Answer:
4 : 5
Step-by-step explanation:
you can divide 120 and 150 by 30 and 8 and 10 by 2.
120/30 = 4
150/30 = 5
8/2 = 4
10/2=5
Answer: 4:5
Step-by-step explanation:
Which of the following integrals will determine the volume of the solid generated by revolving the region bounded by the curves y = 6x, y = x and y = 24 about the y-axis using the shell method?
a) integral^24_0 2 pi x(24 - 5x) dx
b) integral^24_0 5/3 pi y^2 dy
c) integral^4_0 10 pi x^2 dx + integral^24_4 2 pi x(24 - x) dx integral^4_0 25 pi x^2 dx + integral^24_4 2 pi x(24 - x) dx
d) integral^4_0 25 pi x^2 dx + integral^24_4 pi (24 - x)^2 dx
e) integral^24_0 25 pi y^2/36 dy
Answer:
The answer is "Option C."
Step-by-step explanation:
[tex]y=6x, \ \ y=x, \ \ , y=24,\\[/tex]
In this we calculate two points that are (0,4) and(4,24)
on[0,4]
shell radius=x
height = 6x-x
=5x
on[4,24]
shell radius=x
height = 24x-x
6x=24
x=4
Calculating shell volume by shell method:
[tex]v=\int\limits^b_a {2\pi(radius) \cdot(height)} \, dx \\[/tex]
[tex]=\int\limits^4_0 {2\pi(x) \cdot(5x)} \, dx +\int\limits^{24}_4 {2\pi(x) \cdot(24-x)} \, dx \\\\=\int\limits^4_0 {10\pi(x^2) dx +\int\limits^{24}_4 {2\pi x(24-x)} \, dx[/tex]
That's why the answer is "Option C".
The volume of a cylinder varies jointly with the base (area) and the height. The volume is 40 inches^3 when the base (area) is 6 inches^2 and the height is 20 inches. Find the volume of the cylinder (after finding the variation constant) when the base (area) is 8 inches^2 and the height is 12 inches.
Answer: K = ¹/₃, V = 32in³
Step-by-step explanation:
Volume of s cylinder (V) = πr²h where πr² is the base area.
Now from the question,
V ∞ πr²h
V = kπr²h where k is the constant of proportionality which is also the variation constant.
40 = 6 x 20 x k
40 = 120k and
k = ⁴⁰/₁₂₀
= ¹/₃.
Now to find the volume when base area is 8in² and h is 12,
V = 8 x 12 x ¹/₃
V = 32in³
An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?
Answer
[tex]P= 0.144[/tex] ways
the coin can land tails either exactly 8 times or exactly 5 times in
[tex]0.144[/tex] ways
Step by step explanation:
THis is a binomial distribution
Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.
P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹
p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³
p=(9)+p(3)
p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴
P= (0.5)¹⁴ [C(14,9) + C(14,3)]
P= (0.5)¹⁴ [2002 * 364]
P= 1/16384 * (2002 +364)
P= 91091/2048
P= 0.144
Hence,the coin can land tails either exactly 8 times or exactly 5 times in
[tex] 0.144[/tex] ways
Is this strong positive correlation or weak positive or strong negative or weak negative?
Answer:
Weak negative correlation
Step-by-step explanation:
The scatter plot shown in the graph above indicates a negative correlation between the x-variables and the y-variables, because, as the variables on the x-axis increases, the variables on the y-axis decreases.
Also, the if we are to draw a line of best fit to connect some of the data points on a straight line, we would see that a number of the data points would be far apart from each other away from the line. The data points are not much clustered around the line of best fit, therefore, this shows that the negative correlation between the variables is a weak one.
The data represented on the scatter plot show a weak negative correlation.
The temperature is 58° F. It gets warmer by h degrees and reaches to 65° F. Find h.
Answer:
h = 7 degrees
Step-by-step explanation:
To find h, we know that it is positive because it increases in value, not decreases:
h = 65 - 58
h = 7
Answer:
h = 7°F
Step-by-step explanation:
58 + h = 65
h = 65 - 58
h = 7
Check:
68 + 7 = 65
Simplify the following algebraic expression.
square root of 39x^7
Answer: x^3 square root 39x
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Solve the initial value problem y′+y=f(t),y(0)=0 where f(t)={1,−1, if t<4 if t≥4 Use h(t−a) for the Heaviside function shifted a units horizontally.
