The diagram shows a solid triangular prism with a cylindrical hole of radius r cm drilled through it. (i) The ratio of the volume of solid removed : volume of remaining solid is 1 : 6. Find the value of r. Using your answer in part (i), find the total surface area of the solid shown. ​

The required density of the given solid substance is 7.07 g/cm³.

What is the density of a substance?

The density of a substance is the property which is obtained by dividing the mass of the given substance by its volume. Its SI unit is kg/m³.

Calculation for the density of a solid substance

Mass of the given substance = 120 g

Side of cube, a = 2.57 cm

The volume of the given substance = a³

= 2.57³

= 16.97 cm³

The density of the given substance is given by the mass of the substance/volume of the substance

= 120 / 16.97

= 7.07 g/cm³

Hence, the density of the given solid substance is 7.07 g/cm³.

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The cost for her to purchase the fence is $108.

Since she wants to put a wire fence around her garden which is 12 feet long and 6 feet wide, the total perimeter will be:

= 2(length + width)

= 2(12 + 6)

= 36 feet

Therefore, the cost will be:

= Total feet × Amount

= 36 × $3

= $108

Therefore, the cost for her to purchase the fence is $108.

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Option D x+2y+10 .

A trinomial with a constant term will have three terms, and one of those terms will be a constant, which is a number.

we also know about the Constant

A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

Some relatable terms are :

Monomial: Polynomial having a single term.

Binomial: Polynomial having two terms.

Trinomial: Polynomial having three terms.

In given option we'll define

in option A there is no constant .

option B there i sonly given x which is also not constant.

further in option c it is simply binomial in which only two terms are given without constant .

so at last conclusion is in option D there are three terms are given with one constant which is number 10 .

x+2y+10 is trinomial with a constant.

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Answer:

My prediction of the sum is 0.

Hope this helps :)

Step-by-step explanation:

It is 0 because if you owe 2 dollars and you pay it back with 2 dollars then you have 0 dollars owed.

--------------------> 2nd: 2 (positive two - move right)

<-------------------- 1st: - 2 (negative two - move left)

<----------l----------l-----------l----------l----------l--------->

-2 -1 0 1 2

Answer:

The zeros are x =5, -7/2

Step-by-step explanation:

To find the zeros, set the expression equal to zero

(x-5)(2x+7) =0

Using the zero product property

(x-5)=0     (2x+7)=0

Solve each equation

x=5               2x = -7

x=5                  x = -7/2

The zeros are x =5, -7/2

Answer:

5, -7/2

Step-by-step explanation:

[tex]x - 5 = 0 = 5\\\\2x + 7 = 0\\2x + -7 = 0\\\frac{2x}{2} = \frac{-7}{2}\\ x = \frac{-7}{2}\\x = -\frac{7}{2}[/tex]

Thus,

x = 5

x = -7/2

The solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

The fraction expression is given as

-2 1/3 + (-1 3/4) =

Express the terms of the expression as an improper fraction

So, we have

-2 1/3 + (-1 3/4) = -7/3 + (-7/4)

Remove the bracket in the above expression.

So, we have

-2 1/3 + (-1 3/4) = -7/3 - 7/4

Take the LCM in the above expression.

So, we have

-2 1/3 + (-1 3/4) = (-7 * 4 - 7 * 3)/12

Evaluate the difference

-2 1/3 + (-1 3/4) = -49/12

Express the fraction as a mixed fraction

-2 1/3 + (-1 3/4) = -4 1/12

Hence, the solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

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Answer:

26 units

Step-by-step explanation:

By using the Pythagoras Theorem,

C^2 = A^2 + B^2

Substitute in given values for A and B.

C^2 = 10^2 + 24^2

= 100 + 576

= 676

[tex]c = \sqrt{676} \\ = 26[/tex]

Hope this helped! ^^

Sidenote: Pythagoras Theorem can only be used on right-angled triangles.

After simplifying the expression, - ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y), we get the result as - 11 / 2 x + 4 y.

- ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y)

First we will multiply 2 and open the brackets.

