olve the following linear programming problem. Restrict x ≥ 0 and y ≥ 0. Maximize f = 2x + 4y subject to x + y ≤ 7; 2x + y ≤ 12; y ≤ 4.
(x,y)=
f=

cos 59° = ±([tex]\sqrt{1 - sin^2 59}[/tex]) ≈ ±0.515 in terms of the sine function.

To express cos 59° in terms of the sine function, we can use the trigonometric identity:

[tex]sin^2[/tex]θ + [tex]cos^2[/tex]θ = 1

Rearranging this identity, we get:

[tex]cos^2[/tex]θ = 1 - [tex]sin^2[/tex]    θ

Taking the square root of both sides, we get:

cosθ = ±[tex]\sqrt{(1 - sin^2θ)}[/tex]

In the case of cos 59°, we know that sin 59° can be calculated using the sine function since sin 59° is the opposite side of a right triangle divided by its hypotenuse, where the angle opposite to the opposite side measures 59 degrees. Therefore:

sin 59° = 0.85717 (rounded to 5 decimal places)

Substituting sin 59° into the equation for cosθ, we get:

cos 59° = ±([tex]\sqrt{1 - sin^2 59}[/tex]) = ±[tex]\sqrt{(1 - 0.85717^2) }[/tex]≈ ±0.515

Note that since the angle 59° is in the first quadrant, cos 59° is positive. Therefore, we can write:

cos 59° ≈ 0.515 in terms of the sine function.

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The equation of the line passing through (-8, -10) and passing through (x1, f(x1)) is given by y = 5x + 30.


m = (f(x2) - f(x1)) / (x2 - x1)

f(x) = 3x from x1 = 0 to x2 = 5

f(x) = x2 + 2x from x1 = 3 to x2 = 5

m = (f(5) - f(0)) / (5 - 0)

m = (53 + 2(5)) - (03 + 2(0)) / (5 - 0)

m = 25 / 5

m = 5

Therefore, the average rate of change of the function from x1 to x2 is 5.

The equation of the line passing through (-8, -10) and passing through (x1, f(x1)) is given by the equation:


y = mx + b



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



We can find the slope of the line, m, from the average rate of change of the function from x1 to x2 which is 5.



We can find the y-intercept, b, by substituting the coordinates (-8, -10) in the equation of the line.



y = 5x + b



-10 = 5(-8) + b



b = 30



Therefore, the equation of the line passing through (-8, -10) and passing through (x1, f(x1)) is given by y = 5x + 30.

The graph is shown in the image attached.

To solve an equation by graphing, you need to graph the equation on a coordinate plane and find the points where the graph intersects the x-axis. These points correspond to the solutions of the equation, which are the values of x that make the equation true here.

Therefore, to solve the equation by graphing, we plot the graph, locate the points where the graph intersects the x-axis, and read the solutions from the graph.

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Carrie can walk at a speed of 3 mph.

To find out how fast Carrie can walk, we can use the formula distance = speed × time. Let's call the speed at which Carrie walks x, and the time it takes her to walk 6 miles t.

Since she can ride 9 mph faster than she can walk, her biking speed will be x + 9. We can set up the following equations:

6 = x × t (for walking)
24 = (x + 9) × t (for biking)

Since the time it takes her to walk 6 miles and bike 24 miles is the same, we can set the two equations equal to each other:

x × t = (x + 9) × t

Simplifying the equation gives us:

x = x + 9

Subtracting x from both sides gives us:

0 = 9

This is not a valid solution, so we need to go back to our original equations and solve for t:

t = 6/x (for walking)
t = 24/(x + 9) (for biking)

Setting these two equations equal to each other gives us:

6/x = 24/(x + 9)

Cross-multiplying gives us:

6(x + 9) = 24x

Distributing the 6 gives us:

6x + 54 = 24x

Subtracting 6x from both sides gives us:

54 = 18x

Dividing by 18 gives us:

x = 3

So Carrie can walk 3 mph.

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Answer:

Answer is C

Step-by-step explanation:

using long divison:

The mass of the sample decays by a factor of 3/5 every 4.27 months.

In science, decay refers to the natural process of deterioration or breakdown of a substance over time. Decay can occur in many different contexts, such as the decay of radioactive materials, the decay of organic matter, and the decay of physical structures.

In radioactive decay, unstable atoms release energy and subatomic particles as they decay into more stable forms. This process occurs at a predictable rate, which can be used to determine the age of rocks and other materials.

In organic decay, biological matter breaks down into simpler compounds through the action of bacteria and other decomposers. This process is an essential part of the natural cycle of life and death, and it helps to recycle nutrients and other vital substances in ecosystems.