Looks like the function on the right hand side is
[tex]f(t)=\begin{cases}1&\text{for }t<4\\-1&\text{for }t\ge4\end{cases}[/tex]
We can write it in terms of the Heaviside function,
[tex]h(t-a)=\begin{cases}1&\text{for }t\ge a\\0&\text{for }t>a\end{cases}[/tex]
as
[tex]f(t)=h(t)-2h(t-4)[/tex]
Now for the ODE: take the Laplace transform of both sides:
[tex]y'(t)+y(t)=f(t)[/tex]
[tex]\implies s Y(s)-y(0)+Y(s)=\dfrac{1-2e^{-4s}}s[/tex]
Solve for Y(s), then take the inverse transform to solve for y(t):
[tex](s+1)Y(s)=\dfrac{1-e^{-4s}}s[/tex]
[tex]Y(s)=\dfrac{1-e^{-4s}}{s(s+1)}[/tex]
[tex]Y(s)=(1-e^{-4s})\left(\dfrac1s-\dfrac1{s+1}\right)[/tex]
[tex]Y(s)=\dfrac1s-\dfrac{e^{-4s}}s-\dfrac1{s+1}+\dfrac{e^{-4s}}{s+1}[/tex]
[tex]\implies y(t)=1-h(t-4)-e^{-t}+e^{-(t-4)}h(t-4)[/tex]
[tex]\boxed{y(t)=1-e^{-t}-h(t-4)(1-e^{-(t-4)})}[/tex]
Find the exact perimeter (in inches) and area (in square inches) of the segment shown, given that m∠O = 60° and OA = 24 in.
Answer:
A. Perimeter of segment = 49 in.
B. Area of segment = 52 in².
Step-by-step explanation:
Data obtained from the question include:
Radius (r) = 24 in.
Angle at the centre (θ) = 60°
Perimeter of segment =.?
Area of segment =.?
A. Determination of the perimeter of the segment.
Perimeter of segment = length of arc + length of chord
Length of arc = θ/360 x 2πr
Length of chord = 2r x sine (θ/2)
Pi (π) = 3.14
Length of arc = θ/360 x 2πr
Length of arc = 60/360 x 2 x 3.14 x 24
Lenght of arc = 25.12 in
Length of chord = 2r x sine (θ/2)
Length of chord = 2 x 24 x sine (60/2)
Length of chord = 24 in
Perimeter of segment = length of arc + length of chord
Perimeter of segment = 25.12 + 24
Perimeter of segment = 49.12 ≈ 49 in.
B. Determination of the area of the segment.
Area of segment = Area of sector – Area of triangle.
Area of sector = θ/360 x πr²
Area of triangle = r²/2 sine θ
Area of sector = θ/360 x πr²
Area of sector = 60/360 x 3.14 x 24²
Area of sector = 301.44 in²
Area of triangle = r²/2 sine θ
Area of triangle = 24²/2 x sine 60
Area of triangle = 249.42 in².
Area of segment = Area of sector – Area of triangle.
Area of segment = 301.44 – 249.42
Area of segment = 52.02 ≈ 52 in²
What is the y-intercept of the function f(x)=4 - 5x?
-5
-4
4
5
Answer:
y-intercept = (0,4)
Step-by-step explanation:
To find the y-intercept, the place at which the value of x is 0, simply plug zero into your function:
f(x) = 4 - 5x
f(0) = 4 - 5(0)
f(0) = 4
Hence, the y-intercept occurs at (0,4).
The y-intercept of f(x) = 4 - 5x is 4.
Using the slope intercept formula the y-intercept can be found below
y = mx + bwhere
m = slope
b = y-intercept
From the equation:
f(x) = 4 - 5x
According to the slope intercept format,
m = slope = -5
y- intercept = 4
Therefore, the y-intercept of f(x) = 4 - 5x is 4.
read more: https://brainly.com/question/4023516?referrer=searchResults
A local orchestra is holding a charity concert concert at the community center. Each adult ticket $12, and child ticket costs $8. The organizers of the event hope to raise no less than $2,500, and the community center can seat up to 280 people. This graph and system in inequalities represent this situation, where x represents the number of adult tickets and y represents the number of child tickets. 12x + 8y> 2,500. X + y < 280
The answer is (180,80)
To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.
InequalityThe given question is an inequality situation where we are asked to use graph to solve.
The data given are
adult ticket = $12child ticket = $8Total amount raised = $2500Total number of people = 280The inequality for this problem is given is as
[tex]12x + 8y > 2500\\x + y < 280[/tex]
Kindly find the attached image as the graph and solution to this problem.
Learn more on graphically solution for inequality here;
https://brainly.com/question/24372553
#SPJ2
6th grade math, help pleasee:)
Answer:
1/5 cup
Step-by-step explanation:
Sugar: water
1 5
We want 1 cup water, so divide each side by 5
1/5 : 5/5
1/5 : 1
There is 1/5 cup sugar to 1 cup water
SCREENSHOT OF MY QUESTION:
Answer in fraction form = 9/8
Answer in decimal form = 1.125
note: the improper fraction 9/8 converts to the mixed number 1 & 1/8
To get this answer, we divide both sides by 8 to isolate n. The expression 8n really means "8 times n". We divide to undo the multiplication.
Transformation of exponential functions
Answer:
left, 4 units
Step-by-step explanation:
This indicates a shift to the left of 4 units. We know that it's left because the +4 is in the exponent and, it's a +4 not -4.
In △ABC, m∠A=19°, a=13, and b=14. Find c to the nearest tenth.
Answer:
c is either 25.4 or 1.1
Step-by-step explanation:
The Law of Sines is used to find sides and angles when you have a side and its opposite angle. Since the given angle is not opposite the longest given side, there are two possible solutions.
a) sin(B)/b = sin(A)/a
sin(B) = (b/a)sin(A) = 14/13·sin(19°) ≈ 0.350612
B = arcsin(0.350612) or 180° -arcsin(0.350612)
B = 20.525° or 159.475°
Then angle C is ...
C = 180° -A -B = 161° -B = 140.475° or 1.525°
__
Side c can be found from ...
c = sin(C)·a/sin(A)
For C = 140.475°, ...
c = sin(140.475°)·39.9302 ≈ 25.4
For C = 1.525°, ...
c = sin(1.525°)·39.9302 ≈ 1.1
The length of side c could be 25.4 or 1.1.
2. Compare the function ƒ(x) = –x^2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)?
Answer:
g(x)
Step-by-step explanation:
The vertex of g(x) as shwon in the graph is located in the point wich coordinates are (3.5,6.25) approximatively
We need to khow the coordinates of f(x) vertex
Here is a way without derivating:f(x) = -x² + 4x -5
let a be the leading factor, b the factor of x and c the constant:
a= -1b= 4c= -5The coordinates of a vertex are: ([tex]\frac{-b}{2a}[/tex] , f([tex]\frac{-b}{2a}[/tex]) )
-b/2a = -4/ (-1*2) = 4/2 = 2
f(2)= -2²+4*2-4 = -4+4-4 = -4
obviosly f(x) has a minimum wich less than g(x)'s maximum
Answer:
Step-by-step explanation:
g(x) i think
How can you fit data into a pictogram?
Answer:
Step-by-step explanation:
In a pictogram, data can be arranged as follows:
The organization is given in a Cartesian plane, with a vertical and a horizontal axis, images can be introduced. An independent variable is placed on the horizontal axis, usually small numbers. The dependent variable can be placed on the vertical axis, they are usually larger numbers.
Please help I am doing test ! A woman borrows $4,000 at 9% compounded monthly, which is to be amortized over 3 years in equal monthly payments. for tax purposes, she needs to know the amount of interest paid during each year of the loan. find the interest paid during the first year, the second year, and the third year of the loan. [hint: find the unpaid balance after 12 payments and after 24 payments.
Answer:
Monthly Loan Payment
Loan Amount (P) = $6,000
Monthly Interest Rate (n) = 0.75% per month [9.00% / 12 Months]
Number of months (n) = 36 Months [3 Years x 12 months]
Monthly Loan Payment = [P x {r (1+r)n} ] / [( 1+r)n – 1]
= [$6,000 x {0.0075 x (1 + 0.0075)36}] / [(1 + 0.0075)36 – 1]
= [$6,000 x {0.0075 x 1.308645}] / [1.308645 – 1]
= [$6,000 x 0.009815] / 0.308645
= $58.89 / 0.308645
= $190.80
Monthly Loan Amortization Schedule
“Therefore, the total interest paid during the first year will be $465.99”
HOPE this example helps
A food concession owner in a mall sold 120 beef, vegetable, and pork sliders in 7 days. 20% of the sliders sold were beef and 15% were vegetable. How many pork sliders were sold?
Answer:
78 pork sliders
Step-by-step explanation:
The food concession owner sold 120 beef, vegetable and pork sliders.
