Name the following function.

Answer:

[tex]\dfrac{917}{256}=3.58203125[/tex]

Step-by-step explanation:

The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.

The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.  

As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.

The number of partitions is the number of rectangles used.  

Partitions can be of equal length or not of equal length.

Given:

The given partition divides the interval [0, 1] into 3 subintervals:

To calculate the areas of the rectangles, multiply the width of each rectangle by its height.

The width is the difference between the x-values of each subinterval.

The height is the minimum value of the function across the subinterval. For the given function, this is the value of the function for the right side of the subinterval.

First rectangle [0, 1/2]:

[tex]\begin{aligned}\implies \left(\dfrac{1}{2}-0\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{2} \cdot \left(4-\left(\dfrac{1}{2}\right)^3\right)\\\\&=\dfrac{1}{2} \cdot \dfrac{31}{8}\\\\&=\dfrac{31}{16}\end{aligned}[/tex]

Second rectangle [1/2, 3/4]:

[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(4-\left(\dfrac{3}{4}\right)^3\right)\\\\&=\dfrac{1}{4} \cdot \dfrac{229}{64}\\\\&=\dfrac{229}{256}\end{aligned}[/tex]

Third rectangle [3/4, 1]:

[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(1\right)&=\dfrac{1}{4} \cdot \left(4-\left(1\right)^3\right)\\\\&=\dfrac{1}{4} \cdot 3\\\\&=\dfrac{3}{4}\end{aligned}[/tex]

Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:

[tex]\implies \dfrac{31}{16}+\dfrac{229}{256}+\dfrac{3}{4}=\dfrac{917}{256}=3.58203125[/tex]

Answer:

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Since the triangle is isosceles, the two angles opposite to equal sides are congruent:

The sum of the three angles is 180°:

The angle measures are:

If we want to find the volume of the given toy, then the units of our answer will be (A) cm³.

Volume is the amount of space a thing takes up, whereas capacity is the amount of solid, liquid, or gas that it can hold.

Volume is measured in cubic units, although capacity can be expressed in almost any other unit, such as liters, gallons, pounds, etc.

The capacity of an object is measured by its volume.

For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.

The quantity of space occupied by a three-dimensional object can also be used to describe volume.

So, in the description, it is stated that the value is measured in cubic units.

Therefore, if we want to find the volume of the given toy, then the units of our answer will be (A) cm³.

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Answer:

2x4 is 8

Step-by-step explanation:

4 to times so 4+4 =8 thx

There are times when I use or calculate percentages in my personal life or at work. This is true.

The benefits that result from using percentages in this application is that it gives one an idea of the value to be paid as tax. The drawback is that it can be complicated for large number.

A word problem that can Illustrate percentage is that "An income is $1000 and there's a tax of 10%, how much will be paid?"

A number or ratio expressed as a fraction of 100 is called a percentage. Divide the value by the total value to get the percentage, then multiply that number by 100.

For instance, many statistics in the media, bank interest rates, retail discounts, and inflation rates are all expressed as percentages. For understanding the financial aspects of daily life, percentages are crucial.

For example, an income is $1000 and there's a tax of 10%, the tax will be:

= 10% × $1000

= $100

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The pretax rate of return is the profit or loss on an investment before taxes are subtracted.

Pretax financial income, on the other hand, is the amount a firm earns before taxes are taken into account. Taxable income is the amount of income that a corporation must pay taxes on.

Generally speaking, investment income includes, but is not limited to: interest, dividends, capital gains, rental and royalty income, non-qualified annuities, income from firms engaged in trading financial instruments or commodities, and enterprises that are passive for the taxpayer.

The profit or loss on an investment prior to deducting taxes is known as the pretax rate of return. Taxes on investment income are levied by the government on any additional income derived from purchasing or disposing of investments. Securities that are profitably sold are subject to capital gains taxes.

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Answer: Considering both dividends paid and capital gains, Dylan’s pretax profit from his investment is $30. Dylan’s pretax return on investment (ROI) is 24%.

Step-by-step explanation: To determine Dylan’s profit from his investment, add his dividends of $5 and his capital gains of $25.total profit = $25 + $5= $30Before taxes are applied, Dylan can calculate his return on investment (ROI) by dividing his profit by the cost of his investment:30125 = 0.24, or 24%.

The product of -22/5 × - 1/3 is 12/15

A product in math is defined as the result of two or more numbers when multiplied together. For example if 5 is multiplied by 2 , the product is 10 i.e 5 × 2 = 10 , 10 is the product where 5 and 2 are the factors. Also 5×4 = 20, 20 is the product and the 5 and 4 are the products.

