Apply the distributive property to factor out the greatest common factor.9+12n

The table you mentioned shows that the area of the bottom of the box, f(x), is equal to x2 when one side of the box is x feet long.

This can be written as f(x) = x2. You can also use this equation to calculate the area of the bottom of any rectangular box if you know the length of one of its sides. For example, if one side of the box is 4 feet then the area of the bottom of the box is f(4) = 42 = 16 square feet.

The bottom of the box refers to the bottom surface of a rectangular box. It is the surface that is parallel to the surface on which the box is resting. The area of the bottom of a box can be calculated by multiplying the length of one side of the box by the width of the other side. The bottom of the box can be used to hold items, and can also provide a stable platform for stacking items.

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The equation is T(v) = x5 + 2x. The linearity property states that for any two vectors u, v and scalar c, then T(u + cv) = T(u) + cT(v).

Since T is a linear transformation, we can use the linearity property of linear transformations. The linearity property states that for any two vectors u, v and scalar c, then T(u + cv) = T(u) + cT(v).

We can use the linearity property to find T(v) by rewriting v equation as v = u + cv, with u = x2 and c = 2.

So, T(v) = T(u + cv) = T(x2) + 2T(x2) = x3 + 2x3 = x5 + 2x.

The equation is T(v) = x5 + 2x

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1) The percent error in the situation of this:

- Experimental value: 16. 5 sec

- Theoretical value: 17. 1 sec

are : 3.51 %

2) The percent error in this situation:

- Estimated value: 231

- Actual value: 215

are: 7.4 %

1) The steps to find the percent error in the situation where the experimental value is 16.5 sec and the theoretical value is 17.1 sec are:

Subtract the experimental value from the theoretical value:

17.1 - 16.5 = 0.6

Divide the difference by the theoretical value and multiply by 100 to get the percentage:

percent error = (0.6 / 17.1) * 100 = 3.51%

2) The steps to find 7.4% in the situation where the estimated value is 231 and the actual value is 215 are:

Subtract the estimated value from the actual value:

215 - 231 = -16

Divide the difference by the actual value and multiply by 100 to get the percentage:

percent error = (-16 / 215) * 100 = 7.4%

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The numbers 61 (78 times), 32 (77 times), 21, 63 (73 times), 69 (71 times), and 23 are those that appear the most frequently in the New York lottery (70 times).

For instance, reports indicate that the most popular Powerball lottery numbers are 32, 41, 16, 22, 23, and 29. These are the top six MegaMillions numbers: 15, 24, 33, 1, 46, and 39.

According to data, the Powerball numbers that appeared the most frequently over the past seven years were 61 (78 times), 32 (77 times), 21, 63, 69, and 23.

The New York lottery's most frequent numbers are 61 (78 times), 32 (77 times), 21, and 63 (73 times).

The numbers 61 (78 times), 32 (77 times), 21, 63 (73 times), 69 (71 times), and 23 are those that appear the most frequently in the New York lottery (70 times).

Since 2005, a consultant at Ernst & Young has examined the Mega Millions lottery's chosen numbers. The outcomes:

most often winning combinations

14 On 48 winning tickets — 11.6%

36 On 48 winning tickets — 11.6%

48 On 47 winning tickets — 11.4%

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The term of the deposit that the child did was 7 months

It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.

The formula for simple interest and procedure we will use to solve this exercise is:

T = (100 * S.I) / (P * R)

Where:

Information about the problem:

Applying the simple interest formula and isolating the time we get:

T = (100 * S.I) / (P * R)

T = (100 * 11.98) / (250* 8.25)

T = 1198/ 2062.5

T = 0.58 years

Converting the years to month we have:

0.58 years * 12 months/ 1 year = 7 months

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Correctly written question:

A child learning to have money invested a capital of $ 250 at a nominal rate of 0. 0825 (per annum) with simple interest. If he earned $ 11. 98 at the maturity date, how many day was the term of the deposit?

To find the composition of a mixture using a calibration curve, a sample of the mixture must first be prepared. The sample should be of a known concentration or dilution. Then, the sample's absorbance must be measured at a known wavelength.

