A teapot is 1/3 full of tea. When all of the tea is poured into an empty container, the container 2/3 full. What fraction of the tea from a full teapot is needed to fill 1 entire container?

the order from smallest to largest is:

41, 56, 83.

Here we have 3 values, that are:

{83, 56, 41}

To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.

Then the middle number. Which is 56, that is larger than 41 and smaller than 83.

Finally, the largest number, which is 83.

Then the order is:

41, 56, 83.

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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

[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]

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]

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

Based on the calculations, the measure of m∠BDA and m∠BCA are 55° and 70° respectively.

In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle simply refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

First of all, we would determine angle BOA:

∠BOA + ∠BOA = 360° (Angles at a point)

∠BOA + 250° = 360°

∠BOA = 360° - 250°

∠BOA = 110°

Next, we would determine angle BDA:

2 × m∠BDA = ∠BOA (Angle inscribed at the center is twice the angle at the circumference)

2 × m∠BDA = 110°

m∠BDA = 110°/2

m∠BDA = 55°.

The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, angle BCA will be given by this formula:

m∠BCA = ½ × (m<AO - m<BO)

Substituting the given parameters into the formula, we have;

m∠BCA = ½ × (250 - 110)

m∠BCA = ½ × 140

m∠BCA = 70°.

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Answer:

70

Step-by-step explanation:

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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Answer:

15

Step-by-step explanation:

12 / 2 = 6

5 / 2 = 2.5

6 x 2.5 = 15

15 inches²

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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The y-coordinate that completes the point exists 5.

An ordered pair (x, y) denotes the x-and-y coordinates of a general point, where x exists the input value of a function and y exists the output value of a function.

The output value exists y = f(x) and must be found using the rule (function) to the given input value.

In this case the rule exists f(x) = - 3x + 2, and the input value, x, exists - 1 (the first value of the ordered pair).

This exists the mathematical procedure:

x = - 1

f(x) = f (-1)

Then substitute the value x = -1 then

f(-1) = -3 (-1) + 2 = 3 + 2 = 5.

Therefore, the correct answer is option b) 5.

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Answer:

Part 1: 9:18:27

Part 2: 28:42:84

Step-by-step explanation:

Part 1:

54 pigs are split into the ratio 1:2:3. Treating a "1" ratio as x, we have x:2x:3x is 54 pigs. We can add up all parts of the ratio to become the whole. x+2x+3x=54. Solving, x=9. Substituting, our ratio is 9:18:27.

Part 2:

Similar to part 1, we treat a "1" ratio as y. Our ratio is 2y:3y:6y for a total of 154 chickens. Adding all the parts, we have 2y+3y+6y=154, so y=14. Substituting, our ratio is 28:42:84.

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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If the equation is 19-5=3z-11 then the value of z is 15/3.

Given an equation in terms of z is 19-5=3z-11.

We are required to find the value of variable z which exist in equation.

Equation is like a  relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.

The value of z can be find as under:

19-5=3z-11

4=3z-11

3z=4+11

3z=15

z=15/3

Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.

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Answer:

Area=length× berngth

A=5×2x

A=10x square

Any line through the points [tex](a,b)[/tex] and [tex](c,d)[/tex] has

[tex]\gcd(c-a,d-b)+1[/tex]

lattice points. In this case, the count is GCD(45, 264) + 1.

Using Euclid's algorithm, we have

264 = 5•45 + 39

45 = 1•39 + 6

39 = 6•6 + 3

6 = 2•3 + 0

so that GCD(45, 264) = 3. Then there are 3 + 1 = 4 lattice points.

Answer:

Matrix B should be subtracted from Matrix A.

Step-by-step explanation:

Answer:

a.9

b.36

Step-by-step explanation:

Blue beans + orange beans + red beans = 54

6x + 2x-3 + 15-x = 54

6x+2x-x=54+3-15

7x=42

divide both sides by 7

x=6

a. orange beans = 2x-3

but x=6

2(6)-3

12-3

=9

b.blue beans =6x

6(6)

=36

A sample consists of only the 25th student in a group of 1,000 students, called Systematic sampling.

A sample consists of only the 25th student in a group of 1,000 students, called Systematic sampling.

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Answer:

B. (5x + 2)(x + 3)

Step-by-step explanation:

5x times x = 5x^2

5x times 3 = 15x

2 times x = 2x

2 times 3 = 6

15x + 2x = 17x

5x^2 +  17x + 6

P.S. next time please word your question better. Took me a while you meant "5x^2 plus 17x plus 6", since your equation reads "5 times 2 BLANK 17 times 6".

The most appropriate model for a given situation is exponential.

The most appropriate model for a given situation is exponential.

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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 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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By applying Pythagoras theorem, the missing segment lengths of this triangles include:

Since triangle ACD is a right-angle triangle, we would use Pythagoras theorem to find the missing segment lengths of this triangles as follows:

c² = a² + b² ≡ AD² = CD² + AC²

Next, we would use cos trigonometric ratio to find side CD,

cos45 = adjacent/hypotenuse

cos 45 = CD/20

1/√2 = CD/20

CD = 1/√2 × 20

CD = (20√2)/2

CD = 10√2

For side AC, we have:

AD² = CD² + AC²

AC² = AD² - CD²

AC² = 20² - (10√2)²

AC² = 400 - 100(2)

AC = √200

AC = 10√2

From triangle ABC, we have:

cos45 = BC/10√2

BC = 10√2 × cos45

BC = 10√2 × 1/√2

BC = (10√2)/√2

BC = 10

For side AB, we have:

AB² = (10√2)² - 10²

AB² = 200 - 100

AB² = 100

AB = 10.

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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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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)

If the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

A constraint is a condition of an optimization problem that should be satisfied the condition.

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

Therefore, x ≥ 5.6 and x ≤ 24.13  

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

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Answer:

0 ≤ x < 5.6 and 24.13 < x ≤ 32.82

Step-by-step explanation:

The length of the wall of the tank in feet is 62.8 feet.

Circumference is the perimeter of a circular object. Therefore,

circumference = 2πr

where

The fountains pool is enclosed by a circular plastic tank.

The distance from the centre of the pool to the wall of the tank is 10 feet. This is the radius of the circle

Hence,

length of the tank = 2πr

length of the tank = 2 × 3.14 × 10

length of the tank = 20 × 3.14

length of the tank = 62.8 feet.

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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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