A concession stand uses 1/48 of a package of lemonade mix to make 1/6 gallons of lemonade.


How many gallons of lemonade can the concession stand make using the whole package of lemonade mix?


Enter your answer in the box.

Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.

Answer: (4.5, 5.1)

Step-by-step explanation:

The distance between two points (a, b) and (c, d) is:

D = √( (a - c)^2 + (b - d)^2)

Then if we want to find the point on the curve y = √(5*x + 3) that is closest to the point (7, 0) we need to minimize the distance:

D = √( (x - 7)^2 + (y - 0)^2)

D = √( (x - 7)^2 + (√(5*x + 3))^2)

Because we know that D is positive, minimizing D is the same than minimizing D^2

Then we can minimize:

D^2 = (x - 7)^2 + (5*x + 3)

D^2 = x^2 - 14*x + 21 + 5*x + 3

D^2 = x^2 - 9*x + 24

This is a quadratic equation with a positive leading coefficient, then the minimum of this function is at the vertex.

To find the vertex, we need to find the zero of the first derivative, this is:

(D^2)' = 2*x - 9

We need to solve:

0 = 2*x - 9

9 = 2*x

9/2 = x

4.5 = x

To find the correspondent y-value, we need to evaluate the curve in x = 4.5

y = √(5*4.5 + 3)  = 5.1

Then the point is (4.5, 5.1)

This means that the point on the curve y = √(5*x + 3) which is closest to the point (7, 0) is the point (4.5, 5.1)

The horizontally compressed function is \(\(\text{g(x)} = x^2 + 6\)\). The correct option is OC. \(\(\text{g(x)} = x^2 + 6\)\).

To horizontally compress the function \(f(x) = x^2\), we can modify the equation by introducing a horizontal compression factor. Let's call the compressed function \(g(x)\).

The general equation for a horizontally compressed function can be expressed as \(g(x) = f(ax)\), where a is the compression factor.

In this case, we want to compress \(f(x) = x^2\). Let's choose a compression factor of \(\frac{1}{2}\).

Therefore, the equation for \(g(x)\) would be:

\(\[ g(x) = f\left(\frac{x}{2}\right) = \left(\frac{x}{2}\right)^2 \]\)

Simplifying this equation, we have:

\(\[ g(x) = \frac{x^2}{4} \]\)

Hence, the equation of \(g(x)\) is:

\(\[ \text{g(x)} = \frac{x^2}{4} \]\)

So, the correct option is OC. \(\(\text{g(x)} = x^2 + 6\)\).

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Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

The value of the function H(X) is,

H(-1) = -2

H(0) = -3

H(1) =  -4

H(3) = -6

H(4) = -7

To complete the function table, we need to evaluate the function H(x) for each value of x:

A function is a mathematical object that takes an input (or inputs) and produces a corresponding output (or outputs) based on a set of rules or instructions. In other words, a function is a relationship between two sets of numbers, where each input corresponds to exactly one output.

The value of the function at different input values are,

H(-1) = -1 -(-1) - 3 = -2

H(0) =  0 -(0) - 3 = -3

H(1) =  1 -(1) - 3 = -4

H(3) = 3 -(3) - 3 = -6

H(4) = 4 -(4) - 3 = -7

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Answer:

C. 20%

Step-by-step explanation:

4 times out of 20 is 20%

Answer:

22)

\(Area:-\)

-----------

23)

\(perimeter:-\)

\(Area:-\)

----------

24)

----------

25)

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

26)

∴To calculate the perimeter , add the length of its sides.

∴To calculate the area, multiply its height by its width.

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

hope it helps...

have a great day!!

Answer:

The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.

Step-by-step explanation:

The statement is described geometrically in the image attached below by means of a right triangle. All variables are described below:

\(OP\) - Minimum distance between lighthouse and the straight shoreline, in kilometers.

\(PP'\) - Distance along the straight shoreline, in kilometers.

\(\theta\) - Angle of rotation of the lighthouse, in sexagesimal degrees.

To find the rate of change of distance along the straight shoreline (\(\frac{dPP'}{dt}\)), in kilometers per minute, we use the following trigonometric relationship:

\(PP' = OP \cdot \tan \theta\) (1)

Then, we differentiate this expression in time:

\(\frac{dPP'}{dt} = OP\cdot \dot \theta \cdot \sec^{2}\theta\) (2)

Where \(\dot \theta\) is the rate of change of the angle of rotation of the lighthouse, in radians per minute.

The angle at the given instant is calculated by (1): \(OP = 5\,km\), \(PP' = 1\,km\)

\(\theta = \tan^{-1} \left(\frac{PP'}{OP} \right)\)

\(\theta \approx 11.310^{\circ}\)

If we know that \(\dot \theta = 37.699\,\frac{rad}{min}\), \(\theta \approx 11.310^{\circ}\) and \(OP = 5\,km\), then the rate of change is:

\(\frac{dPP'}{dt} \approx 196,035\,\frac{km}{min}\)

The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.