This measured absorbance should then be plotted on the calibration curve. The calibration curve is a graph that shows the relationship between the absorbance of a sample and its concentration. If a linear relationship exists between absorbance and concentration, the calibration curve can be used to determine the concentration of the sample. The concentration of the sample can then be used to calculate the amount of each component in the mixture.

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Mary paid $2.58 for one cup of coffee is  the correct answer.

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Answer:

Step-by-step explanation:

5

It is established that there is always a multiple of 4 between squares of consecutive even numbers.

Take two consecutive even integers into consideration.

If n is an integer, then

The first even number would then be 2n.

Let 2(n+1) be the next consecutive even number.

The following even numbers would follow:

2n, 2(n+1)

Each succeeding even number's square would be:

(2n)² = 2n ×2n = 4n²

[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)

stretching out the brackets

= 4n² +4n +4n+4

[2(n+1)]² = 4n²+8n+4

We would choose values for n and calculate the difference between the squares of each consecutive even number in order to ascertain whether it is always a multiple of 4.

Let n = 1, 2, 3

For n= 1

4n² = 4(1)² = 4×1 = 4

4n²+8n+4 = 4(1)² + 8(1) + 4

= 4+8+4 = 16

The difference between consecutive even numbers' squares is equal to 16/4, or 12.

For n= 2

4n² = 4(2)² = 4×4 = 16

4n²+8n+4 = 4(2)² + 8(2) + 4

= 16+16+4 = 36

36-16 = 20 is the difference between the squares of two consecutive even numbers.

For n= 3

4n² = 4(3)² = 4×9 = 36

4n²+8n+4 = 4(3)² + 8(3) + 4

= 36+24+4 = 64

64-36 = 28 is the difference between the squares of two consecutive even numbers.

12 = 4×3

20 = 4×5

28= 4×7

We can see from the outcomes above that the numbers 12, 20, and 28 are multiples of 4.

As a result, a multiple of four always separates squares of succeeding even integers.

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The missing c-value that makes 12x² + 24x a perfect square trinomial is 12.

Given the expression in the question;

12x² + 24x + c

To determine the perfect square trinomial, first factor out 12 from the expression and find the value of c ;

12x² + 24x

12( x² + 2x )

To find c, divide the coefficient of x by and square the result.

(b/2)² = ( 2/2)² = 1

Now, add 1 to get the perfect trinomial.

12( x² + 2x + 1 )

Simplify using distributive property.

12×x² + 12×2x + 12×1 )

12x² + 24x + 12

Therefore, the perfect square trinomial is 12x² + 24x + 12.

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The circumference of the wheel is 0.5π m

The radius is an important factor in determining the wheel's motion and speed.

In your question, the wheel has a radius of 0.25m and is initially moving at a certain speed.

The distance traveled by a point on the circumference of the wheel is equal to the circumference of the wheel.

The circumference of a wheel can be calculated using the formula,

=> circumference = 2πr

where r is the radius of the wheel.

Thus, the speed of a wheel can be calculated by multiplying the circumference by the number of rotations in a given time.

As the radius of the wheel is 0.25m,

the circumference will be 0.5π m,

and the speed will depend on the number of rotations in a given time.

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a) The relative frequency distribution is 0.3212

b) The percentage of players that had a top speed less than 13.9 km/h = 0.007259 x 100 = 0.7259%

Given that,

Speed (km/hour) Number of players Relative frequency:

10 – 13.9

14 - 17.9

18 – 21.9

22 – 25.9

26 – 29.9

30 – 33.9

4

8

18

76

268

177 4/551=0.007259

8/551=0.01451

18/551=0.03266

76/ 551=0.1379

268/551 = 0.486

177/551=0.3212

Thus, The relative frequency distribution is 0.3212.

