Lewis uses a half-cup of lemon juice for
every pitcher of lemonade he makes. If he
starts with a gallon of lemon juice and makes
19 pitchers of lemonade, is it reasonable to
assume he'll have enough juice left to make at
least 9 more pitchers? Explain.

The multiplicative inverse of 7/5 is 5/7 using the formula of multiplicative inverse like (x)^-1 which equals to 1/x.

let's try to learn what is multiplicative inverse.

1/N or [tex]N^-1[/tex] is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.

One is obtained when a number is multiplied by its own multiplicative inverse.

When a number is multiplied by its original number, the multiplicative inverse of that number, or x^-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2^-1 since it fulfils the formula: 2 x (2^-1) = 2 x (1/2) = 1.It is also known as a number's reciprocal.

Multiplicative inverse of 7/5 is (7/5)^-1 = 1/(7/5) = 5/7.

Given question is incomplete complete question here:

What is the multiplicative inverse of 7/5?

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There are three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

Therefore, the three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

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Answer:

x = 1

Step-by-step explanation:

Immediately, we will simplify like terms on the left side of the equation. This will give us:

[tex]\sqrt{2x-x-1}[/tex]  = 0

Simplifying gives us:

[tex]\sqrt{x-1}[/tex] = 0

Now, an important thing to note, is that for the square root of a number to be 0, the number has to be 0. Therefore, x - 1 must equal 0. So, x = 1. Checking our work gives us:

[tex]\sqrt{2x - x - 1}[/tex] = 0

[tex]\\\sqrt{2 - 1 - 1}[/tex] = 0

[tex]\sqrt{0}[/tex] = 0

It all checks out.

Hope this helped!

The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the function:

y = -(x/3) + 2

At x = -3:

y = -((-3)/3) + 2 = 3

At x = 0:

y = -(0/3) + 2 = 2

At x = 3:

y = -(3/3) + 2 = 1

At x = 6:

y = -(6/3) + 2 = 0

The value of y when x = -3 is 3

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QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.

When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.

In QUAD ABCD, DP equals x + 7 and AC is 4x-13.

4x - 13 is x + 7 + x + 7

4x - 13 = 2x+14

2x-13 = 14.

hence,

The value of x is 13.5.

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The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1

Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]

here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.

We need to find the sum.

We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1

We know that the formula of the sum of n-terms of a geometric sequence is:

[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]

For n = 21, r = -1 and a1 = 1

[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]

Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1

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Jonathan and Oscar will have the same amount of money saved after  2 weeks.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

If they have same amount of money then,

f(x) = g(x)

18x+5 = 8x+25

10x = 20

x = 2 weeks

Therefore, Jonathan and Oscar will have the same amount of money saved after  2 weeks.

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Real value numbers are both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc are all real numbers.

The real number that consist of different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures.Any number that we can think except complex numbers is a real number.

Real numbers encompass three classifications of numbers.Whole numbers, rational numbers, and irrational numbers are all real numbers.Even counting and natural number are all real numbers.

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Step-by-step explanation:

so, clearly, the triangles BCF and DCF are congruent.

that makes the line CF a bisector of the kite figure.

and so, both angles are identical halves of the total angle at C.

therefore,

3x + 13 = 13x - 7

13 = 10x - 7

20 = 10x

x = 20/10 = 2

Because two triangles are said to be congruent when all three of their corresponding sides and all three of their corresponding angles have the same measure, the right answer is SSS.

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found.

In the order below, beginning with triangles DAB and BCD, write the names of the vertices.

AB = CD

DA = BC

Since both triangles' BD sides are the same, BD = BD.

The SSS feature of a congruent triangle allows us to conclude that the triangles DAB and BCD are congruent since they share the same three sides.

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The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.

Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D

where, A --> amplitude

B--> period in form of pi

C--> phase or horizontal shift

D --> vertical shift

We have, the depth of water in a tank oscillates sinusoidally.

The smallest depth of water in tank = 6.6 feet

The largest depth of water in tank = 9.4 feet

We have to determine the formula of depth of water in tank as a function of time in hours .

For sinusoidal function,

Amplitude , A = average depth

= ( largest depth + smallest depth)/2

= (6.6 + 9.4)/2

= 16.0/2 = 8

Now, The period of 8 hours so, B = 2π/8

=> B = 45° = π/4

Also, upward shift , D is 9.4 - 6.6 = 2.8

Horizontal shift, C = 0

So, required function is D = 2.8 + 8 sin(π t/4) .

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The cleaning company would charge $150 for cleaning two rooms according to the fixed charges.

A fixed amount is a fixed amount or amount established by agreement or contract. This amount is usually a specified amount, does not change over time, and is usually paid on demand or by a certain date. Fixed amounts are commonly used in loans, insurance, and other financial contracts.

This cost is calculated by dividing the difference between the total cost of 6 and 8 rooms by the number of rooms cleaned (6 - 2 or 4).

= ($250 - $320)/4

= $40

This will give you a price of for each additional room.

To calculate the cost of two rooms, simply add the fixed amount of the home visit and double the cost ($40) for each additional room. That's a total of $150 for two rooms.

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√6/3 is the value after rationalization of √2/√3

An expression is combination of variables, numbers and operators.

The given expression is √2/√3

Square root two divided by square root three.

