The table shows the number of cups of water required when cooking different amounts of rice.

Amount of
Rice
(cups) Amount of
Water
(cups)
2 5
3 7.5
5 12.5
8 20
Which statements apply to the ratio of rice and water? Choose two options.

The amount of rice is the dependent value.
The amount of water is the dependent value.
The amount of rice is the independent value.
The amount of water is the independent value.
The values cannot be labeled as dependent or independent without a given equation.

Answer:

Step-by-step explanation:

                                       Functions used:

[tex]\displaystyle\\\boxed {(\frac{u}{v})'=\frac{u'v-v'u}{v^2} }\ \ \ \ \ \boxed {(u+v)'=u'+v'}\ \ \ \ \ \boxed {(x^n)'=n*x^{n-1}}[/tex]

[tex]\displaystyle\\f(x)=\frac{x}{x^4-5} \\\\f'(x)=(\frac{x}{x^4-5})'\\ f'(x)=\frac{x'(x^4-5)-(x^4-5)'x}{(x^4-5)^2} \\\\f'(x)=\frac{1(x^4-5)-((x^4)'-5')x}{(x^4-5)^2}\\\\f'(x)=\frac{x^4-5-(4x^3-0)x}{(x^4-5)^2} \\\\f'(x)=\frac{x^4-5-(4x^3)x}{(x^4-5)^2}\\\\f'(x)=\frac{x^4-5-4x^4}{(x^4-5)^2} \\\\f'({x)=\frac{-3x^4-5}{(x^4-5)^2} \\\\[/tex]

[tex]\displaystyle\\f'(x)=\frac{-(3x^4+5)}{(x^4-5)^2} \\\\f'(x)=-\frac{3x^4+5}{(x^4-5)^2}[/tex]

The inverse of the given function f(x) = 3x + 1 is f⁻¹(x) = x/3 - 1/3.

Given the function in the question;

f(x) = 3x + 1

To determine the inverse of the function, write f(x) as y.

f(x) = 3x + 1

y = 3x + 1

Now, interchange the variable

x = 3y + 1

Solve for y by subtracting 1 from both sides

x = 3y + 1

x - 1 = 3y + 1 - 1

x - 1 = 3y

Reorder

3y = x - 1

Divide both term in the equation by 3

3y/3 = x/3 - 1/3

y = x/3 - 1/3

f⁻¹(x) = x/3 - 1/3

Therefore the inverse of the given function f(x) = 3x + 1 is f⁻¹(x) = x/3 - 1/3.

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Based on the given parameters, the slope of the line AC is 5

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

B is the midpoint of AC

A = (2, 4)

B = (6, 24)

Because the point B is the midpoint of AC, then the slope of AC is the slope of AB

The slope of AB is calcilated as

Slope = (y2 - y1)/(x2 - x1)

So, we have

Slope = (24 - 4)/(6 - 2)

Evaluate the quotient

Slope = 5

Hence, the slope of the line AC is 5

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Answer:

B. $375,000 but I could be wrong

Step-by-step explanation:

We do:

1,505(152) = 228,760 (we are multiplying)

2,990 (46) = 137,540

We multiply 1,505 by 152 because 1,505 is the per tank-style water heater unit and we sold 152 of them.

We multiply 2,990 by 46 because 2,990 is the per tankless water heater unit and we sold 46 of them.

Now that we multiply, we add 228,760 and 137,540 together and get a total of $366,300

Since the question is asking for the closest estimate $366,300 is best option to option (B)

Answer:

See below

Step-by-step explanation:

Answer:

d=125

Step-by-step explanation:

since its a vertical angles and vertical angles are congruent (the same)

The value of d would be,

⇒ d = 125 degree

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Two parallel lines are crossed by a transversal.

Now, We have;

Angle d and 125° are vertically opposite angles.

Hence, Both are equal.

Thus, We get;

⇒ d = 125°

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The domain of the given function [tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex] is x < -4096 or x > - 4096.

So, [tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex]:

Therefore, the domain of the given function is x < -4096 or x > - 4096.

