Maddie and Cara each made a bowl of punch. Cara used 6 times as much lemonade as Maddie did. If Maddie used 2/3 of a cup of lemonade, how many cups of lemonade did Cara use?

Write your answer as a fraction or as a whole or mixed number.

Answer:

-1/7

Step-by-step explanation:

Divide the first expression by the second expression.

Answer:

a) -64

0

b) 5

- 5

Step-by-step explanation:

Up square: Multiply the numbers in the right square and left square and write the answer in the up square.

Down square: Add the numbers in the right square and left square and write the answer in the down square.

Left and right square: Factorize the number in the up square and check if it satisfies (add or subtract the factors) the number in the down square.

a) Up square:  -64

                8*(-8) = -64

Down square:  0

            8 + (-8) = 0

b)  Factorize (-25), in such a way that when we add we should get 0.

  -25 = 5 * (-5)

5 + (-5) = 0

Right square:  5

Left square :   -5

c) Right square:   (-3)

       -12 ÷ 4 = (-3)

Down square :  1

   4 + (-3) = 1

\(\sf d) up \ square: \dfrac{-1}{6}\\\\\)

      \(\sf \dfrac{1}{2}*\dfrac{-1}{3}=\dfrac{-1*1}{2*3}=\dfrac{-1}{3}\\\\\\Down \ square : \dfrac{1}{6}\\\\\\\dfrac{1}{2}+\dfrac{-1}{3}=\dfrac{1*3}{2*3}+\dfrac{-1*2}{3*2}\)

                     \(\sf = \dfrac{3}{6}+\dfrac{-2}{6}\\\\=\dfrac{3 + (-2)}{6}\\\\=\dfrac{1}{6}\)

Answer:

1.6667 meters per minute

Step-by-step explanation:

To convert meters per second into meters per minute, let's first think about the difference between seconds and minutes.

There are 60 seconds in one minute, so to find our meters per minute speed, we will divide the distance by 60.

100 / 60 = 1.6667 meters per minute

Hope this helped!

Answer:

it is d my guy :)

Step-by-step explanation:

Dividing in math is the process of finding the quotient of two numbers.

The formula for dividing two numbers is a/b = c, where a and b are the two numbers being divided and c is the quotient.

Division is a mathematical operation that is used to split a whole number into parts. It is the opposite of multiplication, which combines numbers together. The formula for division is A / B = C, where A is the dividend (the number being divided), B is the divisor (the number dividing the dividend), and C is the quotient (the result of the division). To calculate, you divide the dividend by the divisor and the quotient is the resultTo calculate the quotient, you must divide a by b. For example, if we wanted to divide 8 by 4, we would divide 8 by 4 to get 2. The calculation would look like this: 8/4 = 2. As a result, 8 divided by 4 is equal to 2.

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To sketch the curve with polar equation θ = −π/6, we need to plot all the points (r, θ) that satisfy the equation for various values of r. Since θ is fixed at −π/6, all the points will lie on a line at an angle of −π/6 to the positive x-axis.

The value of r can be positive or negative, so we will plot points both above and below the x-axis.

Since r can be any value, we will just choose a few values for illustration purposes. Let's choose r = 1, 2, −1, and −2. Then the corresponding points are:

(1, −π/6), (2, −π/6), (−1, −π/6), and (−2, −π/6)

We can plot these points on a polar coordinate system as follows:

These points lie on a line at an angle of −π/6 to the positive x-axis, as expected. Note that the sign of r determines whether the point lies above or below the x-axis.

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Answer: It is equidistant from the segment's endpoints

Step-by-step explanation:  This can also be called "a locus of point" and this is now the perpendicular bisector theorem.

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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Option 2 has a lower NPV and thus should be chosen as it results in less total payment and better savings. Hence, you would choose option 2 as the Net Present Value of choosing option 2 is -9,903,615.48.

Given:

Purchase price = 12.5 million baht

Down payment = 15%30-year mortgage

We have to calculate the option which is best for us.

Option 1: Mortgage rate = 7.25%

Option 2:Mortgage rate = 6.75%

(a) Monthly Payment of Option 1:

Loan Amount = 12.5 * (100-15)%

= 10,625,000 baht

n = 30 * 12

= 360

i = 7.25%/12

= 0.006042857

Yearly Interest Paid = i * 10,625,000

= 64,515.48 baht

Monthly Interest Paid = 64,515.48 / 12

= 5,376.29 baht

EMI =\([P x R x (1+R)^n] / [(1+R)^n-1]\)

where P = Loan Amount, R= Interest Rate per month, n= total number of payments.

EMI = \([10,625,000 x 0.006042857 x (1+0.006042857)^360] / [(1+0.006042857)^360-1]\)

EMI = 69,677.31 baht

(b) Monthly Payment of Option 2:

Loan Amount = 12.5 * (100-15)%

= 10,625,000 baht

n = 30 * 12 = 360

i = 6.75%/12 = 0.005625

Yearly Interest Paid = i * 10,625,000

= 59,765.63 baht

Monthly Interest Paid = 59,765.63 / 12

= 4,980.47 baht

Point cost = 4% of Loan Amount

= 10,625,000 x 4/100

= 425,000 baht

Loan Amount after Deducting Points = 10,625,000 - 425,000

= 10,200,000 baht

EMI = \([P x R x (1+R)^n] / [(1+R)^n-1]\)

where P = Loan Amount, R= Interest Rate per month, n= total number of payments.

EMI =\([10,200,000 x 0.005625 x (1+0.005625)^360] / [(1+0.005625)^360-1]\)

EMI = 66,128.92 baht

(c) We have to calculate the NPV of the payments to decide which option is better.

We use the formula to calculate NPV:-

NPV = - \([B + (PMT / i) * (1 - (1 + i)^-n)] / ((1 + i)^t)\)

Where B = amount borrowed, PMT = monthly payment, i = interest rate, n = total number of payments, t = year.

NPV =\(- [10625000 + (69677.31 / 0.006042857) * (1 - (1 + 0.006042857)^-360)] / ((1 + 0.006042857)^30)\)

= -9,892,571.85 baht

NPV = \(- [10200000 + (66128.92 / 0.005625) * (1 - (1 + 0.005625)^-360)] / ((1 + 0.005625)^30)\)

= -9,903,615.48 baht

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Answer:

Tan (X) = 72/65. = 1.1

Step-by-step explanation:

tan x = (opposite side) / (adjacent side)

From angle X the adjancent is the closest leg which has the value of 65 and the opposite is the furthest leg with a value of 72. (the line that is connecting the legs which is the biggest line is the hypotenuse and has a value of 97). You will not need the hypotenuse I just gave you extra information for future purposes.

so, since tan x = (opposite side) / (adjacent side):

Tan (X) = 72/65.

Answer: To find the tip amount in dollars for each order, you need to multiply the total bill amount by the tip percentage.

For the first order of 4 dishes, the total bill amount is $8 per dish * 4 dishes = $<<8*4=32>>32.

The tip amount is $32 * 20% = $6.40.

For the second order of 6 dishes, the total bill amount is $8 per dish * 6 dishes = $<<8*6=48>>48.

The tip amount is $48 * 14% = $6.72.

For the third order of 7 dishes, the total bill amount is $8 per dish * 7 dishes = $<<8*7=56>>56.

The tip amount is $56 * 11% = $6.16.

So, the tip amounts from least to greatest are $6.16, $6.40, and $6.72.

Answer:

1

2,3,4

Step-by-step explanation: to

when the number of football is 1 is less expensive than basketball

Since the denominator is the same, we can simply subtract the numerator.

