The function f(x) = x^3 is integrable on [0, 1].
Is there a direct proof that f(x) = x^3 is integrable on [0, 1]?To prove that the function f(x) = x^3 is integrable on the interval [0, 1], we can use Theorem 5.2, which states that if a function is continuous on a closed interval, then it is integrable on that interval.
The function f(x) = x^3 is a polynomial function, and polynomials are continuous for all values of x. Therefore, f(x) = x^3 is continuous on the interval [0, 1]. As a result, by Theorem 5.2, we can conclude that f(x) = x^3 is integrable on [0, 1].
This direct proof relies on the continuity of the function and the application of the given theorem to establish its integrability on the interval [0, 1].
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What is the equation I'm supposed to write?
The equation in slope intercept form is y = -4x/3 + 10
How to determine the equation?The representations are given as:
x represents peachesy represents applesSo, we have:
2 * x + 1.5 * y = 15
Evaluate the product
2x + 1.5y = 15
Subtract 2x from both sides
1.5y = -2x + 15
Divide through by 1.5
y = -4x/3 + 10
Hence, the equation in slope intercept form is y = -4x/3 + 10
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Yasmin designed a square table using a scale drawing. The actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet. Choose the figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet.
The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.
How to calculate the length?From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.
The new length will be:
= 2 × 3 2/3
= 7 1/3
Therefore, the new length is 7 1/3 feet.
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From the given graph, use two points to write an equation in point-slope form and then
change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving for y. Show your
work!
y=mx+b
Step 1
Using the points (2,0) and (-2, -3), we get the slope is
[tex]\frac{-3-0}{-2-2}=\frac{3}{4}[/tex]
Step 2
Using the point (2,0), the equation is
[tex]y=\frac{3}{4}(x-2)[/tex]
Step 3
Using the distributive property, we get [tex]y=\frac{3}{4}x-\frac{3}{2}[/tex].
What's 2 divided by X
Answer:
2/x
Step-by-step explanation:
y
T
N
9
6
U
3
M
What is the value of y?
3√3 units
6√3 units
O
9√3 units
O 12√3 units
The value of y from the given figure is 6√3
Pythagoras theoremFrom the given figure, according to the theorem;
H² = 6² - 3²
H² = 36 - 9
H² = 27
H = 3√3
Determine the value of y using the same theorem;
y² = 9² + ( 3√3)²
y² = 81. + 27
y = √108
y = 6√3
Hence the value of y from the given figure is 6√3
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On a number line, point D is at -3, and point E Is at 6. The point F lies on DE. The ratio of Df to FE ls 2:3. Where does point F lie on the
number line?
Point F is at
. All rights reserved.
on the number line.
Helppp me please
The point F as described in the task content is at point; 0.6 on the number line.
Where does point F lie on the number line?Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.
Consequently, since the ratio of Df to FE ls 2:3
It follows that point F is at -3 + (2/5) × 9.
Point F is therefore at 0.6 on the number line.
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Graph the quadratic function by transforming the graph of f(x) = x^2. Give the minimum or maximum
vertex value and the equation for the axis of symmetry.
For the function g(x) we have:
Maximum y = 5Vertex (-2, 5)Axis of symmetry: x = -2.How to find the graph of g(x)?
The function g(x) is given by applying transformations to f(x), the transformations are:
A reflection: g(x) = -f(x)A translation of 2 units to the left: g(x) = -f(x + 2)A translation of 5 units up: g(x) = -f(x + 2) + 5The function is:
[tex]g(x) = -(x + 2)^2 + 5[/tex]
The graph is the one you can see below:
There you can see that the vertex is at (-2, 5), then the line of symmetry is:
x = -2.
And we have a maximum at the vertex, which is y = 5.
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2. The Kenya Seed Company sold 6 460 t 760 kg of maize seeds to 95 farmers. The farmers bought equal masses of seeds. What mass of seeds did each farmer buy? fond his cous in equal
Using proportions, it is found that each farmer bought 68,008 kg.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:
6460 x 1000 + 760 = 6,460,760 kg
The amount per farmer is:
6,460,760/95 = 68,008 kg.
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mr hassell came home to find that each of the 6 kit kat bars he brought had 1 bar eaten. They each had 3/4 in it.How many bars of kitkat are there in total.