The division of this of the product with any of the factors will give the other factors.

To solve -2 2/5 × -1/3

we first change the mixed fraction to improper fraction.

We then multiply -12/5 with -1/3

-2 2/5 = -12/5

-12/5 × -1/3

= 12/15

therefore the value of -2 2/5 × -1/3 is 12/15

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The probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 25%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of how likely it is that something will happen or be the case. Probability is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can be used to calculate the chances of a certain outcome based on a set of conditions or data. Probability can also be used to make decisions and predictions about the future.

This is because of the Venn diagram that Bart created. If a quadrilateral has four right angles, then it can either have four equal side lengths (which makes it a square) or it can have four unequal side lengths. Since there are 8 quadrilaterals in the set with four equal side lengths (E) and 16 quadrilaterals in the set with four right angles (R), the probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 8/16, which is equivalent to 25%. Therefore, the probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 25%, rounded to the nearest whole percent.

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The correct linear equation which shows a proportional relationship is,

⇒ y equals two thirds times x.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Now,

We know that;

The proportion relationship is,

⇒ y = kx

Where, k is constant of proportional.

By option 1;

The expression is,

⇒ y = 2/3 × x

⇒ y = 2/3x

Hence, It shows the linear equation.

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A horizontal x-axis and a vertical y-axis make up the line graph.

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Answer:

The length would be 29.

Step-by-step explanation:

Follow the distance formula in the image.

-Hope this Helped

Answer:

D) 56

Step-by-step explanation:

[tex]\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56[/tex]

The sum of all possible values of b is 124 in the given question.

If two or more objects have a common centre, they are said to be concentric in geometry.

Concentric shapes include spheres, circles, regular polyhedral, and regular polygons because they all share a central axis. In Euclidean geometry, concentric circles always have different radii but the same centre.

The difference between the areas is [tex]$ \frac{\pi(b^2 - a^2)}{4} = 48 \pi[/tex]

Therefore  b² = a² +1 92

We can write the equation as  (b−a)(b+a)=192

So b−a and b+a are factors of 192

Here are the possibilities:  

 b−a=1, b+a=192 ;

 b−a=2, b+a=96 ;

 b−a=3, b+a=64 ;

 b−a=4, b+a=48 ;

 b−a=6, b+a=32 ;

 b−a=8, b+a=24 ;

and

 b−a=12, b+a=16

Add the pairs of equations and divide by 2 (as long as the sum is even): b=49; b=26; b=19; b=16; and b=14.

49 + 26 + 19 + 16 + 14 = 124

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The rule for the transformation that dilates point B(4, -16) by a scale factor of 3 is: (x, y) --> (3x, 3y)

A transformation is a function that maps points in a given space to points in a different space. There are many types of transformations, including translations, rotations, dilations, and reflections.

A coordinate is a set of numerical values that are used to specify the position of a point in a specific space. In two-dimensional space, a point is typically defined by an ordered pair of numbers (x, y), where x is the horizontal position and y is the vertical position. In three-dimensional space, a point is typically defined by an ordered triple of numbers (x, y, z), where x, y, and z are the positions in the three dimensions.

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The vertex form of parabola y = x² + 9 · x + 8 is the quadratic equation y + 49 / 4 = (x + 9 / 2)².

Herein we find the equation of a parabola in standard form, that is, a quadratic equation of the form:

y = a · x² + b · x + c

Where:

And we are asked to transform this expression into vertex form, that is, a quadratic equation of the form:

y - k = C · (x - h)²

Where:

This can be done by means of algebra properties. First, write the quadratic equation:

y = x² + 9 · x + 8

Second, use algebra properties until a perfect square trinomial is found:

y = x² + 9 · x + 8

y + 49 / 4 = x² + 9 · x + 81 / 4

Third, factor the perfect square trinomial:

y + 49 / 4 = (x + 9 / 2)²

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The first quadrant starts on (12,11)

If the quadrant moves 8 units left it will be located at (12-8, 11) = (4,11)

and if it moves 7 units down it will be located at (4,11-7) = (4,4)

So the new location of the quadrant is (4,4)

It's important to notice that the first quadrant starts on (12,11) and the coordinates are (x,y) where x is on the horizontal axis and y is on the vertical axis. So when it moves left it's decreasing the x value and when it moves down it's decreasing the y value

Step-by-step explanation:

In order to share the money equally

We take the variables as 'x'

This is because the given values are in the form of a ratio

So to do this we plug these values into a equation which is,

[tex]x + 5x + 2x = 32[/tex]

Adding the values we get,

[tex]8x = 32[/tex]

Dividing both sides by 8 we get,

[tex]\frac{8x}{8}= \frac{32}{8}[/tex]

[tex]x = 4[/tex]

Now we multiply the given values by x which is 4 in order to find how much money each ratio get

[tex]x = 4[/tex]

[tex]5x = 5X4 = 20[/tex]

[tex]2x = 2X4 = 8[/tex]

4 + 20 + 8 = £ 32 (Proving)

The container can hold 1.12 pounds

A container can hold a maximum of 17.75 pounds

There are two objects in the container

The first object weights 6.53 pounds

The second object weight 10.1 pounds

The amounts of pounds that the container can hold is

6.53+10.1

= 16.63

17.75-16.63

= 1.12

Hence the container can hold 1.12 pounds

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By analytic geometry, the equations for lines represented by figure are:

In this problem we find the representation of five lines (red - yellow - green - blue - black). There is a horizontal line (green), a vertical line (blue) and three oblique lines (red - yellow - black). According to analytic geometry, we find the following definitions:

The slope for oblique lines is determined by secant line formula:

m = Δy / Δx

Where:

From picture we get the following hints:

Finally, we proceed to find the equations for each line:

Red line

Slope

m = 5 / 2.5

m = 2

Intercept

b = y - m · x

b = 5  - 2 · 0

b = 5

The equation for the red line is y = 2 · x + 5.

Yellow line

Slope

m = - 5 / 1.5

m = - 3.333

Intercept

b = y - m · x

b = 5 - (- 3.333) · 0

b = 5

The equation for the yellow line is y = - 3.333 · x + 5.

Black line

Slope

m = 6 / 3

m = 2

Intercept

b = y - m · x

b = - 6 - 2 · 0

b = - 6

The equation for the black line is y = 2 · x - 6.

Green line

The equation for the green line is y = - 2.

Blue line

The equation for blue line is x = 5.

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Therefore , the solution of the given problem of speed comes out to be

the ball accelerates at 0.33 m/s2.

Speed is a pace that is measured in terms of how far an object travels in a given amount of time. Speed can be measured in a wide range of ways, including in miles an hour, laps every minute, and meters a second. There are connections between the units of time, distance, and speed. Three ways of expressing the relationship are

d = rt, r = dt, and t = dr.

Given -

The ball's initial speed is 0 meters per second.

v = 12 m/s is the ball's final speed.

36 seconds were used.

Determine the ball's acceleration.

Solution:

=> A = (v-u)/t

=>A = (12-0)/36

=> A = 12/36

=> A =1 /3

=> A = 0.33 m/s²

Consequently, the ball accelerates at 0.33 m/s2.

Therefore , the solution of the given problem of speed comes out to be

the ball accelerates at 0.33 m/s2.

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The equation for the temperature at midnight and the solution are Tm = 3T + 5 and -16 degrees Celsius respectively

An equation is a mathematical statement that is made up of two expressions joined by an equal sign.

Let T represent the temperature

The temperature tripled and then rose 5 degrees can be written as:

Tm = 3T + 5

where Tm is the temperature at midnight.

If the temperature at 8:00 AM was –7 degrees Celsius, we have:

Tm = 3(-7) + 5

Tm = -21 + 5

Tm = -16 degrees Celsius

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Answer:

-40 17/40

Step-by-step explanation:

Answer: -40 7/40

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator
40.425=40.4251/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000
40.4251×1000/1000=40425/1000
Find the Greatest Common Factor (GCF) of 40425 and 1000 and reduce the fraction by dividing both numerator and denominator by GCF = 25
40425÷25
1000÷25
=1617/40

Simplify the improper fraction
in conclusion
-40 17/40
you must not forget the minus/negative sign :)

Given that for every hundred pages a thickness of 1/4 inch is added to the book, then the equation is:  y = 1/2 + 1/4*x

Considering that the book's front and back covers each have a thickness of 1/4 inch, adding them together results in a thickness of 1/2 inch for the book, regardless of how many pages it has.

Given that a book's thickness increases by a quarter of an inch for every hundred pages, the equation is:

y = 1/2 + 1/4*x

where y denotes the book's width and x is the number of bond paper pages printed every 100 pages. Y has a length of inches.

Equations that have the same roots or solutions are said to be equivalent.

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The statement that is true about the ratios comparing the width and length of each painting is:

The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

A ratio is a fraction which compares the values of two numbers. Such that they can be expressed as a ratio of one to the other. Example is the ratio of a to b which can be expressed as; a:b or a/ b.