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Answer:

−3.375

Step-by-step explanation:

Hope this helps :)

Answer:

[tex]\boldsymbol{-\dfrac{35}{8}}[/tex]

or, in decimal
-4.375

Step-by-step explanation:

[tex]\textrm{The expression is }\rm -1\frac{1}{2}-\left(+3\frac{1}{2}\right)-\left(-5/8\right)[/tex]

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\\-1\dfrac{1}{2} = -\dfrac{1\cdot 2+1}{2} = -\dfrac{3}{2}\\\\\\+3\dfrac{1}{2} = +\dfrac{3\cdot 2+1}{2} = +\dfrac{7}{2} = \dfrac{7}{2}[/tex]

[tex]\textrm{The expression is }\rm -1\frac{1}{2}-\left(+3\frac{1}{2}\right)-\left(-5/8\right)\\= -\dfrac{3}{2}-\left(\dfrac{7}{2}\right)-\dfrac{-5}{8}\\\\\\= -\dfrac{3}{2}-\dfrac{7}{2}\right)+\dfrac{5}{8}\\\\\\[/tex]

The LCM of 2 and 8 is 8

Multiply each term by 8 and divide the result by 8

We get for numerator:
[tex]8\cdot\dfrac{-3}{2} - 8\cdot \dfrac{7}{2} + 8\cdot \dfrac{5}{8}\\\\= -12 - 28 + 5 = -35\\[/tex]

Denominator is 8

So answer is
[tex]\boldsymbol{-\dfrac{35}{8}}[/tex]

In decimal that would be -4.375

Choose whichever form you like

Answer:

76.83

Step-by-step explanation:

its like 1 plus 1 equals 2 you add the amount of salt present beforehand in the bowl and the one you've added together the sum would equate to 76.73

60  milliliters of 13% vinegar and 150 milliliters of 6% vinegar will give him 300ml of 12% vinegar.

This is further explained below.

Generally, The ratio of their amounts is inversely proportional to the variations in their cost from the mean value when varied quantities of various components are combined to generate a mixture of a mean value, according to the rule of alligation.

In conclusion, How much of each brand is

[tex]x=\frac{13-8}{8-6}\\\\x=5/2[/tex]

For every 2 measures of the 13% vinegar, the Chef needs to add 5 measures of the 6% vinegar (meaning a ratio of 2:5)

2/7 *210=60  milliliters of 13% vinegar

and

150 milliliters of 6% vinegar will give him 300ml of 12% vinegar.

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Answer:

1 cup dry rice makes 4 cups of cooked rice.

Step-by-step explanation:

Comment

Assuming this is a linear relationship, the equation is

cooked rice = k * dry rice

cooked rice = k

dry rice = x

Now all you need do is find k to get the answer.

Givens

x value = 2/3 of a cup.

y value = 2 2/3 cups

k =  ?

Solution

y = k*x

2 2/3 = k * 2/3                    Change to an improper fraction

8 / 3 = k * 2/3                     Multiply both sides by 3

8 = 2k                                 Divide both sides by 2

8/2 = 2k/2

k = 4

Now for one cup of dry rice, we have

y = ?

k = 4

x = 1

y = k*x

y = 4*1

y = 4 cups

The answer should be that the relationship is linear, because it lies between 3 cups (when 3/4 cup of dry rice is used and over 5 cups when 1  abd 1/3 cuprs of dry rice are used,)

Answer:

Option 4

Step-by-step explanation:

The parabola has a y-intercept of -3.

The parabola opens upward, so the leading coefficient is positive.

Answer: -6

Step-by-step explanation:

Answer: 6

2 x3 =6

Step-4by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -5}{2}~~~ ,~~~ \cfrac{ y +2}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(2~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -5}{2}=2\implies x-5=4\implies \boxed{x=9} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +2}{2}=-5\implies y+2=-10\implies \boxed{y=-12}[/tex]

The radical of 80 can be reduced to 4√5

A radical is a symbol that represents a particular root of a number.

A radical expression is defined as any expression containing a radical (√) symbol.

Radical expression can be reduced.

We are asked to reduce the radical of 80.

Hence,

√80 = √16 × 5

where

√16 = 4

Therefore,

√80 = √16 × 5 = 4√5

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The length of AD is option e √229.

Given,

ΔABD and C is a point between B and D. A and C makes a line and there forms another triangle, ΔABC.

∠B is a right angle = 90°

m ∠BAC = 30°

Length of AC = 12

Length of CD = 5

We have to find the length of AD.

First we can consider ΔABC.

Total interior angle of a triangle is 180°

We have given, ∠A as 30° and ∠B 90°.

Then ∠C = 180° - (∠A + ∠B) = 180 - (30 + 90) = 180 - 120 = 60

∠ACB = 60°

Trigonometric Function

Sin θ = (opposite side / hypotenuse)

We can find length of BC using trigonometric function.

In ΔABC,

For sin 30°, AC is the hypotenuse and BC is the opposite side.

So,

Sin 30° = (opposite side / hypotenuse)

Sin 30° = (BC/12)

BC = Sin 30° × 12

BC = 1/2 × 12

BC = 6

Now, we have to find the length of side AB.

For sin 60°, AB is the opposite side and AC is the hypotenuse.

So,

Sin 60° = (opposite side/hypotenuse)

Sin 60° = (AB/12)

AB = Sin 60° × 12

AB = √3/2 × 12

AB = 6√3

Now we can consider ΔABD.

In ΔABD, ∠B is 90°

Length of side AB = 6√3

Length of side BD = BC + CD = 6 + 5 = 11

Now, we can find the length of side AD using pythegorean theorem.

Hypotenuse = [tex]\sqrt{altitude^{2} +base^{2} }[/tex]

Here, AD is the hypotenuse, AB is the altitude and BD is the base.

So,

AD = [tex]\sqrt{AB^{2} +BD^{2} }[/tex]

AD = [tex]\sqrt{(6\sqrt{3} )^{2} +11^{2} }[/tex]

AD = [tex]\sqrt{36(3) + 121}[/tex]

AD = [tex]\sqrt{108+121}[/tex]

AD = √229

That is, the length of side AD is √229.

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The properties used to rewrite the expressions are

The expressions are given as

(8 + 4) + 12 = (4 + 8) + 12

(8 + 4) + 12 = 8 + (4 + 12)

The associative property of expression states that

(x + y) + z = x + (y + z)

This means that the properties used to rewrite the expressions are associative property

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Step-by-step explanation:

a restricting is only necessary, if we need to limit the x values or the y values for various reasons.

the limit for the x values are to eliminate any values that would create an invalid or otherwise undefined result.

otherwise the inequality itself establishes a restriction already.

e.g. sqrt(x) + 3 >= 1 would need an additional restriction

x >= 0 to know we can't even try small negative x to find out verify the solution.

something like

sqrt(x² + 3) >= 1 does not need any further restrictions, because we can use any value for x, from - infinity to +infinity. and the inequality will always be valid.

also consider, that the left side can never get smaller than sqrt(3) which is larger than 1. so, really everything goes.

we could say something like

sqrt(x² + 16) >= 5

we still don't need to give any additional restrictions, but the inequality itself rules out all x that are

-3 < x < 3.

The number of cubes for the 100th term based on the information is 10000.

It should be noted that based on the information given, for:

1 = 1 cube

2 = 4 cubes

3 = 9 cubes

Therefore, we can see that the number of cubes is the square of the appropriate number.

Therefore, for the 100th term, the number of cubes will be:

n² = 100² = 100 × 100

= 10000

The number of cubes will be 10000.

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Considering the given frequency table, the estimate of the mean height is of 7.5 units.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Given a frequency table, for each interval, we consider each observation the halfway point of the interval, hence:

Hence the mean is given by:

M = (21 x 2.5 + 5 x 7.5 + 9 x 12.5 + 3 x 17.5 + 2 x 22.5)/(21 + 5 + 9 + 3 + 2) = 7.5.

Hence the estimate of the mean height is of 7.5 units.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]\cfrac{3x+2y}{5}=1\implies 3x+2y=5\implies 2y=-3x+5 \\\\\\ y=\cfrac{-3x+5}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}} x+\cfrac{5}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so then, a perpendicular line to that will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-3}\implies \cfrac{2}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is 2/3 and it passes through (-9 , -9)

[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-9)}) \implies y +9= \cfrac{2}{3} (x +9) \\\\\\ y+9=\cfrac{2}{3}x+6\implies y=\cfrac{2}{3}x-3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( \cfrac{2}{3}x-3 \right)}[/tex]

[tex]3y=2x-9\implies -2x+3y=-9\implies 2x-3y=9 \\\\\\ 2x-3y=(9)(1)\implies {\LARGE \begin{array}{llll} \cfrac{2x-3y}{9}=1 \end{array}}[/tex]

Equation (A) 3¹ can be placed correctly in Jeremy's work.

So, in the given situation Jeremy determines that: [tex]\sqrt{9}=9^{\frac{1}{2}}[/tex]

Therefore, the equation that should be placed correctly in Jeremy's work is (A) 3¹.

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The complete question is given below:
Jeremy determines that √9= 9^1/2. Part of his work is shown

√9=3=3^1=3^1/2 + ^1/2=____=9^1/2

Which expression or equation should be placed in the blank to correctly complete Jeremy's work?

A: 3¹

B: (3^2)^1

C: 3^1/2 + 3^1/2

D: 3^1/2 x 3^1/2= (3x3)^1/2

E: 3^1/2 x 3^1/2= (3x3)^1/2+^1/2

The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

What is Quadratic equation?

An algebraic equation of the second degree is called a quadratic equation.

Given that;

A quadratic equation is;

3x² = -12x - 15

Now, The equation is written as;

3x² + 12x + 15 = 0

Take 3 common, we get;

3 (x² + 4x + 5) = 0

x² + 4x + 5 = 0

Factorize the equation by using Sridharacharya Formula;

x = - 4 ± √4² - 4*1*5 / 2*1

x = -4 ± √16 - 20 / 2

x = - 4 ± √-4 / 2

Since, √-1 = i

x = -4 ± 2i / 2                            

x = - 2 ± i

It gives two values of x as;

x = - 2 + i

And, x = - 2 - i

Hence, The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

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The equation of the parabola is : y = -6x² + 13x + 2

The general equation for parabola is -

y = ax² + bx + c. We will keep the values of x and y in this equation, to find the coefficients. Once we get the coefficients, again this equation will be used to find the equation of parabola based on given points.

For the point (1, 9)

9 = a(1)² + b(1) + c

9 = a + b + c : equation 1

For the point (2, 4)

4 = a(2)² + b(2) + c

4 = 4a + 2b + c : equation 2

For the point (4, -30)

-30 = a(4)² + b(4) + c

-30 = 16a + 4b + c : equation 3

Subtract equation 2 from equation 1

9 = a + b + c

-4 = 4a + 2b + c

We get: 5 = -3a -b

Rearranging the equation: 3a + b = -5 : equation 4

Subtraction equation 2 from equation 3

-30 = 16a + 4b + c

-4 = 4a + 2b + c

We get: -34 = 12a + 2b : equation 5

Multiplying equation with 2

6a + 2b = -10 : equation 6

Subtract equation 6 from equation 5

12a + 2b = -34

-6a + 2b = -10

6a = -24

a = -6

Keep value a in equation 6 to find the value of b

6(-6) + 2b = -10

-36 + 2b = -10

2b = 36 - 10

2b = 26

b = 13

Keep the value of a and b in equation 1 to find the value of c

-6 + 13 + c = 9

c = 9 - 7

c = 2

Keeping all the coefficients in general equation to find the equation of parabola -

y = -6x² + 13x + 2

Hence, the equation of parabola is : y = -6x² + 13x + 2

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Answer:

The answer is 45points

100-5x

Step-by-step explanation:

80/5=16questions

16-7=9questions

9x5=45points

Answers and Explanation:

- Total of 80 point available.

- Each question is worth 5 points.

If he gets 7 questions wrong --> he loses 7 x 5 points = 35 points.

100 - 35 = 65 --> So, his score would be 65.

If he got x questions wrong --> he would lose 5x points.

So, his score would be 100 - 5x.

--

Have a nice day!

The amount invested at 11% by $1045.31 and investment rate is -

amount invested at 13%. is $13991

amount invested at 11%.  is $7032

Let x represent the amount invested at 13%.

Let y represent the amount invested at 11%.

$21,023 is invested, part at 13 % and the rest at 11%. This means that

x + y = 21023

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested at 13%,

P = x

R = 13%

T =1 year

I = (x × 13 × 1)/100 = 0.13x

Considering the amount invested at 11%,

P = y

R =11%

T = 1 year

I = (x × 11 × 1)/100 = 0.11y

If the interest earned from the amount invested at

13% exceeds the interest earned from the amount invested at

5% by $1045.31, it means that

0.13x - 0.11y = 1045.31 - - -- - - - - -1

Substituting x = 21023 - y into equation 1, it becomes

0.13(121023 - y) - 0.11y = 1045.31

y = 7032

x = 21023 - y = 21023-7032

x = 13991

amount invested at 13%. is $13991

amount invested at 11%.  is $7032

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Answer:

Step-by-step explanation:

y=0.75x+0.00

y=mx+b

Your slope is 0.75 because y=0.75

Your x is the number of times you multiply 0.75.

And there is no b so b=0 because the line would not go through the y line (vertical line)

So to conclude it would be y=0.75x+0

Sorry it took so long, if you are still confused please ask :)

Answer:

The slope would be 4.

Step-by-step explanation:

To find a slope of a line perpendicular to another line, you would find the inverse (+/-) and reciprocal (a & 1/a). So -1/4 is the slope of this line, its inverse is 1/4, and the reciprocal is 4.

Hope this helps! :)