The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars
AlgebraNumber of bars = 6Number of bars eaten = 1Number of bar in each KitKat = 3/4Total bars of KitKat = 6 × 3/4
= (6×3)/4
= 18/4
= 9/2
= 4 1/2 bars
Number of bar remaining after eating 1 bar = 4 1/2 - 1
= 3 1/2 bars
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what formula would i need to use to graph the relationship of volume of surface area of a cylinder?
The formula is illustrated below:
Volume of cylinder = πr²hSurface area = 2πrh + 2πr²How to illustrate the information?It should be noted that a cylinder simply means a three dimensional solid which holds two parallel bases that are joined by a curved surface.
In this case, it can be seen that the formula that can be used to calculate the volume and the surface area of the cylinder is illustrated above.
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There are 400 beads in a box. 20% of them are red, 35% of them are yellow and the rest are green. How many green beads are there in the box
Step-by-step explanation:
400 is the whole = 100%
20% (= 20 out of 100 equal parts of 100%) are red.
how many are that ?
well, again, 400 = 100%
1% = 100%/100 = 400/100 = 4
20% = 20×1% = 20×4 = 80
when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.
400 × 0.2 = 80
now,
35% are yellow.
35% = 35×1% = 35×4 = 140
or
400×0.35 = 140
red + yellow = 80 + 140 = 220
the rest are green
400 - 220 = 180
we would get this also by seeing that
red + yellow = 20% + 35% = 55%.
so, green has then the remaining 100-55 = 45%
and again
45% = 45×1% = 45×4 = 180
or
400×0.45 = 180
Mrs karki purchased a sari for rs 8000 and sold it for Rs 11300 with 13% VAT , find her profit and loss percent.
The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
VAT = 13% = 0.13 * 8000 = 1040
Selling price - VAT = 11300 - 1040 = 10260
Profit = [(10260 - 8000)/8000] * 100% = 28.25%
The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%
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Que tanto por ciento es 20 de 80
Answer:
Step-by-step explanation:
40 por ciento
BP = _______ BC = ________ 13. AP = 3.5, PD = 6, PC = 4
Find BP and BC.
The measure of the length BP and BC are 6 and 10 respectively
Circle theoremThe given figure is a circle containing two chords AD and BC. From the given diagram, the following are true
AP = PC
BP = PD
BC = BP + PC
Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.
Given the following parameters
AP = 3.5,
PD = 6,
PC = 4
According to the expression above;
BP = PD = 6
BC = BP + PC
BC = 6 + 4
BC = 10
Hence the measure of the length BP and BC are 6 and 10 respectively
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Which table shows a function that is increasing only over the interval(-2,1),and nowhere else?
table 1, and table 2 are the answers.
we know that any function is increasing when for an increase in x-values, y-value should also increase
we will verify each table
table-1:
we can see that
x increase as -3, -2, -1 , 0, 1,2
y is also increasing -6,-3,-1,1,3,6
so, this is increasing
table-2:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but it is asking between -2 to 1
y-values are -4,-1,1,4.....which is increasing
so, this is increasing
table-3:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but y changes from -3 to -5 .....which is decreasing
so, this is not increasing
table-4:
we can see that
x increase as -3, -2, -1 , 0, 1,2
but y changes from 7 to 1 .....which is decreasing
so, this is not increasing
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Which of the following best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers?
A) the sum is a constant
B) the sum is a polynomial
C) the sum is an exponential expression
D) nothing can be determined about the sum without more information
The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
Sum of Polynomial expressionPolynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.
ax^2+bx+c and;
mx^2+nx+p
Take the sum of the polynomials
P(x) =. ax^2+bx+c
f(x) = mx^2+nx+p
Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.
Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial
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Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.
What is the maximum length of the seesaw?
1.4 meters
2 meters
0.5 meters
1 meter
Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.
What is the seesaw's maximum length?This can be found as:
Sin 30° = 1 / Maximum length
Solving gives:
Sin 30° = 1 / Maximum length
Ml = 1 / Sin 30°
= 1 / 0.5
= 2 meters
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Find the measure of angle C.
D
118°
C
The measurement of angle C in the given figure is 118°.