So, we get that:

- 7 x + 3 y + 3/2 x + y

Combining the like terms, we get that:

= ( - 14 + 3 ) x / 2 + 3 y + y

Simplifying and solving the expression to obtain the result, we get that:

= - 11 / 2 x + 4 y.

Therefore, after simplifying the expression, - ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y), we get the result as - 11 / 2 x + 4 y.

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Answer:

4

Step-by-step explanation:

The method of altering a graph to produce a different version of the one that came before is known as graph transformation. The graphs are movable in the x-y plane and can be translated. Along with these modifications, they can also be stretched.

Horizontal stretching

Vertical stretching

Vertical translation

Horizontal translation

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The dimensions of the rectangle are:

width = 10 units

length = 17 units

We are given to find the dimensions of a rectangle with an area equal to the parallelogram with vertices (6, 21), (14, 15), (6, 0), and (-2, 6).

If we have two points with coordinates as (a, b) and (c, d) The distance is given by the formula: √[(c - a )² + (d - b)²]

Now, of the coordinates are labelled as;

A(6, 21), B(14, 15), C(-2,6),  (6,0)

Thus;

AB = √(14 - 6)² + (15 - 21)² = √100 = 10 = CD

AC = √(-2 - 6)² + (6 - 21)² = 64 + 225 = √289 = 17 = BD

Thus the dimensions of the rectangle are:

AB = 10 = width

AC = 17 = length

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From the rule for when a relation represents a function, we have that:

16) Is not a function.

17) Is a function.

18) Is not a function.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

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Answer:

x = 3     y = -1

Step-by-step explanation:

x - 5y = 8

x = 5y + 8

replace x with 5y + 8 in the other equation

4(5y + 8) + 5y = 7

20y + 32 + 5y = 7

25y = 7 - 32

25y = -25

y = -25/25

y = -1

x = 5(-1) + 8

x = -5 + 8

x = 3

Deciles are 61.3 and 67.7

What are deciles?

Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts, where each part contains the same number of observations). The decile is a member of the wider family of quantiles.

Given:

Normal distribution =64.5 inches

Standard deviation=σ =2.5 inches

​

So, here the z- score for left decile= -1.28

and for right decile= +1.28

we know,

z= x-[tex]\mu[/tex]/σ

x= zσ + [tex]\mu[/tex]

x=-1.28*2.5 + 64.5

x= 61.3  and,

x= 1.28*2.5 + 64.5

x=67.7

hence, the deciles are 61.3 and 67.7

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The standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.

The population of individuals is always smaller than the entire population, therefore the possibilities for variances will be lower with the sample than with the population. The higher the population, the greater the chances for deviation from the mean.

Therefore, the standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.

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Answer:

Sum of ages is 35

Since there are two persons and it says four years from now, each year 2 more years will be added on to the 35 so year 1: 2years Year 2:4years Year 3:6years Year 4 : 8years

35+8= 43

Remember that Melanie will be 5 years older ( which she should have already been)

so 43+5= 48 ( Melanie's age)

and 48-5 = 43 ( Her brother's age)

Using translation concepts, the note E would be louder with a higher amplitude of y, hence constant a has to be multiplied by a positive constant greater than 1.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the function is given by:

y = asin(1320πx)

The intensity of a sound is given by it's amplitude a, hence, to make the sound stronger, we need to vertically stretch the graph of y, which is done when constant a is multiplied by a positive constant greater than 1.

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Answer:

0.5

Step-by-step explanation:

12/24 = 0.5

6/12 = 0.5

3/6 = 0.5

1.5/3 = 0.5

Answer: 0.5

After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.

Here,

Samuya is multiplying 0.7 by 0.003.

We have to find, zeros will be to the right of the decimal point in the product.

What is Product?

The product of two numbers is the result you get when you multiply them together.

Now,

Product of 0.7 and 0.003 we get;

0.7 x 0.003 = 0.0021

Clearly, there are two zero to the right of the decimal point in the product.

So, After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.

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Answer:

4 years old

Step-by-step explanation:

3x = x + 8

2x = 8

x = 4

Answer:

4 y/o

Step-by-step explanation:

x = age now

  add 8 years

x+8    and this equals   3 times as old as he is now, or  3x

x+8 = 3x       subtract 'x' from both sides

8 = 2x           divide both sides by 2

x = 4 y/o

Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.

A midpoint is simply a point that divides a segment into two equal halves.

Given the data in the question;

Point E is the midpoint of line segment YT, YT is divided into two equal halves. Hence, Two times Line segment YE equals to YT.

2( Line segment YE ) = Line segment YT

Plug in the given values and solve for x.

2( Line segment YE ) = Line segment YT

2( 3x + 1 ) = 14

Expand using distributive property

2 × 3x + 2 × 1 = 14

6x + 2 = 14

Collect like terms

6x = 14 - 2

6x = 12

6x/6 = 12/6

x = 12/6

x = 2

Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.

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The real distance between Hooperville and Michael's home town is 116.667 miles.

Scales are ratios commonly used to contain great extensions of land in images and maps and offer a quick though efficient manner to estimate distances. The real distance between Hoopersville and Michael's home town can be found thorugh this formula:

d' = d / r      

Where:

If we know that d = 3.5 in and r = 1.5 in / 50 mi, then the real distance between Hooperville and Michael's hown town is:

d' = 3.5 in / (1.5 in / 50 mi)

d' = 116.667 mi

The real distance between Hooperville and Michael's home town is 116.667 miles.

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The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

To find the equation:

When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:

[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]

The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:

As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]

Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

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The correct question is given below:

Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.

The maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀ is given as -

Polarization is the property of wave oscillations having a definite direction relative to the wave's propagation direction. Transverse waves that can be polarized are EM waves. The polarization direction is defined as the direction parallel to the EM wave's electric field.

The effect of a polariser on polarised light is described by Malus' law, which states that-

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The correct question is -

What is the maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀.

Answer:

19

Step-by-step explanation:

5w+3°=98°

5w=98°-3°

5w=95°

therefore w=95/5=19

I'm assuming the equation is

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1[/tex]

Let me know if the equation is different so I can update the solution.

-----------------

Fractions are a pain to deal with, so it's best to eliminate them whenever we can. In equations like this, we can multiply both sides by 4 since this is the LCD (which stands for "lowest common denominator").

If we multiply both sides by 4, then all the denominators of 4 will cancel.

We'll have these steps:

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1\\\\4\left(\frac{3}{4}y - \frac{2}{4}y+7\right) = 4\left(\frac{2}{4}y-1\right)\\\\3y - 2y + 28 = 2y - 4 \ \ \text{ ... denominators cancel after distributing}\\\\y + 28 = 2y - 4\\\\y- 2y =- 4-28\\\\-y = -32\\\\y = \frac{-32}{-1}\\\\y = 32\\\\[/tex]

Answer:

[tex]y=32[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{3}{4}y-\frac{2}{4}y+7=\frac{2}{4}y-1[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y+7-7=\frac{2}{4}y-1-7[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y=\frac{y}{2}-8[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y-\frac{y}{2}=\frac{y}{2}-8-\frac{y}{2}[/tex]
[tex]-\frac{y}{4}=-8[/tex]
[tex]4\left(-\frac{y}{4}\right)=4\left(-8\right)[/tex]
[tex]\frac{-y}{-1}=\frac{-32}{-1}[/tex]
[tex]y=32[/tex]

Therefore "y = 32."

Hope this helps.

Answer:

[tex]\large\boxed{\textsf{The Circumference is the Perimeter of the circle.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to identfy what the Circumference is.}}[/tex]

[tex]\Large\underline{\textsf{What is the Circumference?}}[/tex]

[tex]\textsf{The Circumference is a fancy word to describe the sum of the arcs of a circle.}[/tex]

[tex]\textsf{The total of the area 'on' the circle is commonly referred to as the Perimeter.}[/tex]

[tex]\mathtt{Circumference = (diameter)\pi }[/tex]

Now, it is not a function, same domain has different ranges