A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.

We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08.  The unit price for each bottle will be: The bottle having the lower price will be:-

30-ounce bottle = $6.00

One ounce bottle = 30 / 6.00 = $5.00

and

24-ounce bottle = $4.08

One ounce bottle = $24/ 4.08 = $5.88

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

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The lines that carry the rectangle onto itself are x = 0 and y = 1

The graph that completes the question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The rectangular graph

The coordinates of one end of the graph are

(-3, 3) and (-3, -1)

Next, we calculate the midpoint of these ends

So, we have

Midpoint = 1/2(x₁ + x₂, y₁ + y₂)

Substitute the known values in the above equation, so, we have the following representation

Midpoint = 1/2(-3 + 3, -1 + 3)

Evaluate the like terms

Midpoint = 1/2(0, 2)

So, we have

Midpoint = (0, 1)

So, we have

x = 0 and y = 1

Hence, the reflection lines are x = 0 and y = 1

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Answer:

Some points that are on this line are:

(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)

Answer:

The number of degrees Celsius goes down 6 every week. (-6)

Step-by-step explanation:

If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).

The equation will look something like this:

w ÷ t = c

Fitting the numbers into this equation will look something like this:

2 ÷ -12 = -6

Every week, it changed -6 degrees Celsius.

Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.

The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.

Given :

Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,

Let g(x) = f(x) − 5.

g(x) = (x−p)(x−q)(x−r)(x−s)h(x)

The condition f(t) > 5 translates to g(t) > 0.

Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :

the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }

The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.

Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have

f(x)=x(x−1)(x−3)(x−4)+5

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Full question ;

Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?

a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]

b.  [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]

a. The derivative of a cubic function

[tex]y=ax^3+bx^2+cx+d[/tex]  is  [tex]y'=3ax^2+2bx+c[/tex].

Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.

b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].

Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]

A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.

A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3

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A)

A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.

So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414

It is believed that the machine is underfilling the bags.

So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414

Given,

n= 8

Population standard deviation (б) = 18

x= 407

We will use the t-test since n > 8 and we are given the population standard deviation.

t=x-μ / (б/[tex]\sqrt{n-1}[/tex])

t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]

t= -1.028

Use the t table to find p value

p-value = 12.706

Level of significance α = 0.025

p-value>α

It is a two-tailed test.

So, we fail to reject the null hypothesis.

So, its bag-filling machine works correctly at the 414-gram setting.

B)

Let μ be the population mean amount of ozone in the upper atmosphere.

As per the given, we have

[tex]H_{0}[/tex]    : μ = 4.8

[tex]H_{1}[/tex] : μ ≠ 4.8

Sample size: n= 26

Sample mean = 4.6

Standard deviation = 1.2

Since population standard deviation is now given, so we use a t-test.

t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]

t= -0.2/0.24

t= -0.833

It is a two-tailed test.

We are accepting the null hypothesis.

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Answer:

[tex]27x^6y^6[/tex]

Step-by-step explanation:

The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex].  So,

[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].

Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex].  So,

[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]

The value of the c in the function c = 19m - 15 when m=10 is 175.

A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.

Given the function;

c = 19m - 15,

where m represents the number of months and c represents the total number of car sent to New York.

To find the value of c:

when m = 10,

Substitute the value of m to the function;

c = 19 (10) - 15

c = 190 - 15

c = 175.

Therefore, the value of c is 175.

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Interest is the price you pay to borrow money or the cost you charge to lend money.

To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.

310-285 = 25

So, Polly will pay $25 in interest.

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The binary representation of each of these hexadecimal numbers is given as follows:

a) 80E = 100000001110

b) 135AB = 00010011010110101011

c) ABBA = 1010101110111010

d) DEFACED = 1101111011111010110011101101

To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:

Then, for example:

80E hexadecimal = 100000001110.

As:

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Answer:

x=5

Step-by-step explanation:

If p and q are parallel, then the two angles in question should be equal to one another.

So,

(3x+15)°=(8x-10)°

(3x+15)°+10°=(8x-10)°+10°

(3x+25)°=(8x)°

(3x+25)°-(3x)°=(8x)°-(3x)°

25°=5x°

5=x

So, the two angles should be (8(5)-10)° and (3(5)+15)°.  Both of these expressions equal 30°.  This makes sense, as the illustration shows that the two angles are acute.

The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]

Given that,

Length of the ladder is, [tex]l=9ft[/tex]

Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.

Now, from triangle ABC,

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

[tex]h^{2} +b^{2} =l^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = 81               (Equation-1)

Differentiating the above equation with respect to time, 't'.

So,

We can write,

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0

[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0

[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0                (Equation-2)

In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.

Let us assume,

h = 3 ft and db/dt = 3 ft/s

We can substitute values in equation-1,

[tex]3^{2} +b^{2}[/tex] = 81

9 + [tex]b^{2}[/tex] = 81

[tex]b^{2}[/tex] = 81-9

[tex]b^{2}[/tex] = 72

b = [tex]\sqrt{72}[/tex]

b = 8.48 ft

Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]

3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0

3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0

3*[tex]\frac{dh}{dt}[/tex] = - 25.44

[tex]\frac{dh}{dt}[/tex] = -25.44/3

[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s

Therefore,

The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

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The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

We have the room as a cuboid.

And its length is 6 meters and height is 3 meters.

The volume of the cuboid = length x height x width

90 = 6 x 3 x width

width = 90 / 18

width = 5 meter.

To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:

12 x width = 12 x 5 = 60 rupees.

Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.

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(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.

Below table showing calculation of Point Estimate of Mean and Standard Deviation:

Score                                  X-X’                                  (X-X’)^2

87                                         5                                         25

91                                         9                                         81

86                                         4                                         16

82                                         0                                         0

72                                        -10                                       100

91                                         9                                         81

60                                        -22                                       484

77                                        -5                                         25

80                                        -2                                         4

79                                        -3                                         9

83                                         1                                         1

96                                         14                                       196

984                                                                                   1022

Mean(X’) = Total Score/n

n = Total number = 12

X’ = 984/12 = 82

Standard Deviation (σ) = √∑(X-X’)^2/(n-1)

σ = √1022/(12-1)

σ = √1022/ 11

σ = 9.6389

(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389

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Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.

It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.

Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.

Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."

∀xA⇒A(x↔a}

for every formula A and every term a, where A(x↔a}  is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of

∀xA.

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The solution is D = 200 feet

The diameter of the circular store is = 200 feet

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the diameter of the circle be represented as = D

Let the radius of the circular store be = r

D = 2r

Now , the area of the circular store be = A

The value of A = 31,415 feet²

The area of the circular store is given by the formula

Area of the circle = πr²

Substituting the values in the equation , we get

31415 = 3.1415 x r²

Divide by 3.1415 on both sides of the equation , we get

r² = 10000

Taking square roots on both sides of the equation , we get

r = 100 feet

Now , the diameter of the store = 2 x radius of the store

Diameter of the store D = 2 x 100 feet

Therefore , diameter of the store D = 200 feet

Hence , The diameter of the circular store is = 200 feet

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Answer: B & A

Step-by-step explanation: I think?

280 is the number which is 16 2/3% more than 240

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.

(1/6) th of 240 = 240/6 = 40

40 more than 240 = 280

So, 280 is the number which is 16 2/3% more than 240

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The correct option is b) ii only

From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.

What is meant by distribution?

The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.

What are the 3 types of distribution?

The Three Types of Distribution

What are the 5 factors of distribution?

Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.

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Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;

T = mx + b

Where:

Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;

f(x) = T = 9.25x + 3

When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;

f(1) = T = 9.25(1) + 3

f(1) = T = 9.25 + 3

f(1) = T = $12.25.

In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.

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Complete Question:

The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?

The equation of the line that has the slope of 7/3 is:  y = (7/3) x - 27/49

Finding the slope and y-intercept is necessary to express the equation of a graphed line in y-intercept (y=mx+c) form, which can then be used to get the equation of the line. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.

Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

Given that,

slope (m) = 7/3

Putting (7,-9) into the equation: y =mx+c

or, -9 = (7/3) × (7) + c

or, -9 = 49 /3 + c

or, c = (-9) × (3/49)

or, c = -27/49

Thus, the equation becomes:

or, y = (7/3) x + -27/49

or, y = (7/3) x - 27/49

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The complete answer: A domain is a set of input data in a relationship.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

An input value and an output value are matched in a relation.

A relation is a function where each input value yields one and only one output value.

Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,

while the range is the set of output values.

The domain of a function or relation is the set of all possible independent values that it can have.

Therefore,  a domain is a set of input data in a relationship.

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Answer:

Step-by-step explanation:

Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7

Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306

Degree of freedom {df}=18

We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t

It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]

As we know, t distribution provides the cumulative probability

As the value of the total area under the t distribution will 1

So, we can write it as:

[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]

Now, using excel, we can easily calculate the t-critical value as follows

=T. INV ( Probability, DF)

Where Probability is the area and DF is the degree of freedom,

Now we will enter these values in excel:

=T. INV (0.95,18)

t-critical value can also be found using t table

Look up for df = 18, in very first column

Now look up for 0.05 in one tail row

Now intersect both of them to get the t-critical value

We will get it as: 2.306

So t-critical value will be =2.306

[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]

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The two inequalities that describe the total cost and no. of guests are

18a + 9c ≤ 2475 and

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let 'a' be the no. of adults and 'c' be the no. of children.

The expense for this event must not exceed $2,475.00.

Therefore, 18a + 9c ≤ 2475...(i)

The venue can hold no more than 150 guests.

Therefore, a + c ≤ 150...(ii)

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Step-by-step explanation:

x = second number

first number = x - 6

third number = 4x

x - 6 + x + 4x = 96

6x - 6 = 96

6x = 102

x = 102/6 = 17

first number = x - 6 = 17 - 6 = 11

second number = x = 17

third number = 4x = 4×17 = 68

Answer:

A.[tex] \frac{7}{6} \sqrt{x} [/tex]

Step-by-step explanation:

Solution Given:

[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]

Bye using indices formula

[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]

we get

[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]

[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]

[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]

[tex] \frac{7}{6} \sqrt{x} [/tex]

Answer:

[tex]2x^2+7x+C[/tex]

Step-by-step explanation:

Find the antiderivative of f'(x)=4x+7

[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]