20% were beef.
15% were vegetable.
The percentage of pork sliders sold is:
100 - (20 + 15) = 100 - 35 = 65%
The number of pork sliders sold is therefore:
65/100 * 120 = 78
78 pork sliders were sold.
A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. On a coordinate plane, points are at (negative 5, negative 7) and (3, 1). What is the solution to the system of equations? (–6, –4) (0, –1) (0, –2) (2, 0)
Answer:
(2,0)
Step-by-step explanation:
From the information the first equation is y = 0.5 x - 1 and the the line through (3,1) and (-5,-7) is
y = x - 2 . From those two equations you get
x - 2 = 0.5 x -1 and x = 2 , y = 0. So it is the last point. (2,0)
Answer:
D. (2,0)
Step-by-step explanation:
URGENT
What is the length of?
Answer:
option (c) 4
Step-by-step explanation:
sides opposite to equal angles are equal
so ML = MN
that is 4x = x+3
4x - x = 3
3x = 3
x= 1
ML= 4x = 4*1 = 4 units
MN = x+3= 1+3= 4 units
so answer is option (c) 4
hope this answer help you
Pleased help with this
Answer:
A
Step-by-step explanation:
How many different isosceles triangles have integer side lengths and perimeter 23?
Answer:
6 different isosceles triangles.
Step-by-step explanation:
This is a AMC 8 2005 question. (You can search up their solution)
There are 6 triangles:
6, 6, 11
7, 7, 9
8, 8, 7
9, 9, 5
10, 10, 3
11, 11, 1
There are only 6 because if there was an isosceles triangle with side lengths such as 5, 5, 13 the triangle would be impossible since the two smaller side lengths must sum up to be greater than the longest side length.
The number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
What is the isosceles triangle?In an isosceles triangle, two sides and angles are equal. The sum of the angle of the triangle is 180 degrees.
Given
Isosceles triangles have integer side lengths and a perimeter of 23.
Let x be the isosceles side and y be the other side. Then
[tex]\rm 2x + y = 23[/tex] ...1
And we know that the sum of the two sides of the triangle must be greater than the third side. Then
[tex]\rm 2x >y[/tex] ...2
From equations 1 and 2, we have
x > 5.75
But the value of x is an integer then x will be 6. Then
All possibilities are
[tex]6 + 6 > 11\\\\7 + 7 > 9\\\\8+8>7\\\\9+9>5\\\\10+10>3\\\\11+11>1[/tex]
Thus, the number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
More about the Isosceles triangle link is given below.
https://brainly.com/question/7915845
Helppppp............
Answer:
A (15/16)
D (0.45)
E (1/14)
F (0)
Step-by-step explanation:
Allowable values for probabilities (p) are numbers greater than or equal to zero and smaller than or equal to one:
[tex]0\leq p\leq 1[/tex]
Therefore you can select answers:
A (15/16)
D (0.45)
E (1/14)
F (0)
Answer:
0, 1/2, 0.1, 15/16 are the answers
Step-by-step explanation: I don't think negative numbers count as a probability
Please answer this correctly without making mistakes my work is due today
Answer:
24.24
Step-by-step explanation:
brainlist plzzzzzzzzzzz
Alexandria ate at most two hundred fifty calories more than twice the number of calories her infant sister ate. Alexandria ate eighteen hundred calories. If i represents the number of calories eaten by the infant, which inequality represents the situation? A. 1,800 less-than-or-equal-to 250 + 2 i B. 1,800 less-than 250 + 2 i C. 1,800 + 250 greater-than 2 i D. 1,800 + 250 greater-than-or-equal-to 2 i
Hey there! I'm happy to help!
The words at most means that there is a maximum point that is included as a probability. This means that we will use the less than or equal sign (≤) in our inequality.
Let's write this all out as an inequality now. We will use i to represent how much the baby ate.
1,800≤2i+250
This inequality shows that Alexandria's 1,800 calories is at most 250 more than twice those of her baby sister. Therefore, the correct option is A. 1,800≤250+2i .
Have a wonderful day!
Answer:
The correct option is A. 1,800≤250+2i.
