each unit square of a $3\times 3$ grid of unit squares is to be colored either blue or red. for each square, either color is equally likely to be used. find the probability of obtaining a grid that does not have a $2\times 2$ red square.

The scale factor in scale drawing from figutre A to figure B is 4

In a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.

In the given scale drawing, the object is scaled up from 7 cm to 28 cm.

Therefore, the scale factor can be calculated as follows:

scale factor = size of object in drawing / size of corresponding object in real life

scale factor = 28 cm / 7 cm

scale factor = 4

So, the scale factor in this scale drawing is 4.

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The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.6321.

Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1.

The exponential probability distribution with a mean of 12 seconds is given by

f(x) = (1/12) × e^(-x/12)

where x represents the time between arrivals of vehicles.

To find the probability that the arrival time between vehicles is 12 seconds or less, we need to integrate the probability density function from 0 to 12

P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] f(x)dx

=  [tex]\int\limits^{12}_0[/tex]  (1/12) × e^(-x/12) dx

= [(-e^(-x/12))]_[0,12]

= (-e^(-12/12)) - (-e^(0/12))

= 1 - e^(-1)

≈ 0.6321

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The given question is incomplete, the complete question is:

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. What is the probability that the arrival time between vehicles is 12 seconds or less?

In this problem, we are given the angle A, and the side lengths a and b of triangle ABC. Using the   Geometry concept of Law of Sines, we can solve for the remaining angles and side lengths of the triangle. We find that sin(B) ≈ ∠B ≈ ° and ∠C ≈ °, and we can calculate that c ≈ 9.69. This gives us one possible triangle that satisfies the given conditions.

However, the problem states that there are two triangles that satisfy these conditions. To find the second triangle, we must first construct a triangle with angle A₁ = 180° - A and sides a₁ and b₁ such that a₁/b₁ = a/b. This is possible because the Law of Sines tells us that this ratio is constant for all three sides of a triangle. We then apply the Law of Sines to this new triangle to solve for its remaining parts. We find that sin(B₁) ≈ ∠B₁ ≈ ° and ∠C₁ ≈ °, and we can calculate that c₁ ≈ 12.02. This gives us the second possible triangle that satisfies the given conditions.

Now, to show that the areas of the two triangles are proportional to the sines of their respective angles C and C₁, we use the area formula for a triangle, which is 1/2 * base * height. The height of each triangle can be calculated using the sine of the angle opposite the base. Therefore, we have:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (1/2 * a * c * sin(C)) / (1/2 * a₁ * c₁ * sin(C₁))

We can simplify this expression by substituting a1/b1 for a/b and simplifying:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (a/b) * (c/c₁) * (sin(C)/sin(C₁))

Using the Law of Sines, we know that a/b = sin(A)/sin(B) and c/c₁ = sin(C)/sin(C₁), so we can substitute these values into our expression:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (sin(A)/sin(B)) * (sin(C)/sin(C₁)) * (sin(C)/sin(C₁))

Using the fact that the angles in a triangle sum to 180°, we can solve for sin(A) and sin(B):

sin(A) = sin(180° - B - C) = sin(B + C)

sin(B) = sin(180° - A - C) = sin(A + C)

Substituting these values into our expression, we get:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (sin(B + C)/sin(B)) * (sin(C)/sin(C₁)) * (sin(C)/sin(C₁))

Simplifying this expression, we get:

Area of ΔABC/ Area of ΔA₁B₁C₁ = sin(C)/sin(C₁)

Therefore, the areas of the two triangles are proportional to the sines of their respective angles C and C₁

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The time since the rock reached its closure temperature is approximately 579.8 years. When the rock was discovered, it had 4.375 grams of europium-151.

To find the time since the rock reached its closure temperature, we can use the following formula

t = t(1/2) * log(N0/Nt)

where t is the time elapsed, t(1/2) is the half-life, N0 is the initial amount of the isotope, and Nt is the amount of the isotope at the time it was discovered.

Substituting the given values, we get

t = 96.6 * log(5/0.625) ≈ 579.8 years

Therefore, the time since the rock reached its closure temperature is approximately 579.8 years.

To find the amount of europium-151 in the rock when it was discovered, we can use the fact that the total amount of samarium-151 and europium-151 in the rock is constant.

Since the rock originally contained 5 grams of samarium-151, it must have contained 5 - 0.625 = 4.375 grams of europium-151 when it was discovered.

Therefore, the rock had 4.375 grams of europium-151 when it was discovered.

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Answer:

3p^2 -6p +3

Step-by-step explanation:

(3p-3) ( p-1)

We can FOIL

first : 3p*p = 3p^2

outer: 3p * -1 = -3p

inner: -3*p = -3p

last: -3*-1 = 3

Add them together : 3p^2 -3p -3p +3

                                  3p^2 -6p +3

Answer:

4th answer is correct

Step-by-step explanation:

( 3p - 3 ) ( p - 1 )

Multiply each term in ( p - 1 ) by 3p and -3.

3p ( p - 1 ) - 3 ( p - 1 )

Solve the brackets.

3p² - 3p - 3p + 3

Combine like terms.

3p² - 6p + 3

A hexagonal pyramid has seven vertices.

A hexagonal pyramid contains 12 edges.

A hexagonal pyramid has seven faces.

A hexagonal pyramid is a type of pyramid that exists. A hexagonal pyramid has a hexagonal foundation and isosceles triangles as the faces that join the pyramid together at the top.

A hexagonal pyramid is a 3D pyramid with a hexagonal foundation and sides or faces in the shape of isosceles triangles that form the hexagonal pyramid at the apex or top of the pyramid. A hexagonal pyramid has six sides and six isosceles triangular lateral faces. Heptahedron is another name for a hexagonal pyramid. A hexagonal pyramid has seven faces, twelve edges, and seven vertices. For your convenience, an image of a hexagonal pyramid is provided below.

A hexagonal pyramid has seven vertices in toa

\x linking the triangle edges to the primary vertex and six base edges.

A hexagonal pyramid has seven faces, one for each side of the triangle, and one base.

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The Monthly Budget for fast food is Option A. $136.

To determine how much money you should budget for fast food, we need to calculate the total amount of money you spend on fast food each week. To do this, we simply multiply the cost of one fast food meal by the number of meals you buy in a week, which is four in this case.

$850 x 4 = $3400 per week

Next, we need to figure out how much money you spend on fast food per month. To do this, we need to multiply the weekly amount by the number of weeks in a month. Most months have around four weeks, so we will use that as an estimate.

$3400 x 4 = $13600 per month

Therefore, the answer is Option A. $136. You should budget around $136 per month for fast food if you buy it four times a week and it costs you about $850 each time.

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Marcus is using a plant food to fertilize his garden his garden is a rectangle Marcus uses 1 cup of plant food for every square yard of his garden.

To solve it, we need to first find the area of Marcus's garden in square yards, and then multiply it by 1 cup of plant food per square yard. Finally, we need to convert the total cups to ounces using the given conversion rate.

Let the length of Marcus's garden is l yards and the width is w yards. Then the area of his garden in square yards is

A = lw.

If Marcus uses 1 cup of plant food per square yard, then he will use A cups of plant food in total.

To convert cups to ounces, we can use the given conversion rate of 4 cups per 28 ounces.

1 cup = 28/4 ounces

Therefore, the total weight of plant food Marcus uses in ounces is

Total weight = A * (28/4) ounces

By substituting A = lw, we get

Total weight = lw * (28/4) ounces

Total weight = 7lw ounces

Hence, the total weight of plant food Marcus uses to fertilize his garden is 7 times the product of the length and width of his garden, measured in yards.

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Therefore, the solution to the system of equations is: x = 13/12, y = -3/4 that is option C.

In mathematics, an equation is a statement that asserts the equality of two expressions, separated by an equals sign (=). The expressions on either side of the equals sign are referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between variables and to solve problems.

Here,

To solve the system of equations:

4y + 12x = 10 ...(1)

2y - 6x = -8 ...(2)

We can use the method of elimination or substitution.

Method of elimination:

We can eliminate x by multiplying equation (2) by 2 and adding it to equation (1) to obtain:

4y + 12x = 10

(4y - 12x = -16)

8y = -6

Dividing both sides by 8, we get:

y = -6/8

y = -3/4

Substituting this value of y in equation (1), we get:

4(-3/4) + 12x = 10

Simplifying and solving for x, we get:

-3 + 12x = 10

12x = 13

x = 13/12

So the answer is C. x = 13/12, y = -3/4.

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If the perimeter of a rectangular living room is 38 meters, the length of the living room is 105 meters.

The perimeter of a rectangle is the sum of the lengths of all its sides. Let's denote the length of the living room as "L". The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

We know that the width of the living room is 9 meters, and the perimeter is 38 meters. Substituting these values in the formula, we get:

38 = 2(L + 9)

Dividing both sides by 2, we get:

19 = L + 9

Subtracting 9 from both sides, we get:

L = 105

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By Tangent function, to the nearest foot, the plane has flown approximately 28,333 feet.

A closed, two-dimensional shape, a circle is also a curve. The radius of the circle or the line connecting the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying figure.

We are aware of our side and degree. We must determine how far the aircraft has traveled.

To determine how far the plane has traveled, we can utilize the sine function. Keep in mind that the sine function's definition is

tan(θ) = opposite/adjacent = height/distance.

tan(3) = 850/d

Solving for d, we get:

d = 850/tan(3)

d ≈ 28,333 feet

Tangent figure given below:

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The protein requirement may be slightly higher, around 1.0 to 1.2 g/kg, this would put his daily protein needs between 72.6 and 87.1 grams.

As a healthy 20-year-old college student who jogs at a moderate pace 3 days per week for 20 minutes, John has an active lifestyle that requires a certain amount of protein to maintain his body.

Protein is an essential nutrient that is needed for the growth and repair of muscles, bones, and other tissues in the body.
According to the Dietary Reference Intake (DRI), the recommended daily allowance of protein for an adult male is 56 grams per day.

However, this amount can vary depending on a person's body weight, activity level, and other factors.
In John's case, he weighs 160 lbs and exercises moderately 3 days per week. Based on this information, he would need approximately 72-80 grams of protein per day.

This is because athletes and people who exercise regularly need more protein to repair and build muscle tissue.
To meet his daily protein requirements, John can include protein-rich foods in his diet such as lean meats, fish, eggs, dairy products, nuts, and beans.

It is also important for him to spread out his protein intake throughout the day rather than consuming all of it in one meal.
John needs approximately 72-80 grams of protein per day to support his active lifestyle and maintain his overall health.

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Answer:

Side AC Is Parrellel to BD

Side BA is Parallel to DC

Step-by-step explanation:

Parallel is the opposing side.

Sam will have to borrow $7840.

If Sam puts 20% down on a car that costs $9800, the down payment would be 20% of $9800 which is $1960.

The amount he will have to borrow is the difference between the cost of the car and the down payment. So, $9800 - $1960 = $7840.

This calculation can be done by first finding the percentage of the total cost that is required as a down payment and then subtracting that amount from the total cost to find the remaining amount that needs to be borrowed.

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Sev needs to run 9 miles as per the below calculations to complete his target.

The target that Sev needs to achieve is 18 miles in a week. A week has 7 days. Sev is already done running for 5 days.
Day 1: 1.4 miles

Day 2: 1.4 miles

Day 3: 1.4 miles

Day 4: 2.4 miles

Day 5: 2.4 miles

Thus, Sev has run for 1.4*3 = 4.2 miles in the first 3 days.

Sev has run for 2.4*2 = 4.8 miles in the last 2 days.

So far, she has run 4.2 + 4.8 = 9 miles. Since her goal is to run 18 miles, she needs to run an additional: 18 - 9 = 9 miles to meet her goal.

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Answer:

y = 2.50x + 5.25

FORMULA FOR SLOPE INTERCEPT

y = mx + b

IM SO SORRY IF THIS DOES NOT MAKE SENSE!

The quality of milk reaching the ultimate consumer is largely determined at the plant, where processing and handling occurs. a

Once milk is collected from the farm, it is transported to processing plants where it undergoes a series of treatments to ensure that it is safe for consumption.

This includes pasteurization, homogenization, and standardization.
The pasteurization process involves heating the milk to a specific temperature for a certain amount of time to kill harmful bacteria.

Homogenization helps to evenly distribute the milk's fat content, while standardization ensures that the milk meets certain regulatory requirements for fat content and nutritional value.
The plant, milk undergoes rigorous quality control testing to ensure that it meets certain standards.

This includes testing for bacterial count, somatic cell count, and antibiotic residue.

Any milk that fails to meet these standards is discarded.
The USDA and FDA also play a role in ensuring that milk reaching consumers is of high quality.

The USDA sets standards for milk production, while the FDA regulates the use of antibiotics and other drugs in milk production.

The primary responsibility for ensuring milk quality rests with the processing plant.
The USDA and FDA do play a role in ensuring the quality of milk reaching consumers, the majority of the responsibility lies with the processing plant.

It is at the plant where the milk undergoes treatments to ensure that it is safe for consumption and undergoes rigorous quality control testing to meet certain standards.

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The probability of rolling an even number on a dice is 1/2, since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes (1, 2, 3, 4, 5, and 6).

The probability of landing on tails when flipping a coin is also 1/2, since there are only two possible outcomes (heads or tails) and they are equally likely.

To find the probability of both events happening together, we need to multiply their probabilities:

1/2 (probability of rolling an even number) x 1/2 (probability of landing on tails) = 1/4

Therefore, the probability of rolling an even number on a dice and landing on tails when flipping a coin is 1/4 or 0.25 (25%).

~~~Harsha~~~

De acuerdo a la información, el área total de la placa es de 10800 centímetros cúbicos.

El área que debe cubrir la placa es un área en forma de rectángulo. Por está razón, el área que se va a cubrir puede ser calculada utilizando la siguiente formula:

Área = largo x altura

De acuerdo a lo anterior, encontremos el área reemplazando los valores correspondientes:

60 cm x 180 cm = 10800 centímetros cúbicos

Por lo tanto, el área de la zona a cubrir por la placa es de  10800 centímetros cúbicos.

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation [tex]x_1-x_2[/tex], we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

[tex]1(x_1=22.8)[/tex] and deducting it from the mean of Sample [tex]2(x_2=20.1)[/tex].

With the use of the equation [tex]df=n_1+n_2-2[/tex], it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because [tex]n_1[/tex] = 20 and [tex]n_2[/tex] = 30.

We must apply the formula to determine the margin of error at 95% confidence [tex]ME=t*\sqrt[s]{n}[/tex].

The sample standard deviation (s) is equal to the average of [tex]s_1[/tex] and [tex]s_2[/tex] (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of [tex]n_1[/tex] and [tex]n_2[/tex] (25). When these values are entered into the formula, we get [tex]ME=1.67*\sqrt[3.4]{25}=1.7[/tex].

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means [tex]CI=x_1-x_2+/-ME[/tex].

The confidence interval's bottom limit in this instance is [tex]x_1-x_2-ME2.7-1.7=0.0[/tex] and the upper limit is [tex]x_1+x_2+ME=2.7+1.7=5.4[/tex].

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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There are 36 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To find the number of ways the letters d, i, g, i, t can be arranged so that the two i's are not next to each other, follow these steps:
Consider the four non-i letters: d, g, t.

There are 3! (3 factorial) ways to arrange these letters, which is equal to 3 x 2 x 1 = 6 ways.

Since we want to prevent the two i's from being next to each other, we can think of placing them in the "gaps" between the non-i letters.

There are 4 possible gaps for the i's to be placed: (i) d (i) g (i) t (i).
Since there are two i's, we need to choose 2 of the 4 gaps to place them in.

This can be done in 4C2 ways (combination), which is equal to 4! / (2! x (4-2)!) = 6 ways.
Multiply the number of ways to arrange the non-i letters (step 1) with the number of ways to place the i's (step 3): 6 x 6 = 36.

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There are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To arrange the letters d, g, i, t, and i so that the two i's are not next to each other, follow these steps:

Step 1: Treat the two i's as one entity for now (denoted as [i]). So, we have 4 entities: d, g, t, and [i].
Step 2: Arrange these 4 entities (d, g, t, and [i]) in any order. There are 4! (4 factorial) ways to do this, which is 4 x 3 x 2 x 1 = 24 ways.
Step 3: Now, we need to separate the two i's. There are 3 spaces between the other letters (d, g, and t) where we can place the second i.
For example: if the arrangement is d-[i]-g-t, the second i can be placed in any of the three spaces indicated by the dashes.
Step 4: For each of the 24 arrangements from Step 2, there are 3 possible ways to place the second i. So, the total number of arrangements is 24 x 3 = 72 ways.

Thus, there are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

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The actual distance from Marcus's house to the peak is 0.328 miles and the Skye's distance is 0.330 miles

Given that

The actual distance between Marcus and Skye's houses is 1 1/2 miles.

So, we have

Ratio = 0.246 : 1 1/2

Scale : Actual = 0.246 : 1 1/2

For Marcus, we have

2 : Actual = 0.246 : 1 1/2

So, we have

Actual = 0.246/(1 1/2) * 2

Evaluate

Actual = 0.328

For Skye, we have

2.015 : Actual = 0.246 : 1 1/2

So, we have

Actual = 0.246/(1 1/2) * 2.015

Evaluate

Actual = 0.330

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The cosine function that could model the height of the Ferris wheel is given as follows:

y = cos(4π).

The cosine function is defined as follows:

y = cos(Bx).

In which the period of the function is given by 2π/B.

The car completes 4 whole rotations in a time period of 2 minutes, hence it completes 2 rotations per minute, thus the period of the function is of 0.5 minutes.

Considering the period of 0.5 minutes, the coefficient B is given as follows:

2π/B = 0.5

0.5B = 2π

B = 2π/0.5

B = 4π.

Hence the function is given as follows:

y = cos(4π).

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The amount of fluid that a person should drink per day can vary depending on factors such as their age, sex, weight, activity level, and climate.

The Institute of Medicine recommends that men should consume about 3.7 liters (125 ounces) of fluid per day, while women should consume about 2.7 liters (91 ounces) of fluid per day. This includes fluid from all sources, including water, other beverages, and food.

It is important to note that individual fluid needs may vary and may be influenced by factors such as health conditions, medications, and pregnancy or breastfeeding. It is always a good idea to consult with a healthcare professional to determine the appropriate amount of fluid intake for your specific needs.

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A client's daily fluid intake should be around 3,700 ml for men and 2,700 ml for women, keeping in mind that individual needs may vary.

Remember to round to the nearest whole number if necessary.

As a concise answer bot, I cannot provide a 200-word response.

How many ml of fluid a client should drink per day, we need to consider general guidelines for daily fluid intake.
The general recommendation for daily fluid intake is approximately:
- For men: 3,700 ml (about 13 cups)
- For women: 2,700 ml (about 9 cups)
These amounts include fluids from all sources, such as water, beverages, and food.

Please note that individual needs may vary depending on factors such as age, activity level, and climate.

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Answer:

It'd be 4300 mililiters

Step-by-step explanation:

3.8× 100= 3800

3800+500=4300

Answer:

k is usually called the spring constant

Step-by-step explanation:

sorry if its not right, that is just what i have learned.

have a good day !!!

only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

How to solve the question?

The mathematical term "indirectly proportional" refers to a relationship in which two variables are related in such a way that when one increases, the other decreases, and vice versa. In other words, the two variables vary in opposite directions.

Out of the four equations given, only one shows an indirect proportional relationship. This equation is:

y=1/x

In this equation, y and x are indirectly proportional. As x increases, the value of 1/x decreases, and therefore, the value of y decreases as well. Similarly, as x decreases, the value of 1/x increases, and the value of y increases as well. This relationship is commonly known as an inverse relationship, where the two variables vary in opposite directions.

On the other hand, the other three equations do not show an indirect proportional relationship. The equation y=5x shows a direct proportional relationship, where y increases as x increases and vice versa. The equation y=-2x+1 is a linear equation with a negative slope, where y decreases as x increases, and y increases as x decreases. Lastly, the equation y=3x+5 is also a linear equation with a positive slope, where y increases as x increases, and y decreases as x decreases.

In summary, only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

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The surface area of the rectangular prism which is given above would be = 130ft²

To calculate the surface area of the rectangular prism the formula that should be used;

=2( wl+hl+wh)

where;

w = 5ft

l = 10ft

h = 1 ft

surface area = 2(5×10+1×10+5×1)

= 2(50+10+5)

= 2×65 = 130ft²

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If on Tuesday, Friday,  Saturday, and Sunday, she collected 43 cans each day. Tina got $14.15 for her cans last week.

Tina collected 37 cans on Monday, Wednesday, and Thursday, which is a total of 37 x 3 = 111 cans. She collected 43 cans on Tuesday, Friday, Saturday, and Sunday, which is a total of 43 x 4 = 172 cans. The total number of cans she collected last week is 111 + 172 = 283 cans.

Since Tina gets 5 cents for every can she recycles, she made 5 x 283 = $14.15 for recycling all of the cans she collected last week.

Therefore, Tina got $14.15 for her cans last week.

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Complete question is:

Tina collects cans to recycle at the supermarket. Last week, on Monday, Wednesday and Tursday, she collected 37 cans each day. On Tuesday, Friday,  Saturday, and Sunday, she collected 43 cans each day. Tina gets 5 cents for every can she recycles.  How much money did Tina get for her cans last week?