4x + 5 - 5x = -x + 5

The answer is B

Answer:

[-6 , 0]

Step-by-step explanation:

If the absolute value of an expression is equal to a number, that means that the expression itself could be equal to either the negative equivalent to that number or the positive equivalent.

for example, if my inequality is |x| > -3

x could either be:

-3 or 3

So,

| 2(x - 1) + 8 |  ≤  6

can be separated into two separate inequalities:

      2(x - 1) + 8  ≤   6

or,  2(x - 1) + 8  ≥ - 6

we solve these inequalities separately.

2(x - 1) + 8 ≤ 6

2x - 2 + 8  ≤ 6               [distribute 2]

2x  ≤ 0              [add 2 to both sides, subtract 8 from both sides]

x ≤  0   [finalize isolating x by dividing both sides of the equation by 2]

expressed as [in interval notation]:

(-∞, 0]

now, let's solve for the other inequality.

2(x - 1) + 8  ≥  - 6

2x - 2 +  8   ≥  - 6         [distribute 2]

2x  ≥  -12                   [add 2 to both sides, subtract 8 from both]

x  ≥  -6          [divide both by 2 to isolate x]

expressed as [in interval notation]:

[-6 , ∞)

So, our answer for x is going to be

-6 ≤ x ≤ 0

or, expressed in interval notation:

[-6 , 0]

*[ includes number]

*( is not equal to number)

Answer:

Liz got a higher score than Austin.

Step-by-step explanation:

Since 42 divided by 50 is 82, as a percentage is then 82%. Austin has a 80% which most likely means, if on the same quiz, that he got a 40 out of 50.

Answer:

You can either use substation or you can use elimination on both of the problems

Step-by-step explanation:

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

For x = 1.648, the mentioned logarithmic functions f(x) and quadratic g(x) are comparable.

Now, the functions that are provided with in question are

f(x) = ㏒₃ 2x

g(x) = -4x² + 3x + 7

Desmos was used to create the graphs for both of the functions.

The graph unequivocally demonstrates that both functions are still equal at the time of curve convergence.

At the point x = 1.648, f(x) = g.(x).

Both the functions f(x) and g(x) are therefore equivalent for x = 1.648.

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    5 (4 + √3)/13 is the solution linear equation.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

5/4 - √3

Multiply by 4 + √3 in nominator and dinominator .

\(\frac{5}{4 - \sqrt{3} } * \frac{4 + \sqrt{3} }{4 + \sqrt{3} }\)

=   5 (4 + √3)/(4)² - (√3)²

=  5 (4 + √3)/16 - 3

=   5 (4 + √3)/13

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As a result, the simplified formulation with a rationalized denominator is as follows:

= \(\frac{20 + 5\sqrt{3} }{`13} \\\)

deno

To rationalize the denominator, multiply both the numerator and the denominator by the denominator's conjugate, which is 4 + sqrt(3):

\(\frac{5}{(4-\sqrt{3} ) } * \frac{(4+\sqrt{3} )}{(4+\sqrt{3} )}\)

Using the distributive property to simplify the numerator and denominator, we get:

= \(\frac{5(4+\sqrt{3} )}{(4-\sqrt{3} )(4+\sqrt{3} ) } }\)

= \(\frac{20 + 5\sqrt{3} }{`16-3} \\\)

= \(\frac{20 + 5\sqrt{3} }{`13} \\\)

As a result, the simplified formulation with a rationalized denominator is as follows:

= \(\frac{20 + 5\sqrt{3} }{`13} \\\)

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The statement that best describes "willing suspension of disbelief" is: A dynamic in which the audience agrees to accept the fictional world of the play on an imaginative level while knowing it to be untrue.

The concept of "willing suspension of disbelief" is an essential element in experiencing and appreciating works of fiction, particularly in theater, literature, and film. It refers to the voluntary act of temporarily setting aside one's skepticism or disbelief in order to engage with the fictional narrative or performance. It involves consciously accepting the imaginative world presented by the creator, even though it may contain unrealistic or fantastical elements. By willingly suspending disbelief, the audience allows themselves to become emotionally invested in the story and characters, making the experience more enjoyable and meaningful. This dynamic acknowledges the inherent fictional nature of the work while acknowledging that the audience is aware of its fictional status. It creates a mutual understanding between the audience and the creators, enabling the audience to fully immerse themselves in the narrative and connect with the intended emotions and themes of the work.

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Answer:

5.5 feet

Step-by-step explanation:

Circumference of a circle is given by

C = πd where d is the diameter of the circle

Therefore, if we know  C we can calculate d = C/π

Given C = 17.27 feet
d = 17.27/π = 5.497 feet

Rounded to 2 decimal places that would be 5.5 feet

Answer:

The vertex of the parabola is (5, -4).

Hope this helps!

Answer:

I'll help

Step-by-step explanation:

Answer:

\(\left \{ {{y=10} \atop {x=5}} \right.\)  \(\left \{ {{y=11} \atop {x=4}} \right.\) \(\left \{ {{y=12} \atop {x=3} \right.\) \(\left \{ {{y=14} \atop {x=1}} \right.\)

x-restaurant gift cards ;

y-movie theater gift cards

Step-by-step explanation:

x+y=15

50x+20y≤450

\(\left \{ {{x\leq 5} \atop {y\geq 10}} \right.\)

so,\(\left \{ {{y=10} \atop {x=5}} \right.\)  \(\left \{ {{y=11} \atop {x=4}} \right.\) \(\left \{ {{y=12} \atop {x=3} \right.\) \(\left \{ {{y=14} \atop {x=1}} \right.\)

Mr. Thomsen can by 5 restaurant cards and 10 movie theater gift cards

System of equations

When there are multiple unknowns and providing necessary information to set up solutions in those unknowns, systems of equations are being used to solve applications.

How to determine the each type of gift card Mr. Thomsen buy?

Consider \(x\) as the number of restaurant gift cards.

Let's take \(y\) as the numbers of movie theaters gift card.

The cost of each restaurant gift cards is 50$

The cost of each movie theater gift cards is 20$

He has 450$ to spend on 15 gift cards.

Therefore, the system of equation to find the each type of gift card will be:

\(50x+20y=450\)

How to find the value of \(x\) :

Here, we know that : \(x+y=15\)

So, the value of \(x\) will be:

\(x=15-y\)

\(50(15-y)+20y=450\)    

Expand the equation

\(750-50y+20y=450\)

Add similar elements

\(-50y+20y=-30y\)

Therefore, the equation will be:

\(750-30y=450\)

Then subtract 750 from both sides as follow:

\(750-30y =450-750\)

\(-30y=-300\)

Simplify the equation:

\(-30y=-300\)

Divide the both sides by \(-30\)

\(\frac{-30y}{-30} =\frac{-300}{-30}\)

Simplify:

\(y=10\)

Therefore the value of \(x\) will be:

\(x=15-10\)

\(x=5\)

Therefore, Mr. Thomsen can by 5 restaurant cards and 10 movie theater gift cards.

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Answer:

you bad

Step-by-step explanation:

ferfrfvrgb rg bg bb

Answer:

Step-by-step explanation:

When WWI began in Europe in 1914, many Americans wanted the United States to stay out of the conflict. So they won't get dragged into it plus it would cause drama between them and Europe and it would go on and on until the other team wins.

Answer:

What war? If your referring to WW2 then because they were provoked from the japanese. IF they attacked the US, then they feared that later in the future they will be overrun when germany plus japan imperialism will be too strong for them.

The printer has a unit rate of 1/2 pages per second , where the slope of the line is m = 1/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let y represent the number of pages printed by the printer

Let x represent the time taken is second

Let the first point be P ( 2 , 1 )

Let the second point be Q ( 4 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 1 ) / ( 4 - 2 )

Slope m = 1/2

Therefore , the value of m is 1/2 pages per second

Hence , the printer has a unit rate of 1/2 pages per second

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