By just adding the given areas, we conclude that the definite integral is equal to 3.026
How to calculate the definite integral?
The integral will be equal to the sum of the four areas between points a and c.
The areas above the horizontal axis are positive areas, these are A and C.
While the areas below the horizontal axis are negative areas, these are B and D.
Then the definite integral will be:
I = A - B + C - D
Here we know that:
A = 1.311
B = 2.229
C = 5.545
D = 1.601
Replacing that, we conclude that the definite integral is
I = 1.311 - 2.229 +5.545 - 1.601 = 3.026
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Which expression is equivalent to?
Answer: [tex]\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{\frac{16}[81}} \sqrt[4]{\frac{x^{11}y^{8}}{x^{7}y^{6}}}\\\\=\frac{2}{3} \sqrt[4]{x^{4}y^{2}}\\\\=\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]
Luigi is navigating a maze. He gets to a junction and has 3 directions he can go in. For each of these choices, he eventually gets to another junction where he has 6 choices of direction.
How many different possible paths are there?
Darren wins a coupon for $4 off the lunch special for each of 5 days. He pays $75 for his 5 lunch specials. Write and solve the equation to find the original price p for one lunch special.
Answer:
19
Step-by-step explanation: (75/5) + 4= p
15+4=p
19=p
The original price for one lunch meal is $19
p = $15 + $4
p = $19
For the following pair of lines, identify the system by type.
consistent
inconsistent
equivalent
Considering that the two lines intersect at only one point, the system of equations described by them is consistent.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
According to the number of solutions, the system is classified as follows:
Consistent: One solution.Equivalent: Infinite solutions.Inconsistent: No solutions.In this graph, each equation is described by a line, and they intersect once, meaning that there is one solution and the system is consistent.
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Create one symmetrical (normal) and one asymmetrical set of data, and explain why each fit the definition.
- Knowing the type of distribution and the skewness of the data, is it possible to draw conclusions about the mean and the median?
- Why would it be best to use particular measures of center and spread if the data is symmetrical or asymmetrical?
- What measures would you use in each case?
If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.
If the data is asymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.
What are symmetrical and asymmetrical data?A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.
A histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.
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what is ratio (maths short definition)
Answer:
division
Step-by-step explanation:
ratio means those 2 nunbers are being divided
division is how the numbers are related or compared
much of it is describing some of all something
like 2 out 3 dentists like chrwing gum
At a restaurant, Isabel and Nancy received a bill for $12.42. If they leave a tip of 15%, how much will each girl pay if they equally divide the total amount? Round where necessary.
Answer:
$7.14
Step-by-step explanation:
Given:
Isabel , Nancy = 2 humans
Bill = $12.42
Tip = 15%
To Find:
How much will each girl pay if they equally divide the total amount?
Solve:
$12.42 × 15% = 1.863
1.863 ≈ 1.86
$12.42 + 1.86 = 14.28
14.28 ÷ 2 = 7.14
Therefore each girl pays $7.14 .
~Kavinsky
What is 11% of 15?
1.65
1.56
2.5
pretty please what is g(x)
The value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x). This can be obtained by finding composite of (h ° g) (x) using the formula for composition.
Find the value of g(x):
Composition of a function : A composite function is created when one function is substituted into another.
f composite of g is denoted as (f ° g)
The formula to find the composite of a function,
(f ° g)(x) = f(g(x))For example,
f(x) = x + 2, and g(x) = 3x
(f ° g)(x) = f(g(x)) = g(x) + 2 = 3x +2 (g ° f)(x) = g(f(x)) = 3(f(x)) = 3(x+2) = 3x + 6
In the question,
Given that, f(x) = (8x³ - 1)³, h(x) = x³
f(x) = (h ° g) (x)
⇒ (8x³ - 1)³ = h(g(x))
⇒ (8x³ - 1)³ = (g(x))³
Taking cube roots on both sides,
⇒ ∛(8x³ - 1)³ = ∛(g(x))³
⇒ (8x³ - 1) = (g(x))
⇒ g(x) = 8x³ - 1
Hence the value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x).
