How is using mental math to add money like using mental math to add whole numbers? How is it different?

Based on the calculations, the ratio of water to cement (W:C) is equal to 1:1.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Given the following data:

Substituting the given parameters into the formula, we have;

Therefore, the ratio of water to cement is given by:

Ratio of water to cement, W:C = 3:3

Ratio of water to cement, W:C = 1:1.

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The width of the banner of the Friday’s pep rally is 3 feet.

To calculate a percentage, divide the value by total value and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.

Calculating a percentage means determining a portion of a whole in terms of 100. A percentage can be calculated in two ways:

For the given expression;

The length of the Friday’s pep rally banner is 18 feet.

Let the width be 'b'.

The given condition is;

The length of the banner is made 6 times the width.

Then,

6 time the width  = length

6×w = 18

w = 18/6

w = 3

Therefore, the width of the banner is found as 3 feet.

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Answer: WX, ZY and WX and AB.

The 2nd one is correct.

[tex]8.35 \times {10}^{9} [/tex]

or

[tex]835 \times {10}^{7} [/tex]

Answer:

D. 2z^3/y

Step-by-step explanation:

xyz^2 = 2z^4

z(xyz) = z(2z^3)

xyz = 2z^3

xz = (2z^3)/y

Answer:

Step-by-step explanation:

Answer:

50!!

Step-by-step explanation:

The teacher buys enough pencils for 10 of her students. She gives each student 5 pencils. How many pencils did she give away altogether?

10 x 5 = 50

Answer:

write any one positive aspect of your religion

25 times 789 is 19725

the answer:19,725

The total change in the weight of Callie's cat will be 1 5/8 pounds.

It should be noted that weight is a measurement of the force an acceleration field, particularly the gravitational field of the Earth near the surface, exerts on a particle or object.

From the information that was given, it should be noted that Callie's cat lost 4 1/2 pounds before having surgery and two weeks after having surgery, her cat gained 2 7/8 pounds.

Therefore, based on the information that was illustrated, it should be noted that the change in weight will be the difference between the weights given.

The change in weight will be:

= 4 1/2 pounds - 2 7/8 pounds

= 4 4/8 - 2 7/8 pounds.

= 1 5/8 pounds

Therefore, the change in weight of Callie's cat will be 1 5/8 pounds.

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The critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.

The critical point is a single value at which the function is not differentiable

The inequality is given as:

(x² - 9 x) / (x - 5) < 0.

Factorize the numerator

x (x - 9) / (x - 5) < 0.

Equate it to 0, we get that:

x (x - 9) = 0 or x - 5 = 0

x = 0 or x - 9 = 0 or x - 5 = 0

So, the critical points will be:

x = 0 or x = 9 or x = 5.

Therefore, the critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.

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Answer:

19/20*30/20=19/20 x

570/400=19/20 x

57*20=40*19x

1140=760x

x=30/20 or 3/2

a) The simple average of the unit prices is $10.45.

b) The total number of units purchased during the first six months is 115.898 units.

c) The average cost of the units purchased is $10.35.

d) The value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19.

An average refers to the mean of a data set.

The average is computed as the total value divided by the number of values in the data set.

Month    Unit Price     Total  Value    Units

February   $10.00             $200         20.000

March          10.60               200          18.868

April             11.25               200           17.778

May              9.50               200          21.052

June            9.20               200           21.739

July             12.15               200           16.461

Total prices $62.70     $1,200          115.898

Simple Average = $10.45 ($62.70/6)

The average cost of the purchased units = $10.354 ($1,200/115.898)

Thus, the value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19 (115.898 x $11.90).

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Answer:

Step-by-step explanation:

it is Payment: Uniform Payment Series: (F/P, i, ∞) = ∞. (A/F, i, ∞) = 0.

Answer: The answer would be 0.4 or 4/10

Step-by-step explanation:

Answer:

B. {-4, -2, 0, 2, 4}

Step-by-step explanation:

A definition for the word domain is the "input" of a function, also called the x values.

A definition for the word range is the "output" of a function, also called the y values.

With this knowledge, looking at the question, it is asking for the range of the relation, which means we are looking at the y values.

A is incorrect because it shows all values from -4 to 4, however some are not in the relation shown.

B is correct because it is showing all of the y values given in the table and no others.

C is incorrect because it is just showing the bounds of the relation, but not all values between.