The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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According to the data, it can be inferred that Lin is faster than Andre because she is going at 0.3 km/min speed while he is going at 0.25 km/min speed.

To calculate who goes faster we must divide the time into the distance traveled by each character as shown below:

According to the above, the point K of each would be equal to the distance that each of them travels in one minute. As shown in the graph, after 5min (Lin) and 8min (Andre), each one reaches their respective destination located 1.5km and 2km away, respectively, taking the point (0,0) as the starting point.

The graph is attached.

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Given in the question that the temperatures in Alaska was : -18° F

In Honolulu the same day, the temperature was 83° higher .

To get the temperature in Honolulu, you perform addition as:

-18° F + 83° F = 65°F

Answer

A. 65

9514 1404 393

Answer:

  k = 1/3

  ∠D ≅ ∠P

  ∠E ≅ ∠Q

  ∠F ≅ ∠R

  ∠G ≅ ∠S

Step-by-step explanation:

The scale factor is the ratio of corresponding side lengths. It is convenient to choose one of the sides that has length 1.

  k = QR/EF

  k = 1/3

__

Corresponding angles are listed in the same order by the similarity statement.

  ∠D ≅ ∠P

  ∠E ≅ ∠Q

  ∠F ≅ ∠R

  ∠G ≅ ∠S

Answer:

m<ABD = 37°

m<DBC = 58°

Step-by-step explanation:

m<ABD + m<DBC = m<ABC

2x + 23 + 9x — 5 = 95

11x + 18 = 95

     -18     -18

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

11x = 77

/11      /11

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

x = 7

Now, plug this into the equation for m<ABD and m<DBC to find their values.

m<ABD = 2x + 23

= 2(7) + 23

= 14 + 23

= 37

m<DBC = 9x — 5

= 9(7) — 5

= 63 – 5

= 58

Now, check to see if our values are right or not.

2x + 23 + 9x — 5 = 95

2(7) + 23 + 9(7) — 5 = 95

14 + 23 + 63 – 5 = 95

100 – 5 = 95

95 = 95 CORRECT

x=6

\(5x + 20 > 50 \\ 5x > 50 - 20 \\ 5x > 30 \\ \frac{5x}{5} > \frac{30}{5 } \\ x > 6\)

Answer:

Hope I helped!~

Step-by-step explanation:

To find the equation of the line, we can use the slope-intercept form of the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Using the two data points given, we can calculate the slope:

m = (11.25 - 8.35) / (1995 - 1993) = 1.95

To find the y-intercept, we can use one of the data points:

8.35 = 1.95(1993) + b

b = -3884.65

So the equation of the line is:

y = 1.95x - 3884.65

To predict the price of a box of two pieces on July 1, 1999, we can substitute x = 6 (since 1999 is 6 years after 1993) into the equation:

y = 1.95(6) - 3884.65

y = 11.7 - 3884.65

y = -3872.95

This gives us a negative price, which obviously does not make sense. It is likely that the price of a box of two pieces was not linearly increasing during this time period, or that there were other factors influencing the price. Therefore, we cannot use this equation to accurately predict the price of a box of two pieces on July 1, 1999.

Answer:

Hope you can understand my handwriting though

Answer:

agreed

Step-by-step explanation:

agreed...............................

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Solution

Given that

Comparing the indiced,

a = 11, b = 7

Option A

Answer:

Hope this helps ;)

Step-by-step explanation:

If you stretch the square root function F(x)=√x vertically by four units, the new function can be represented by the equation:

G(x) = 4 * √x

This can be written as:

G(x) = 2 * √(2x)

Alternatively, you can write the equation as:

G(x) = √(4x)

Either way, the vertical stretch of the square root function by four units is given by the equation G(x) = 4 * √x or G(x) = 2 * √(2x) or G(x) = √(4x).

Therefore, the minimum percentage of stores that sell a gallon of milk for between $3.27 and $3.83 is 75%, rounded to one decimal place.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It measures how spread out the data is from the mean or average value. A low standard deviation indicates that the data is closely clustered around the mean, while a high standard deviation indicates that the data is more spread out. It is calculated as the square root of the variance, which is the average of the squared differences from the mean.

Here,

Chebyshev's theorem states that for any dataset, regardless of its distribution, at least 1 - 1/k² of the data will fall within k standard deviations of the mean, where k is any positive number greater than 1. To find the minimum percentage of stores that sell a gallon of milk for between $3.27 and $3.83, we can first find how many standard deviations away from the mean these prices are:

$3.27 is (3.27 - 3.55)/0.14 = -2 standard deviations from the mean

$3.83 is (3.83 - 3.55)/0.14 = 2 standard deviations from the mean

Thus, the distance between $3.27 and $3.83 is 4 standard deviations (2 in each direction).

Using Chebyshev's theorem with k = 2 (since we want to know the minimum percentage within 2 standard deviations), we have:

=1 - 1/2²

= 1 - 1/4

= 0.75

This means that at least 75% of stores sell a gallon of milk for between $3.27 and $3.83.

