A pygmy hippo and a regular hippo were recently born. The pygmy hippo had a mass of 5 1/2 kg at birth. The regular hippo had a mass of 24 1/2 kg at birth. Complete the comparison. At birth, the regular hippo massed ? times as much as the pygmy hippo.

The gallons needed to paint the silo is 10.

A cylinder is a three-dimensional object. It is a prism with a circular base. The total surface area of cylinder can be determined by adding the area of all its faces.

Total surface area of the cylinder excluding its base = 2πrh +πr²

Where:

TSA = (2 x 3.14 x 10 x 30) + (3.14 x 10²)

314 + 1884 = 2198 ft²

Number of gallons needed = 2198 / 224 = 9.81 = 10 gallons

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The ratio of the volume of pipe a to the volume of pipe b is 27:1  .

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

Given that,

Radius of pipe a is 6 cm, and the radius of pipe b is 2 cm.

We know that the volume of cylinder is :- [tex]\pi r^{2}h[/tex]

where r is radius and h is height of the cylinder.

If two figures are similar then ratio of volume is equal to the cube of any dimension.

The ratio of the volume of Pipe a to the volume of Pipe b  :-

[tex]\frac{V(a)}{V(b)}=\frac{6^{3} }{2^{3} }[/tex]

       = [tex]\frac{27}{1}[/tex]

Hence, The ratio of the volume of pipe a to the volume of pipe b is 27:1 .

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Answer:

let the angles be 3x,4x&5x

Now,

perimeter (p)=sum of all sides

or, 96=3x+4x+5x

or, 96=12x

or,96/12=x

or,8=x

or,x=8

Then,

3x=3*8

=24

4x=4*8

=32

5x=5*8

=45

The equilibrium expression is written as  [NH3]^2/[N2] [H2]^3.

A reaction involves the conversion of reactants to products. Now we know that the number that shows us the extent to which we can convert the reactants to products is given by the equilibrium constant. If the equilibrium constant is large and positive, then the reaction tends towards the conversion of reactants to products. on the other hand, when the reaction has a small equilibrium constant, then the reaction tends towards the reactants.

Thus, the magnitude of the equilibrium constant tells us how easily reactants are converted into products and this is necessary when we are trying to predict the direction in which a reaction will go or make calculations.

Given a reaction; N₂(g) + 3H₂(g) ----> 2NH3(g) we can now write the expression for the equilibrium of the reaction as;

K = [NH3]^2/[N2] [H2]^3

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The range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

All the possible set of x-values that are plotted on the horizontal axis (x-axis) are the domain of a function. In order words, they are the inputs of the function.

On the other hand, all the corresponding set of x-values that are plotted on the vertical axis (y-axis) are the range of a function. In order words, they are the outputs of the function.

In the graph given below that shows a function, s is plotted on the vertical axis (y-axis), and its values starts from 20, up to 100. The range can be said to be all values of s that are from 20 to 100.

Therefore, the range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

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Answer:

D.

Step-by-step explanation:

Based on the table, the minutes a person has to run to burn 100 calories is 20 minutes

Ratio shows the equivalent relationship that exists between two or more numbers. A ratio table can be described as table that shows equivalent relationship between two numbers.

The first step is to determine the ratio between the minutes run and the calories burned. To do this, divide any of the minutes run on the table by the corresponding calories burned.

Ratio = minutes run / calories burned

8 / 40 = 1/5

Now, multiply this ratio by 100

1/5 x 100 = 20 minutes

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Answer:

s is antecedent t is consepuent

Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. Thus the steps taken by Tyler are correct if x = 22.

ii. Tyler made no mistake.

Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. The value of the alphabet in the expression would be determined by applying mathematical operations appropriately.

To solve the question given to Tyler, we have:

[tex]\sqrt{x + 3}[/tex] = -5

square both sides of the equation to have;

(x + 3) = [tex](-5)^{2}[/tex]

x + 3 = 25

collect like terms to get;

x = 25 - 3

  = 22

x = 22

1. Thus the equation is true if x = 22.

2. Tyler did not make any mistake in solving for x.

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The most appropriate model for a given situation is exponential.

The most appropriate model for a given situation is exponential.

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Answer:

Step-by-step explanation:

Simplify both sides of the equation:

4 (2 + a) = 24

( 4 )( 2 ) + ( 4 )( a )  =  24   (Distribute)

8 + 4a = 24

4a  +  8 = 24

subtract 8 from both sides:

4a + 8 − 8 = 24 − 8

4a = 16

Divide both sides by 4:

4 a/4     =     16/4

a  =  4

Multiple bracket out first:

4 x 2 =8

4 x a = 4a

8 +4a = 24

-8

4a. = 16

÷4

a = 4

Hope this helps!

