Standard 6.NS.B.3:
15. A recipe for 8 servings calls for 3/4 cup
of sugar. How much sugar is needed for 10
servings?
2. Can anyone pls help me? this is due today

Determine whether the scalar triple product of the vectors formed by the points a, b, and c with the vector formed by the point d is equal to zero. If so, the points lie in the same plane; otherwise, they do not.

To determine whether the points a, b, c, and d lie in the same plane, we can use the scalar triple product. The scalar triple product of three vectors is defined as the dot product of one vector with the cross product of the other two vectors.

Let's choose any three of the given points as our vectors. Suppose we take a, b, and c as the three vectors. Then the scalar triple product is:

a · (b x c)

= (1, 3, 2) · [(2, -3, 8) x (6, 0, 1)]

= (1, 3, 2) · (-3, 46, 18)

= -3 + 138 + 36

= 171

The scalar triple product is non-zero, which means that the three vectors are not coplanar. Therefore, the points a, b, and c do not lie in the same plane.

Similarly, we can calculate the scalar triple product for the other possible combinations of three points. If we find that the scalar triple product is zero for all combinations, then the four points a, b, c, and d lie in the same plane. However, in this case, we have already found that the scalar triple product is non-zero for one combination, so we can conclude that the points do not lie in the same plane.

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The solution is: The measure of angle x is 74°

Here,

we know that

The inscribed angle measures half of the arc that comprises

so

∠ABC=(1/2)[arc ADC]

substitute the given values

150°=(1/2)[4x+4]

300°=[4x+4]

4x=300-4

4x=296

x=74°

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complete question:

Find the value of x if m arc ADC = (4x + 4)° and m angle ABC = 150°.

The following parts can be answered by the concept of Standard deviation.

a. We find that P(X ≤ 86) is approximately 0.0004.

b. We find that P(80 ≤ X ≤ 100) is approximately 0.1151.

c. We find that x such that P(X ≤ x) = 0.40 corresponds to a z-score of approximately -0.25. Therefore, x is approximately μ + (z-score × σ) = 120 + (-0.25 × 20) = 115.

d. Using Table 1, we find that x such that P(X > x) = 0.90 corresponds to a z-score of approximately 1.28. Therefore, x is approximately μ + (z-score × σ) = 120 + (1.28 × 20) ≈ 146.4.

a. To find P(X ≤ 86), we first need to calculate the z-score, which is given by (86 - μ) / σ. Plugging in the given values, we get (86 - 120) / 20 = -1.7. Using Table 1, we look for the closest z-score to -1.7, which is -1.69, and corresponding to it, we find the probability 0.0459. However, since we need to find P(X ≤ 86), we need to add the area to the left of -1.69 in the table, which is 0.0004.

b. To find P(80 ≤ X ≤ 100), we first need to calculate the z-scores for 80 and 100 using the same formula as above. The z-score for 80 is (80 - 120) / 20 = -2, and the z-score for 100 is (100 - 120) / 20 = -1. Plugging these values into Table 1, we find the probabilities corresponding to -2 and -1, which are 0.0228 and 0.1587 respectively. To find the probability for the range 80 ≤ X ≤ 100, we subtract the probability corresponding to -2 from the probability corresponding to -1, which is 0.1587 - 0.0228 = 0.1359.

c. To find x such that P(X ≤ x) = 0.40, we need to find the z-score corresponding to a cumulative probability of 0.40 in Table 1. The closest z-score to 0.40 is -0.25. We can then use the formula z = (x - μ) / σ and rearrange it to solve for x: x = μ + (z-score × σ) = 120 + (-0.25 × 20) = 115.

d. To find x such that P(X > x) = 0.90, we first need to find the z-score corresponding to a cumulative probability of 0.90 in Table 1, which is approximately 1.28. We can then use the formula z = (x - μ) / σ and rearrange it to solve for x: x = μ + (z-score × σ) = 120 + (1.28 × 20) ≈ 146.4, rounded to one decimal place. Therefore, x is approximately 146.4.

