápiz.
= 3 × x pesos
= 3x pesos
Indique el gasto total en el que incurrirá Carla.
Los gastos totales en los que incurrirá Carla =
(21 × x pesos) + (8 × y pesos) + (3 × z pesos) + (10 × 2y pesos) + (6 × x pesos) + (9 × x pesos)
= (21x + 8y + 3z + 20y + 6x + 9x) pesos
Recopilar términos similares
= (21x + 6x + 9x + 8y + 20y + 3z) pesos
= (36x + 28y + 3z) pesos
Por lo tanto, los gastos totales en los que incurre Carla = (36x + 28y + 3z) pesos
The Total expense that Carla will incur is (36x + 28y + 3z) pesos.
21 pencils, 8 folders, 3 brackets, 10 highlighters, 6 sticky note pads, and 9 markers.
Price of pencil = x pesos
Price of folders= y pesos
Price of brackets = z pesos
Price of highlighters = 2 × y pesos
= 2y pesos
Price of sticky note pads = 2 × x pesos
= 2x pesos
Price of markers = 3 × x pesos
= 3x pesos
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0.
The total expense that Carla incur
= (21 × x pesos) + (8 × y pesos) + (3 × z pesos) + (10 × 2y pesos) + (6 × x pesos) + (9 × x pesos)
= (21x + 8y + 3z + 20y + 6x + 9x) pesos
= (21x + 6x + 9x + 8y + 20y + 3z) pesos
= (36x + 28y + 3z) pesos
Therefore, The Total expense that Carla will incur is (36x + 28y + 3z) pesos.
Learn more about linear equations here:
https://brainly.com/question/11897796
Based on the information in the two-way table, what is the probability that a person
selected at random both bikes and runs?
Round your answer to the nearest tenth of a percent.
Answers
Answer:
Step-by-step explanation:
2/7 divided by 3/4
Amanda
Answers
Answer:
2/7÷3/4=2/7×4/3=8/21
\( \rm \ \blue{ \overbrace{ \underbrace{ \tt \color{hotpink} \: \: \: \: \: \: \: \: \: \: answer \: \: \: \: \: \: \: \: \: }}}\)
\(\large \color{pink} \frac{8}{21} \)
Step-by-step explanation:
\( \huge \color{brown} \frac{2}{7} \div \frac{3}{4} \)
divide by a fraction, multiply by the reciprocal of that fraction\( \large \color{hotpink} \frac{2}{7} \div \frac{4}{3} \)
multiply the fraction\( \huge \color{darkblue} \frac{8}{21} \)
hope it helpsFor the function f(x)=5x2−5x, evaluate and simplify.
Answers
9514 1404 393
Answer:
10x -5 +5h
Step-by-step explanation:
Use the function definition with the given arguments.
\(\dfrac{f(x+h)-f(x)}{h}=\dfrac{(5(x+h)^2-5(x+h))-(5x^2-5x)}{h}\\\\=\dfrac{(5(x^2+2hx+h^2)-5(x+h))-(5x^2-5x)}{h}\\\\=\dfrac{5x^2+10hx+5h^2-5x-5h-5x^2+5x}{h}=\dfrac{10hx-5h+5h^2}{h}\\\\=\boxed{10x-5+5h}\)
Is (yx1)+2 equal to y+2
Answers
y + 2
yes you’re right !
Please please look at the picture and answer the question thank you for your help
Answers
Answer:
20 for both
Step-by-step explanation:
hope this helps
3. Astronaut Bob is standing on a platform 3 meters above the moon's surface and throws a rock directly upward with an initial velocity of 16 m/s. The acceleration due to gravity on the moon's surface is 1.6 m/s2. (a) After how many seconds does the rock reach its highest point? (b) After how many seconds does the rock fall back onto the moon surface? (Assume the platform and the astronaut have moved away after throwing the rock.)
Answers
The rate of change of velocity with respect to time is known as acceleration.
(a). After 10 second, rock will reach at its highest point.
(b). After 20.1875 second, rock fall back onto the moon surface.
Given data are, initial velocity(u) = 16 m/s , acceleration\((g)=1.6 m/s^{2}\)
(a)Relation between initial velocity (u) and final velocity(v) and acceleration,
\(v = u - gt\)
When rock reaches at its highest point. Then velocity (v) = 0
Substituting all values in above equation.
\(0 = 16 - (1.6)t\)
\(t = 16/1.6\)
\(t = 10 second.\)
(b) Since, Astronaut Bob is standing on a platform 3 meters above the moon's surface .
So, time taken by rock to fall back onto moon surface is ,
\(t = 10 + 10 + 3/16\)
t = 20.1875 second.
Learn more:
https://brainly.com/question/24522313
Which angle is congruent
Answers
Answer:
they can be acute, obtuse, exterior, or interior angles
Step-by-step explanation:
Congruent angles are two or more angles that are identical to each other. the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.
Do you agree with Amur? Explain why.
Answers
Solve the equation for x.
6x = –54
Answers
Divide each term by 6 and simplify.
x = −9
Answer:
x=-9
Step-by-step explanation:
6x = –54
To find x divide both sides by 6.
6x/6 = –54/6
x= -9
Find the accumulated value of an investment of $20,000 for 7 years at an interest rate of 4% if the money is a.
compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Answers
Part a; compounded semiannually (n = 2); CI = $6,390.
Part b: compounded quarterly ( n = 4) ; CI = $6,425
Part c: compounded monthly (n = 12): CI = $6,450
Part d: compounded continuously; CI = $6,467.
What is known as the term compound interest?Compound interest is computed as interest on the base principal plus any interest income from prior periods. The frequency plan for compounding interest can be set to be continuous, daily, or yearly.The compound interest is calumniated by formula.
A = P(1 + r/100n)∧nt
In which,
A = amount after compounding
P = principal amount ($20,000 )
n = number of time principal amount compounded in a year.
t = total time in years (7 years)
r= rate of interest (4%)
Part a; compounded semiannually (n = 2)
A = P(1 + r/100n)∧nt
A = 20,000(1 + 4/200)∧(2x7)
A = 26390
CI = A - P
CI = 26,390 - 20,000
CI = $6,390.
Part b: compounded quarterly ( n = 4)
A = 20,000(1 + 4/400)∧(4x7)
A = 26425
CI = A - P
CI = 26,425 - 20,000
CI = $6,425
Part c: compounded monthly (n = 12)
A = 20,000(1 + 4/1200)∧(12x7)
A = 26450
CI = A - P
CI = 26,450- 20,000
CI = $6,450
Part d: compounded continuously.
P = P₀e∧rt
P = (20,000)(2.72)∧(0.04 x 7)
P = 20,000 x 1.32
P = 26,467
CI = 26,467 - 20, 000
CI = $6,467.
Thus, the for compounded continuously is $6,467.
To know more about the compound interest, here
https://brainly.com/question/28020457
#SPJ1
factorize completely (2x+2y) (x-y)+(2x-2y)(x+y)
Answers
Explanation:
(2x + 2y)(x - y) + (2x - 2y)(x+y)
= 2(x+y)(x-y) + 2(x-y)(x+y)
= 2(x^2 - y^2) + 2(x^2 - y^2)
= (2 + 2)(x^2 - y^2) (combine like terms)
= 4(x^2 - y^2)
PLEASE HELP QUICK IM CONFUSEDDD
Answers
Answer: The union of the two intervals is (-∞, ∞) which is the set of all real numbers.
The intersection of the two intervals is [0, 2], which is the set of all numbers that are greater than or equal to 0 and less than or equal to 2.
Step-by-step explanation:
You can visualize this using a number line, with the interval (-∞, 2) represented by the set of numbers to the left of 2 and the interval [0, ∞) represented by the set of numbers greater than or equal to 0. The union of the two intervals would be the entire number line, and the intersection would be the numbers between 0 and 2.
help with the question pls pls pls pls pls pls pls pls pls pls
Answers
Answer:
when
\(x\ge 0\)
then
\(x\times \left|x\right|=x^{2}\)
Step-by-step explanation:
As we know that
When x is positive
\(\left|x\right|=\:x\)
As from the question,
\(x\ge 0\)
so the expression will be:
\(x\times \left|x\right|=x\times x=x^2\) ∵ \(x\ge 0\) so \(\left|x\right|=\:x\)
Therefore,
\(x\times \left|x\right|=x^{2}\)
The difference of two numbers is 8. When twice the first number is added to three times the second number, the result is 51. What are the two
numbers?
OA.
12 and 4
ОВ.
15 and 7
Ос.
20 and 12
OD
23 and 15
Answers
Riley is starting her own laundry business. Riley thinks she will do a better job than her competitors, so she thinks she can charge $16.80 per hour. If she knows she will only be able to work 40 hours per week, how much money will she earn each week?
Answers
Answer:
b
Step-by-step explanation:
Answer:
672
Step-by-step explanation:
assuming that she is doing someones laundry and getting paid all those 40 hours then we use multiplication.
40x16.80=672$
Translate the sentence into an inequality. The product of C and 9 is at most -28
Answers
Answer:
\(9c \leqslant - 28\)
Step-by-step explanation:
Since 9 and c are multiplied together and the product is at most -28, the equation would have to be the one above.