D is incorrect because it is the domain of the function, or the x values.

Therefore, you were correct, and your answer is B.

Answer: B? Although its supposed to be {4, 2, 0, -2, -4}

Answer:

Child ticket: 12 dollars

Total price: 64 dollars

Step-by-step explanation(Child ticket price):

[tex]T = X(1 - P\%)\\T = 20(1 - 40\%)\\T = 20(1 - 0.4)\\T = 20(0.6)\\T = 12[/tex]

-----------------------------------------------------------------------------------------------------------

Step-by-step explanation(Total price):

[tex]T(12) * 2 + (20.00 * 2) = \$64[/tex]

Hope this helps.

Answer:

no

Step-by-step explanation:

Put them as fractions that have equivalent denominators.

3/4 :27/36 (multiply 9 to both numbers)

12/9 :48/36(multiply 4 to both numbers)

Since the numerators are not the same the answer is no.

If they were equal both numerator and denominator would be the same

Answer:

[tex]{ \tt{ \frac{3x}{7} - 2 = 15 }} \\ \\ { \tt{3x - (2 \times 7) = (15 \times 7)}} \\ { \tt{3x - 14 = 105}} \\ { \tt{3x = 119}} \\ { \tt{x = 39.67}} \\ { \tt{ 39\frac{2}{3}}}[/tex]

Answer:

[tex] \sf \large \: x = \frac{119}{3} [/tex]

Step-by-step explanation:

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

3x/7−2=15

Step 1: Simplify both sides of the equation.

3x/7−2=15

3/7x+−2=15

3/7x−2=15

Step 2: Add 2 to both sides.

3/7x−2+2=15+2

3/7x=17

Step 3: Multiply both sides by 7/3.

(7/3)*(3/7x)=(7/3)*(17)

x=119/3

Answer:

0.745/9.089

Multiply numerator and denominator by 1000

=745/9089

The proportion of Trick-or-treaters not dressed as Snow white are 5/9.

A proportion may be defined as the way of representation of numbers or letters in the form of ratios which are made equal to each other. For example, if there are 1 mango and 2 bananas then the ratio is written as 1:2 that is for every 1 mango there are 2 bananas and there are 1/3 mangoes and 2/3 bananas.

Total number of Trick-or-treaters = 9

Total number of Trick-or-treaters dressed as Snow white = 4

Total number of Trick-or-treaters not dressed as Snow white = 9-4 = 5

Thus, Proportion of Trick-or-treaters not dressed as Snow white = 5/9

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let x be the real part of z

let y be the imaginary part of z

[tex]arg(x +i y - 1) = arg(x + iy + 3i) \\ arg(x - 1 + iy) = arg(x + (y + 3)i) \\ arctan( \frac{y}{x - 1} ) = arctan( \frac{y + 3}{x} ) \\ arctan( \frac{ (\frac{y}{x - 1} ) - ( \frac{y + 3}{x}) }{1 +( \frac{y}{x - 1} )( \frac{y + 3}{x} )} ) = 0 \\ arctan( \frac{ \frac{xy - (x - 1)(y + 3)}{x(x - 1)} }{ \frac{x(x - 1) + y(y + 3)}{x(x - 1)} } ) = 0[/tex]

[tex]arctan( \frac{xy - xy - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y } ) = 0 \\ \frac{ - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y} = tan(0) = 0 \\ - 3x + y + 3 = 0 \\ y = 3x - 3[/tex]

[tex] \frac{x - 1}{y} = \frac{x - 1}{3x - 3} = \frac{x - 1}{3(x - 1)} = \frac{1}{3} \\ [/tex]

Answer:

[tex]\dfrac{x-1}{y}=\dfrac{1}{3}[/tex]

Step-by-step explanation:

Sums of real and imaginary numbers are known as complex numbers:  

[tex]\large\boxed{z = x + iy}[/tex]

(where x is the real number and iy is the imaginary number).

Complex numbers can be represented on an Argand diagram.

z = x + iy is represented on the diagram by the point P(x, y).

[tex]\textsf{Argument of a complex number $= \boxed{\arg z}$}[/tex]

It is the angle between the positive real axis and the line joining that number to the origin on an Argand diagram, measured in an anticlockwise direction.

[tex]\textsf{For \;$z = x + iy$, \;the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x}$.}[/tex]

[tex]\textsf{Given: \quad $\arg (z-1)=\arg(z+3i)$}[/tex]

[tex]\textsf{If $z$ is a complex number then $z = x + iy$}.[/tex]

[tex]\textsf{Substitute this into the given equation}:[/tex]

[tex]\begin{aligned} \arg(z-1)&=\arg(z+3i)\\\implies \arg(x + iy - 1) &= \arg(x + iy + 3i)\\\implies \arg((x - 1) + iy) &= \arg(x + i(y + 3))\end{aligned}[/tex]

[tex]\textsf{If the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x} \implies \theta=\tan^{-1}\left(\dfrac{y}{x}\right)$}:[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)=\tan^{-1}\left(\dfrac{y+3}{x}\right)[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)-\tan^{-1}\left(\dfrac{y+3}{x}\right)=0[/tex]

[tex]\boxed{\begin{minipage}{6.2cm}\underline{Trigonometric identity}\\\\ $\tan^{-1}(a)-\tan^{-1}(b)=\tan^{-1}\left(\dfrac{a-b}{1+ab}\right)$\\ \end{minipage}}[/tex]

Use the arctan identity:

[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{y}{x-1}-\dfrac{y+3}{x}}{1+\left(\dfrac{y}{x-1}\right)\left(\dfrac{y+3}{x}\right)} \right)=0[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{1+\dfrac{y(y+3)}{x(x-1)}} \right)=0[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{\dfrac{x(x-1)+y(y+3)}{x(x-1)}} \right)=0[/tex]

[tex]\implies \tan^{-1}\left({\dfrac{xy-(y+3)(x-1)}{x(x-1)+y(y+3)} \right)=0[/tex]

[tex]\implies \tan^{-1}\left({\dfrac{xy-xy+y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]

[tex]\implies \tan^{-1}\left({\dfrac{y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]

[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=\tan(0)[/tex]

[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=0[/tex]

[tex]\implies y-3x+3=0[/tex]

[tex]\implies y=3x-3[/tex]

[tex]\textsf{Substitute\;\; $y=3x-3$ \;\;into \;\;$\dfrac{x-1}{y}$}:[/tex]

[tex]\begin{aligned}\implies \dfrac{x-1}{y}& =\dfrac{x-1}{3x-3}\\\\ & =\dfrac{x-1}{3(x-1)}\\\\ & =\dfrac{1}{3}\end{aligned}[/tex]

[tex]\textsf{Therefore, the value of\; $\dfrac{x-1}{y}$\; is\; $\dfrac{1}{3}$}.[/tex]

The numbers 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer

The numbers are given as:

0.5, −13, 0.62, 3.14, 19%

Numbers that can be represented as a fraction of two integers are rational numbers

The given numbers can be represented as a fraction of two integers

i.e.

0.5 = 5/10

0.62 = 62/100

3.14 = 314/100

19% = 19/100

This means that 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer (because it has no decimal point and it is negative)

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Answer:

  f(2) = 3

Step-by-step explanation:

You want the value of f(2), given the graph of f(x).

The value of the function for a given argument is found by locating the point on the graph with an x-coordinate equal to the argument. The y-coordinate of that point is the function value.

See the attachment.

The y-coordinate associated with the point that has an x-value of 2 is 3.

  f(2) = 3

Considering the algorithm to divide a number by a fraction, she must multiply x by -12/5 to find the answer of the division of x by -5/12.

To divide a number, or even another fraction, by a fraction, we need to multiply the numerator by the inverse of the denominator.

Taking the following division of fractions as an example, we have that:

(a/b)/(c/d).

Hence the quotient is:

a/b x d/c.

For this problem, the division is:

x/(-5/12).

Hence:

Thus the quotient is given by:

-12x/5.

Meaning that she must multiply x by -12/5 to find the answer of the division of x by -5/12.

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The RS line segment will be 16 units long.

The collinear points are Q, R, S, and T.

The collinear's condition will then be determined:

The points Q, R, S, and T all lie on the same line segment in that order, so the QR:RS:ST ratio is 1:4:5. If QT = 40.

The value of the variable x will then be:

The length of the line segment RS will then become:

Therefore, the RS line segment will be 16 units long.

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The correct question is given below:

The points Q, R, S, and T all lie on the same line segment, in that order, such that the

ratio of QR:RS: ST is equal to 1:4:5. If QT = 40, find RS.