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find the size of each of the angles marked with letter
Answer:
f = 78 , g = 32 , h = 74
Step-by-step explanation:
f and 78° are alternate angles and are congruent , then
f = 78
---------------------------
h and 74° are alternate angles and are congruent , so
h = 74
--------------------------
the sum of the 3 angles in the triangle = 180°
sum the 3 angles and equate to 180
78 + g + h = 180
78 + g + 74 = 180
152 + g = 180 ( subtract 152 from both sides )
g = 28
Suppose you set up a function to show how many hot dogs you will purchase for a dinner when you have already bought two packages but must buy more, . What is the domain of this function?
The domain of the function is:
h > 0, only integers.
Then the correct option is the first one.
What is the domain of the given function?For a function f(x), we define the domain as the set of the possible values of x that we can use as inputs in the given function.
Here the function is:
f(h) = 6*h + 12
Where h is the number of packages that you buy.
Then h can be only integers larger than zero (as you can't buy half a package or something like that).
Then we conclude that the correct option is the first option.
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PLEASE HELP, I THINK IT’S EITHER B OR C.
(09.01 LC)
A function is shown in the table.
x g(x)
-2 2
-10
02
1 8
Which of the following is a true statement for this function? (5 points)
The function is decreasing from x = 0 to x = 1.
The function is decreasing from x = -1 to x = 0.
The function is increasing from x = 0 to x = 1.
The function is increasing from x = -2 to x = -1.
its c! there isnt a decrease between x = -1 and x = 0, as when x = -1 y = 0 and when x = 0 y = 2, showing an increase of +2.
Solve for x: 12x2 – 6 (a2 + b2)x + 3a2b2 = 0
Answer:
x:12×2−6(a2+b2)x+3a2b2=0
Step-by-step explanation:
equation
PLEASE HELP IM STUCK PLS
Answer:
x - intercept: (3, 0)
y - intercept: (0, 9)
Step-by-step explanation:
This equation is written in standard form,
To find the intercepts it would be easier to put the equation in
slope-intercept form y = mx + b
x and y are the variablesm is slope, slope = rise / runb is the y - intercept, when x = 0the x - intercept is when y = 09x + 3y = 27
subtract 9x from both sides
(9x - 9x) + 3y = 27 - 9x
3y = 27 - 9x
Divided both sides by 3
3y / 3 = 27 - 9x / 3
y = 27 / 3 - 9x / 3
y = - 3x + 9
Now we can plug in x = 0, to find y - intercept:
y = - 3(0) + 9
y = 0 + 9
y = 9
Now we can plug in y = 0, to find x - intercept:
0 = - 3x + 9
0 - 9 = - 3x + 9 - 9
-9/3 = -3x/3
-3 = -x
3 = x
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Determine what type of model best fits the given situation: A. none of these B. exponential C. linear D. quadratic
The option c is correct. Linear model suits best to this graphical representation out of the exponential and quadratic model.
According to the statement
We have given that a model in the graphical representation and we have to tell that which type of model used in this representation.
So,
According to this representation,
A linear representation is a representation on a category of vector spaces or similar.
The other meaning is that when the growth increases linearly or at the constant speed.
In this graphical representation, linear representation is used because it increases or decreases linearly not suddenly.
linear representation explain this graph perfectly.
So, Linear model suits best to this graphical representation.
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c= 6x+100 and c=10x+80
what number does x have to be for c to be the same on each equation?
Answer:
x= 5 , for c to be same on each eqn
Which of the following is a solution to the equation
3/4
x-12 = -18?
1) 4.5
2) -8
3) -22.5
4) -40
Answer: B) -8
Step-by-step explanation:
We add 12 both sides
3/4 x = -18 + 12Add −18 and 12 to get −6.
3/4 x = -6Multiply both sides by 3/4 by the reciprocal of 3/4.
x = -6 × (3/4)Express a -6 x (3/4) as a single fraction.
x = -6 × 4 / 3Multiply −6 and 4 to get −24.
x = -24 / 3Divide −24 by 3 to get −8.
x = -8Answer: Option "2" is correct. ✅
Type SSS, SAS, ASA, AAS, or HL to justify why AABC = ADEF.
AC FD and AB = DE
The theorem that justifies why triangles ABC and DEF are congruent is: HL.
What is the Hypotenuse-Leg Congruence Theorem (HL)?The hypotenuse-leg congruence theorem (HL) states that if two triangles that are right triangles have a pair of congruent hypotenuse and a pair of corresponding congruent legs, then both right triangles are proven to be congruent to each other. This means both right triangles are have the same shape and size.
Given that:
angle ABC = angle DEF = 90° (congruent right angles, this means both triangles are right triangles)
AC = FD (a pair of congruent hypotenuse)
AB = DE (a pair of congruent legs)
Thus, we can conclude that since triangle ABC and triangle DEF have a pair of congruent hypotenuses and a pair of congruent legs, therefore, the two right triangles, triangle ABC and triangle DEF are congruent to each other by the HL congruent theorem.
Thus, the theorem that justifies why both triangles are congruent is: HL.
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Evaluate the double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d
The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
What is the double integral 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d?Generally, the equation for is mathematically given as
The area denoted by the letter D that is bordered by y=0, y=x2, and x=7
The equation for the X-axis is y=0.
y=x² ---> (y-0) = (x-0)²
Therefore, the equation of a parabola is y = x2, and the vertex of the parabola is located at the point (0,0), and the axis of the parabola is parallel to the Y axis.
The equation for a straight line that is parallel to the Y-axis and passes through the point (7,0) is x=7.
[tex]\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA[/tex]
Integrating we have
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
If x equals zero, then we know that u equals zero as well.
When x equals seven, we know that u=72=49.
Therefore, by changing x2=u into our integral, it becomes from
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
[tex]7/2 \int^49_0 sin u dx[/tex]
Hence
=7/2(-cos49+1)
In conclusion,
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
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can someone help me pls
Explanation:
The sector is the pizza slice. We subtract off the area of the triangle to find the yellow shaded area.
78.6794 - 70.4956 = 8.1838
Cory saw 27 animals in the woods. two-thirds of them were insects. one-third of the insects were ants. the rest of the insects were flies. cory saw two times as many squirrels as rabbits. cory also saw a family of deer: a buck, a fawn, and a doe. how many of each animal did cory see?
Number of ants = 6
Number of flies = 12
Number of buck = 1
Number of fawn = 1
Number of doe = 1
Number of squirrels = 3
Number of rabbit = 6
What is the number system?
A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
A system for representing numbers is called a number system. It also defines a set of numbers to represent a quantity and is referred to as the system of numeration.
Given,
Total number of animals Cory saw = 27
Number of insects = [tex]27 \times \frac{2}{3}[/tex]
[tex]= 18[/tex]
Remaining number of animals = [tex]27-18[/tex]
= [tex]9[/tex]
From the insects-
Number of ants = [tex]18 \times \frac{1}{3}[/tex]
[tex]=6[/tex]
Number of flies = [tex]18-6[/tex]
= [tex]12[/tex]
Number of buck = 1
Number of fawn = 1
Number of doe = 1
Let the number of squirrels be [tex]x[/tex]
Then, the number of rabbits = [tex]2x[/tex]
Remaining animals = [tex]2x+x[/tex]
⇒ [tex]9=3x[/tex]
⇒ [tex]x= 3[/tex]
Therefore,
Number of squirrels = 3
Number of rabbits = [tex]2x[/tex]
= 6
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A trander an article at 10% loss. If he had sold it for Rs.540 more , he would have gain 5% . Find the cost price of the articles.
The answer is :3600
Answer:
3600
Step-by-step explanation:
Reason is because you put the answer in your question.
Answer:
Rs.10800
Step-by-step explanation:
loss of article(L%)=10%
s.p=?
c.p of an article (c.p)=c.p
Now,
s.p=100-L%×c.p
_____
100
= 100-10 ×c.p
_____
100
=90 ×c.p
___
100
=0.9 × c.p
if article sold with Rs. 540 more
Article profit =5%
s.p =c.p + 540 =100+p%×c.p
______
100
or, c.p +540=105×c.p
______
100
or, c.p +540=1.05×c.p
or,c.p +540=1.05c.p
or, 540=1.05c.p-c.p
or,540=0.05c.p
or, 540=c.p
____
0.05
Therefore, c.p =Rs. 10800
A and B are two cylinders that are mathematically similar.
The area of the cross-section
of cylinder A is 18 cm².
Work out the volume of cylinder B.
+
18 cm²
A
5 cm
1
B
61%
10 cm
The Volume of the Cylinder B is gotten as; 720 cm³
What is the Volume of the Cylinder?We are given 2 similar cylinders with;
ratio of heights = a : b
Thus;
ratio of areas = a² : b²
We are given that;
Height of A is 5cm.
Height of B is 10cm.
Thus;
Ratio of heights = 5 : 10 = 1 : 2
Therefore;
ratio of areas = 1² : 2² = 1 : 4
The cross sectional area of B is 4 times the cross sectional area of A. Thus;
Cross sectional area of B = 4 × 18 = 72 cm²
Volume of cylinder = cross section area × height
Volume of cylinder B = 72 × 10 = 720 cm³
The complete question is;
A and B are two cylinders that are mathematically similar.
The area of the cross-section of cylinder A is 18cm².
Height of A is 5cm.
Height of B is 10cm.
Work out the volume of cylinder B
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Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm!
Using a quadratic regression equation, it is found that the prediction of the number of songs that Kimberly will download on Month 9 is of:
c. 16.
How to find the equation of quadratic regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that the function initially decreases, then it increases , which means that it is a quadratic function. The points (x,y) to be inserted into the calculator are given as follows:
(1,8), (2,6), (4,5), (6,7), (7,9)
Inserting these points into the calculator, the prediction of y for a value of x is given as follows:
y = 0.391x² - 2.937x + 10.455
Hence, when x = 9, the prediction is:
y = 0.391 x 9² - 2.937 x 9 + 10.455
y = 15.69
Rounded to 16, hence option c is correct.
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Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Step-by-step explanation:
we have 2 blocks, as the graphic shows.
the surface areas of both blocks are the sum of their 6 sides each.
the special thing about seeing them as "composite figure" is that 2 sides (one for each block) are partly or even completely blocking each other off from being seen, so these parts and whole side are not part of the combined surface area.
let's start with the large block :
it is 5cm × 6cm × 20cm.
its surface area is the sum of
top and bottom 5×6
front and back 20×5
left 20×6
visible right (20 - 12)×6 = 8×6
it is (20-12)cm long, because the short block
is 12cm high.
so, we have
2 times 5×6 =2×30 = 60 cm²
2 times 20×5 = 2×100 = 200 cm²
20×6 = 120 cm²
8×6 = 48 cm²
in total : 428 cm²
now the small block :
it is 4cm × 6cm × 12cm.
its surface area is the sum of
top and bottom 4×6
front and back 4×12
no left (completely covered by the large block)
right 6×12
so, we have
2 times 4×6 = 2×24 = 48 cm²
2 times 4×12 = 2×48 = 96 cm²
6×12 = 72 cm²
in total : 216 cm²
the complete surface area of the composite figure is
428 + 216 = 644 cm²
What is the eleventh term in the sequence 17, 24, 31, 38…?
Answer:
87
Explanation:
This is an arithmetic sequence with common difference: 7 and first term: 17
Arithmetic sequence:
a + (n - 1)d where n is term position, d is difference, a is first term
17 + (n - 1)7
7n + 10
The eleventh term:
7n + 10
7(11) + 10
77 + 10
87
To Find :-
Eleventh term of the sequence.Solution :-
Given A.P.,
17 , 24 , 31 , 38 …First term (a) is 17.
Common difference (d) = 24 - 17 => 7
We know that :
tn = a + (n - 1) dHere n would be 11.
>> t11 = 17 + (11 - 1) 7
>> t11 = 17 + (10) 7
>> t11 = 17 + (10) × 7
>> t11 = 17 + 70
>> t11 = 87
Therefore, eleventh term in the sequence is 87.
In kickboxing, it is found that the force, fneeded to break a board, varies inversely with the length, of the board. If it takes 8 pounds of pressure to break a board that is 3 feet long, how long is a board that requires 5 pounds of pressure to break?
The board with a length of 4.8 feet would require 5 pounds of pressure to break.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let p represent the pressure and l represent the length.
l ∝ 1/p
l = k/p (k is constant)
When l = 3, p = 8, hence:
3 = k/8
k = 24
For p = 5:
l = k/p = 24/5 = 4.8 feet
The board with a length of 4.8 feet would require 5 pounds of pressure to break.
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Two 6-sided dice, one red and one green, are rolled. What is the probability that the red die shows a 2 and the green die shows a 5
The probability that the red die shows a 2 and the green die shows a 5 is 1/36
How to determine the probability that the red die shows a 2 and the green die shows a 5?The sample space of a die is
S = {1, 2, 3, 4, 5, 6}
This means that
Red die = {1, 2, 3, 4, 5, 6}
Green die = {1, 2, 3, 4, 5, 6}
On the dice, we have
P(Red = 2) = 1/6
P(Green = 5) = 1/6
The probability that the red die shows a 2 and the green die shows a 5 is
P = P(Red = 2) * P(Green = 5)
Substitute the known values in the above equation
P = 1/6 *1/6
Evaluate the product
P = 1/36
Hence, the probability that the red die shows a 2 and the green die shows a 5 is 1/36
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Find all subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2•
All subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2 is
{( 0,1) (-1,1)}
{(1,0)(0,1)}
{(1,0)(-1,1)}
A fixed A is a subset of some other set B if all elements of set A are factors of set B. In other phrases, set A is contained within set B. The subset relationship is denoted as A⊂B.
Subsets are a part of one of the mathematical ideas known assets. a hard and fast is a set of items or factors, grouped within the curly braces, consisting of {a,b,c,d}. If a set A is a set of even numbers and set B includes {2, 4,6}, then B is stated to be a subset of A, denoted by B⊆A and A is the superset of B.
In mathematics, set A is a subset of a fixed B if all factors of A are also elements of B; B is then a superset of A. It's far possible for A and B to be equal; if they may be unequal, then A is a proper subset of B. The relationship of one set being a subset of every other is known as inclusion.
A set which is (is linearly independent andoil generates/ spans the space (like R) is called a baris.
S= (1,0), (0,1), (-1))}
option-1
As, dimension of R²=2, so, Ary set
conists of three vectors cannot be baris for R²
so, option-1 is wrong.
option-2
As, dimention of R2-2.
{(10), (-11)} is a linearly independent
subset of S. so And as, this subset
has 2 vectors so it will as also
span R se, it will be a baris
of IR?
So, option-6 is correct
{(0,1)} is linearly independent subset
option-7
As (LO) has one vector. So, it cannot
Span/generate R so, it also cannot be balis
for R2
of S.
But it cannot span R²
So ut cannot
be a baris of R2
se, option-2 is wrong.
Option-3
AS, {(0,1), (-1,1)} is linearly independent
So, option -7, is wrong.
Answer
[as fox amy KER, (-1,1) K (0,1)] subset of s
And also as dim {(0,1), (-11)}=2
which is same as the dimention of IR2
so {(0,1), (-11)} forms a baris of R2
{(1,0), (0,1), (-11)}
{(1,0)}
So, option-3 is
Connect
option-4
{(1,0), (3, 1)} is standard balis of R2
which is subset of S.
10
[{(1,0), (0,1)}]
So, option-4 is correct.
option-5
{(-11)}
consists of one vertex,
so, ut cannot span R², so, ut cannot
be a baris of R²
9090
LO {(1,0), (-1,1)}]
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Of the following, which reads the same forwards, backwards, and upside down (when viewed on a calculator screen)?
(A) 6889
(B)1991
(C)1961
(D) 1881
Answer: D 1881
Step-by-step explanation: 6889 and 1961 don't read the same forwards and backward. 1991 upside down is 1661. So, only 1881 works