The percentage of players who had top speed between 14 and 17.9 km/h was = 0.01451 x100 = 1.451%

The percentage of players that had a top speed less than 13.9 km/h = 0.007259 x 100 = 0.7259%

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(a) Relative frequency distribution:

Speed (km/hr) Number of players Relative frequency

10-13.9 44 0.114

14-17.9 77 0.199

18-21.9 1414 0.368

22-25.9 5959 0.153

26-29.9 324324 0.084

30-33.9 181181 0.046

(b) Frequency histogram:

      |

      |

      |  X

      |  X

      |  X  X

      |  X  X

_______|__X__X

10     14     18     22     26     30

(c) Relative frequency histogram:

      |

      |

      |   X

      |   X

      |   X   X

      |   X   X

_______|___X___X

0.1   0.2   0.3   0.4   0.5   0.6   0.7

(d) Percentage of players with a top speed between 18 and 21.9 km/h:

0.368 * 100 = 36.8%

(e) Percentage of players with a top speed less than 13.9 km/h:

0.114 * 100 = 11.4%

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Answer:

The silo holds 22608 ft³ of the corn

Step-by-step explanation:

Assume the cylindrical silo is a perfect cylinder.

Volume of cylinder = πr²h

Volume = 3.14 × (12)² × 50

Volume = 22608 cubic feet

The values of x and y are given as follows:

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In this problem, we have that the right angle is bisected, and thus it is divided into two angles of 45º.

As the angle of 45º has the same value for the sine and the cosine, the sides of the triangle BDC have the same length, hence the value of x is given as follows:

x = 3.

Applying the Pythagorean Theorem, the value of y will be given as follows:

y² = 3² + 3²

y² = 2 x 9

[tex]y = 3\sqrt{2}[/tex]

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Answer:

[tex]x=\dfrac{9}{4}=2.25[/tex]

[tex]y=\dfrac{15}{4}=3.75[/tex]

Step-by-step explanation:

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

[tex]\boxed{\sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}}[/tex]

From inspection of the given right triangle:

Therefore:

[tex]\implies \dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]

[tex]\implies \dfrac{3}{x}=\dfrac{4}{3}[/tex]

[tex]\implies 3 \cdot 3 = 4 \cdot x[/tex]

[tex]\implies9 = 4x[/tex]

[tex]\implies x=\dfrac{9}{4}[/tex]

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment segment directly opposite the leg.

[tex]\boxed{\sf \dfrac{hypotenuse}{leg\:1}=\dfrac{leg\:1}{segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{hypotenuse}{leg\:2}=\dfrac{leg\:2}{segment\;2}}[/tex]

From inspection of the given right triangle:

Therefore:

[tex]\implies \dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]

[tex]\implies \dfrac{4+x}{y}=\dfrac{y}{x}[/tex]

[tex]\implies x(4+x)=y^2[/tex]

Substitute the found value of x:

[tex]\implies \dfrac{9}{4}\left(4+\dfrac{9}{4}\right)=y^2[/tex]

[tex]\implies y^2=\dfrac{225}{16}[/tex]

[tex]\implies y=\sqrt{\dfrac{225}{16}}[/tex]

[tex]\implies y=\dfrac{\sqrt{225}}{\sqrt{16}}[/tex]

[tex]\implies y=\dfrac{15}{4}[/tex]

The equation can be used to find the value of the car on January 1, 2018, which is A term in an arithmetic sequence and A= 25000*(1-0.15)^8

The given data is:

Price of car = $ 25,000

Rate of depreciation = 15 %

Formula used:

A= P(1-r)^n-----(1)

where p= price of the car

A= new price of a car after depreciation

r = rate of depreciation i.e. 15/100 = 0.15

n= time in years 2018 - 2010 = 8 years

Putting values in formula:

A= 25000*(1-0.15)^8

A= 25000*(0.85)^8

A= $6812.263

So, the Equation that can find the value of the car on January 1, 2018, is:

A= 25000*(1-0.15)^8 and the value of the car after 8 years is $6812.263

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To find the volume of the solid using the slicing method, we need to find the area of each cross-sectional square and then multiply it by the length (or height) of the solid.

Let's call the height of the solid h and the side length of each square cross-section s. The radius of the base of the solid is 15, so the diameter of the base is 2 * 15 = 30. Half of the diameter is the chord of the semicircular base, and it's also equal to the side length of the square cross-section.

So, s = 30 / 2 = 15

Since the cross sections are squares, the height of the solid (h) is equal to the side length of the square (s).

Now we can find the area of each cross-sectional square:

A = s^2 = 15^2 = 225

Finally, to find the volume of the solid, we need to multiply the area of each cross-sectional square by the height of the solid:

V = A * h = 225 * 15 = 3375

So, the volume of the solid is 3375 cubic units.

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Let's call the height of the solid h and the side length of each square cross-section s. The radius of the base of the solid is 15, so the diameter of the base is 2 * 15 = 30. Half of the diameter is the chord of the semicircular base, and it's also equal to the side length of the square cross-section.

Now we can find the area of each cross-sectional square:

A = s^2 = 15^2 = 225

V = A * h = 225 * 15 = 3375

For data at the interval​ level, we cannot calculate meaningful differences between data entries. The statement is false.

Interval:

The interval of a numerical value generally represents the maximum and minimum value between which the numerical value belongs, it is the amount of time that has passed between the beginning and end of the event which is also known as elapsed time.

The various ways of showing intervals are Inequalities, interval notations, and number lines, the amount of time between two given times is known as the time interval.

Data at the ordinal level can be qualitative or quantitative.  A true statement is​ "For data at the interval​ level, you can calculate meaningful differences between data​ entries."

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Answer:
Ez ahh question, the answer for A  is $2125 and B $2000 (better give me brainliest)
Step-by-step explanation:

A. Suppose the price $X
- to make a profit of 25%
$1700 x (1 + 25%) = $x
1700 x 1.25 = $2125
B. Suppose the price $y
$y x (1+25%) = $2500
$y = $2500 divided by 1.25
= $2000

The most consistent player is Player A, with a standard deviation of 1.4.

To compare the variability of the two players' data, we can use either the interquartile range (IQR) or the standard deviation.

The interquartile range (IQR) is a measure of the spread of the data that takes into account the values of the first quartile (Q1), the median, and the third quartile (Q3). It is calculated as the difference between Q3 and Q1. A smaller IQR indicates that the data is more tightly clustered and, therefore, more consistent.

The standard deviation is a measure of the average spread of the data from the mean. A smaller standard deviation indicates that the data is more tightly clustered around the mean and, therefore, more consistent.

In this case, we can calculate the IQR and standard deviation for each player's data. After sorting the data and finding the quartiles, we get the following:

Player A:

Q1: 1.5

Median: 2

Q3: 3

IQR: 1.5

Standard deviation: 1.4

Player B:

Q1: 2

Median: 4

Q3: 5

IQR: 3.5

Standard deviation: 2.9

From the calculations, we can see that Player A has a smaller IQR (1.5) and a smaller standard deviation (1.4) compared to Player B (IQR = 3.5, Standard deviation = 2.9). This means that Player A's data is more tightly clustered around the median, indicating that he is more consistent in his performance.

Therefore, the correct answer is (C).

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--The given question is incomplete; the complete question is

"The table shows the number of goals made by two hockey players during the season's games.

Player A                  Player B

2, 3, 1, 3, 2, 2, 1, 3, 6  1, 4, 5, 1, 2, 4, 5, 5, 11

Which measure of variability is best for the data, and which player is more consistent?

A) Player A is the most consistent, with an IQR of 1.5.

B) Player B is the most consistent, with an IQR of 3.5.

C) Player A is the most consistent, with a standard deviation of 1.4.