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Answer:

Step-by-step explanation:

To solve the equation x/6=(x+10)/42 for x, we can cross-multiply and simplify:

x/6 = (x+10)/42

42x = 6(x+10) (multiply both sides by 42)

42x = 6x + 60 (distribute on the right side)

36x = 60 (subtract 6x from both sides)

x = 5/3 (divide both sides by 36)

Now that we have found x, we can substitute it into the expression 6x+10 and evaluate:

6x + 10 = 6(5/3) + 10 = 10 + 10 = 20

Therefore, 6x+10 equals 20 when x/6=(x+10)/42 and x is 5/3.

Answer:

04x=24

Step-by-step explanation:

04x=24

divide both sides by 4 to let x stand alone

04x÷4=24÷4

x=6

We need to calculate the probability using the Cumulative Normal Distribution Table. We are given the population proportion (p=0.326), the sample size (n=140), and we want to find the probability that the sample proportion is less than 0.29.

First, we need to calculate the standard error (SE) using the formula:
SE = sqrt((p * (1 - p)) / n)
SE = sqrt((0.326 * (1 - 0.326)) / 140)
SE ≈ 0.0386
Next, we calculate the z-score using the formula:
z = (sample proportion - population proportion) / SE
z = (0.29 - 0.326) / 0.0386
z ≈ -0.9338
Now, we use the Cumulative Normal Distribution Table to find the probability associated with the z-score of -0.9338. The table value is approximately 0.1753.
So, the probability that the sample proportion of tax returns for which no tax was paid is less than 0.29 is 0.1753.

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When we fail to reject the null hypothesis, it means we reject the alternative hypothesis.

When we fail to reject the null hypothesis, it means that we do not have enough evidence to support the alternative hypothesis. Another theory implies that there is a significant relationship between the two variables. Whereas, the null hypothesis states that there is no relationship between the two variables. In statistics, we often come across different opinions.

In general, the purpose of alternative hypothesis testing is to show that, under certain conditions, there is sufficient evidence to support the null hypothesis rather than certain test results (null hypothesis). It is often followed as a research hypothesis because it is based on However, research hypotheses sometimes overlap with the null hypothesis. Therefore, it does not necessarily mean that we accept the alternative hypothesis, but rather we simply cannot reject the null hypothesis.

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The length of DE is equal to length CE since their corresponding angles are equal.

To prove that line DE is equal to line CE, we will take the following steps as shown below.

In the given figure;

line AD = line BC

angle ADC = angle BCD

let the line DB divide angle ADC equally and let line AC divide angle BCD equally.

then our new triangle becomes EDC

so angle EDC = angle ECD, since the angles are divided equally.

If the two angles (m∠EDC = m∠ECD), then their lengths must be equal since the triangle forms an isosceles triangle.

So length DE = length CE, proved.

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we have: COP = Q / P_in = -1200 W / 500 W

= -2.4.

what is unit rate?

A unit rate is a ratio in which the denominator is 1. It is a rate that compares a quantity to one unit of another quantity.  

To find the rate of cooling, we need to calculate the heat removed per unit time, which is given by:

Q = P_in - P_out

where Q is the rate of cooling, P_in is the power input, and P_out is the power discarded to the ambient.

So, we have:

Q = P_in - P_out

= 500 W - 1.7 kW

= -1200 W (note that the negative sign indicates heat removed)

Therefore, the rate of cooling is 1200 W.

To find the coefficient of performance, we use the formula:

COP = Q / P_in

where COP is the coefficient of performance, Q is the rate of cooling, and P_in is the power input.

So, we have:

COP = Q / P_in

= -1200 W / 500 W

= -2.4

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If we give a cup of water to a very thirsty person and double what is left, the individual will be unable to finish what is left.