To find the time it takes for the mass to decay by a factor of 3/5, we can set up the following equation:

M(t) = (3/5)M(0)

[tex]120(\frac{625}{81} )^{t} = \frac{3}{5} \\\frac{625}{81}= \frac{3}{5}^{\frac{1}{t} } \\ln(\frac{625}{81})=ln(\frac{3}{5}^{\frac{1}{t} })\\[/tex]

[tex]t=\frac{ln(\frac{625}{81})}{ln(\frac{3}{5})} = 4.27months[/tex]

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The composite functions f ∘ g and g ∘ f are:
domain of f = (-∞, ∞)
domain of g = (-∞, ∞)
domain of f ∘ g = (-∞, ∞)
domain of g ∘ f = (-∞, ∞)

The composite functions f ∘ g and g ∘ f are formed by plugging one function into the other. To find f ∘ g, we plug the function g into the function f:

f ∘ g = f(g(x)) = f(x2/3) = (x2/3)3 = x2

To find g ∘ f, we plug the function f into the function g:

g ∘ f = g(f(x)) = g(x3) = (x3)2/3 = x2

The domain of a function is the set of all possible values of x that make the function defined. The domain of f is all real numbers, since the function f(x) = x3 is defined for all values of x:

domain of f = (-∞, ∞)

The domain of g is also all real numbers, since the function g(x) = x2/3 is defined for all values of x:

domain of g = (-∞, ∞)

The domain of f ∘ g is the intersection of the domain of f and the domain of g, which is all real numbers:

domain of f ∘ g = (-∞, ∞)

The domain of g ∘ f is also the intersection of the domain of g and the domain of f, which is all real numbers:

domain of g ∘ f = (-∞, ∞)

Therefore, the answers are:

domain of f = (-∞, ∞)
domain of g = (-∞, ∞)
domain of f ∘ g = (-∞, ∞)
domain of g ∘ f = (-∞, ∞)

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The number of pounds of peaches sold is given as follows:

65 pounds, option 2.

The amount is obtained solving a system of equations, for which the variables are given as follows:

She sold a total of 165 pounds, hence:

x + y = 165

x = 165 - y.

She made $337.50, hence:

1.75x + 2.5y = 337.50.

Replacing the first equation into the second, the value of y is obtained as follows:

1.75(165 - y) + 2.5y = 337.50

0.75y = 48.75

y = 48.75/0.75

y = 65 pounds.

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Answer:

How to calculate 8 + 3(5 - 7)​

Use Pemdas

Pemdas

8 + 3(5 - 7)​

5 - 7

= -2

8 + 3 ⋅ -2

Pemdas

8 + 3 ⋅ -2

3 x -2

= -6

8 + -6

Pemdas

8 + -6

Step-by-step explanation:

You're welcome.

Answer:

8+3(5-7)=-2

You will use the"Bracket Of Division Multiplication Addition and Subtraction(BODMAS)" method. Hence solve the one in the bracket first. So it's going to be 5-7 which is -2.Then you continue with the multiplication of 3 by the -2 you got making -6. Finally add the 8 to the -6 making 2.

Answer: 14/3 or 3/4 are in 7/2

Step-by-step explanation:

Answer:

Step-by-step eEIKxplanation:

The corner point (8, 4) and is equal to 550

The minimum value of P = 50x + 75y exists at the corner point (3, 0) and is equal to 150. The maximum value of P = 50x + 75y exists at the corner point (8, 4) and is equal to 550.

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8×4=32

11-8=3

4×3=12

12÷2=6

32+6=38

=38inch^2

it might b wrong tho?

The linear demand function is given by Q = -1.09P + 76.4, the revenue function is R = -1.09P^2 + 76.4P, and the price that yields maximum revenue is $34.95.

To create the linear demand function, we use the two points given: (35, 34.75) and (36, 33.06). We can find the slope of the line between these two points using the slope formula: (33.06 - 34.75)/(36 - 35) = -1.69. This slope represents the change in quantity demanded per dollar change in price. To find the intercept, we can use either of the points and solve for it: 35 = -1.69(34.75) + b, giving us b = 131.15. Thus, the demand function is Q = -1.69P + 131.15, which we can simplify to Q = -1.09P + 76.4.

To find the revenue function, we multiply the demand function by the price: R = P(Q) = P(-1.09P + 76.4) = -1.09P^2 + 76.4P. To find the price that yields maximum revenue, we can take the derivative of the revenue function with respect to price and set it equal to zero: dR/dP = -2.18P + 76.4 = 0, giving us P = $34.95. Therefore, the price that yields maximum revenue is $34.95.