Given that are two lines intersecting at a point making 4 angles, 118°, C, D and B.
B and D are opposite to each other and C and 118° are opposite to each other.
We need to find the measurement of angle C.
To find the measurement of angle C, we can use the concept of vertical angles.
Vertical angles are a pair of non-adjacent angles formed when two lines intersect.
They are always congruent, meaning they have the same measure.
In this case, angle 118° and angle C are vertical angles. So, their measures are equal:
Angle C = 118°
Therefore, the measurement of angle C is 118°.
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The wall around a playground is 410 m.if one wall along the length is 80 m what is the length of the wall along the breadth what is the area of playground.
The length of the wall = 125m
The area of the Playground = 10000[tex]m^{2}[/tex]
What is geometry?
A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.
Given data:
Perimeter of the playground=410m
length of the wall = 80m
The playground's width can be calculated as follows if its length is 80 meters:
(Formula of Perimeter of a rectangle)
P=2(L+B)
410=2(80 +B)
410= 160 + 2B
2B= 410-160
2B= 250
B= 125 m
This results in a 125 m length for the playground.
The area of playground.
Area = Length x Width
Area = 80 x 125
area = 10000[tex]m^{2}[/tex]
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Pls help solve for part b)iii.
Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;
a. The height of the tree is approximately 31.2 m.
b. i. The distance of Q from the base of the tree is 50•√5 m.
ii. The angle of elevation of the top of the tree from Q is approximately 15.6°
iii. The bearing of the tree from Q is 296.565°
How can the distances and bearing of the tree from Q be found?a. tan(32°) = Height/50
Height = 50 × tan(32°) = 31.243 m.
Height of the tree ≈ 31.2 m.b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;
d = √(100² + 50²) = 50•√5
The distance of Q from the base of the tree, d = 50•√5 m.ii. The angle of elevation is given by trigonometric ratios as follows;
[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]
Which gives;
[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]
The angle of elevation of the top of the tree from Q ≈ 15.6°iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;
Angle = arctan(50/100) ≈ 26.565°
The angle between the direction north of Q and a line from Q to the tree is therefore;
90° - 26.565° = 63.435°
The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;
Bearing = 360° - 63.435° = 296.565°
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Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = StartFraction B C Over 9 EndFraction
sin(45°) = StartFraction 9 Over B C EndFraction
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = StartFraction B C Over 9 EndFraction
Applying the trigonometric ratios, the equations that can be used are:
sin 45 = BC/9
cos 45 = BC/9
How to Apply the Trigonometric Ratio?In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:
To find AC, use the cosine ratio, CAH.
To find BC, use the sine ratio, SOH.
sin 45 = opp/hyp = BC/9
sin 45 = BC/9
cos 45 = adj/hyp = BC/9
cos 45 = BC/9
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Answer: A, E
Step-by-step explanation: Sin(45)=BC/9 ; cos(45)=Bc/9
suppose you are performing an experiment where you randomly assign people to one of three experimental conditions
The analysis which would be most appropriate for randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control) are-
ANOVAthe general linear modelWhat is ANOVA?A statistical test called an analysis of variance, or ANOVA, is used to compare the means of more than two groups.
One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.A statistical technique called analysis of variance, or ANOVA, divides observed variance data into various components for use in further testing. When there are three or more data groups, a one-way ANOVA is used to find out how the dependent and independent variables are related.What is general linear model?A helpful framework for analysing how various variables affect various continuous variables is the general linear model (GLM).
GLM generalises the ANOVA's linear model by enabling any other kind of resual distribution id(and optimises the likelihood function, which only allows a t-test based on an estimated error of the coefficients). An GLM is therefore an ANOVA, but a GLM is not exclusively a GLM.To know more about ANOVA, here
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The complete question is -
Suppose you are performing an experiment where you randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control). Which analysis would be most appropriate?
Practice with Laws of Logic
Provide the valid conclusion to the argument below.
If I am sick, then I will not come to school.
If I do not come to school, then I am sad.
Answer:
if I am sick, then I will not come to school.
Step-by-step explanation:
please help me !! due today:(
Answer:
[tex]\huge\boxed{\sf x = 65 \textdegree}[/tex]
Step-by-step explanation:
Using trigonometric ratio cos.
Here,
Theta = θ = xAdjacent = 12Hypotenuse = 28Finding x:[tex]\displaystyle cos \theta =\frac{adjacent}{hypotenuse} \\\\cos \ x =\frac{12}{28} \\\\cos \ x = 0.43\\\\x = cos^{-1} 0.43\\\\x = 65 \textdegree\\\\\rule[225]{225}{2}[/tex]
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion? assume that past data are not available for developing a planning value for p*. (round your answer up to the nearest whole number.) the answer is not 384. i already submitted that answer and it was incorrect
The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.
Given margin of error of 0.05 and confidence interval of 95%.
We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.
Margin of error is the difference between real values and calculated values.
The formula of margin of error is as under:
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where
z is the critical value of z for given confidence level
n is sample size
σ is population standard deviation
We have not given population standard deviation so we will use the following formula:
Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]
We have to find z value for 95% confidence level.
z value=1.96
We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2
put [tex]\sqrt{p(1-p)}[/tex]=1/2
Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]
0.05=1.96*0.5/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=0.98/0.05
[tex]\sqrt{n}[/tex]=19.6
squaring both sides
n=384.16
After rounding off we will get
n=384.
Hence the sample size needed to obtain a margin of error of 0.05 is 384.
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Please help me solve this, random answers will be removed
[tex]ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065[/tex]
Answer:
Step-by-step explanation:
I need help with this!!
Answer: $18.51
Step-by-step explanation:
1015cm^3/7.95cm^3/g = 127.67g
127.67g/1000g = .128
.128*$.29 = $.037
$.037*500 = $18.51
Answer:
$1170
Step-by-step explanation:
1. We know that each steel part has a volume of 1015 cubic centimeters, and the machinist wants to make 500 of these. Then the total volume of the steel part the machinist will make will be 1015 x 500.
--> 1015 x 500
--> 507500 cubic centimeters.
2. The density of the steel part is 7.95 grams per one cubic centimeter. Then the total density of the 500 steel parts will be 507500 x 7.95.
--> 507500 x 7.95
--> 4,034,625 grams.
3. For every kilo of steel part, the cost is $0.29. We should first change the 4,034,625 gram to kilo. Since 1000 grams is a kilo, we divide 4,034,625 by 1000.
--> 4,034,625 grams / 1000 = 4034.625 kilograms.
Now we multiply 4034.625 by 0.29 to find the total cost.
--> 4034.625 x 0.29
--> 1170.04125.
Since the question specifically asked to round it to the nearest dollar, our final answer becomes $1170.
Find a linear differential operator that annihilates the given function. (Use D for the differential operator.) 4 ex cos 3x
If the function is
[tex]y = 4 e^x \cos(3x)[/tex]
then we have derivatives
[tex]Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)[/tex]
[tex]D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)[/tex]
Now consider the linear ODE
[tex]aD^2y + bDy + cy = 0[/tex]
Substituting [tex]y[/tex] and its derivatives reduces the equation to
[tex](-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0[/tex]
Now,
[tex]-24a - 12b = 0 \implies b = -2a[/tex]
[tex]-32a + 4b + 4c = 0 \implies c = 10a[/tex]
Then the minimal ODE with the given solution is
[tex]aD^2y -2a Dy + 10ay = 0[/tex]
or
[tex]\boxed{D^2y -2 Dy + 10y = 0}[/tex]
Which expression illustrates the associative property of addition? (3 19) – 12 = (3 12) – 19 3 (19 – 12) = 3 (19 12) (3 19) – 12 = 3 (19 – 12) 3 (19 –12) = 3 – (19 12)
Answer:
Associative Property
For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.
Answer:
3rd Option!
Step-by-step explanation:
EDGE 2022; good luck
A sweatshirt costs $48 at Hollister. The sales tax rate is 7%. How much will it cost to buy the sweatshirt?
Answer:
$ 51.36
Step-by-step explanation:
To find the sales tax multiply the tax rate by the cost of the product and then add to the cost.
Sales tax = tax rate * cost price
= 7% * 48
= 0.07 * 48
= $ 3.36
Cost price = cost of product + sales tax
= 48 + 3.36
= $ 51.36