The teacher kept track of what students drank at a school picnic. For 3 grades, the ratios of the amount of water consumed to the amount of fruit juice consumed were equivalent. Complete the table

Answer:

7 and 1/3

O___O

The question is testing on indices. Write 49 in its prime factors. By power rule (a^m)^(1/n)=a^(m/n). By factors, 49 = 7×7

49^(1/2)

(7^2)^(1/2) = 7^(2×1/2) = 7

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The expression can be simplified through division of the exponential (power).

In the given expression, if the powers have the same base, we can actually divide the power.  In order to carry out the division of the exponential (power), we can subtract their exponential.

In the general form, a-m=1/am

As there are two different base terms x and y in the numerator and denominator, we will subtract the powers of x terms and powers of y terms.

Let us simplify the x terms,

x¹/₂÷x³/₄=x(1/2)-(3/4)  

Solving the powers,(½)–(¾)=(2/4)–(¾)=(2-3)/4=-1/4

x¹/₂÷ x³/₄=x(1/2)-(3/4)= x-1/4  

Let us simplify the y terms,

y⁻¹/₃÷y¹/₂= y(⁻¹/₃)-(¹/₂)

Solving the powers, (-1/3)-(1/2)=(-2/6)-(3/6)=-5/6

y⁻¹/₃÷y¹/₂= y(⁻¹/₃)-(¹/₂)=y-5/6

Putting the terms together gives us,

x-1/4 *y-5/6

It can be expressed as a fraction as a-m=1/am

x-1/4 *y-5/6=1/x1/4y5/6

Hence, x¹/₂ y⁻¹/₃ / x³/₄ y¹/₂= x-1/4 *y-5/6=1/x1/4y5/6

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Angles <6 and <12 are  alternate interior angle.

An interior angle is an angle that is inside a shape. It can also be described as an angle that lie in the area bounded between two parallel lines that are intersected by a transversal. In the given image, angles 6 and 11 are interior angles. The sum of interior angles is 180 degrees.

An alternate interior angle is an angle that is formed when two parallel lines are crossed by a transversal. The angle formed on the inner side of the parallel lines, and on the opposite sides of the transversal are called alternate interior angles. The alternate interior angles are angles 6 and 12.

A corresponding angle is an angle that is on  the same side of one of two lines cut by a transversal and on the same side of the transversal. Angle 4 and 12 are  corresponding angles.

An alternate exterior angle is the two angles that is formed  the outer side of the two parallel lines but on the opposite side of the transversal. Angles 4 and 14 are alternate exterior angle.

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172.16.0.0/20 is the required network address with a prefix if you need 16 subnets.

Given that,
If you require 16 subnets, your new network address with a prefix should be something different from the old one, which is 172.16.0.0/16. To determine the prefix corresponding to the 16 subnets.

Here,
Original network address with a prefix  = 172.16.0.0/16,
After 16 subnets the address would become,
New network address with the prefix with 16 subnets =  172.16.0.0/20.

172.16.0.0/20 is the required new address with prefix be if you need 16 subnets.

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The expression as a single logarithm is log (2/3).

In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.

The general properties of logarithm for a fixed base are:

Now from the above properties of logarithms we can calculate:

log 8-2 log 6+log 3

=log 8 + log 3 - 2log6

We know that logₐx+logₐy=logₐxy and logₐxⁿ=n logₐx

∴log(8×3) -log(6²)

=log 24 - log 36

Again we know that logₐx-logₐy=logₐ(x/y)

=log(24/36)

=log(2/3)

Therefore the given expression written as a single logarithm is log(2/3).

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The  values of for which the rocket's height is 29 meters are 0.75 and -0.67.

Velocity can be described as a vector quantity having both direction and magnitude which is the distance traveled per time.

We were given the  rocket's height h  as [tex]h=57t-5t^2[/tex] which is an equation, and we were been given the height which is the value that can be input into the equation as  is 29 meters , then we can proceed to simplify the equation as

[tex]h=57t-5t^2[/tex]

29=57t-5t^2

then we will have  [tex]57t-5t^2-29=0[/tex]

with the use of quadratic formula the values of t are : 0.75 and -0.67

Then we can chose 0.75 seconds

Therefore, after the calculation with the use of the quadratic equation, we can come into conclusion that the values that are required in the question are 0.75 and -0.67.

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NOTE: This is a complete question, there were no given options, even on the internet.

The value of given expression for x=0 is 0, x=-2 is -20 and x=2 is 20.

Given the expression is (10x)⁺¹.

Firstly, we will simplify the given expression (10x)⁺¹ for x=0.

Substitute the value x=0 in given expression, we get

(10x)⁺¹=(10×0)⁺¹

As we know that something multiply to zero is 0.

So, we get

(10x)⁺¹=0

Now, we will simplify the given expression (10x)⁺¹ for x=-2.

Substitute the value x=2 in given expression, we get

(10x)⁺¹=(10×2)⁺¹

Now, we will know that if we multiply any number with 2 we get twice of it, we get

(10x)⁺¹=(20)⁺¹

(10x)⁺¹=20

Furthermore, we will simplify the given expression for x=-2.

Substitute the value x=-2 in given expression, we get

(10x)⁺¹=(10×(-2))⁺¹

Now, we will know that if we multiply any number with 2 we get twice of it, we get

(10x)⁺¹=(-20)⁺¹

(10x)⁺¹=-20

Hence, the value of expression (10x)⁺¹  for x=0, 2 and -2 is 0, 20 and -20.

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Step-by-step explanation:

per the laws of intersecting lines the angles on one side of any of the lines must be the same as the angles on the other side of that line - just left-right mirrored.

for that reason, CGE = DGF.

also to remember : the sum of all angles around a point on one side of a line is always 180° (because they represent a half-circle with that point being the center). in other words, these angles are supplementary (together 180°).

therefore,

180 = 62 + 32 + DGF

DGF = CGE = 180 - 62 - 32 = 86°

The value of x = -4

The given linear function is f(x) = -4x+8

We have to find the x corresponding to f(x) = 24

For our convenience, let f(x) = y

Then y = -4x + 8

This equation implies y in terms of x.

Isolating x to one side of the equation, we get,

x = (y - 8)/-4 = (8-y)/4

This equation gives x in terms of y.

So when f(x) = y = 24,

x = (8-24)/4

⇒ x = -4

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The equation 3x - 1 = 1 - 3x has a solution x = 1/3

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

The expression is given as;

3x - 1 = 1 - 3x

Now, To check the solution is exist or not we can solve the equation as;

3x - 1 = 1 - 3x

Add '3x' both side,

3x - 1 + 3x = 1 - 3x + 3x

6x - 1 = 1

Add '1' both side,

6x - 1 + 1 = 1 + 1

6x = 2

Divide '6' both side,

x = 1/3

Hence, The equation 3x - 1 = 1 - 3x has a solution x = 1/3.

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[tex]A(\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{k}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{k +1}{4} ~~ = ~~\stackrel{\stackrel{\textit{sllope of AB}}{\downarrow }}{5}\implies k+1=20\implies \boxed{k=19}[/tex]

Answer:

19

Step-by-step explanation:

74+21=95       95/5=19

The percentage loss is 25 %.

It is given that initial value of company stock is $28 and final value is $21 . Put these values in equation (1) , we get

     [tex]Percentage=\frac{21 - 28}{28} \times100\\\\Percentage=\frac{-7}{28} \times100\\\\Percentage=-25 \%[/tex]

Negative sign indicates loss in the percentage.

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Answer:

There are 3/16 groups of 2

Step-by-step explanation:

3/8 / 2 = 3/16

Answer:

$123.20

Step-by-step explanation:

Hey there!

To find the price for 308 bags of chips FOR 308 people, we need to first know what the price for 1 bag is

It says that it is 2 dollars for 5 bags

Now, we need to divide 2 by 5 to see how much money 1 bag is

2/5 is 0.4 and in this case 0.40 since we're dealing with money

Now that we know this, all we need to do is multiply 0.40 by 308 because we are buying for 308 people

0.40 x 308 is 123.2

This means that for 308 people, it would cost $123.20 to supply them all with a bag of chips!

Answer:

I think the length remains the same

Step-by-step explanation:

The value of the variable x and y are 12 and 31 respectively.

Line a and b are parallel lines.

These parallel lines are cut by a transversal.

The traversal forms angle relationship as follows:

5x - 7 = 3x + 17 (alternate angles)

The variable x and y can be found as follows

5x - 7 = 3x + 17

5x - 3x = 17 + 7

2x = 24

x = 24 / 2

x = 12

Therefore,

4y + 3 + 3x + 17 = 180

4y + 3 + 3(12) + 17 = 180

4y + 3 + 36 + 17 = 180

4y = 124

y = 124 / 4

y = 31

Therefore, the value of the variable x and y are 12 and 31 respectively.