The expected result will depend on the quantity of water present in the first cup. If the cup of water is small, the thirsty person may not be satisfactorily hydrated by taking three cups.

However, if the size of the cup is large and the water content is also large, the individual will be hydrated after just a cup of water. So, the response to this question depends on the size of the cup and the amount of water contained therein.

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Therefore , the solution of the given problem of surface area comes out to be Height =11/7 yards and Length = 79.5 yards

The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

One parallelogram's area is equal to 267 / 2 = 133.5 square yards.

Thus, by dividing the area by the height of a parallelogram, we may determine its base:

One parallelogram's base is equal to its area times its height, or

=> 133.5 / (11/7)

=> 103.5 square yards

We can use the formula for a parallelogram's area to get the length of one side of the mirror now that we know its base and height:

=> Base x Height = parallelogram's area.

One mirror's side's length is calculated as follows:

=>  base / height

=> (103.5 / (11/7)) = 79.5 yards

The other side of the mirror is 79.5 yards long because it is composed of two parallelograms that are congruent with one another.

As a result, the mirror's measurements are:

Height =11/7 yards.

Length = 79.5 yards

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The radius of the cylinder is 3. 95 cm

The formula for calculating the volume of a cylinder is expressed with the equation;

V = πr²h

Such that the parameters are;

From the information given, we have;

Substitute the values

1225 = 3.14× r² × 25

Multiply the values, we get;

1225 = 78.5r²

Divide by the coefficient

r² = 15. 60

Find the square root of both sides

r = 3. 95 cm

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the value of the given iterated integral is 0.

To evaluate the iterated integral 3 2 4z 0 ln(x) 0 xe−y dy dx dz, we need to follow the order of integration dz, then dx, then dy.

Starting with dz:

∫ from 0 to 4 of ∫ from 0 to ln(2z) of ∫ from 0 to 3xe^(-y) dy dx dz

Simplifying the middle integral with respect to y:

∫ from 0 to 4 of ∫ from 0 to ln(2z) of -3x(e^(-ln(2z))-e^(-0)) dx dz

= ∫ from 0 to 4 of ∫ from 0 to ln(2z) of -3x(2z-1) dx dz

= ∫ from 0 to 4 of [-3/2 * x^2 * (2z-1)] evaluated from 0 to ln(2z) dz

= ∫ from 0 to 4 of [-3/2 * (ln(2z))^2 * (2z-1)] dz

= -3/2 * ∫ from 0 to 4 of (ln(2z))^2 * (2z-1) dz

Using integration by substitution with u = ln(2z), du/dz = 1/(z*ln(2)), and dz = du/(ln(2)), we get:

= -3/2 * ∫ from 0 to ln(8) of (u^2/ln^2(2)) * (2e^u - 1) du

= -3/2 * [(2u^2e^u)/ln^2(2) - (2u^2)/ln^4(2) - (2ue^u)/ln^2(2) + (2u)/ln^4(2) - (e^u)/ln^2(2)] evaluated from 0 to ln(8)

= -3/2 * [(64e^ln(8))/ln^2(2) - (64)/ln^4(2) - (8e^ln(8))/ln^2(2) + (8)/ln^4(2) - (e^ln(8))/ln^2(2)] + 3/2 * [0]

= -3/2 * [48 + 32/ln^2(2) - 8 - 8/ln^2(2) - 1/ln^2(2)]

= -3/2 * [40 + 24/ln^2(2)]

= -60 - 36/ln^2(2)

Therefore, the value of the iterated integral 3 2 4z 0 ln(x) 0 xe−y dy dx dz is -60 - 36/ln^2(2).
To evaluate the given iterated integral, which is ∫₀³∫₀²∫₀ˡⁿ(x) (4z * x * e^(-y) dy dx dz), we will solve it step by step, starting with the innermost integral.

1. First, we evaluate the integral with respect to y:

∫₀ˡⁿ(x) (4z * x * e^(-y) dy) = -4zx(e^(-y))|₀ˡⁿ(x) = 4zx(e^(-ln(x)) - e^0) = 4zx(1/x - 1)

2. Next, we evaluate the integral with respect to x:

∫₀² (4zx(1/x - 1) dx) = 4z ∫₀² (1 - x) dx = 4z [x - (1/2)x²]|₀² = 4z(2 - 2) = 0

3. Finally, we evaluate the integral with respect to z:

∫₀³ (0 dz) = 0

Thus, the value of the given iterated integral is 0.

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The allele frequency for the f allele in this population's gene pool is 0.6. This means that out of all the alleles in the gene pool, 60% of them are the f allele.

The total number of rabbits carrying the f allele (60) can be divided by the total number of alleles in the gene pool to arrive at this figure (100).

As a result, 0.6 or 60% of the population's gene pool contains the f allele. With frequencies of 0.2 and 0.2, respectively, for the other two alleles, ff and ff, it may be concluded that the f allele is more prevalent.

This also indicates that the f allele, which has the highest frequency, is the most prevalent allele in the population.

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The inequality for the provided sentence is (x+9)/(-4) >-2, and x>-1 is the obtained inequality's solution.
Given that, a maximum of -2 results when a number multiplied by 9 and split by -4.

What is inequality?
In mathematics, inequality is a concept that describes a relationship between two values. It is commonly expressed using symbols such as ">", "<", "≥", "≤", or "≠", and can be used to compare two numbers, variables, expressions, or sets. Inequality can be used to describe a range of values, such as "x is greater than 0 but less than 10", or "x is not equal to 0". Inequality is an important concept in mathematics, and it is used in many areas, such as problem solving, analysis, and statistics.

Let x be the unknowable integer.

x+9 is the result of adding 9 to an integer.

Divided by -4, the outcome is (x+9)/.(-4)

Up to a limit of -2

(x+9)/(-4) >-2

On both sides of the discrepancy, multiply -4 to get

x+9>8

Subtract  9 on both the sides of inequality, we get

x>-1

Therefore, the inequality for the given phrase is (x+9)/(-4) >-2 and the solution for the inequality obtained is x>-1.

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Answer:

To find a circle given its diameter, you can use the following formula:

C = πd

where C is the circumference of the circle, d is the diameter, and π (pi) is a mathematical constant approximately equal to 3.14.

If you want to find the area of the circle, you can use the following formula:

A = πr²

where A is the area of the circle, and r is the radius (which is half the diameter).

Answer:

area of circle or round of it?

p > 1 (Option B)

To determine all values of p for which the infinite series Σ n=1 [infinity] n/(n^p+1) converges, we can use the p-series convergence test. This test states that the series converges if p > 1.

Your answer: The infinite series Σ n=1 [infinity] n/(n^p+1) converges for all values of p where p > 1 (Option B).

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From the given fractions change in percentage is 50 percent.

The two given fractions are 1/3 and 1/6.

Difference of given fractions = 1/3 - 1/6

= 1/6

The percentage change = Difference of fractions/Original fraction ×100

= 1/6 ÷ 1/3

= 1/6 × 3/1

= 0.5 ×100

= 50%

Therefore, from the given fractions change in percentage is 50 percent.

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In mathematics, the focus point is a special point related to a curve or shape. The method for finding the focus point depends on the specific curve or shape in question.

Here are a few examples of finding focus points:

For a parabola, the focus point is a fixed point that lies on the axis of symmetry and is equidistant from the vertex and the directrix. The focus point is given by the formula (h, k + 1/4a), where (h, k) is the vertex and a is the distance between the vertex and the directrix.

For an ellipse, the focus points are the two points on the major axis that are equidistant from the center. The distance from the center to each focus point is given by c = ✓(a² - b²), where a is the length of the major axis and b is the length of the minor axis. The focus points are then located at (h + c, k) and (h - c, k), where (h, k) is the center of the ellipse.

For a hyperbola, there are two focus points that are equidistant from the center. The distance from the center to each focus point is given by c = ✓(a² + b²), where a is the distance from the center to each vertex and b is half the distance between the two branches of the hyperbola. The focus points are then located at (h + c, k) and (h - c, k), where (h, k) is the center of the hyperbola.

In general, the focus point of a curve or shape can be found by using its definition and properties. It is always a good idea to consult a reference or textbook for specific formulas and techniques.

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The total area of the figure is 216 m².

What is a quick rectangle answer?

A square shape is a kind of quadrilateral that has its equal sides equivalent to one another and all the four vertices are equivalent to 90 degrees. Consequently, it is likewise called an equiangular quadrilateral. A parallelogram is another name for a rectangle because its opposite sides are parallel and equal.

The rectangle has a length of 8 meters and a width of 18 meters, so its area is:

8 meters × 18 meters = 144 square meters

The triangle has a base of 18 meters and a height of 8 meters, so its area is:

(1/2) × 18 meters × 8 meters = 72 square meters

The total area of the six-sided composite figure is the sum of the areas of the rectangle and the triangle:

144 square meters + 72 square meters = 216 square meters

Therefore, the total area of the figure is 216 m².

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Answer:

4 + 9 = 13

Step-by-step explanation:

Start by prime factorizing 108. 108 is equal to [tex]2^2 \cdot 3^3[/tex]. This conveniently makes the a and b we need, as we are looking for [tex]a^2 \cdot b^3[/tex]. We get [tex]a=2,b=3[/tex]. Now, plug this into [tex]2a+ 3b[/tex]. We get [tex]2 \cdot 2 + 3 \cdot 3 = 4 + 9 = 13[/tex].

The true velocity of the vector of drone is V = -4i + 4j

Given data ,

Let the velocity of a drone relative to the air is modeled by v = 3i - j

Now , the drone encounters wind with velocity modeled by w = -7i + 5j

And , The true velocity vector of the drone, taking into account both the velocity of the drone relative to the air and the velocity of the wind, is the vector sum of the drone's velocity and the wind's velocity.

Given the velocity of the drone relative to the air as v = 3i - j, and the velocity of the wind as w = -7i + 5j, we can add these vectors together to obtain the true velocity vector of the drone:

v + w = (3i - j) + (-7i + 5j)

To add vectors, we add their corresponding components. In this case, adding the i-components and j-components separately, we get:

(3i - 7i) + (-1j + 5j) = -4i + 4j

Hence , the component vector is V = -4i + 4j

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To solve these problems, we need to first find the total number of possible combinations of six integers that can be selected from the given range of positive integers. This can be found using the formula for combinations:

n C r = n! / r!(n-r)!

where n is the total number of integers in the range and r is the number of integers to be selected (in this case, r = 6).

A. For integers not exceeding 40, we have n = 40. So, the total number of possible combinations of six integers is:

40 C 6 = 40! / 6!(40-6)! = 3,838,380

Now, we need to find the probability of selecting none of the correct six integers. Since there are six correct integers, there are 34 incorrect integers in the range. So, the probability of selecting none of the correct six integers is:

34 C 6 / 40 C 6 = 1,090,584 / 3,838,380 = 0.2844

B. For integers not exceeding 48, we have n = 48. So, the total number of possible combinations of six integers is:

48 C 6 = 48! / 6!(48-6)! = 12,271,512

Now, we need to find the probability of selecting none of the correct six integers. Since there are six correct integers, there are 42 incorrect integers in the range. So, the probability of selecting none of the correct six integers is:

42 C 6 / 48 C 6 = 2,251,799 / 12,271,512 = 0.1836

C. For integers not exceeding 56, we have n = 56. So, the total number of possible combinations of six integers is:

56 C 6 = 56! / 6!(56-6)! = 32,468,436

Now, we need to find the probability of selecting none of the correct six integers. Since there are six correct integers, there are 50 incorrect integers in the range. So, the probability of selecting none of the correct six integers is:

50 C 6 / 56 C 6 = 1,081,575 / 32,468,436 = 0.0333

D. For integers not exceeding 64, we have n = 64. So, the total number of possible combinations of six integers is:

64 C 6 = 64! / 6!(64-6)! = 19,068,840

Now, we need to find the probability of selecting none of the correct six integers. Since there are six correct integers, there are 58 incorrect integers in the range. So, the probability of selecting none of the correct six integers is:

58 C 6 / 64 C 6 = 170,544 / 19,068,840 = 0.0089

Therefore, the probability of selecting none of the correct six integers decreases as the range of positive integers increases.

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The resulting function 1 unit is y=6e⁵ˣ + 1.

To understand how to vertically compress, reflect across the y-axis, and shift a function, we first need to understand what each of these transformations does to a function individually.

Vertically compressing a function by a factor of k means multiplying the output (y) of the function by k. In this case, the function y = e⁻⁵ˣ will be compressed by a factor of 6, so the new function will be y = 6e⁻⁵ˣ.

Reflecting a function across the y-axis means switching the signs of the x-values. In this case, the function y = 6e⁻⁵ˣ will be reflected across the y-axis to create y = 6e⁵ˣ.

Shifting a function up 1 unit means adding 1 to the output (y) of the function. In this case, the function y = 6e⁵ˣ will be shifted up 1 unit to create y = 6e⁵ˣ + 1.

Therefore, the resulting function after vertically compressing by a factor of 6, reflecting across the y-axis, and shifting up 1 unit is y = 6e⁵ˣ + 1.

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Answer:

x=21

Step-by-step explanation:

Tales Theorem:

TW/TU=TV/TS

If TW=x, TU=x+9, TV=14, and TS=14+6=20

Then:

x/x+9=14/20

Cross multiply:

20x=14(x+9)

20x=14x+126

6x=126 / Divide both sides by 6

x=21

Hope this helps!

Therefore, the derivative of the cross product of two differentiable functions is equal to the cross product of the derivatives of the two functions.

The derivative of the cross product of two differentiable vector functions, u(t) and v(t), can be found using the product rule of differentiation as follows:

d/dt [u(t) X v(t)] = u(t) X v'(t) + u'(t) X v(t)

Then, using the property of the cross product that u(t) X v'(t) = u'(t) X v(t), the equation simplifies to:

d/dt [u(t) X v(t)] = u'(t) X v'(t)

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based on the graph provided, the correct option that describes the pattern of association between the variables is: There is a negative nonlinear association. Thus, option C is correct.

The graph shows that as the age of the person increases, the number of hours they sleep generally decreases, indicating a negative association.

However, the relationship between age and sleep hours is not linear, as the points on the graph do not form a straight line. Instead, the points appear to follow a nonlinear pattern, where the rate of decrease in sleep hours slows down as age increases.

This suggests a negative nonlinear association, where the decrease in sleep hours is not constant, but varies with age.

Therefore, based on the graph provided, the correct option that describes the pattern of association between the variables is: There is a negative nonlinear association.

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Answer apply this formula

csquare=asquare plu bsquare

Step-by-step explanation:

use pythogorean theorum to find the hy potonuse and then solve

Answer:

3rd answer 70 1/8

Step-by-step explanation:

What is the area of a right triangle with a height of 8 yards and a base of 17 yards?

base times height times .5

8.25*17*.5=70.125= 70 1/8

Answer: To find the area of a trapezoid, we use the formula:

Area = (1/2) × (b1 + b2) × h

where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.

Substituting the given values, we get:

Area = (1/2) × (49 + 24) × 16

Area = (1/2) × 73 × 16

Area = 584

Therefore, the area of this section of the deck is 584 square feet.

Step-by-step explanation: Hope this helps! :D

Answer: YEAI THINK 584SQAURE

Step-by-step explanation: