Answer:
The capacity of the container is 2546.78 cm³.
Step-by-step explanation:
The volume of the frustum of a cone is:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
The information provided is:
r = 16/2 = 8 cm
R = 24/2 = 12 cm
h = 8 cm
Compute the capacity of the container as follows:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
[tex]=\frac{\pi\cdot8}{3}\cdot[(12)^{2}+(12\cdot 8)+(8)^{2}]\\\\=\frac{8\pi}{3}\times [144+96+64]\\\\=\frac{8\pi}{3}\times304\\\\=2546.784445\\\\\approx 2546.78[/tex]
Thus, the capacity of the container is 2546.78 cm³.
The body paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 11/2hours.
What is the probability that the painting time will be less than or equal to an hour?
What is the probability that the painting time will be more than 50 minutes?
Determine the expected painting time and its standard deviation.
Answer:
a. [tex]\mathbf{P(Y \leq 60) = 0.3333}[/tex]
b. P(Y>50) = 0.8889
c. E(y) = 67.5 and Standard deviation [tex]\sigma[/tex] = 12.99
Step-by-step explanation:
From the information given :
an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to [tex]1\frac{1}{2}[/tex]hours.
The objective is to determine the probability that the painting time will be less than or equal to an hour?
since 60 minutes make an hour;
[tex]1\frac{1}{2}[/tex]hours = 60 +30 minutes = 90 minutes
Let Y be the painting time of the automobile; then,
the probability that the painting time will be less than or equal to an hour ca be computed as :
[tex]P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333[/tex]
What is the probability that the painting time will be more than 50 minutes?
The probability that the painting will be more than 50 minutes is P(Y>50)
So;
[tex]P(Y>50) = \int \limits ^{90}_{50} f(y) dy[/tex]
[tex]P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy[/tex]
[tex]P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}[/tex]
[tex]P(Y>50) = (\dfrac{90-50}{45})[/tex]
[tex]P(Y>50) = \dfrac{40}{45}[/tex]
P(Y>50) = 0.8889
Determine the expected painting time and its standard deviation.
Let consider E to be the expected painting time
Then :
[tex]E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}[/tex]
[tex]E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}[/tex]
To determine the standard deviation, we need to first know what is the value of our variance,
So:
Variance [tex]\sigma^2[/tex] = E(x²) - [E(x)]²
Variance [tex]\sigma^2[/tex] = 4725 - (67.5)²
Variance [tex]\sigma^2[/tex] = 4725 - 4556.25
Variance [tex]\sigma^2[/tex] = 168.75
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{variance}[/tex]
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{168.75}[/tex]
Standard deviation [tex]\sigma[/tex] = 12.99
If a TV set is bought on the installment plan there is a down payment of $25 and 12 monthly payments of $15 each. The same set may be bought for cash at 12% less than the installment price. The amount saved by making a cash payment is:
Answer:
Amount saved by making a cash payment is $24.6
Step-by-step explanation:
We start by calculating the amount to be paid if payment was by installments.
We are told that there would be a down payment of $25 and $15 every month for 12 months.
So total installment payment would be;
$25 + 12($15) = $25 + $180 = $205
Now let’s try and figure out the cash payment
For the cash payment, we have 12% less than installment payment.
Kindly note that 12% is same as 12/100 = 0.12
Thus, 12% less payment would be;
205-0.12(205) = 205 - 24.6 = $180.4
Thus, the amount saved if payment was cash would be;
$205 - $180.4 = $24.6
Geometry, please answer question ASAP
Answer:
Yes, PQR ~ TSV with a scale of 1 : [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Yes the triangles are congruent for the statement given in option C
The scale 1 : [tex]\sqrt{3}[/tex] shows that the side lengths are proportional
PQ/TS = QR/SV
3[tex]\sqrt{3}[/tex]/6/[tex]\sqrt{3}[/tex] and that's simplified as 1/[tex]\sqrt{3}[/tex]
A sector of a circle has an arc measurement of 110°. The area
of the sector is 117 cm What is the diameter of the circle?
Answer:
22.08 cm
Step-by-step explanation:
Area = pi*r^2*(angle/360)
r=11.04, d=22.08
2x-15=3(2x+3)
It’s multi step equations
Answer:
x = -6
Step-by-step explanation:
Hello!
2x - 15 = 3(2x + 3)
Distribute the 3
3 * 2x = 6x
3 * 3 = 9
2x - 15 = 6x + 9
Subtract 2x from both sides
-15 = 4x + 9
Subtract 9 from both sides
-24 = 4x
Divide both sides by 4
-6 = x
Hope this helps!
Multiply.
(7c+6)(-5c-4)
Simplify your answer.