Answer:

15, 11, 60

Step-by-step explanation:

Let Joe's amount be x

x + x - 6 + 4x = 96

6x - 6 = 96

6x = 90

x = 15

Joe has 15

Kaitlin has 11

Miguel has 60

Answer:

Area=length× berngth

A=5×2x

A=10x square

The characteristic that  is necessary to create a table that compares two functions  is D. Choose the same values for each functions .

The Mathematical tables can be regarded as the lists of numbers which is used in showing the results of a calculation  and these can have  varying arguments.

It should be noted that when necessary to creating a table that compares two functions it  is important to Choose the same values for each functions .

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The total displacement of the honeybee as it travels west, south and north is 219.2 m.

The total displacement of the honeybee is calculated as follows;

total horizontal displacement, x = 100 m due west

total vertical displacement, y = 200 m - 5 m = 195 m

total displacement, d = √x² + y²

d = √(100² + 195²)

d = 219.2 m

Thus, the total displacement of the honeybee as it travels west, south and north is 219.2 m.

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When to use the law of cosine is explained below.

Using the labelled triangle, we have: sin D/d = sin E/e = sin F/f.

Using the sine law, the measure of angle M is: 74.9°.

The cosine law is given as, c = a² + b² - 2ab(cos C). It is used to solve a triangle with missing angle or side.

When we are given two sides and an angle between the two sides, and we need to find the third side.

When we are given the all three sides of a triangle and we need to find the angles of the triangle.

Using the labelled triangle DEF in the diagram below, the law of sines is:

sin D/d = sin E/e = sin F/f.

m∠N = 56°

n = 8.5 cm

m = 9.9 cm

Plug in the values into sin N/n = sin M/m:

sin 56/8.5 = sin M/9.9

sin M = (sin 56 × 9.9)/8.5

sin M = 0.9656

M = sin^(-1)(0.9656)

M = 74.9°

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Average speed (v) :

[tex]\qquad❖ \: \sf \:v = \cfrac{total \: \: distance \: \: covered}{total \: \: time \: \: taken} [/tex]

[tex]\qquad❖ \: \sf \:v = \dfrac{16.4}{1.5} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:v = 11 \: \: kmph[/tex]

The fraction (1/3)⁻⁴ is equal to 81.

Given that:

Fraction: (1/3)⁻⁴

Rewrite the expression by applying the rule that states a negative exponent is equal to the reciprocal of the positive exponent:

(1/3)⁻⁴= 1 / (1/3)⁴

Now, let's simplify (1/3)⁴:

(1/3)⁴ = (1/3) × (1/3) × (1/3) × (1/3)

(1/3)⁴ = 1/81

So, the expression becomes:

1 /(1/3)⁴ = 1 / (1/81)

Now, dividing by a fraction is equivalent to multiplying by its reciprocal:

1 / (1/81) = 1 × 81 = 81

Therefore, the fraction (1/3)⁻⁴ is equal to 81.

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Answer:

2/3

Step-by-step explanation:

Let's solve your equation step-by-step.

9a=(√3)a+2

9a=1.732051a+2

Solve Exponent.

9a=1.732051a+2

log(9a)=log(1.732051a+2)(Take log of both sides)

a*(log(9))=(a+2)*(log(1.732051))

a=(log(1.732051)/log(9))*(a+2)

a=0.25*(a+2)

a=0.25a+0.5(Simplify both sides of the equation)

a−0.25a=0.25a+0.5−0.25a(Subtract 0.25a from both sides)

0.75a=0.5

0.75a/0.75=0.5/0.75

(Divide both sides by 0.75)

a=0.666667

a=2/3

0.666667=2/3

Hope this helps :)

Answer:

2/3

Step-by-step explanation:

9^a = sqrt(3)^a * sqrt(3)^2

9^a = 3^((a/2)+1)

3^(2a) = 3^((a/2)+1)

2a = (a/2)+1

1.5a=1

a=1/(3/2) = 2/3

Answer:

The value of x = 14 ...

The value of ∠AED = ( 7x + 15) = 7(14) + 15 = 113

The value of ∠AEB = 5x-3 = 5(14) -3 = 67

Step-by-step explanation:

=> ∠BEC = ∠AED { vertically opposite angles }

∠AED = (7x + 15)°

=> ∠AEB + ∠BEC = 180° { linear pair }

=> ( 5x-3) + ( 7x+15) = 180°

=> 5x -3 + 7x + 15 = 180°

=> 12x + 12 = 180°

=> 12( x +1 ) = 180°

=> x+1 = 180/12

=> x +1 = 15

=> x = 15-1

=> x = 14

Answer:

Hope you like my answer

Answer:

radius = 10 feet

Step-by-step explanation:

C represents the circumference.

C = 2πr  ,where r is the radius.

We are given C = 62.8 ft

Equating the two expressions of C :

2πr = 62.8

Then

2 × 3.14 × r = 62.8

Then

6.28 × r = 62.8

Then

[tex]r = \frac{62.8}{6.28} = 10[/tex]

Step-by-step explanation:

20 gallons of gasoline

gas is $ 2.50 per gallons

2.50 × 20

{(2×2)(0×.5)(0)}

domain=200

range=2.5

If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.

Given that m∠ABF=41° and BF is an angle bisector.

We are required to find the angle m∠BCE if BF is an angle bisector.

Angle bisector basically divides an angle into two parts.

If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.

In this way ∠ABC=2*∠ABF

∠ABC=2*41

=82°

In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.

∠BCE+∠CEB+EBC=180  (Sum of all the angles in a triangle is 180°)

∠BCE+90+82=180

∠BCE=180-172

∠BCE=8°

Hence if BF is an angle bisector then angle m∠BCE=8°.

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The smallest surface area of cubic rectangular boxes = 96 ft²

An object with three dimensions is solid and has both height and depth. A sphere and a cube, for instance, have three dimensions, whereas a circle and a square do not.

A three-dimensional shape's total surface area equals the sum of its side's surface areas. The measured area of all surfaces of three-dimensional solids, such as cubes, spheres, prisms, and pyramids, is expressed in square units.

Since it is a closed rectangular box so, there will be two equal sides.

Volume = 64 ft³

Volume of rectangular cube = hx²

Surface area of rectangular cube = 2x²+4hx

Equating the above equation we get, hx² = 64

                                                               h=64/x²

Put the value of h in surface area formula,

S = 2x² + 4(64/x²)*x

S = 2x² + 256/x

For the surface area to be minimum,

ds/dx = 0

4x - (256/x²) = 0

4x³ = 256

x³ = 64

x = 4 ft

Therefore, the smallest surface area

= 2(4)² + (256/4)

S = 32 + 64

= 96 ft²

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Answer: 60 oranges

Step-by-step explanation:

Given information

Weight = 75 g / orange

Total = 4.5 kg

Given formula

Total = Number of oranges × Average weight

Convert Kilogram unit to Gram

1 kg = 1000 g

4.5 kg = 4.5 × 1000 = 4500 g

Substitute values into the given formula

Total = Number of oranges × Average weight

Number of oranges = Total / Average weight

Number of oranges = 4500 / 75

Simplify by division

[tex]\Large\boxed{Number~of~oranges~=~60}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

60 oranges

Step-by-step explanation:

    The average weight of an orange ⇒ 75g

     Total weight of oranges ⇒ 4.5 kg

      Number of oranges                       Weight ( in grams)

              1                                                   75 g

              x                                                   (4.5 × 1000) g

        1  ⇒  75

        x  ⇒ 4500

      Use cross multiplication and find the value of x.

         75x = 4500 × 1

         75x = 4500

     Divide both sides by 75.

           x = 60

Answer:

option c

Step-by-step explanation:

option c is a correct answer

Answer:

(-5, 2)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}[/tex]

Both equations are linear equations.

Rearrange Equation 1 to make y the subject:

[tex]\implies -2x-5y=20[/tex]

[tex]\implies -5y=2x+20[/tex]

[tex]\implies y=-\dfrac{2}{5}x-4[/tex]

Therefore, the graph of this equation is a straight line with a negative slope and a y-intercept of (0, -4).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)[/tex]

[tex]x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)[/tex]

Plot the found points and draw a straight line through them.

The graph of this equation is a straight line with a positive slope and a y-intercept of (0, 2).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)[/tex]

[tex]x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)[/tex]

Plot the found points and draw a straight line through them.

The solution(s) to a system of equations is the point(s) of intersection.

From inspection of the graph, the point of intersection is (-5, -2).

To verify the solution, substitute the second equation into the first and solve for x:

[tex]\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4[/tex]

[tex]\implies \dfrac{6}{5}x=-6[/tex]

[tex]\implies 6x=-30[/tex]

[tex]\implies x=-5[/tex]

Substitute the found value of x into one of the equations and solve for y:

[tex]\implies \dfrac{4}{5}(-5)+2=-2[/tex]

Hence verifying that (-5, -2) is the solution to the given system of equations.

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First simplify first one

Another one is

On first line

at x=0

At x=5

On second line

At x=0

At x=5

Graph attached

Solution is (-5,-2)