Find the volume of a pyramid with a square base, where the perimeter of the base is 4.1 m and the height of the is pyramid 3.6 m. Round your answer to the nearest tenth of a cubic meter.

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The density in pounds per cubic meter is 83 pounds per cubic metre.

The density is mass of a unit volume of a material substance.

In other words, density is the ratio between mass and volume or mass per unit .

Therefore, density can be represented mathematically as follows:

density = mass / volume

Hence,

mass = 5 ounces

5 ounces = 0.3125 pounds

1 gallon = 0.00378541 pounds

Therefore,

density = 0.3125 / 0.00378541

density = 82.5538052681

density = 83 pounds per cubic metre.

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Step-by-step explanation:

Well first let's find the derivative in using the power rule

h'(t) = (-4.9)t + 157

h'(t) = -9.8t + 157

we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.

h'(1452.602) = -9.8(1452.602) + 157

h' = 14,078.500

Using it's formula, the area of the right triangle is of 750 inches squared.

The area of a right triangle is given by half the multiplication of the two legs, which are the two smaller sides.

In this problem, the two legs are 25 inches and 60 inches, hence the area of the triangle is:

A = 0.5 x 25 x 60 = 750 inches².

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Answer:

[tex]\huge\boxed{\sf 81x^4 - 16y^4}[/tex]

Step-by-step explanation:

= (3x - 2y)(3x + 2y)(9x² + 4y²)

= [(3x)² - (2y)²] (9x² + 4y²)

= (9x² - 4y²)(9x² + 4y²)

Using the above formula again

= (9x²)² - (4y²)²

[tex]\rule[225]{225}{2}[/tex]

The days of the year (excluding Sundays) paul attends school is 183 days

Months Paul skipped school = January, February, June, July August

= 31 + 28 + 30 + 31 + 31

= 151 days

Days he attend school excluding Sunday = Total days in a year - (Months Paul skipped school + Sundays)

= 365 - (151 + 31)

= 365 - 182

= 183 days

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Answer:

Domain:[-4,∞)

Range:[0, ∞)

Thus, choice C is the exact answer

10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit. This can be obtained by multiplying 10 with the tens digit and adding unit digit.

Given that, in a two digit number,

t = the tens digit

u = the ones digit

The expression for the digit will be ,

10×t + u = 10t + u

The value of its reversal,

u = the tens digit

t = the ones digit

10×u + t = 10u + t is the required expression

For example,

37 = 10×3 + 7 = 30 + 7 and its reverse 73 = 10×7 + 3 = 70 + 3

Hence 10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit.

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Answer:

(2x + 20) ft^2.

Step-by-step explanation:

Area  = length * width

         =   2 * (x + 10)

         = (2x + 20) ft^2.

The volume of the cuboid is 132 cubic inches.

Given length of cuboid 7 1/3 inches, breadth being 6 2/3 inches , height being 2 7/10 inches.

Volume is amount of liquid a container can hold in its capacity. Cuboid is a 3 dimensional figure having length , breadth and height.Volume of cuboid is the product of length, breadth and height of cuboid.

We have to calculate volume of cuboid.

We have to make a simple fraction showing length , breadth and height.

Length=(3*7+1)/3=22/3

Breadth=(3*6+2)/3=20/3

Height=(10*2+7)/10=27/10

Volume=22/3*20/3*27/10

=11880/90

=132 cubic inches.

Hence the volume of cuboid having length of 22/3 inches, breadth of 20/3 inches and height of 27/10 is 132 cubic inches.

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Question is incomplete as it should include figure.

When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.

Systematic random sampling is known to be a form of a random sampling method that needs one to select samples using a system of intervals where one has ranges of numbered population.

Note that When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.

See options below

a. stratified sample

b. comprehensive sample

c. random sample

d. Systematic sample

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The length of the belt around the two pulleys is approximately 49.2 centimeters.

In this question we must determine the perimeter of a belt around two pulleys, whose centers are 10 centimeters apart. This perimeter is the sum of part of the circumference of small pulley, part of the circumference of the big pulley and two times the segment tangent to the two pulleys.