Х
Answer:
120c
Step-by-step explanation:
7c(-5c)*(-4+6)
7c+5c*4+6
12c*10
120c
Answer:
the answer can be step by step explanation will be found in the answer was Matilda by 776 7 x 6 then the answer you will you - with the answer dancer used you New divide the answer that answer the simple your answer if we multiply you can contact me and say me in which is correct or wrong and I am a teacher
Given equation x-y=2. Find x and y.
PLEASE help me with this question. This is really URGENT
Answer:
c. p(10)=26,327(1+0.024)^10
Step-by-step explanation:
its just the answer
Answer:
[tex]\boxed{\sf Option \ 3}[/tex]
Step-by-step explanation:
The problem is exponential growth.
[tex]a(1+r)^t[/tex]
[tex]a = \sf initial \ amount[/tex]
[tex]r = \sf rate[/tex]
[tex]t= \sf time[/tex]
The third option is right.
[tex]P(10)=26237(1+2.4\%)^{10}[/tex]
[tex]P(10)=26237(1+0.024)^{10}[/tex]
I need help fast please
Answer:
Difference : 4th option
Step-by-step explanation:
The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.
x² + 3x + 2 - Break the expression into groups,
( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,
x( x + 1 ) + 2( x + 2 ) - Group,
( x + 2 )( x + 1 )
This is the same as the denominator of the other fraction, and therefore we can combine the fractions.
x - 1 / ( x + 2 )( x + 1 )
As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.
Help please, I would really appreciate it. :)
Answer:
9, 13, 17, 21
Step-by-step explanation:
If x=2,
y=1+4(2)
y=9
This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.
Consider the following polynomial expression: 4x5 - 16x2 + 13x8.
Part D: what is the leading term ?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]13x^8[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]4x^5 - 16x^2 + 13x^8[/tex]
The leading term contains the highest power of 'x'.Since 8 is greater than 5 and 2, the leading term in the give in polynomial would be [tex]13x^8[/tex].⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
3 x 5(0 + 2) - 4
O Α. Ο
ling
B.
11
O C. 26
O D. 33
Answer:
26 is the answer
Step-by-step explanation:
hope this helps you
Please help, 50 points! :) Please do all parts
you WILL get brainiest
PDF attached below
1. The first step here is to arrange the data set's form least to greatest,
Sherelle: 26, 39, 56, 58, 60, 62, 65, 66, 66, 68, 71, 72, 72, 73, 74, 75, 81, 83, 84, 85
Venita: 44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79
Now we can determine our 5 - number summary based on the numbers respective positions.
First Data Set,
(Five - Number Summary) - Minimum : 26, Quartile 1 : 60, Median : 69.5, Quartile 3 : 75, Maximum : 85
Second Data Set,
(Five - Number Summary) - Minimum : 44, Quartile 1 : 53, Median : 63.5, Quartile 3 : 73, Maximum : 79
2. This part is based on your drawings of the box and whisker plots, so you would have to figure that part out by yourself.
3. First off we know that our data set is composed of the years from 1900, so let's rewrite the set based off of the actual year -
Sherelle: 1926, 1939, 1956, 1958, 1960, 1962, 1965, 1966, 1966, 1968, 1971, 1972, 1972, 1973, 1974, 1975, 1981, 1983, 1984, 1985
Venita: 1944, 1945, 1951, 1951, 1953, 1953, 1955, 1957, 1958, 1962, 1965, 1966, 1969, 1969, 1970, 1973, 1975, 1977, 1978, 1979
( a ) Now in Sherelle's defence, she can say that the lowest coin date in her group is 1926, comparative to Venita's group - the lowest coin date in hers being 1944. Therefore, she is more likely to have the 1916 coin, after all that date is the lowest overall in both their data set.
( b ) In Venita defence, she can say that the mean of her data set is lower than the mean of Sherelle's data set. Take a look at the calculations below,
Sherella's Mean : [tex]\frac{39336}{20}[/tex] = [tex]\frac{9834}{5}[/tex] = 1966.8,
Venita's Mean : [tex]\frac{39250}{20}[/tex] = [tex]\frac{3925}{2}[/tex] = 1962.5
( c ) I would say Sherella's bag would most likely contain the 1916 coin. The mean is a prominent factor, but their mean(s) only differ by a very small quantity. That too, Sherella's bag contains the lowest coin in both their groups, and though that is not a prominent factor, it could be that she does have the 1916 coin.
which of the following shows maximum rise in temperature?
a} 23 to 32
b} [ -10] to 1
c} [-18] to [-11]
d} [-5] to 5
Answer:
b) (-10) to 1Step-by-step explanation:
it shows the maximum rise in temperature.
Answer:
b answer, will show the rise in temperature
{3, 6, 9, 12, 15, 18, 21, ...)