We need to rationalize the denominator

To rationalize multiply numerator and denominator by √3

√2/√3×√3/√3

√2×3/3

√6/3

Hence, √6/3 is the value after rationalization of √2/√3

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Step-by-step explanation:

y = 2x + 1 -------- (I)

y = 4x + 6 --------(ii)

from eqn (I)

y = 2x + 1

sub y = 2x + 1 in eqn (ii)

2x + 1 = 4x + 6

2x - 4x = 6 - 1

-2x = 5

x = -5/2

sub x = -5/2 in eqn (I)

y = 2(-5/2) + 1

y = -5 + 1

y = -4

Therefore, (x, y) = (-5/2, -4)

A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.

The correct answer is an option (A)

Consider plot A.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 6, 6, 7, 7, 10

Using the formula of mean, the mean of Plot A would be:

mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10

mean = 57/10

mean = 5.7

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 6)/2

            = 11/2

            = 5.5

Consider plot B.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 5, 6, 6, 6, 7

mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10

mean = 51/10

mean = 5.1

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 5)/2

            = 5

Hence, both the mean and median are greater for Plot A than for Plot B.

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The complete question is:

Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.

Answer:

a)

24 = 2³ × 3

40 = 2³ × 5

b)

LCM = 120

Step-by-step explanation:

a)

                 24                                      40

              /       \                                  /      \

            2         12                           2         20

                      /     \                                   /      \

                    2       6                               2      10

                           /     \                                     /    \

                        2         3                               2       5

24 = 2³ × 3

40 = 2³ × 5

b)

LCM = 2³ × 3 × 5

LCM = 120

The slope is $125 and the slope tells the annual due payment of $125.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take two points from the graph as (2, 400) and (4, 650)

Then, the slope of line is

slope, m = ( 650- 400) / ( 4- 2)

slope, m = 250 /2

slope , m = 125

Hence, the slope is 125.

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Answer: length of EF is 18 units.

Step-by-step explanation:

similar triangles (as displayed in the photo) have the same angle measures, but can have different side lengths. however, these side lengths are proportional to each other, meaning that with similar triangles, there will ALWAYS be a number you can multiply the first triangle by to get its similar triangle.

you can find this number by dividing one side length of whichever triangle is bigger with its corresponding side on the other triangle (for example, sides DF and AC correspond, so you'd divide whichever value's bigger by the smaller one. in this case you'd divide 21 by 14.) this gives you 1.5, which tells you that triangle DEF is 1.5 times larger than triangle ABC. so to get EF, just multiply BC (which is 12) by 1.5. this gives you 18. so, EF equals 18. hope this helped :3

Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day

Two or more expressions with an Equal sign is called as Equation.

The billing cycle for the month = 28 days

Current beginning balance = x

Annual percentage rate (APR) = 24%

Monthly percentage rate (MPR) = 2% (24% ÷ 12)

Purchase on the last day = $1,400

Total finance charge for the month = $51

Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)

Finance charge for the beginning balance = $50 ($51 - $1)

The current beginning balance, x = $2,500 ($50 ÷ 2%)

Equation for current beginning balance, x = 51 - 1 ÷ 0.02

Total finance charge for the last-day purchase = $28 ($1,400 x 2%)

Savings in finance charge by purchasing on the last day = $27 ($28 - $1)

Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.

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The comparison operator "≥" in logic means that the number is either greater than or equal to a number , the greater than equal to symbol is used to describe the relationship between two terms .

What is a Comparison Operator ?

The Comparison operator in logic is used to compare logic statements ,such as [tex]a > b[/tex] or [tex]a < b[/tex] , by using a , b as variables, the operator compares their values, returns true and false.

The Comparison Operator "≥" , in logic is read as " greater than equal to" , For Example : if the statement is [tex]a \geq b[/tex] , then if the variable is greater than or equal to b , then the operator will return TRUE and if not then it will return FALSE .

The given question is incomplete , the complete question is

What does the comparison  operator "≥"(greater than equal to) mean in logic ?

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The value of p is 12.322

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here p=-log(2.1×10¹²)

                  p= - ( log(2.1) +12 log10)

                  p= -(0.322+12)

                  p=12.322

Hence, the value of p is 12.322

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Answer:

A. The ratios are both identical (three fifths and three fifths).

Step-by-step explanation:

ratio means fraction

ratio also means division

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"SOHCAHTOA"

sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent

mathworldwolframcom

sine equals opposite over hypotenuse

sine X equals 3 over 5

cosine equals adjacent over hypotenuse

cosine Y equals adjacent over hypotenuse

cosine Y equals 3 over 5

side thats 3 is adjacent for y but

side thats 3 is also opposite for x

both identical, aka C on their question is right

its the 1st option for flvs

Answer:

60 because their a 2 induivedinal in 1 sock.

Step-by-step explanation:

30 x 2 = 60

Answer:

17%

Step-by-step explanation:

Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%

The correct option is option C which states that , less than 80% power to detect the standard deviation is 0.4.

We know that the power is less and the effect size is small therefore we can say that all other things given as equal, it's harder to detect than the larger effect. As a result power is reduced.

Statistical power is a measure of research efficiency that is estimated before the study begins . This is done so as to predict the likelihood of discovering an actual effect rather than receiving a false negative result or, in the worst case scenario, overestimating the effect by identifying noise in the data.

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Answer: 102.4

Given ratio 5:8

Let's assume the answer to be x

5÷8 should be equal to 64÷x

∴ x= (64×8) ÷ 5

=102.4

The number that has the same ratio to 64 as 5:8 is gotten as; 40

How to Calculate Ratio?

We have the ratio 5:8.

Now, we want to find the number that has the same ratio to 64 as 5:8. Thus, we will use proportion to get this;

x/64 = 5/8

Cross multiply to get;

x = 64 * 5/8

x = 40