D) Player B is the most consistent, with a standard deviation of 2.9."--

Derivative of arcsin x is 1/√1-x²

The derivative of arcsin x is denoted by d/dx(arcsin x) (or) d/dx(sin-1x) (or) (arcsin x)' (or) (sin-1x)'. Its value is 1/√1 - x². We will prove it in two methods in the upcoming sections. The two methods are:

Using the chain rule

Using the first principles

Derivative of arcsin x Formula

The derivative of the arcsin function is,

d/dx(arcsin x) = 1/√1 - x² (OR)

d/dx(sin^-1x) = 1/√1 - x²

Derivative of Arcsin

d/dx(arcsinx) (or) d/dx(sin^-1x)

=1/√1-x²

arcsinx=1/√1-x²

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These functions have restricted domains: f(x) is defined only for x >= 3 and g(x) is defined only for x < 3.

A function is a mathematical concept that assigns exactly one output (or "output value") to each input (or "input value"). It provides a way to describe the relationship between inputs and outputs and can be thought of as a machine that takes inputs and produces outputs. Functions can be represented using equations or graphs.

In mathematical terms, a function can be formally defined as a set of ordered pairs (x,y), where x is the input (independent variable) and y is the output (dependent variable). The output value for a given input value is unique, and a single input value cannot correspond to multiple output values.

Functions are widely used in mathematics, science, and engineering to model real-world phenomena and to describe mathematical relationships. There are many types of functions, including linear functions, polynomial functions, exponential functions, logarithmic functions, and trigonometric functions, among others.

The equation y = 2|x - 3| + 5 can be rewritten as two separate linear functions, f(x) and g(x), as follows:

f(x) = 2(x - 3) + 5, for x >= 3

g(x) = -2(x - 3) + 5, for x < 3

So, for x >= 3, y is given by the linear function f(x) = 2(x - 3) + 5, and for x < 3, y is given by the linear function g(x) = -2(x - 3) + 5.

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Answer:

The cost of the other two panes should be $5.70.

Step-by-step explanation:

Given that,

Now based on the above information, the calculation is as follows:

= 14.25 x 2 ÷ 5

= $5.70

Therefore we can conclude that the cost of the other two panes should be

$5.70.

The y values are also equal at x=-2. Thus, f(-2) = g(-2) is true. D is the right answer, thus.

Quantity and their permutations, relationships and associated tissues, shapes and their locales, and locations in which they are found are all components of the mathematics classroom. The relationship among a group of inputs, each of which has a productivity commission, is referred to by the term "function." A function is a relationship involving inputs and outputs where each input produces a single, unique result. Every function has an area and a codomain, often known like a scope. F is typically used to describe functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, yet another functions, many-to-one functions, within functions, and on functions.

given

In the given graph, the two lines intersects at x = -2

And intersection point is that point , where the y values of the two graphs are equal .

That is  f(x) = g(x)

The y values are also equal at x=-2. Thus, f(-2) = g(-2) is true. D is the right answer, thus.

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Answer:

Step-by-step explanation:

Because all of the other sides are equal so it makes that equal

Answer:omak sus

Step-by-step explanation:

The solution is, the side lengths that are possible are from 6 to 30. as, The inequality is, 6 ≤  x ≤ 30.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

given that,

Natasha wants to plant a square garden and enclose it with a fence.

She has 120 feet of fencing available

and she wants the sides of her garden to be at least 6 feet long.

now, we have to Write and solve the inequality that describes the side lengths that are possible,

so, we have,

the garden is square, so, perimeter = 4 * side length

now. let, the length of side = x

we get,

perimeter = 4x = y

so, we get,

x ≥ 6 ......(1)

and, y ≤ 120

i.e. 4x ≤ 120

or, x ≤ 30 .....(2)

so, from 1 & 2 we get,

The inequality is, 6 ≤  x ≤ 30

Hence, The solution is, the side lengths that are possible are from 6 to 30. as, The inequality is, 6 ≤  x ≤ 30.

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The number of observations in the sample, minus one, serves as the denominator in the formula for a sample's variance.

The formula for a sample's variance is the sum of the squared variances between each observation and the mean, divided by the sample's observation count, minus one. This is referred to as the sample size minus one (n-1). Rather than relying on the sample size The denominator in the formula for a sample's variance is equal to the number of observations in the sample, minus one. The denominator facilitates the calculation of a population variance, which is used to determine a sample variance (n). This is true because the population variance is a fair approximation of the population variance and the denominator helps with bias correction.

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A total of 3703 square inches of paint will be required to cover the table completely.

It deals with the dimensions, regions, and densities of the various 2D and 3D shapes.

A cylinder can be used to represent the table's top, and rectangular prisms can be used to represent the table's legs.

The surface area of the cylinder will be

SA of cylinder = 2πr² + 2πrh

substitute the values in the above equation, we get

SA of cylinder = 2π (18² + 18 × 3)

simplifying the equation, we get

SA of cylinder = 2375 square inches

The surface area of the prism will be

SA of prism = 4 [WL + 2(WH + LH)]

substitute the values in the above equation, we get

SA of prism = 4 [2 x 6 + 2 (2 x 20 + 6 x 20)]

simplifying the equation, we get

SA of prism = 4 [12 + 2 x 160]

SA of prism = 4 [12 + 320]

SA of prism = 1328 square inches

The total surface area of the table will be

Total surface area = SA of prism + SA of cylinder

simplifying the equation, we get

Total surface area = 1328 + 2375

Total surface area = 3703 square inches

In order to completely cover the table, 3703 square inches of paint will be required.

Therefore, the correct answer is option B. 3,703.

The complete question is:

The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.

Estimate the amount of paint needed to cover all parts of the table, to the nearest square inch.

A.2,375

B.3,703

C.2,707

D.4,014

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The amount of paint needed to cover all parts of the table will be 3703 square inches.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.

There are numerous shapes and dimensions in geometry, including sphere, cube, cuboid, cone, cylinder, etc. Each form has its own volume and surface area. However, we can only measure the area that two-dimensional shapes like squares, circles, rectangles, triangles, etc. cover; there is no volume available.

The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.

The table is shown below.

The surface area of the cylinder will be

SA of cylinder = 2πr² + 2πrh

SA of cylinder = 2π (18² + 18 × 3)

SA of cylinder = 2375 square inches

Then the surface area of the prism will be

SA of prism = 4 [WL + 2(WH + LH)]

SA of prism = 4 [2 x 6 + 2 (2 x 20 + 6 x 20)]

SA of prism = 4 [12 + 2 x 160]

SA of prism = 4 [12 + 320]

SA of prism = 1328 square inches

Then the total surface area of the table will be

Total surface area = SA of prism + SA of cylinder

Total surface area = 1328 + 2375

Total surface area = 3703 square inches

Thus, the amount of paint needed to cover all parts of the table will be 3703 square inches.

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Answer:

3/4

Step-by-step explanation:

[tex] \sqrt{ \frac{9 }{16?} \ } [/tex]

[tex] \sqrt{9 } [/tex]

=3

[tex] = 3[/tex]

[tex] \sqrt{16} [/tex]

[tex] = 4[/tex]

ans=3/4

Answer:

Hindus from India invented zero to represent the idea of the power of the cosmos and universe as they expand into infinity. They called this the sunya which means empty in Sanskrit. The book Brahma Sphuta Siddhanta was published in c. 628 by Brahmagupta which defines zero as the subtraction of a number by itself, e.g. 5-5 =0.

The builder has 17  grey bricks and 18 red bricks. The total weight of the bricks is 298 kilograms.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.

Assume that the builder has x number of red bricks and y number of gray bricks.

The weight of 1 red brick is 9 kilograms.

The weight of x red bricks is 9x kilograms.

The weight of 1 gray brick is 8 kilograms.

The weight of y red bricks is 8y kilograms.

The weight of x red bricks and y red bricks is 9x + 8y kilogram.

The total number of bricks is 35 whose weight is 298 kilograms.

According to the question,

x+y = 35 ......(i)

9x + 8y = 298 .....(ii)

Solve the equations by using the elimination method:

Multiply 9 with equation (i) and subtract equation (ii) from it:

9x+9y = 315

9x + 8y = 298

(-)  (-)       (-)

_______________

         y = 17

Putting y = 17 in equation (i)

x+17 = 35

x = 18

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