Answer:
Below
Step-by-step explanation:
5)
The sequence includes the terms 3,6,9,12,15.. and so on
Notice that each time we add 3.
The first term is 3.
We can see it in a different way
● 3 = 3×1
● 6 = 3×2
● 9 = 3×3
● 12 = 3×4
Let 1 be n. Notice what happens
● 3 = 3n
● 6 = 3 × (n+1)
● 9 = 3 × (n+2)
● 12 = 3 × (n+3)
So we can express it as.
● a1 = 3 × 1 =3
● a2 = 3×2 =6
● a3 = 3×3 = 9
So the third term is a3 wich is 9
● a6 = 3×6 = 18
So the sixth term is 18 .
■■■■■■■■■■■■■■■■■■■■■■■■■■
6)
the sequence is defined by:
● f(n-1) = -0.5 f(n)
Repalce n-1 with n and n with n+1
● f(n) = -0.5 f(n+1)
So to get a term you must multiply the next one by -0.5
The first term in the sequence is 120.
● 120 = -0.5 f(n+1)
● f(n+1) = 120/-0.5
● f(n+1) = -60
So the second term is -60
How to work out the medium in maths
Answer:
To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
It's the middle value of a list of numbers arranged in order.
For example the median of the list 1 2 3 4 5 is 3.
If there are an even number of values, the median is the mean of the middle two. For example:
1 3 4 5 7 9:
The middle 2 numbers are 4 and 5 so
the median is (4 + 5) / 2 = 4.5
1/3(12-6x)=4-2x I need help pls
Answer:
no solution
Step-by-step explanation:
1/3(12-6x)=4-2x
4-1.3x=4-2x
4=4-0.7x
0=0.7x
ns
The research chemists at MegaClean created a new cleaner that keeps car and truck tires shiny and clean for one year. They believe that this product will be highly successful and will attract customers to purchase their existing line of household cleaning products.
Answer:
Complementary effect
Step-by-step explanation:
Complementary goods service is another good or item used in conjunction with the service. In general, complementary goodness does not matter when eaten alone, but when combined with another good or service, it increases the overall value of the offering. When a product shares a lucrative relationship with another product offering it is considered an affiliate, for example, an iPhone and apps used with it, so that this is good example of Complementary effecthelp with math again please
ANSWER:
It is C
NO EXPLANATION
choose the equation below that represents the line passing through the point (1,-4) with a slope of 1/2
PLS HELP ON THIS QUESTIN I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The bars in a _____________ do not touch since data is ______________.
A. bar graph ; continuous
B. bar graph ; discrete
C. histogram ; discrete
D. histogram ; continuous
Answer:
I believe it's D. histogram ; continuous
Step-by-step explanation:
[tex]2 |3 \sqrt{2} - 2 \sqrt{3} | + |3 \sqrt{8} - 8 \sqrt{3} | + 2 \sqrt{12} [/tex]
.......................
Answer:
hope it helps
Step-by-step explanation:
Answer:
SEE THE IMAGE FOR SOLUTION..
In ΔEFG, the measure of ∠G=90°, EG = 11, FE = 61, and GF = 60. What ratio represents the sine of ∠F?
Answer:
sinF = [tex]\frac{11}{61}[/tex]
Step-by-step explanation:
sinF = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{EG}{FE}[/tex] = [tex]\frac{11}{61}[/tex]
The ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].
What is sine of an angle?In a right angled triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse.
Formula for sine of an anglesin θ = opposite side w.r.t θ / hypotenuse
According to the given question
We have
A right angle triangle EFG, in which
∠G = 90 degree
EG = 11
FE = 61
and, GF = 60
Now, the opposite side with respect to ∠F is GE
and the hypotenuse is EF
Therefore, sine of ∠F = side which is opposite w.r.t ∠F/ hypotenuse
⇒ [tex]sinF=\frac{GE}{EF}[/tex]
⇒ [tex]SinF=\frac{11}{61}[/tex]
Hence, the ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].
Learn more about sine of an angle here:
https://brainly.com/question/13656175
#SPJ2
Simplify 3(2x - 5). 1)-6x - 15 2) 6x - 15 3) 6x - 8 4) 5x - 2
Answer:
[tex] \boxed{ \bold{ \: 6x - 15}}[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \mathsf{3(2x - 5)}[/tex]
Distribute 3 through the parentheses
⇒[tex] \mathsf{3 \times 2x - 3 \times 5}[/tex]
Calculate the product
⇒[tex]6x - 15[/tex]
Hope I helped!
Best regards!!
Writing equations in standard form:
(1,-6) and (-7,2)
How would I write this in standard form? I already tried but I keep getting x+y=7 and it says it’s wrong so could someone help?
Answer:
[tex]x + y = - 5[/tex]
Step-by-step explanation:
hopefully it is clear and makes sense
:)
Someone pls help me . I also need to show work just in case my teacher ask me to send her a photo of my notebook .
Answer: (i) 3
(ii) 10
(iii) 1080
Step-by-step explanation:
(i) Coefficient is the number written before any variable.
Coefficient of x in [tex]3x+10=36[/tex] is 3.
(ii) Constant is a numerical term written without any variable.
Constant in [tex]2x+10=5x[/tex] is 10.
(iii) Let x be the number of miles Katie's family drive.
Since they charge $30 combined with $0.25 per mile drive.
So, Total charge = 0.25 x +30 ( in dollars)
If they charged $300, then
[tex]0.25 x +30 =300[/tex]
Subtract 30 from both sides, we get
[tex]0.25x=270[/tex]
Divide both sides by 0.25, we get
[tex]x=1080[/tex]
Hence, Katie drove 1080 miles.
Monica wants to save at least $399 to buy a new laptop computer. She has $284 saved
already. Which option below will allow her to have enough money to buy the computer?
a. She spends $22 and earns $93.
b. She is given $38 and earns $42.
c. She spends $82 and earns $94.
d. She earns $580 and spends $422.
Answer:
D. She earns $580 and spends $422.
Step-by-step explanation:
The option of Monica earning $580 and spending $422 will allow her to have enough money to buy the new computer.
First, add $580 to the $284 that she already has saved:
284 + 580
= $864
Then, subtract $422 from this:
864 - 422
= $442
So, this option will leave her with $442. Since she only needed to save at least $399 to buy the computer, this means she has enough money for it.
The option that will let her buy the computer is D. She earns $580 and spends $422.
First Question The following table shows the length and width of a rectangle: Length Width Rectangle A 4x + 5 3x − 2 Which expression is the result of the perimeter of rectangle A and demonstrates the closure property? A.14x + 6; the answer is a polynomial B.14x + 6; the answer may or may not be a polynomial C.2x + 6; the answer is a polynomial D.2x + 6; the answer may or may not be a polynomial
Answer: A.14x + 6; the answer is a polynomial
Step-by-step explanation:
Since all of the variables have integer exponents that are positive this is a polynomial.
EXTRA POINTS. WILL GIVE A BRAINLIEST AND A THANK YOU. ANSWER ASAP... I want a clear, grammatically correct answer please, Part A and Part B separate; This is an essay, please write it as such. All steps! Easy to understand! Josh and his friends bought vanilla wafers for $4 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $45 to buy a total of 27 packets of wafers of the two varieties. Part A: Write a system of equations that can be solved to find the number of packets of vanilla wafers and the number of packets of chocolate wafers that Josh and his friends bought at the carnival. Define the variables used in the equations. (5 points) Part B: How many packets of chocolate wafers and vanilla wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)
Answer:
Part A:
[tex]x+y=27 \\4x+y = 45[/tex]
Part B:
Number of vanilla wafers packets bought = 6 and
Number of chocolate wafers packets bought = 21
Step-by-step explanation:
Given:
Cost of each packet of vanilla wafer = $4
Cost of each packet of chocolate wafer = $1
Total number of packets bought = 27
Total money spent = $45
Part A:
To write a system of equations for the given situation.
Here, we do not know the number of packets bought for each type of wafer.
We just know that total number of packets bought and the total money spent in buying those packets.
Let us suppose,
Number of packets of vanilla wafers bought = [tex]x[/tex] and
Number of packets of chocolate wafers bought = [tex]y[/tex]
Total number of packets = Number of packets of vanilla wafers bought Plus Number of packets of chocolate wafers bought:
i.e. [tex]x+y=27 ...... (1)[/tex]
Money spent on vanilla wafers packets = [tex]4 \times x[/tex]
Money spent on chocolate wafers packets = [tex]1 \times y[/tex]
Total money spent = [tex]4x+y = 45 ...... (2)[/tex]
So, the system of equations is:
[tex]x+y=27 \\4x+y = 45[/tex]
Part B:
To find number of packets bought for each flavor = ?
Here, we have two equations and two variables [tex]x[/tex] and [tex]y[/tex].
As, the coefficients of [tex]y[/tex] in both the equations are same.
Let us subtract equation (1) from (2):
[tex]4x+y-x-y=45-27\\\Rightarrow 3x = 18\\\Rightarrow \bold{x =6}[/tex]
By equation (1), putting the value of [tex]x[/tex] and solving for [tex]y[/tex]:
[tex]6+y=27\\\Rightarrow \bold{y =21}[/tex]
So, number of vanilla wafers packets bought = 6 and
number of chocolate wafers packets bought = 21
I need help bc I am not smart
Answer:
1) one and two-thirds hour
2) 2.4 miles