Solve the following system of equations. Express your answer as an ordered pair in the format (a,b). 3x+4y=17 -4x-7y=-18
Answer:
Step-by-step explanation:
3x+4y = 17 _______ equation 1
-4x -7y= -18 _______ equation 2
muliply by 4 in equation 1
12x + 16y = 68 ______ equation 3
multiply by 3 in equation 2
-12x - 21y = -54 ________ equation 4
add equation 3 & 4
- 5y = 14
y = - 14/5
substitute y in equation 1
3x + 4 (-14/5) =17
3x = 17+ (56/5)
3x =( 85 + 56) / 5
3x = 141/5
x = 47/5
hence (a,b) = (47/5, -14/5)
What is the vertex of the graph of the function f(x) = x2+8x-2?
Answer:
the answer is (-4,-18)
Answer:
The vertex is at (-4, -18).
Step-by-step explanation:
f(x) = x^2 + 8x - 2
Covert to vertex form:
f(x) = (x + 4)^2 - 16 - 2
f(x) = (x + 4)^2 - 18.
So the
vertex is (-4,18
Please help asap.
A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures $90$ degrees If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.) What is the degree measure of the fifth slice Larry eats?
Answer:
The answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Step-by-step explanation:
Given that pizza is divided into six unequal slices.
Largest slice has an angle of [tex]90^\circ[/tex].
He eats the pizza from largest to smallest.
Let the difference in angles in each slice = [tex]d^\circ[/tex]
1st angle = [tex]90^\circ[/tex]
2nd angle = 90-d
3rd angle = 90-d-d = 90 - 2d
4th angle = 90-2d-d = 90 - 3d
5th angle = 90-3d-d = 90 - 4d
6th angle = 90-4d -d = 90 - 5d
We know that the sum of all the angles will be equal to [tex]360^\circ[/tex] (The sum of all the angles subtended at the center).
i.e.
[tex]90+90-d+90-2d+90-3d+90-4d+90-5d=360\\\Rightarrow 540 - 15d = 360\\\Rightarrow 15d = 540 -360\\\Rightarrow 15d = 180\\\Rightarrow d = 12^\circ[/tex]
So, the angles will be:
1st angle = [tex]90^\circ[/tex]
2nd angle = 90- 12 = 78
3rd angle = 78-12 = 66
4th angle = 66-12 = 54
5th angle = 54-12 = 42
6th angle = 42 -12 = 30
So, the answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Facespace is a popular form of social media. Recent reports show that the mean time spent on Facespace is 35 minutes a day with a standard deviation of 6 minutes a day. The data is normally distributed. If 1100 people are on in one sitting, how many of them lie within one standard deviation below the mean and two standard deviations above the mean?
Answer:
897
Step-by-step explanation:
I think it deleted my prior solution because I linked the Wikipedia article for the empirical rule... So to retype this:
We'll be using the empirical, or 68-95-97.5 rule of normal distributions which says that 68% of data in a normal distribution is within 1 standard deviation, 95% is within two, and 97.5% is within three. Graphical representations of the rule can be found online and may be helpful to understand it more easily.
The first part of the problem is relatively straightforward, to get the two pieces within one standard deviation, that's 68% of the total population of 1100. So, 0.68*1100=748.
The second part is a bit trickier, since it is just the part of the second standard deviation out that is above the mean. To get this, we need to think about the difference between one standard deviation out and two, percentage-wise. Since two standard deviations out is 95% of the data, the difference between one and two is 95%-68%, or 27% of the data. However, since we only want the upper half of that, we'll just be using 13.5%. So our second piece is 13.5% of 1100, or 148.5.
Add together our two pieces, 748+148.5=896.5 and round up to 897.
10. Here is a list of 25 scores on a Math midterm exam: 38.5, 41.5, 52, 52.5, 61, 63, 63.5, 68, 69, 69, 78.5, 79, 80, 83, 87, 88.5, 88.5, 91, 91.5, 92, 92.5, 94, 94, 97, 97 Find P36:
Answer:
69
Step-by-step explanation:
Since the values in the data set has been ranked already from smallest to largest, as shown in the question.
Then calculate the index,
To find the 36th percentile using the data set,
Multiply k (36/100) by n (25) to reach an index of 9.
Then since the index is whole number,
To calculate percentile according to the 'greater than' method, count the values in the data set from smallest to largest until you reach the number ranked 9th
Which is 69.
Since the value for the 36th percentile must be greater than the first nine values, the 10th ranked value would be the kth (36th) percentile. In this data set, that value is 69.
Alternatively, using the 'greater than or equal to' method, after getting the 9th rank,
Include the ninth-ranked value, (69) in this data set.
The kth (36th) percentile is then calculated by taking the average of that value in the data set (69) and the next ranked value (69). (59 + 69) / 2 = 69.