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The solution of the heat equation subject to the boundary and the initial conditions is u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt).

The heat equation with the given boundary conditions is:

∂u/∂t = k ∂^2u/∂x^2

where k is a constant. We can use separation of variables to solve this equation. Let:

u(x, t) = X(x)T(t)

Substituting this into the heat equation, we get:

X(x)T'(t) = k X''(x)T(t) / X(x)T(t)

Dividing both sides by X(x)T(t) and rearranging, we get:

X''(x)/X(x) = T'(t)/(kT(t))

The left-hand side depends only on x, while the right-hand side depends only on t. Since they are equal, they must be equal to a constant:

X''(x)/X(x) = -λ

T'(t)/(kT(t)) = λ

where λ is a constant. The boundary conditions u(0,t) = u(1,t) = 0 imply that X(0) = X(1) = 0. The general solution for X(x) is then:

X(x) = A sin(nπx)

where A is a constant and n is a positive integer. The eigenvalues λ are:

λ = -(nπ)^2

The general solution for T(t) is:

T(t) = B exp(-kλt)

where B is a constant. The solution for u(x, t) is then:

u(x, t) = Σ[ A_n sin(nπx) exp(-(nπ)^2 kt) ]

where the sum is taken over all positive integers n.

We can now use the initial condition u(x,0) = 4sin3πx+8sin6πx to determine the constants A_n. Since the solution only contains sine terms, we can use the Fourier sine series to expand the initial condition:

4sin3πx+8sin6πx = Σ[ A_n sin(nπx) ]

where the sum is taken over all positive odd integers for n = 3 and all positive even integers for n = 6. The coefficients A_n are:

A_3 = 4π/3

A_6 = 16π/6

Substituting these values into the solution for u(x, t), we get:

u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt)

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Using algebraic expressions, the expression that is equivalent to 9(4w) is: 36w.

Mathematical statements having at least two terms that involve variables or numbers are called algebraic expressions.

Every combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is a recognised algebraic expression (or variable expression).

We just join like terms in an algebraic expression to make it simpler. Hence, related variables will be combined. Now, the identical powers will be merged from the similar variables.

Now in the given case,

9(4w)

= 9×4×w

=36w.

Therefore, the expression that is equivalent to 9(4w) is: 36w.

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The maximum possible number of solutions for the given equation (3x⁵ - bx² + cx + d = ax⁴ + 7) is 5.

Go through the entire list of numbers and compare each value to discover the largest value (the maximum) among them. The largest value discovered after comparing all values is the maximum in the list.

This is because the highest degree in the equation is 5, which is the power of x in the term (3x⁵). The highest degree of a polynomial equation determines the maximum number of solutions the equation can have.

Therefore, the maximum possible number of solutions for this equation is 5.

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The following exponential rule is called the Product Rule.

What is exponential rule ?

Exponential rules are mathematical rules that govern the manipulation of exponential expressions, which involve terms that have a base raised to a power. Exponential rules are important in many areas of mathematics and science, particularly in algebra, calculus, and statistics.

According to the question:
The following exponential rule is called the Product Rule. It states that when multiplying two powers with the same base, you can add their exponents. The rule is:

[tex]a^m * a^n = a^(m+n)[/tex]

For example, [tex]2^3 * 2^4 = 2^(3+4) = 2^7 = 128[/tex]. This rule is fundamental in simplifying expressions and solving equations involving exponential functions.

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If Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.

The balance is the sum οwing οn an accοunt in banking and accοunting. The term "balance" in bοοkkeeping refers tο the difference between the tοtal οf debit entries and the tοtal οf credit entries made intο an accοunt οver the cοurse οf a certain financial periοd. The accοunt shοws a debit balance when tοtal debits exceed tοtal credits.

Net debt is represented by an accοunt balance that is less than zerο. An accοunt with a minus sign (-) at the end οf the amοunt typically has a negative balance οr is in debt.

Given,

The fee charged when the balance falls belοw zerο = $5.95/day

The current balance in Lin's sister's accοunt = −$2.67

We are asked tο find her accοunt balance after 22 days if nο transactiοns are made.

Since the current balance in her accοunt is belοw zerο, a fee will be charged.

The fee charged fοr 22 days = 5.95 × 22 = $130.9

Then the current balance = -2.67 - 130.9 = -$133.57

Therefοre if Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.

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[tex]\dfrac{y-(-3.5)}{-3.5-6.5} = \dfrac{x-0}{0-(-1)}[/tex]

[tex]\dfrac{y+3.5}{-10} = \dfrac{x}{1} \iff y +3.5 = -10x\\[/tex]

[tex]\implies y = -10x - 3.5[/tex]

The cost per square foot of the remaining sheet metal is $4.10.

To find the cost per square foot of the remaining sheet metal, we can first calculate how much sheet metal is remaining by solving the equation:

7.6X - 3.5X = 65.6

where X is the amount of sheet metal remaining in square feet.

Simplifying the left side of the equation gives:

4.1X = 65.6

Dividing both sides by 4.1 gives:

X = 16

Therefore, the amount of sheet metal remaining is 16 square feet.

To find the cost per square foot, we can divide the cost of the remaining sheet metal by the amount of sheet metal remaining:

$65.60 / 16 sq. ft. = $4.10 per square foot.

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The data point 1.8 falls outside the range of 1.798, so it can be considered an outlier.

An outlier is a data point that is significantly different from other data points in a data set. Outliers can occur due to errors in data collection or measurement, or they can be legitimate data points that are simply far outside the range of the other data. In statistical analysis, it is important to identify outliers and decide whether to remove them from the data set or keep them and analyse them separately.

There are several methods for identifying outliers, including graphical methods and statistical methods such as the use of z-scores or the interquartile range.

To identify outliers in this data, we can start by calculating some basic statistical measures such as the mean and standard deviation.

The mean of the given data is:

(1.11 + 1.13 + 1.40 + 1.32 + 1.14 + 1.28 + 1.13 + 1.8 + 1.10 + 1.20) / 10 = 1.304

The standard deviation of this data is:

sqrt(((1.11 - 1.304)²  + (1.13 - 1.304)² + (1.40 - 1.304)² + (1.32 - 1.304)² + (1.14 - 1.304)² + (1.28 - 1.304)² + (1.13 - 1.304)² + (1.8 - 1.304)² + (1.10 - 1.304)² + (1.20 - 1.304)^2) / 9) = 0.247

One common rule of thumb for identifying outliers is to consider any data point that falls more than 2 or 3 standard deviations from the mean to be an outlier. Using this rule, we can identify any values that fall outside the range:

1.304 - 2 * 0.247 = 0.81

1.304 + 2 * 0.247 = 1.798

1.304 - 3 * 0.247 = 0.563

1.304 + 3 * 0.247 = 2.045

Based on this rule, we can see that the data point 1.8 falls outside the range of 1.798, so it can be considered an outlier.

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(a) The F statistic for testing that all effects equal 0 is given by:
F = [(R2 / k) / ((1 - R2) / (n - k - 1))]
where R2 is the coefficient of determination, k is the number of predictor variables, and n is the total number of observations.
To derive this expression, we start with the definition of the F statistic:
F = [(SSR / k) / (SSE / (n - k - 1))]
where SSR is the sum of squares for regression and SSE is the sum of squares for error.
We know that R2 = SSR / SST, where SST is the total sum of squares. Therefore, we can rewrite SSR as:
SSR = R2 * SST
Substituting this back into the F statistic, we get:
F = [(R2 * SST / k) / (SSE / (n - k - 1))]
We also know that SST = SSR + SSE, so we can substitute this back into the F statistic:
F = [(R2 * (SSR + SSE) / k) / (SSE / (n - k - 1))]
Simplifying the expression, we get:
F = [(R2 / k) / ((1 - R2) / (n - k - 1))]
This is the expression for the F statistic in terms of the R2 value.

(b) The F statistic for comparing nested models is given by:
F = [(R2_2 - R2_1) / (k_2 - k_1)] / [(1 - R2_2) / (n - k_2 - 1)]
where R2_1 and R2_2 are the R2 values for the smaller and larger models, respectively, and k_1 and k_2 are the number of predictor variables in the smaller and larger models, respectively.
To derive this expression, we start with the definition of the F statistic:
F = [(SSR_2 - SSR_1) / (k_2 - k_1)] / [(SSE_2 / (n - k_2 - 1))]
where SSR_1 and SSR_2 are the sum of squares for regression for the smaller and larger models, respectively, and SSE_2 is the sum of squares for error for the larger model.
We know that R2 = SSR / SST, so we can rewrite SSR_1 and SSR_2 as:
SSR_1 = R2_1 * SST
SSR_2 = R2_2 * SST
Substituting these back into the F statistic, we get:
F = [((R2_2 * SST) - (R2_1 * SST)) / (k_2 - k_1)] / [(SSE_2 / (n - k_2 - 1))]
Simplifying the expression, we get:
F = [(R2_2 - R2_1) / (k_2 - k_1)] / [(1 - R2_2) / (n - k_2 - 1)]

This is the expression for the F statistic for comparing nested models in terms of the R2 values.

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1. The y-intercept of y = -3/2x - 4, is -4, which would be marked at y = -4 on the y-axis.

2. The slope (m) = 3; y-intercept (b) = -86;

The equation for the situation is: y = 3x - 86

3. Median of class A = 40; Median of class B = 8

The difference is: 32

In a linear equation, the y-intercept is the point at which the graph of the equation intersects the y-axis. It is the value of y when x is equal to zero.

1. The y-intercept of the equation, y = -3/2x - 4, is -4. This means the y-intercept on the graph would be at when y = -4 on the y-axis.

2. The slope (m) = unit rate = 3 degrees every hour

The starting value = y-intercept (b) of the situation = -86

To write an equation for the situation substitute m = 3 and b = -86 into y = mx + b:

y = 3x - 86

3. Median is the middle value of a data set, therefore:

Median of class A = 40

Median of class B = 8

The difference between the medians of the class = 40 - 8 = 32

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The number of adults is 120, and the total money made from ticket sales is £1120.

The mathematical connection between two or more numbers is called a ratio, and it is represented as the product of the division of two values. Several formats, such as fractions, decimals, or percentages, can be used to express ratios. Mathematicians employ ratios in many different areas, including geometry, probability, and finance. The connection between the lengths of two or more sides of a form is described in geometry using ratios. Ratios, sometimes in the form of odds, are used in probability to indicate the possibility of an event occurring.

Let x be the number of adults.

Given that, ratio of children to adults is 2 : 3.

Thus,

2/3 = 80/x

Cross-multiplying gives:

2x = 240

x = 120

The number of adults is 120.

Each child ticket costs a quarter of the adult ticket, so the cost of a child ticket is:

1/4 * £8 = £2

The total money made from child tickets is:

£2 * 80 = £160

The total money made from adult tickets is:

£8 * 120 = £960

Total money made from ticket sales is:

£160 + £960 = £1120

Hence, the total money made from ticket sales is £1120.

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Throughout the hour, 70 percentage of customers add chocolate creamer to their coffee.

Find the proportion of consumers who selected chocolate creamer and add up all of the customers who visited throughout the hour to determine the appropriate percentage.

The number of clients who selected chocolate creamer is calculated by dividing the total number of customers by 100.

Here it is,

For one hour, the manager of a coffee shop counted the number of patrons who added vanilla or chocolate creamer to their coffee.

The question given is:

                         Vanilla      Chocolate    

Age 18 - 30            2               6

Age 30 +                4               8      

2 + 4 + 6 + 8 Equals 20 clients in this instance.

6 + 8 = 14 is the number of clients who select chocolate creamer.

Customers that used chocolate creamer made up: [14/20] / 100 = 70%

As a result, 70% of consumers at that time add chocolate creamer to their coffee.

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The complete question is:

The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?

Answer:

70%

Step-by-step explanation:

i did the quiz lol

The required,
(a) The missing terms of the first sequence are -7, 6, and 19.
(b) The missing terms of the second sequence are 71, 88, and 105.
(c) The missing terms of the third sequence are 2, -6, and -14.

Arithmetic progression is the series of numbers that have common differences between adjacent values

To find the missing terms of each arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence:

an = a₁ + (n - 1)d

where an is the nth term, a₁ is the first term, n is the number of terms, and d is a common difference.

Sequence 1,

a₁ = -20, an = 19

n = ? (unknown)

d = (an - a1) / (n - 1)

19 = -20 + (n - 1)d
39 = (n - 1)d

d = 39 / (n - 1)

We also know that a₂, a₃, and a₄ are missing, and there are four terms in total. Therefore, n = 4.

d = 39 / (4 - 1) = 13

Using the formula, we can now find the missing terms:

a₂ = a₁ + d = -20 + 13 = -7

a₃ = a₂ + d = -7 + 13 = 6

a₄ = a₃ + d = 6 + 13 = 19

So the missing terms of the first sequence are -7, 6, and 19.

Similarly,

The missing terms of the second sequence are 71, 88, and 105.
The missing terms of the third sequence are 2, -6, and -14.

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Answer:

The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.

Plugging x=0 into the given function, we get:

f(0) = 320(0.90)^0 = 320(1) = 320

Therefore, the initial price of the store item was $320.

Answer:

8 small and 14 large is the answer

Step-by-step explanation: