in the equation y= -x-1/2
the slope is -1/1 which can also be shown as -1.
Find the volume of the solid of revolution formed by rotating
about the x-axis each region bounded by the given curves.
f(x) =(1/3)x + 2, y = 0, x = 1, x = 3
The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .
Let us think of any region that is enclosed by a function g(x) and the x-axis between x=a and x=b. If this region is rotated about the x-axis, the solid of rotation that results can be thought of as consisting of thin cylindrical discs with a width of dx and a radius of g (x). Therefore, by integrating the volume of this disc, the whole volume of the solid will be revealed.
Volume=[tex]\int^{a}_{b}\pi [g(x)]^2dx[/tex]
The given function is g(x)=(1/3)x+2 ranging from x=1 to x=3
Therefore volume of the solid formed is:
[tex]\int^{3}_{1}\pi [\frac{1}{3}x]^2dx\\=\int^{3}_{1}\pi [\frac{1}{9}x^2]dx\\=\pi \int^{3}_{1} [\frac{1}{9}x^2]dx\\\\=\pi [\frac{1}{27}x^3 ]^3_1\\= \frac{26}{27} \pi[/tex]
The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .
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What is the constant of proportionality between y and x in the graph?
Answer: 4/3 or 2/1.5
Step-by-step explanation:
The constant of proportionality is also known as the slope. This can be found with change in y over change x.
Since we have a graph with distinct points, we can use rise over run. For this graph, we will count 3 units up from (0, 0) and 4 units right to (4, 3). This becomes 4/3 or 2/1.5. This is the constant of proportionality.
ok im sorry but does anyone know 7+(-12)+(-7)??
Answer:
-12
Step-by-step explanation:
Given the following question:
7 + (-12) + (-7)
Using PEMDAS:
(-12) + (-7) = -19
7 + -19 = -12
= -12
Hope this helps.
=========================================================
Explanation:
Let's simplify the 7+(-12) portion first
Draw a vertical number line. Plot a point at 7. Then move down 12 units to arrive at -5
Or you could start at -12 and move up 7 units to arrive at -5
This tells us that 7+(-12) = -5
So the overall 7+(-12)+(-7) turns into -5+(-7)
-----------
Draw another vertical number line, or use the one already drawn in the previous section.
Plot a point at -5. Then move down 7 units to arrive at -12
Or start at -7 and move down 5 units to arrive at -12
Therefore, -5 + (-7) = 7+(-12)+(-7) = -12 is the final answer
-----------
Shortcut:
The 7 and -7 in the original expression add to 0. They cancel each other out. So we're left with -12
What is p2 + 13 if p = −4?
29
17
−3
−21
The value of the expression p² + 13 will be A. 29.
How to compute the expression?It should be noted that the expression given is that p² + 13 and we are told that p = -4.
Therefore, we have to put the value of p into the expression. This will be:
p² + 13
= (-4)² + 13
= 16 + 13.
= 29
The value is 29.
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A group of 2129 students were surveyed about the courses they were taking at their college with the following results:
921 students said they were taking History.
987 students said they were taking Dance.
1012 students said they were taking Psychology.
474 students said they were taking Dance and History.
466 students said they were taking Psychology and History.
457 students said they were taking Dance and Psychology.
235 students said they were taking all three courses.
a) How many students took Dance or didn't take Psychology?
b) How many students took Dance & Psychology or took Psychology & History?
c) How many students took Dance, Psychology, or History?
d) How many students took Dance or History, but not Psychology?
e) How many students took none of the courses?
f) How many students took Psychology and History, but not Dance?
Using the Venn sets, the amounts are given as follows:
a) 1358 students.
b) 688 students.
c) 1758 students.
d) 746 students.
e) 371 students.
f) 771 students.
What are the Venn Sets?For this problem, we consider the following sets:
Set A: students taking History.Set B: students taking Dance.Set C: Students taking Psychology.235 students said they were taking all three courses, hence:
(A ∩ B ∩ C) = 235.
457 students said they were taking Dance and Psychology, hence:
(B ∩ C) + (A ∩ B ∩ C) = 457
(B ∩ C) = 222.
466 students said they were taking Psychology and History, hence:
(A ∩ C) + (A ∩ B ∩ C) = 466
(A ∩ C) = 231.
474 students said they were taking Dance and History, hence:
(A ∩ B) + (A ∩ B ∩ C) = 474
(A ∩ B) = 239.
1012 students said they were taking Psychology, hence:
C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 1012
C + 231 + 222 + 235 = 1012
C + 688 = 1012
C = 324.
987 students said they were taking Dance, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 987
B + 239 + 222 + 235 = 987
B + 696 = 987
B = 291.
921 students said they were taking History, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 921
A + 239 + 231 + 235 = 921
A + 705 = 921
A = 216.
The number of students who took no courses is given as follows:
None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 2129
None + 216 + 291 + 324 + 239 + 231 + 222 + 235 = 2129
None + 1758 = 2129
None = 2129 - 1758
None = 371.
For item a, the amount is:
Dance + None = 987 + 371 = 1358 students.
For item b, the amount is:
(B ∩ C) + (A ∩ B ∩ C) + (A ∩ C) = 457 + 231 = 688 students.
For item c, the amount is the total subtracted by none, hence:
2129 - 371 = 1758 students.
For item d, the amount is:
A + B + (A ∩ B) = 216 + 291 + 239 = 746 students.
For item e, the amount is of 371, as we found previously.
For item f, the amount is:
A + C + (A ∩ C) = 216 + 324 + 231 = 771 students.
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graph the linear inequality 9x-y<9
The line has a slope of 9 and y-intercept of -9
Linear inequality graphA linear equation is a equation that has a linear degree of 1.
Given the inequality expression 9x-y<9
Write in slope-intercept form
-y < -9x + 9
y > 9x - 9
From the equation, we can see that the line has a slope of 9 and y-intercept of -9
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What is the decimal rule?
1.2 x (-5) = ?
I got -60 but it’s saying it’s the incorrect answer and I’m not sure what I’m doing wrong.
Answer:
-6
Step-by-step explanation:
1 x -5 is still -5, and the do .2 x -5 = -1 -1+-5= -6
Does the mapping diagram represent a function? Why or why not?
x -7 -1 8
y -4 4
A. No; the input values x = -7 and x= -1 are paired with the same output value.
B. No; each input pairs with only one output. C. No; the output value y = -4 pairs with two different input values.
D. Yes; each input pairs with only one output.
Answer:
D
Step-by-step explanation:
A relation is a function is each input maps onto no more than one output.
step by step explanation
The sum of the given infinite geometric series is; 32
What is the sum of the geometric series?The general formula for finding the sum of an infinite geometric series is s = a₁/(1 - r)
where;
s is the sum
a₁ is the first term of the series
r is the common ratio.
To find the common ratio, use the formula: r = a2⁄a1
where a2 is the second term in the series and a1 is the first term in the series.
Thus;
r = 2²/4²
r = 1/2
Thus;
S = 4²/(1 - 1/2)
S = 16/(1/2)
S = 32
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help i have no clue how to do this pls help
Answer:
4
Step-by-step explanation:
the sequence is like [tex]1^{2}[/tex],[tex]2^{2} ,4^{2},8^{2} ,16^{2} ,32^{2}[/tex]
If u get it correct I’ll give brainlest
Answer:
pretty sure it’s addition property of equality since you’re adding 5 to 10
a plank of wood is 220 cm long.I cut it in 14cm pieces. what lenght of wood i will have left over?
The required Length is 10cm.
What is length?
Length is a measure of distance. In the International System of Amounts, length is a volume with dimension distance. In utmost systems of dimension a base unit for length is chosen, from which all other units are deduced.Length is generally understood to mean the most extended dimension of a fixed object. still, this isn't always the case and may depend on the position the object is in.Varied terms for the length of a fixed object are used, and these include height, which is the perpendicular length or perpendicular extent, and range, breadth, or depth. Height is used when there's a base from which perpendicular measures can be taken. range or breadth generally relates to a shorter dimension when the length is the longest one.220 / 14 gives us 15.
You have to understand that this means 15 whole 14 cm pieces and a Length of 1 piece.
thus 14 * 15 = 210
So 220- 210 = 10
where you know 220- 210 is< 15
Hence, The correct Length is 10cm.
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Find the earnings for selling the same number of each type of sandwiches. Use x to represent the number of each type of sandwiches sold. Pretzel ham sandwich cost $2.25, pretzel turkey sandwich cost $1.55, bagel ham sandwich cost $2.00, bagel turkey sandwich cost $1.30
Total earnings for selling the same number of each type of sandwiches are $7.10x. This is a simple sum.
Here, the number of each type of sandwiches sold is x.
Pretzel ham sandwich cost $2.25. so, the earnings for selling Pretzel ham sandwich is $2.25x.
Similarly, earnings for selling pretzel turkey sandwich is $1.55x, earnings for selling bagel ham sandwich is $2.00x and earnings for selling bagel turkey sandwich is $1.30x. The total earning can be found by a simple sum of all individual earning of each type of sandwiches.
Therefore, Total earnings for selling the same number of each type of sandwiches are = $2.25x + $1.55x + $2.00x + $1.30x = $7.10x
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the best graph to use for nominal or ordinal data is
Bar charts and pie charts are the best graphs to use for nominal or ordinal data.
What is defined as the Bar charts?Bar graphs are graphical representations of data (usually grouped) in the form of horizontal or vertical rectangular bars, with the length of the bars proportional to the data measure.
They are also referred to as bar charts. In statistics, bar graphs are one method of data handling.The drawn bars are uniform in width, as well as the variable quantity is depicted on one of the axes. The variable's measure is also depicted on other axes. The heights or lengths of the bars represent the variable's value, and these graphs are also employed to compare different quantities.Thus, for nominal and ordinal variables, bar charts or even pie charts are most commonly used.
Line charts as well as histograms are the most common ways to represent scale variables.
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Find the 50th percentile from the following sorted list of 34 data
128 134 144 146 153
190
207 209
220
221
237
256
263 265
271
273
283
324 350
371
389 401 416 417
422
424 443 444
448 466
486
487 490 500
50th percentile =
Enter an integer or decimal number [more..]
Question Help: Message instructor
The 50th percentile value is 303.5.
What is a percentile?
A percentile is a term used in statistics to express how a score compares to other scores in the same set. While there is technically no standard definition of percentile, it's typically communicated as the percentage of values that fall below a particular value in a set of data scores.
Percentiles are commonly used to report values from norm-referenced tests (in which the average is determined by comparing a set of results in the same group) as the percentages of scores that fall below those of the average of the set.
For calculation we have to add all the given numbers.
(128+134+144+146+153+190+207+209+220+221+237+256+263+265+271+273+283+324+350+371+389+401+416+417+422+424+443+444+448+466+486+487+490+500) divided by 34
hence 50th percentile is 303.5
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Please solve this! I need it asap!
The differentiation of the given function is expressed as; 2x - √3(y) = 0
How to carry out Differentiation?
We want to differentiate the function;
x² - √3(xy) + 2y² = 12
To differentiate this means to express as;
x²(dy/dx) - √3(xy)(dy/dx) + 2y²(dy/dx) = 12(dy/dx)
This gives us;
2x - √3(y) + 0 = 0
2x - √3(y) = 0
Thus, the differentiation of the given function is expressed as;
2x - √3(y) = 0
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Round the decimal to the given place value.
124.123474
hundred-thousandth
Answer: 124.12347
Step-by-step explanation:
A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Violet measures the distance
from the pole to the stake and from the pole to the tower, as shown in the diagram
below. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot is 48 ft.
What is mean by foot of Maths?A unit of length (or distance) in US units equal to 12 inches. The abbreviation is: ft. Or sometimes the single quote mark: ' Example: 10 feet can be written 10 ft, or just 10' A foot is exactly 0.3048 meters in the Metric System (the foot is defined that way).
Step-by-step explanation:
Here, we want to find the length of the wire
from the diagram, we can identify two similar triangles
The smaller one and a bigger one
Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal
We can start by getting the height of the tower
we have this as:
8/11 = 28/x
8 * x = 28 * 11
8x = 308
x = 308/8
x = 38.5 ft
So as we can see, the wire represents the hypotenuse of the larger triangle that measures 28 ft base and 38.5 ft height
So we can use the Pythagoras’ theorem to get the hypotenuse
Let us call this g mathematically;
According to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
thus, we have it that;
g^2 = 38.5^2 + 28^2
g^2 = 2,266.25
g = √2,266.25
g = 47.61 which is approximately 48 ft
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Arun says if he adds together two mixed numbers, his answer will always be less than the sum of the whole-number parts plus 1. Say 2 counter-examples to show Arun's statement is not true. A counter statement is any example that shows a statement is false
The two examples can be 1 1/2 & 1 3/4 and 2 2/3 & 1 2/3.
According to Arun,
Sum of two mixed numbers < Sum of the whole number part + 1
Now, lets take the example as 1 1/2 and 1 3/4
Their sum will be:
1 1/2 + 1 3/4 = 3 / 2 + 7 / 4
= 13 / 4 = 3 1/4
The sum of whole parts = 1 + 1 = 2
Adding 1 to it = 2 + 1 = 3
We can clearly see that 3 1/4 > 3.
It contradicts Arun's statement.
Another example can be:
2 2/3 + 1 2/3 = 8 / 3 + 5 / 3
= 13 / 3 = 4 1/3
Sum of whole part + 1 = 2 + 1 + 1 = 4
4 1/3 > 4
It contradicts Arun's statement.
Therefore, the two examples can be 1 1/2 & 1 3/4 and 2 2/3 & 1 2/3.
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Rs=3x st=6x-5 rt=58 find st
The value of st is 30.4
As S is the point in RT, it implies that RS+st=Rt. Therefore according to the question,
3x+6x-5=58
⟹9x=58-5
or
9x=53
⟹x=5.9
RS = 3×5.9=17.7
st=(6×5.9)-5=35.4-5=30.4
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An 8-ounce cup of juice costs $1.20. A 12-ounce cup of the same juice costs
$1.44. Can the relationship between cost and ounces of juice be described
by a constant rate? Explain.
Answer: It can.
Step-by-step explanation:
If an 8 oz. cup of juice cost $1.20 and a 12 oz. cup of juice cost $1.44, there is a $0.24 difference between the money and cups of juice in ounces. If there were to be a constant rate of change, a 16 oz. cup of juice MUST cost $1.68
No, the relationship between cost and ounces of juice cannot be described by a constant rate.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Cost of 8 ounce juice= $1.20
Cost of 12 ounce juice= $1.44
Now,
If the relationship between cost and ounces of juice was described by a constant rate, then the cost per ounce would be the same for both the 8-ounce cup and the 12-ounce cup. However, we can see that the cost per ounce is different for each cup:
For the 8-ounce cup: cost per ounce = $1.20 / 8 ounces = $0.15 per ounce
For the 12-ounce cup: cost per ounce = $1.44 / 12 ounces = $0.12 per ounce
Therefore, by algebra the cost per ounce is different for each cup, the relationship between cost and ounces of juice cannot be described by a constant rate.
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c. A parallelogram
has an area of 7 square units. If the height that corresponds to
a base is unit, what is the base?
If a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units, then the base is 28 units.
As per the question statement, a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units.
We are required to find out the base of the parallelogram.
To solve this question, we need to know the formula to calculate the area of a parallelogram, which goes as
Area of Parallelogram = (Base * Height)
Putting our data obtain from the question statement, in the above-mentioned formula, we can calculate the value of the base of our concerned parallelogram, i.e.,
[tex]7=(base*\frac{1}{4})\\or, base=(7*4)\\or, base = 28[/tex]
Therefore, base of our concerned parallelogram is 28 units.
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Solve the following equation. x/9 = 1Then place the correct number in the box provided.
Answer:
9
Step-by-step explanation:
x/9 = 1
Multiply both sides by 9
x = 9
Also, any number over itself is equal to 1.
What is 9.06 divided by 6?
Answer:
9.06 ÷ 6 = 1.51
Hope this helps :)
Check:
1.51
× 6
-------
9.06
Move decimal 2 times to the left un 9.06 because in the number 1.51 there are 2 numbers behind the decimal.
Q1: What is the inverse of the statement?
If you have read many books, then you have learned many words.
A) If you have learned many words, then you have read many books.
B) If you have read many books, then you have learned many words.
C) If you haven't learned many words, then you haven't read many books.
D) If you haven't read many books, then you haven't learned many words.
Q2: The given figure is a rectangular prism.
Which edges are parallel to QP¯¯¯¯¯ ?
Select all answers that are correct.
A) TR¯¯¯¯¯ (Maybe this?)
segment T R
B) PH¯¯¯¯¯¯
segment P H
C) QT¯¯¯¯¯
segment Q T
D) JA¯¯¯¯¯ (And this?)
segment J A
Answer: The answer for #2 is JA and TR I took the test:)
Step-by-step explanation:
Q1 option D is the correct answer: The inverse of the statement, If you have read many books, then you have learned many words, is If you haven't read many books, then you haven't learned many words.
Q2 Edges parallel to QP are
option Aoption DWhat is inverse of a statement?The inverse of a statement refers to a statement that has opposite to the original statement to which the inverse is required. For example:
the statement: John is coming
inverse of the statement: John is not coming
How to get parallel edgesThe edge refers to a side of the prism while parallel refers to a property of line that implies that the edges are equally spaced apart and will never intersect.
The diagram for Q2 is attached
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Translate the sentence into an equation.
The sum of 8 times a number and 9 is 7.
Use the variable b for the unknown number.
Answer:
8 x b + 9 = 7
Step-by-step explanation:
sum is to add and 8 times means to multiply it by 8
At a school fundraiser Ms. Navaro sold 24 plates of cookies, which is 80% of the total number of plates of cookies she baked. How many plates of cookies did Ms. Navaro bake?
Answer:
. Onusko made 60 cookies for a bake sale. She sold 2/3 of them and gave 3/4 of the remaining cookies to the students working at the sale. How many
Approximate 13 plus cube root of 9 to the nearest tenth.
14.5
15.1
16.0
17.3
Answer:
15.1
Step-by-step explanation:
7. Alicia and Dexter are each walking on a straight path. For a particular -second window of time, each has their velocity (in feet per second) measured and recorded as a function of time. Their respective velocity functions are plotted in .
Figure 1.4.14. The velocity functions and for Alicia and Damon, respectively.
Determine formulas for both and .
What is the value and meaning of the slope of ? Write a complete sentence to explain and be sure to include units in your response.
What is the value and meaning of the average rate of change of on the interval ? Write a complete sentence to explain and be sure to include units in your response.
Is there ever a time when Alicia and Damon are walking at the same velocity? If yes, determine both the time and velocity; if not, explain why.
Is is possible to determine if there is ever a time when Alicia and Damon are located at the same place on the path? If yes, determine the time and location; if not, explain why not enough information is provided.
(a) The formula for velocity functions is:
f(t)=0.4t+4
g(t)=0.9t
(b) The slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec². The slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².
(c) Damon is accelerating with 0.9 ft/sec² in intervals [4,8].
(d) Both are walking at a velocity of 7.2 ft/sec at t=8 sec.
What is velocity?
The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.(a) For Alicia,
m=(Δv/Δt)=(8-4)/(10-0)=4/10=0.4
f(t)=0.4t+4
for Damon,
m=(Δv/Δt)=(9-0)/(10-0)=9/10=0.9
g(t)=0.9t
The formula for velocity functions is:
f(t)=0.4t+4
g(t)=0.9t
(b) Value and meaning of the slope is
m for Alicia =0.4
Slope is determined (Δv/Δt)=(8-4)/(10-0)=4/10=0.4 ft/sec².
So, the slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec².
m for Damon=0.9
Slope is determined (Δv/Δt)=(9-0)/(10-0)=9/10=0.9 ft/sec².
So, the slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².
(c) Value and meaning of the average rate of change on the interval:
the average rate of change of Δ on the interval [4,8] =
[tex]\frac{Velocity\ at\ 8\ sec - Velocity\ at\ 4\ sec}{Time\ interval\ (8-4)\ sec}[/tex]
=(7.2-3.6)/(8-4)=(3.6/4)=0.9 ft/sec²
So, Damon is accelerating with 0.9 ft/sec² in intervals [4,8].
(d) Let both are walking with the same velocity at t sec.
So, Let's equate their velocities
0.4t+4=0.9t
t=4/0.5 = 8 sec
The velocity of Alicia at 8 sec = 0.4(8)+4 = 7.2 ft/sec
The velocity of Damon at 8 sec = 0.9(8) = 7.2 ft/sec
So, both are walking at a velocity of 7.2 ft/sec at t=8 sec.
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What is the domain of the function expressed by this formula?
Y= 1/x - 7
Answer:
x cannot equal seven, there's a mark for it in RSM menu
Step-by-step explanation:
so the answer is y = -7