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The zeros of the polynomial function are y = 4/5, y = -4/5 and y = ±4/5√i and the polynomial as a product of the linear factors is f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The polynomial equation is given as

f(y) = 625y^4 - 256

Express the terms as an exponent of 4

So, we have

f(y) = (5y)^4 - 4^4

Express the terms as an exponent of 2

So, we have

f(y) = (25y^2)^2 - 16^2

Apply the difference of two squares

So, we have

f(y) = (25y^2 - 16)(25y^2 + 16)

Apply the difference of two squares

So, we have

f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

Set the equation to 0

So, we have

(5y - 4)(5y + 4)(25y^2 + 16) = 0

Expand the equation

So, we have

5y - 4 = 0, 5y + 4 = 0 and 25y^2 + 16 = 0

This gives

5y = 4, 5y = -4 and 25y^2 = -16

Solve the factors of the equation

So, we have

y = 4/5, y = -4/5 and y = ±4/5√i

Hence, the zeros of the polynomial function are y = 4/5, y = -4/5 and y = ±4/5√i

How to write the polynomial as a product of the linear factors?

In (a), we have

The polynomial equation is given as

f(y) = 625y^4 - 256

Express the terms as an exponent of 4

So, we have

f(y) = (5y)^4 - 4^4

Express the terms as an exponent of 2

So, we have

f(y) = (25y^2)^2 - 16^2

Apply the difference of two squares

So, we have

f(y) = (25y^2 - 16)(25y^2 + 16)

Apply the difference of two squares

So, we have

f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

Hence, the polynomial as a product of the linear factors is f(y) = (5y - 4)(5y + 4)(25y^2 + 16)

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Answer: I think it's 9: 48

Step-by-step explanation: hope this helps!

Answer:

8:45

because the small hand (hour hand) is a little passed 8

and the long hand (minute had) is at 45 minutes

Step-by-step explanation:

The answer should be parallel to each other

step by step

from plotting the graph line AB is parallel to Line DF

Answer: AB and DF are parallel.

Step-by-step explanation:

A=(-2,-11)

B=(6,5)

D=(-7,-10)

F=(2,0)

Slope (AB)=5-(-11) =

                    6-(-2)  =2

Slope (DF)=8-(-10)=

                    2-(-7) =2

Slope of AB=Slope of DF

AB and DF are parallel.

Area of base = 52

height = 5

Volume = 260

To find the volume of a rectangular prism all you need to do is multiply the length * width * height.

the area of base is the length * width = 13 * 4 = 52

then you multiply that by the height = 52 * 5 = 260

The vertices that would minimize the objective function N = 7x + are (4, 0)

The objective function is given as

N = 7x + 2y

Next, we substitute the values in the options in the objective function

So, we have

A. (4,0)

N = 7(0) + 2(4)

N = 8

B. (6,3)

N = 7 x 6 + 2 x 3

N = 48

C. (3,9)

N = 7 x 3 + 2 x 9

N = 39

D. (0,12)

N = 7 x 0 + 2 x 12

N = 24

The smallest result in the above computations is 8

Hence, the vertices that would minimize the objective function N = 7x + are (4, 0)

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Answer:

96.8 fps

Step-by-step explanation:

the formula is

x * 1.46666667

66 * 1.46666667

≈96.8

The given exponential function  y = 3 eˣ is a exponential growth.

An exponential function is simply function that is used in a variety of real-world applications. It is primarily used to determine exponential decay as well as exponential growth, as well as to calculate investments, model populations, and so on.

Now, as per the given exponential functions;

y = 3 eˣ

The value of the exponent 'e' = 2.72.

This for any value of x > 0. this function will be of exponential Growth.

Therefore, the given function  y = 3 eˣ shows the exponential Growth.

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After expanding logarithm is [tex]\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa.

The basic form of the logarithm function can be written as  .

    [tex]log_ax =N[/tex]

where, a is the base of function or equation

          x define expression

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]log_b\frac{\sqrt{x} \sqrt{3} }{y^2 \sqrt{6z^2} } \\\\= log_b \sqrt{x} \sqrt{3} - log_b {y^2 \sqrt{6z^2} }\\\\= log_b\sqrt{x} + log_b\sqrt{3} - log_by^2 - log_b \sqrt{6z^2} \\\\= \frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - \frac{1}{2} log_b{(6z^2)} \\\\=\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]

Thus, after expanding logarithm is [tex]\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]

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Answer:

69

Step-by-step explanation:

The function y = 100 ( 0.25 ) ˣ is an exponential decay function.

An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.

We are given a function:

y = 100 ( 0.25 ) ˣ

We need to tell whether is is a exponential growth or decay function.

We can see that the value of a ˣ = (0.25) ˣ

So, the value of a = 0.25.

Since, it is a decimal and not an integer, its value will decrease with the increase in exponent x.

So, it will be a exponential decay function.

Therefore, we get that, the function y = 100 ( 0.25 ) ˣ is an exponential decay function.

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