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Answer:

\(\frac{31}{45}x\)

__________________________________________________________

Step-by-step explanation:

We are given:

3\(\frac{1}{5}x\) + 10\(\frac{7}{9}x\) - 2\(\frac{2}{5}x\) - 10\(\frac{8}{9}x\)

Concepts used:

Evaluating Mixed fractions and Adding like terms

Simplifying the Mixed Fractions:

to simplify these mixed fractions, we will multiply the whole number part with the fraction's denominator and add that to the numerator.

The number formed will be given the same denominator as of the fraction part in the number

After simplifying these mixed fraction, we get:

\(\frac{16}{5}x + \frac{97}{9}x - \frac{12}{5}x - \frac{98}{9}x\)

Adding and Subtracting the like terms:

to simplify our calculations, we will pair the numbers with the same denominator

\((\frac{16}{5}x - \frac{12}{5}x) + (\frac{97}{9}x - \frac{98}{9}x)\)

Simplifying the terms in the brackets

\(\frac{4}{5}x - \frac{1}{9}x\)

Taking the LCM and simplifying

\(\frac{36}{45}x - \frac{5}{45}x\)

Since the denominators are equal, the numerators can now be subtracted

\(\frac{31}{45}x\)

Therefore, simplifying the given series of number gives us 31x/45

the two planes will be at the same altitude of approximately 5675.48 feet after 49.45 seconds.

A plane is a flat two-dimensional surface that extends infinitely in all directions. In geometry, a plane is defined as a surface that is completely flat and has no thickness. It is often represented as a coordinate system with two perpendicular axes, usually labeled as the x-axis and y-axis.

Assuming that the two planes maintain their rates of ascent, we can use the following equations to determine when the planes will be at the same altitude:

altitude of plane A = 4000 + 33.5t

altitude of plane B = 3146 + 50.75t

where t represents time in seconds.

To find the time at which the two planes will be at the same altitude, we can set the two equations equal to each other and solve for t:

4000 + 33.5t = 3146 + 50.75tSubtracting 3146 from both sides, we get:

854 + 33.5t = 50.75t

Subtracting 33.5t from both sides, we get:

854 = 17.25t

Dividing both sides by 17.25, we get:

t = 49.45 seconds

Therefore, it will take approximately 49.45 seconds for the two planes to be at the same altitude. To find the altitude at which they will meet, we can substitute this value of t into either equation. Using the equation for plane A, we get:

altitude of plane A = 4000 + 33.5(49.45) = 5645.08 feet

Using the equation for plane B, we get:

altitude of plane B = 3146 + 50.75(49.45) = 5675.48 feet

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a) The Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.

b) The total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.

a. Nash Equilibrium: A Nash Equilibrium is a set of strategies such that each player's strategy is a best response to the strategies of the other players.

In this game, each person i chooses their effort level x i to maximize their own payoff, which is the worth of the project divided by 2. Their individual payoff is given by:

pi = (2x1x2) / 2 = x1x2

By taking the derivative of pi with respect to xi and setting it to zero, we get the following first-order condition:

dpi/dx i = x2 - xi = 0

Since xi is in the range [0,1], we have xi = x2.

Thus, the Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.

b. Total Payoff: The total payoff of the project is given by:

pt = x1x2 + x1x2 = 2x1x2

By factoring the total payoff function, we get:

pt = 2x1x2 = 2x1x1 = 2x12

So, the total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.

Since the Nash Equilibrium is when both players put in the same effort level, there is no effort level that yields a higher total payoff than the Nash Equilibrium.

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Answer:

  D. a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold

Step-by-step explanation:

You want to know possible changes to radius and height that will double the volume of a cylinder.

The volume of a cylinder is given by the formula ...

  V = πr²h

This tells you the volume is proportional to the height, and proportional to the square of the radius.

This proportionality tells you that the volume can be doubled by ...

We note that doubling the radius will multiply the square of the radius by 4:

  R = 2r

  R² = (2r)² = 4(r²)

The second option above (double height only) matches choice D.

<95141404393>

Answer:

P = 0.309

Step-by-step explanation:

Answer:

f(x)

Step-by-step explanation:

Because f(x) = 4x + 5

Answer:

f(x)

Step-by-step explanation:

g(x) intercept Is shown to be 2

f(x) if u sub 0 into x to find the y intercept gives you 5

h(x) I you sub 0 into the equation in place of x to find the y intercept it gives you -1.84

and if you look at all ghe y intersect values f(x) is the greatest

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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The function represented by the graph with the given transformations is |–x| + 2.

The function represented by the given transformations is |–x| + 2.

Let's analyze the transformations step by step:

Reflection across the x-axis:

Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.

Translation right 2 units:

Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.

Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.

Thus, the function represented by the graph with the given transformations is |–x| + 2.

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Answer: -lx-2l

Step-by-step explanation: