The equation of the line through (0, 1) and (c, 0) is
y - 0 = (0 - 1)/(c - 0) (x - c) ==> y = 1 - x/c
Let L denote the given lamina,
L = {(x, y) : 0 ≤ x ≤ c and 0 ≤ y ≤ 1 - x/c}
Then the center of mass of L is the point [tex](\bar x,\bar y)[/tex] with coordinates given by
[tex]\bar x = \dfrac{M_x}m \text{ and } \bar y = \dfrac{M_y}m[/tex]
where [tex]M_x[/tex] is the first moment of L about the x-axis, [tex]M_y[/tex] is the first moment about the y-axis, and m is the mass of L. We only care about the y-coordinate, of course.
Let ρ be the mass density of L. Then L has a mass of
[tex]\displaystyle m = \iint_L \rho \,\mathrm dA = \rho\int_0^c\int_0^{1-\frac xc}\mathrm dy\,\mathrm dx = \frac{\rho c}2[/tex]
Now we compute the first moment about the y-axis:
[tex]\displaystyle M_y = \iint_L x\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}x\,\mathrm dy\,\mathrm dx = \frac{\rho c^2}6[/tex]
Then
[tex]\bar y = \dfrac{M_y}m = \dfrac{\dfrac{\rho c^2}6}{\dfrac{\rho c}2} = \dfrac c3[/tex]
but this clearly isn't independent of c ...
Maybe the x-coordinate was intended? Because we would have had
[tex]\displaystyle M_x = \iint_L y\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}y\,\mathrm dy\,\mathrm dx = \frac{\rho c}6[/tex]
and we get
[tex]\bar x = \dfrac{M_x}m = \dfrac{\dfrac{\rho c}6}{\dfrac{\rho c}2} = \dfrac13[/tex]
The center of mass for a uniform triangular shape is on its centroid. The y-coordinate of the center of mass of the lamina is 1/3 (independent of c).
What is the center of mass for a triangular shape?If the surface is plane triangle approximately and mass is uniformally distributed, then its center of mass will lie on the centroid of that triangle.
What is centroid of a triangle and its coordinates?The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
If the triangle has its vertices as [tex](x_1, y_1), (x_2, y_2) , \: (x_3, y_3)[/tex], then the coordinates of the centroid of that triangle is given by:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)[/tex]
For this case, the triangular lamina has vertices (0, 0), (0, 1) and (c, 0)
Assuming its mass is spread regularly, the coordinates of its center of mass would be:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)\\\\(x,y) = \left( \dfrac{0+0+c}{3} + \dfrac{0+1+0}{3} \right) = (c/3, 1/3)[/tex]
Thus, the y-coordinate of the center of mass of the lamina is 1/3 (independent of c).
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Question 19 of 20:
Select the best swer for the question
19. The distance from the center of a round table top to the edge of the table top is 4 ft what is the area of the table top
Answer:
50.26 ft^2
Step-by-step explanation:
Area=pi*r^2
Area=pi*(4)^2=pi*16=50.26
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Task: Population of a Species
The population of a species in the wild in Asia has been decreasing exponentially since 1980. This function represents the wild population of the species t years after 1980: W(t)=20000(0.95)t.
The Wildlife Refuge Foundation noticed this trend before 1980
and decided to try to help reduce the population decline by
breeding the species in captivity. The graph shows the number
of these animals that have been born in captivity since 1980.
(Note: The function W(t) and the graph are not the same function!)
[15 points] Use the graph to create a function to represent the number of the species that have been born in captivity, C(t).
Answer:
C(t) = 20t
Step-by-step explanation:
The graph of C(t) appears to be linear
The y intercept is 0
The slope is 200/10 = 20
y = mx+b where m is the slope and b is the y intercept
y = 20x+0
y = 20x
C(t) = 20t
Answer:
the answer is c (t) = 20 t
Step-by-step explanation:
[tex]\sf{}[/tex]
:,-)
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
Please help brainliest will be given
Complete the equation describing how
x and y are related.
x
-1
5
0 1 2 3 4
3 8
V 2
13
18
23
28
y = 5x + [?]
Enter the answer that belongs in [?].
a radion station usa 1\6 of its time for the news. in a 12 hour day, how many hours are used for music & entertainment?
Answer:
10 hours
Step-by-step explanation:
In order to answer this question, you must assume that all air time not spent on news is spent on music & entertainment. That would usually not be the case, as there would usually be advertisements and public service programming along with everything else.
The time spent on news is ...
(1/6)(12 hours) = 2 hours
If the rest is spent on music and entertainment, then ...
12 -2 = 10 . . . hours are used for music and entertainment
g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.
Answer:
The correct option is D.
But option B is correct if P(A) = P(B).
Step-by-step explanation:
P(A|B) is read as "The probability of A given B".
It is different from the options A, B, and C.
It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).
a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit
Answer:
$900
Step-by-step explanation:
To begin with let us estimate the total cash value of the prices
$1000 x 1= 1000
$500 x 1= 500
$50 x 2= 100
Total = $1600
Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets
2.5*1000= $2,500
Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600
Then the expected profit is = $2,500-$1600= $900
The highest attendance at this stadium was in 2007 when 91,547 people attended. The average cost of a ticket was $57. How much money was made on ticket sales for that game?
Answer:57*91547
Step-by-step explanation:
If Tristan wants to stretch the spring by 9 inches, how many kilograms of weight must he apply to it? I need help with it please.
Answer:
9/3 = 3x/3
3 = x
The spring stretches 9 inches with 3 kilograms of weight attached to it
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3
Answer:The spring stretches 9 inches with 3 kilograms of weight attached to it.
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3:
The spring stretches 9 inches with 3 kilograms of weight attached to it.
What is the value of x to the nearest tenth?
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
Factor of
x2 – 14x + 24
A. (x - 6)(x - 4)
B. (x - 8)(x - 3)
C. (x - 12)(x - 2)
D. (x - 24)(x - 1)
Answer: The answer is C.
Step-by-step explanation:
Hi, there!!!
The answer is option C.
The solution is in picture.
I hope it helps....
What is the lateral surface area of a right hexagonal prism whose base is a regular hexagon with sides measuring 8 inches long and altitude measuring 6 inches tall?
Answer:
288 square inches
Step-by-step explanation:
Assuming your "altitude" is the height of the prism--the distance between bases, the lateral area is the sum of the areas of the six rectangular faces. Each of those has an area of ...
(8 in)(6 in) = 48 in^2
so the 6 of them will have an area of ...
lateral area = 6×48 in^2 = 288 in^2
_____
Comment on nomenclature
'Altitude' is usually associated with the height of a triangle. In the case of a regular polygon, the 'altitude' of a triangular section of the polygon is called the 'apothem', and is often designated using the letter 'a'. If the polygon is regular, the apothem can be calculated from the side length and the number of sides, but it is often given in problems involving area, perimeter, and/or volume.
The distance between the parallel bases of a prism is often referred to as the prism height or length. The use of the word 'altitude' is confusing in this case.
Since the lateral area is the product of the perimeter of the base and the distance between bases, we have to assume that your 'altitude' refers to the distance between bases. Otherwise, there is not sufficient information to work the problem.
In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard. Compute the test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Answer:
The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.
Step-by-step explanation:
We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.
In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.
Let [tex]p_1[/tex] = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.
[tex]p_2[/tex] = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}
The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = [tex]\frac{24}{90}[/tex] = 0.27
[tex]\hat p_2[/tex] = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = [tex]\frac{42}{380}[/tex] = 0.11
[tex]n_1[/tex] = sample of cars driven at high altitudes = 90
[tex]n_2[/tex] = sample of cars driven at low altitudes = 380
So, the test statistics = [tex]\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }[/tex]
= 3.234
The value of z-test statistics is 3.234.
Find the measure of a.
A. 20
B. 70
C. 80
D. 40
A circle is a curve sketched out by a point moving in a plane. The measure of a is 70°. The correct option is B.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In the given circle, the line AC is the diameter of the circle, therefore, the measure of ∠ABC will be 90°.
∠ABC = 90°
This is because a triangle formed on the diameter of the circle such that all the vertices of the triangle intersect the circle, then the angle opposite to the diameter is a right angle.
Now, in ΔABC, the sum of all the angles of the triangle can be written as,
∠ABC + ∠BCA + ∠BAC = 180°
90° + a + 20° = 180°
110° + a = 180°
a = 180° - 110°
a = 70°
Hence, the measure of a is 70°.
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Find 900 ÷ 90.
plz help
Answer:
the answer is 10
Step-by-step explanation:
900 ÷ 90
=> 10 [tex]\sf{}[/tex]
Answer:
The answer is 10.
Step-by-step explanation:
900/90=cut 0 of numerator and denominator then 90 divide by 9 is 10.
Someone help me understand
Answer:
f¯¹(x) = 23/ (6x + 3)
Step-by-step explanation:
f(x) = (23 – 3x)/6x
The inverse, f¯¹, for the above function can be obtained as follow:
f(x) = (23 – 3x)/6x
Let y be equal to f(x)
Therefore, f(x) = (23 – 3x)/6x will be written as:
y = (23 – 3x)/6x
Next, interchange x and y.
This is illustrated below:
y = (23 – 3x)/6x
x = (23 – 3y)/6y
Next, make y the subject of the above expression. This is illustrated below:
x = (23 – 3y)/6y
Cross multiply
6xy = 23 – 3y
Collect like terms
6xy + 3y = 23
Factorise
y(6x + 3) = 23
Divide both side by (6x + 3)
y = 23/ (6x + 3)
Finally, replace y with f¯¹(x)
y = 23/ (6x + 3)
f¯¹(x) = 23/ (6x + 3)
Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is
f¯¹(x) = 23/ (6x + 3)
the bold answer is incorrect. what is the right answer?
Yuko added a 15 percent tip when she paid her cab driver. If the fare was $25.50, what was the total amount she paid? A. $28 B. $30 C. $31
Answer:
B. $30
Step-by-step explanation:
First, find the amount of the tip.
Multiply the tip rate and taxi fare.
tip rate * taxi fare
The tip rate is 15% and the taxi fare is $25.50
15% * 25.50
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100=0.15
15.0 ---> 1.5 ---> 0.15
0.15 * 25.50
3.825
The tip amount is $3.825
Next, find the total amount she paid.
Add the taxi fare and the tip amount.
taxi fare + tip amount
The taxi fare is $25.50 and the tip amount is $3.825
$25.50 + $3.825
$29.325
Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.
Therefore, the best answer choice is B. $30
A recent survey asked 1200 randomly selected U.S. adults if they believe that the U.S. federal government is doing enough to keep U.S. elections safe from outside interference. After analyzing the results, the researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe. Which statement BEST describes how to interpret these results
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is D
Step-by-step explanation:
From the question the question we are told that
The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.
Generally a confidence interval states to what extent the chances of the true population is within the a given range
So the 95% confidence interval given in the question as 52.5% and 59.5% means that the chances of the true population mean being with this given range is 95%
So given that the the true population mean is within this range then it means that the population mean will be greater than 50%
So the statement that best describe and interprets this result is
The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.
find the missing side. round your answer to the nearest tenth. PLEASE HURRY!
Answer:
44.8
Step-by-step explanation:
Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8
I hope this helped! :D
Find the slope of the line whose x-intercept is 4 and the y- intercept is -9
Answer:
y = (9/4)x - 9
Step-by-step explanation:
The x-intercept is (4, 0) and the y-intercept is (0, -9).
As we move from (0, -9) to (4, 0), x (the 'run' increases by 4 and y (the 'rise' increases by 9. Thus, the slope of the line connecting these two points is m = rise/run = 9/4, from which we can write the desired equation in the form y = mx + b:
y = (9/4)x - 9
What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?
k = –k equals negative StartFraction 3 Over 2 EndFraction.
k = –k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 3 Over 2 EndFraction.
Answer: k = 2/-3
Step-by-step explanation: Option (B)
Taking the test as we speak
How many gallons of a 5% bleach solution must be
added to 10 Gallons of a 20% bleach solution to
produce that is 15% bleach
Answer:
Step-by-step explanation:
10 gallons of the 20% solution contain 2 gallons of bleach.
x gallons of the 5% solution contain 0.05x gallons of bleach.
If the two are combined, the resulting 10+x gallons contain 2+0.5x gallons of bleach. The concentration is (2+0.05x)/(10+x).
(2+0.05x)/(10+x) = 15%
2+0.05x = 0.15(10+x)
2+0.05x = 1.5+0.15x
0.5 = 0.10x
x = 5
5 gallons of 5% solution is added to the 10 gallons of 20% solution.
How to solve this question
hopefully this answer can help you to answer the next question. can you choose this answer as the brainliest answer and give five stars
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that fewer than 13 have vcrs?
Answer:
The probability is [tex]P(x < 13) = 0.8732[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.70
The sample size is [tex]n = 15[/tex]
Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )
The probability of failure is mathematically evaluated as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.70[/tex]
[tex]q = 0.30[/tex]
The probability that fewer than 13 have vcrs is mathematically represented as
[tex]P(x < 13) = 1- [P(13) + P(14) + P(15)][/tex]
=> [tex]P(x < 13) = 1-[( \left 15 } \atop {}} \right. C_{13} *p^{13}* q^{15-13})+ (\left 15 } \atop {}} \right. C_{14} *p^{14}* q^{15-14}) +( \left 15 } \atop {}} \right. C_{15} *p^{15}* q^{15-15}) ][/tex]
Here [tex]\left 15 } \atop {}} \right. C_{13}[/tex] means 15 combination 13 and the value is 105 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{14}[/tex] means 15 combination 14 and the value is 15 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{15}[/tex] means 15 combination 15 and the value is 1 (obtained from calculator)
So
[tex]P(x < 13) = 1-[(105 *p^{13}* q^{2})+ (15 *p^{14}* q^{1}) +(1*p^{15}* q^{0}) ][/tex]
substituting values
[tex]P(x < 13) = 1-[(105 *(0.70)^{13}* (0.30)^{2})+ (15 *(0.70)^{14}* (0.30)^{1}) +(1*(0.70)^{15}* (0.30)^{0}) ][/tex]
[tex]P(x < 13) = 0.8732[/tex]
Write each expression in a simpler form that is equivalent to the given expression. Let g be a nonzero number. 1/g^1 or 1/g-1
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Apply rule : [tex]a^1 =a[/tex]
[tex]\displaystyle \frac{1}{g^1 } =\frac{1}{g}[/tex]
[tex]\displaystyle \frac{1}{g^{-1}}[/tex]
Apply rule : [tex]\displaystyle a^{-b}=\frac{1}{a^b}[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }[/tex]
Apply rule : [tex]\displaystyle \frac{1}{\frac{1}{a} } =a[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }=g[/tex]
Answer:
[tex]\frac{1}{g^1}[/tex]
= [tex]\frac{1}{g}[/tex]
[tex]\frac{1}{g - 1}[/tex]
= [tex]\frac{g^1}{1}[/tex]
= [tex]\frac{g}{1}[/tex]
= g
Hope this helps!
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
In a triangle ABC,AB=9 and BC =12 which of the following Cannot be the length of AC.
Step-by-step explanation:
mark it as the brainliest
Answer:
i need help with this too
Step-by-step explanation:
find the HCF of 72,108 and 180
Answer:
36 is the answer
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
72: 2×2×2×3×3
108: 2×2×3×3×3
180: 2×2×3×3×5
here, common factors are 2,2,3 and 3 ..
so.. HCF: 2×2×3×3
•°•HCF=36 ..