From the first dimension of the canvas size, we have;

length = 6 feet

width = 4 feet

So that,

the ratio comparing the width and length = 4/ 6

                                                      = 0.6667

From the second dimensions of the canvas size, we have;

length = 3 feet

width = 2 feet

the ratio comparing the width and length = 2/ 3

                                                       = 0.6667

Therefore, the statement that is true about the ratios comparing the width and length of each panting is; The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

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The closest number of 2 is 63/32. By using the subtraction operation, we can compute it.

What are numbers?

A number is a mathematical object that can be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original examples. Number words can be used to represent numbers in language.

Given numbers are [tex]1\frac{15}{16}[/tex], 17/8, 63/32

Now find the difference between the given numbers from 2.

The difference of   [tex]1\frac{15}{16}[/tex] from 2 is

2 - [tex]1\frac{15}{16}[/tex]

= 2 - 31/16

= 1/16.

The difference of 17/8 from 2 is

|2 - 17/8|

= |(16 - 17)/8|

=| -1/8|

= 1/8

The difference of 63/32 from 2 is

2 - 63/32

= (64 - 63)/32

= 1/32

The numerator of the difference is the same. The greater denominator represents a less number.

Thus 63/32 is close to 2.

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Answer:

  7.  VS = 17

  8.  QR = 6

  9.  UT = 17

Step-by-step explanation:

You have trapezoid QRTU with midsegment VS parallel to bases QR and TU. Given dimensions for two of these parallel lines, you want the measure of the third.

The markings on the parts of segments QU and RT indicate that points V and S are their midpoints, respectively. This makes segment VS a "midsegment", one that joins the midpoints of opposite sides. As such, its length is the average of the lengths of QR and TU:

  VS = (QR +TU)/2

This is the relation that is used for problem 7.

For problems 8 and 9, this is rearranged to give the values of QR and UT:

  QR = 2VS -UT

  UT = 2VS -QR

From above, ...

  VS = (QR +UT)/2 = (12 +22)/2

  VS = 17

From above, ...

  QR = 2VS -UT = 2(9) -12

  QR = 6

From above, ...

  UT = 2VS -QR = 2(11) -5

  UT = 17

__

Additional comment

You will note that the line segments form an arithmetic sequence: the difference in length between adjacent segments is the same.

  7: 12, 17, 22

  8: 6, 9, 12

  9: 5, 11, 17

The given series consists of prime numbers starting from 2. So, the missing term is the prime number after 11, which is 13.

So, None of the above will be the correct answer.

A×(B∩C)=(A×B)∩(A×C)

We have B∩C={1,2,3,4}∩{5,6}=ϕ

∴ L.H.S = A×(B∩C)=A×ϕ=ϕ

A×B={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)}

A×C={(1,5),(1,6),(2,5),(2,6)}

∴R.H.S.=(A×B)∩(A×C)=ϕ

∴L.H.S=R.H.S

Hence A×(B∩C)=(A×B)∩(A×C)

To verify: A×C is a subset of B×D

A×C={(1,5),(1,6),(2,5),(2,6)}

B×D={(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),

(3,8),(4,5),(4,6),(4,7),(4,8)}

which is 13.

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''Start with a line and point K on that line'' is the next step in constructing a line perpendicular to a segment

Whenever two lines cross at a right angle, they are perpendicular or orthogonal. All four of the angles created by two perpendicular lines are 90 degrees.

If and only if the slope product of two non-vertical lines is negative one, those lines are perpendicular. In other words, two perpendicular lines' slopes are the negative reciprocals of one another. A vertical line is perpendicular to only horizontal lines and has an infinite slope (which have slope 0).

This provides a way to determine if two lines are parallel by using their equations. Additionally, this enables us to discover the equations of lines that are perpendicular to another line.

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8. The ratio of the adjacent over the hypotenuse is 8:17

10. The ratio of the adjacent over the hypotenuse is 1:√2

From the question, we are to calculate the ratio of the adjacent over the hypotenuse in the given triangles

8.

Using angle A as the reference angle

Adjacent = 16

Hypotenuse = 34

Thus,

The ratio of the adjacent over the hypotenuse = 16/34

The ratio of the adjacent over the hypotenuse =  8/17

Hence, the ratio is 8:17

10.

First,

We will calculate the hypotenuse, H

From the Pythagorean theorem, we can write that

H² = 4² + 4²

H² = 16 + 16

H² = 32

H = √32

H = 4√2

Now,

Using angle A as the reference angle

Adjacent = 4

Hypotenuse = 4√2

Thus,

The ratio of the adjacent over the hypotenuse = 4/4√2

The ratio of the adjacent over the hypotenuse =  1/√2

Hence, the ratio is 1:√2

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