Now we proceed to determine the parts of the perimeter of the belt:

Big pulley

s' = (214.92° / 180°) · π · (6 cm)

s' ≈ 22.506 cm

Small pulley

s'' = (145.08° / 180°) · π · (3 cm)

s'' ≈ 7.596 cm

Tangent segments

l = (10 cm) · sin 72.54°

l ≈ 9.539 cm

Lastly, the perimeter of the belt is:

L = s' + s'' + 2 · l      (1)

L = 22.506 cm + 7.596 cm + 2 · (9.539 cm)

L = 49.180 cm

The length of the belt around the two pulleys is approximately 49.2 centimeters.

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Answer:

[tex]BC=5\sqrt{2}[/tex], [tex]AC=5\sqrt{4}[/tex]

Step-by-step explanation:

In a 45-45-90 relation triangle the two shortest sides will have equal length, meaning:

[tex]BC=5\sqrt{2}[/tex]

To find the hypotenuse we must multiply the shortest side by [tex]\sqrt{2}[/tex], both sides are equal so it doesn't matter which we multiply.

[tex]AC=5\sqrt{2} \sqrt{2} \\AC=5\sqrt{4}[/tex]

Answer:

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

Step-by-step explanation:

Standard form for equation of line: y = mx + c

where m = gradient or slope

c = y-intercept

From the question we know that,

x = 2

y = 3

m = - 0.5

We will substitute these values into the equation to find c.

3 = (-0.5)(2) + c

3 = - 1 + c

c = 3 + 1 = 4

Therefore the equation of this line is [tex]y = -\frac{1}{2} x+4[/tex]

Answer:

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR   (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.

Answer:Divide your speed in feet per minute by 60

Step-by-step explanation:

The correlation coefficient r between the two data sets is 0.33

From the table of values, we make use of the following representations:

Using the above representations, we can now plot our data values in the Excel software

From the Excel application, we have the following summary:

X Values

∑ = 424

Mean = 21.2

∑(X - Mx)2 = SSx = 101.2

Y Values

∑ = 151.8

Mean = 7.59

∑(Y - My)2 = SSy = 8.238

X and Y Combined

N = 20

∑(X - Mx)(Y - My) = 9.54

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

This gives

r = 9.54 / √((101.2)(8.238))

Evaluate

r = 0.3304

Approximate

r = 0.33

Hence, the correlation coefficient r between the two data sets is 0.33

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Answer:

20

Steps-by-step explanation:

sorry mistake

Answer:

12

Explanation: I just counted them! :) and there was 6 in the middle and on the outside so 6 + 6 = 12! :)

The ratio of its width to its length is; 5 :9.

The ratio of its length to its perimeter is; 9: 28.

1). From the task content, the land measures 4.5 km long and 2.5 km wide. Hence, the ratios is; 2.5: 4.5.

Therefore, we have; 5: 9 by expression as whole number ratios.

2) Since the perimeter of the rectangle is; 2(2.5+4.5) = 14.

The ratio of length to perimeter expressed simply is therefore; 9: 28.

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Answer:

Distributive property

Step-by-step explanation:

In order to solve this equation we first need to distribute 3 into 2y+5, we use the distributive property to do this.

Let [tex]y=\cos(2x)[/tex], with first two derivatives

[tex]Dy = -2\sin(2x)[/tex]

[tex]D^2y = -4\cos(2x)[/tex]

Consider the linear ODE

[tex]aD^2y + bDy + cy = 0[/tex]

Substitute [tex]y[/tex] and its derivatives and solve for the unknown coefficients [tex]a,b,c[/tex].

[tex]-4a\cos(2x) - 2b\sin(2x) + c\cos(2x) = 0[/tex]

[tex]\implies \begin{cases}-4a+c=0 \\ -2b=0 \end{cases}[/tex]

[tex]\implies b=0 \text{ and } c= 4a[/tex]

Then the minimal ODE with this solution is

[tex]aD^2y + 4ay = 0 \implies \boxed{D^2y + 4y = 0}[/tex]

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]=[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]

Therefore,

125 = 5³

27 = 3³

Hence,

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} }[/tex]

Hence,

Both cube root are the same now,

Therefore, we have to add them together.

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

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Putting the other player's king in check is always a good move. true

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Using the concept of vertical and horizontal asymptotes, it is found that the function will have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 for a = -1 and m = 1.

In this problem, the function is:

[tex]f(x) = \frac{2x^m}{x + a}[/tex]

It has a vertical asymptote at x = 1, hence:

x + a = 0

1 + a = 0

a = -1

It has a horizontal asymptote at y = 2, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x + a} = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x} = 2[/tex]

[tex]2^{m-1} = 2[/tex]

Then, since we want to simplify, the exponents at the numerator and the denominator have to be equal, hence m = 1.

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Answer:

1.11

Step-by-step explanation:

Answer:

b.  -x + y = 0

Step-by-step explanation:

Direct variation:

Direct variation means "y varies directly as x”:

[tex]y \propto x \implies y=kx[/tex]

where k is the (non-zero) constant of variation.

To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.

Equation a

[tex]y=\dfrac{4}{3}x-2[/tex]

This is not a direct variation equation as there is an addition of -2.

Equation b

[tex]-x+y=0[/tex]

[tex]\implies y=x[/tex]

This is a direct variation equation where the constant of variation is 1.

Equation c

[tex]xy=8[/tex]

[tex]\implies y=\dfrac{8}{x}[/tex]

This is not a direct variation equation as y is inversely proportional to x.

Equation d

[tex]y=14[/tex]

This equation does not include the variable x, and so is therefore not a direct variation equation.

If y varies inversely with x then the line must be linear and increasing

And the y intercept must be 0 in y=mx+c

#1

c=-2

#2

Yes

#3

No

#4

Parallel to x axis no direct variation

The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).

According to the question,

The circle with center at (-1,-4) that passes through the point (-4,0).

To find the radius of the circle:

Radius r = √[(-4 - (-1))² + (0- (-4))²]

=√(-4+1)² + (4)²

=√9+16

=√25

=5.

In order to find the standard equation of the circle is

(x - (-4))² + (y - (0))² = (5)²

(x + 4)² + (y )² = 25

x² + 8x + 16 + y² = 25

x² + y² + 8x + 16 = 25

x² + y² + 8x = 25 - 16

x² + y² + 8x = 9

x² + y² + 8x - 9 = 0

Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.

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The number of minutes it take to complete the same job if sandy and randy work together than if sandy works alone is 18mins.

According to this question, Sandy rakes and bags the leaves on her front lawn in 30 mins while Randy does the same job in 20 mins.

To calculate the time it will take both of them to work together, we use the following expression;

1/30 + 1/20 = 1/x

x = 12mins

Therefore, it will take 30 - 12 = 18 mins, to complete the same job if sandy and randy work together than if sandy works alone.

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Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

Answer:

53

Step-by-step explanation:

Let yazid's score be x

x + x + 17 + 2x = 161

4x + 17 = 161

4x = 144

x = 36

jack = x + 17

jack = 53

Answer:

Jack:  36

Bonus:  Yazid:  53 and Susan:  72

Step-by-step explanation:

Let J, Y, and K stand for Jack, Yazin, Susan's scores.

We are told that:

J = Y + 17  [Jack scored 17 marks more than Yazid]

S = 2Y  [Susan scored twice Yazid's score]

J + Y + S = 161  [total score is 161]

Substitute the first two expressions into the last equation:

J + Y + S = 161

(Y+17) + Y + (2Y) = 161

4Y = 144

Y = 36

Use Y = 36 to find the other scores:

J = Y + 17

J = 36 + 17

J = 53

S = 2Y

S = 2*(36)

S = 72

CHECK:

Does 36+53+72 = 161?

YES

Answer:

{x:x is a real number}

Since any value can replace x to give an integer.

{x:x is a real number}