Can someone help me please

The next number in the sequence is 9.

The given sequence of numbers are perfect squares of decreasing numbers in descending order. Specifically, the given sequence consists of the squares of the first five counting numbers in descending order, starting from 8², then 7², 6², 5², and 4².

Therefore, the next number in the sequence should be the square of the next counting number in descending order, which is 3. Thus, the next number in the sequence should be 3², which is equal to 9.

To further explain, the sequence can be written as follows:

64 = 8²

49 = 7²

36 = 6²

25 = 5²

16 = 4²

The next number in the sequence is the square of the next counting number in descending order, which is 3. Therefore, the next number in the sequence should be 3², which is equal to 9. Thus, the next number in the sequence is 9.

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The statement "the first number of my ordered pair is 50" implies that all the points are of the form (50, y), where y can be any real number.

Therefore, the set of points that satisfy this statement is infinite, and it is not possible to list all of them.

However, if you need 20 specific points, you can choose any 20 values for y and pair them with 50 to obtain 20 points that satisfy the given condition.

For example, some of the points that satisfy this statement are (50, 0), (50, 1), (50, -2), (50, π), and (50, 10^6).


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The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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A dot plot that represent this data set is shown in the image attached below.

In Mathematics and Statistics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of crosses or dots.

Based on the information provided about this data points, we can reasonably infer and logically deduce that the number with the highest frequency is 1.

In this scenario, we would use an online graphing calculator to construct a dot plot with respect to a number line that accurately fit the data set.

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The equation of the line with given coordinates in slope intercept form is given by y = 6x.

Use the slope-intercept form of the equation of a line,

y = mx + b,

where m is the slope of the line

And b is the y-intercept.

The slope of the line is equals to,

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line.

Using the coordinates (-3, -18) and (3, 18), we get,

⇒m = (18 - (-18)) / (3 - (-3))

⇒m = 36 / 6

⇒m = 6

So the slope of the line is 6.

Now we can use the slope-intercept form of the equation of a line .

Substitute in the slope and one of the points, say (-3, -18) to get the y-intercept,

y = mx + b

⇒ -18 = 6(-3) + b

⇒ -18 = -18 + b

⇒ b = 0

So the y-intercept is 0.

Putting it all together, the equation of the line in slope-intercept form is,

y = 6x + 0

⇒ y = 6x

Therefore, the slope intercept form of the line is equal to y = 6x.

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Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.

Let's start by using variables to represent the unknown quantities in the problem. Let m be the number of slices of pizza Michael received, a be the number of slices Amy received, and au be the number of slices Mr. Au received.

We know that Miss Chang gave Michael 60 slices of pizza in total, so we can write:

m = 60

We also know that Amy received twice as many slices of pizza as Michael, so we can write:

a = 2m

Finally, we know that Mr. Au received three times the sum of what Miss Chang gave to Michael and Amy, so we can write:

au = 3(m + a)

We also know that Miss Chang gave 60 slices of pizza in total, so we can write:

m + a + au = 60

Now we can substitute the expressions we found for a and au into the last equation to get:

m + 2m + 3(m + 2m) = 60

Simplifying this equation, we get:

m + 2m + 3m + 6m = 60

12m = 60

m = 5

So Michael received 5 slices of pizza, and we can use the equations we found for a and au to determine how many slices Amy and Mr. Au received:

a = 2m = 2(5) = 10

au = 3(m + a) = 3(5 + 10) = 45

Therefore, Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.

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The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.

The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.

Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]

Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for  [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]

Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]

So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

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After 666 days, the video will receive approximately 33,621,452 views.

We are given the function V(d) = 4^(1.25d), where d represents the number of days since the video was uploaded and V(d) represents the number of views the video has received at that time. To find the number of views the video will receive after 666 days, we need to evaluate V(666).

Plugging in d = 666 into the function, we get V(666) = 4^(1.25*666). Using a calculator, we can simplify this to V(666) ≈ 33,621,452. Therefore, after 666 days, the video will receive approximately 33,621,452 views.

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To find the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π), follow these steps:

1. Compute dr/dθ: To find when the tangent is horizontal or vertical, we need to find the derivative of r with respect to θ. Start by differentiating r = 1 + cos(θ) with respect to θ:

dr/dθ = -sin(θ)

2. Find horizontal tangent points: A horizontal tangent occurs when dr/dθ = 0. In this case, -sin(θ) = 0. Solve for θ:

θ = nπ, where n is an integer

Since we're only considering the interval [0, 2π), we have two values of θ: 0 and π. Now, find the corresponding r-values for these points:

r(0) = 1 + cos(0) = 1 + 1 = 2
r(π) = 1 + cos(π) = 1 - 1 = 0

So, the coordinates for horizontal tangents are (2, 0) and (0, π).

3. Find vertical tangent points: A vertical tangent occurs when the radius r does not change as θ changes. Since dr/dθ = -sin(θ), we are looking for values of θ where sin(θ) is undefined. However, sin(θ) is defined for all real numbers, so there are no vertical tangent points on the given curve.In conclusion, the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π) are (2, 0) and (0, π).

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U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:

Find the slopes of sides UQ, QA, and UA:

Determine which segments are perpendicular and how we know they are perpendicular:

To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.

Find the lengths of each side:

Use the Pythagorean Theorem to show that it is a right triangle:

Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.

Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.

U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

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The value of Isabel's investment after 5 years is 2512.08 euros.

To calculate the value,

The formula for calculating compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have

P = 2000 euros

r = 0.043 (4.3% as a decimal)

n = 2 (compounded biannually)

t = 5 years

So, the formula becomes:

A = 2000 (1 + 0.043/2)^(2*5) = 2512.08 euros

Therefore, after 5 years, Isabel's investment will be worth 2512.08 euros.

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Answer:

V = 1,728 mi³

SA = 864 mi²

Step-by-step explanation:

We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.

First, we can solve for the area of one of the triangle sides:

A(triangle) = (1/2) · b · h

A(triangle) = (1/2) · 24 · 18

A(triangle) = 12 · 18

A(triangle) = 216 mi²

Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.

V = A(triangle) · depth

V = 216 · 8

V = 1,728 mi³

__

We can find the surface area by finding the area of each side, then adding all of those areas together.

We already know that the area of each of the triangle sides is 216 mi².

Now, we can solve for the area of the base.

A(base) = length · width

A(base) = 24 · 8

A(base) = 192 cm²

Then, we can find the area of the top side.

A(top) = length · width

A(top) = 30 · 8

A(top) = 240 mi²

Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.

SA = (2 · A(triangle)) + A(base) + A(top)

SA = 2(216) + 192 + 240

SA = 432 + 192 + 240

SA = 624 + 240

SA = 864 mi²

The answer is 2143.6.

Yes, if there are more concordant pairs in the rank order, it makes sense that the Kendall correlation will be positive, as it suggests a tendency for the two variables to move in the same direction more often.

In Kendall correlation,

Rank values of each observation for the two variables are compared to determine the level of agreement or disagreement between them.

A concordant pair is when the rank order of the two variables is the same both increase or decrease together.

A discordant pair is when the rank order is different one variable increases while the other decreases.

If there are more concordant pairs, it means that the two variables tend to move in the same direction more often.

Which suggests a positive correlation relationship between them.

Conversely, if there are more discordant pairs, it means that the two variables tend to move in opposite directions more often.

Which suggests a negative  relationship between them.

Example ,

two variables, X and Y, that are positively correlated.

If we plot the observations of X and Y on a scatter plot.

Expect to see a pattern where as the values of X increase, the values of Y also tend to increase.

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The magnitude of the resultant force is approximately 119.89 pounds, and the direction angle is approximately S12.2°W.

To solve the problem, we can use vector addition.

Let F1 be the vector representing the first force, and F2 be the vector representing the second force. Then, we can find the resultant force R by adding the two vectors:

R = F1 + F2

To add two vectors, we need to resolve them into their x and y components. Let's do that first.

For F1:

Magnitude = 80 pounds

Direction = S58°E

To resolve F1 into its x and y components, we can use trigonometry:

Fx1 = 80 cos 58° = 42.57 pounds (east)

Fy1 = 80 sin 58° = 68.13 pounds (south)

For F2:

Magnitude = 50 pounds

Direction = N76°E

To resolve F2 into its x and y components, we can again use trigonometry:

Fx2 = 50 cos (180° - 76°) = -16.92 pounds (east)

Fy2 = 50 sin (180° - 76°) = 48.76 pounds (north)

Note that we used (180° - 76°) for the angle because the direction is N76°E, which means it is 76° east of due north.

Now we can add the x and y components separately:

Rx = Fx1 + Fx2 = 42.57 - 16.92 = 25.65 pounds (east)

Ry = Fy1 + Fy2 = 68.13 + 48.76 = 116.89 pounds (south)

To find the magnitude and direction of the resultant force, we can use trigonometry again:

Magnitude = sqrt(Rx^2 + Ry^2) = sqrt(25.65^2 + 116.89^2) = 119.89 pounds (rounded to the nearest hundredth)

Direction angle = atan(Rx/Ry) = atan(25.65/116.89) = 12.2° (rounded to the nearest tenth)

The direction angle is approximately S12.2°W, and the resultant force has a magnitude of about 119.89 pounds.

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The two types of transformations that are produced by the matrix include:

We can see that a 90° counter-clockwise rotation followed by a dilation produces a transformation that stretches and rotates the figure.

On the other hand, a 90° counter-clockwise rotation followed by a reflection in the vertical axis produces a transformation that reflects and rotates the figure.

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The numbers chocolate chip cookie would be assigned to the group is equals to the 40 belongs to 60-100. So, right choice is option(a).

We have a data values for a random number ranges within 1 to 100 need to be assigned for each event.

Probability for the chocolate cookies purchased for a fundraiser = 0.40

Probability for the butter cookies purchased for a fundraiser = 0.15

Probability for the peanuts butter cookies purchased for a fundraiser = 0.15

Probability for the lemon cookies purchased for a fundraiser = 0.30

The number would be assigned to the chocolate chip cookie group = 0.40× 100

= 40%

The difference between 60-100 is 40.

Hence, required number is 60-100.

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Complete question:

The above figure complete the question.

the probability distribution table shows the probability for the type of cookies purchased for a fundraiser. to conduct a simulation to determine the type of cookies purchases, random number ranges within 1 to 100 need to be assigned for each event. what numbers would be assigned to the chocolate chip cookie group?

a) 60-100

b) 71-100

c) 20-100

The solution to the equation 30 + q = 43 is q = 13.

Given the equation in the question:

30 + q = 43

To determine the value of q in the equation 30 + q = 43, isolate q on one side of the equation by performing the same operation on both sides of the equation.

30 + q = 43

q + 30 = 43

Next, we can isolate q by subtracting 30 from both sides of the equation:

q + 30 - 30 = 43 - 30

q = 43 - 30

Subtract 30 from 43

q = 13

Therefore, the value of q is 13.

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The value of the gauge needle is, 9.01 cm

Given that;

The fuel gauge of a car represents how much gasoline is left in the tank. If the area of the sector represented by the fuel gauge is 10.6 square centimeters.

Now, We can formulate;

A = θ/360 πr

10.6 = (135/360) 3.14 x r

3816 = 423.5r

r = 9.01

Thus, The value of the gauge needle is, 9.01 cm

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The amount of  bird food in cubic centimeters will fit in the container is

11, 398. 2 cubic centimeters

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

V = π(d/2)²h

Such that the parameters of the given equation are;

Now, substitute the values into the formula, we have;

Volume = 3.14 (22/2)² 30

divide the values

Volume = 3.14(121)30

Now, multiply the values and expand the bracket

Volume = 11, 398. 2 cubic centimeters

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a) To express ∂z/∂u and ∂z/∂v as functions of u and v, we first need to express z directly in terms of u and v. We are given that:

z = tan^-1(x/y)

And that:

x = ucosv
y = usinv

Substituting these expressions for x and y into the equation for z, we get:

z = tan^-1((ucosv)/(usinv))
z = tan^-1(cotv)

Now we can use the chain rule to find ∂z/∂u and ∂z/∂v:

∂z/∂u = ∂z/∂cotv * ∂cotv/∂u
∂z/∂v = ∂z/∂cotv * ∂cotv/∂v

To find ∂cotv/∂u and ∂cotv/∂v, we use the quotient rule:

∂cotv/∂u = -cosv/u^2
∂cotv/∂v = -csc^2v

Substituting these into the chain rule expressions, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+cot^2v))
∂z/∂v = (-csc^2v) * (1/(1+cot^2v))

Simplifying these expressions using trig identities, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+(cosv/usinv)^2))
∂z/∂v = (-1/sinv^2) * (1/(1+(cosv/usinv)^2))

b) To evaluate ∂z/∂u and ∂z/∂v at (u,v) = (1.3, pi/6), we simply plug in these values into the expressions we derived in part (a):

∂z/∂u = (-cos(pi/6)/(1.3)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))
∂z/∂v = (-1/sin(pi/6)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))

Simplifying these expressions using trig functions, we get:

∂z/∂u = (-sqrt(3)/1.69^2) * (1/(1+(sqrt(3)/1.3)^2))
∂z/∂v = (-4) * (1/(1+(sqrt(3)/1.3)^2))

Plugging in the values and evaluating, we get:

∂z/∂u ≈ -0.5167
∂z/∂v ≈ -1.5045
To answer this question, we'll first express z directly in terms of u and v, and then apply the chain rule to find the partial derivatives ∂z/∂u and ∂z/∂v.

Given:
z = tan^(-1)(x/y)
x = u*cos(v)
y = u*sin(v)

First, let's express z in terms of u and v:
z = tan^(-1)((u*cos(v))/(u*sin(v)))

Now, we can simplify the expression:
z = tan^(-1)(cot(v))

Next, we'll find the partial derivatives using the chain rule:

a) ∂z/∂u:
Since z doesn't have a direct dependence on u, we have:
∂z/∂u = 0

b) ∂z/∂v:
∂z/∂v = -csc^2(v)

Now let's evaluate the partial derivatives at the given point (u,v) = (1.3, π/6):

∂z/∂u(1.3, π/6) = 0
∂z/∂v(1.3, π/6) = -csc^2(π/6) = -4

So, the partial derivatives at the given point are:
∂z/∂u = 0 and ∂z/∂v = -4.

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Answer: 10 pencils and 5 notebooks.

Step-by-step explanation:

       We will create a system of equations using the information given. Let n be equal to the number of notebooks and p be equal to the number of pencils.

She spent $23.25 on notebooks and pencils. Notebooks cost $2.49 each and pencils cost $1.08 each.

       $2.49n + $1.08p = $23.25

She bought a total of 15 notebooks and pencils.

       n + p = 15

Next, we will solve for p by substituting.

       n + p = 15 ➜ n = 15 - p

       $2.49n + $1.08p = $23.25

       $2.49(15 - p) + $1.08p = $23.25

       $37.35 - $2.49p + $1.08p = $23.25

       $37.35 - $1.41p =  $23.25

       -$1.41p =  -$14.10

       p = 10 pencils

Lastly, we will solve for n by substituting:

       n = 15 - p

       n = 15 - 10

       n = 5

The initial condition y(5) = 4 tells us that we should use the positive square root.

To find the particular solution to the given differential equation, we can use separation of variables. First, we rearrange the equation to get:

y dy = 2x dx

Next, we integrate both sides with respect to their respective variables:

∫y dy = ∫2x dx

This gives us:

y^2/2 = x^2 + C

where C is the constant of integration. To find the value of C, we use the initial condition y(5) = 4:

4^2/2 = 5^2 + C

8 = 25 + C

C = -17

So the particular solution to the differential equation dy/dx = 2x/y with the initial condition y(5) = 4 is:

y^2/2 = x^2 - 17

or

y = ±√(2x^2 - 34)

Note that there are two possible solutions, one with a positive square root and one with a negative square root, but the initial condition y(5) = 4 tells us that we should use the positive square root.

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It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.

A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.

On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.

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To find the average temperature of the coffee during the first half hour, we need to find the temperature of the coffee at t = 0 (when the coffee is just brewed) and at t = 30 (after half an hour has passed).

At t = 0, T(0) = 20 + 75e^0/50 = 20 + 75 = 95 C. At t = 30, T(30) = 20 + 75e^-30/50 ≈ 42.5 C.

So, the temperature of the coffee decreases from 95 C to 42.5 C during the first half hour.

The average temperature during this time period can be found by taking the average of the initial and final temperatures:

Average temperature = (95 C + 42.5 C) / 2 = 68.75 C.

Therefore, the average temperature of the coffee during the first half hour is 68.75 C.

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Answer:

The answer is 5.8cm to 1 d.p

Step-by-step explanation:

volume of cube=L³

200=L³

cube root both sides

³√200=³√L³

L=5.8cm to 1 d.p

a.  You will pay 80% of the original price.

b. $14.40 is the discount price of the t-shirt.

c. The sale price of the gaming system is $288.

d. $22.50 is the regular price of the hat.

a. When a store offers a 20% discount, you will pay 80% of the original price. This is because the discount is taken off the original price, leaving you to pay the remaining percentage.

b. If the regular price of a t-shirt is $18, the discount price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.

Discount price = Regular price x (1 - Discount percentage)

Discount price = $18 x (1 - 0.20)

Discount price = $18 x 0.80

Discount price = $14.40

Therefore, $14.40 is the discount price of the t-shirt.

c. If the regular price of a gaming system is $360, the sale price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.

Sale price = Regular price x (1 - Discount percentage)

Sale price = $360 x (1 - 0.20)

Sale price = $360 x 0.80

Sale price = $288

Therefore, the sale price of the gaming system is $288.

d. If the discount price of a hat is $18 and the discount percentage is 20%, we can find the regular price by dividing the discount price by the percentage you will pay after the discount, which is 80%.

Regular price = Discount price / (1 - Discount percentage)

Regular price = $18 / (1 - 0.20)

Regular price = $18 / 0.80

Regular price = $22.50

Therefore, the regular price of the hat is $22.50.

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When the subject or predicate is missing from a sentence, the sentence error is a sentence fragment.

Sentence Errors are errors related to grammar and mechanics within sentences in Standard Written English.

An example of a sentence error will be "The children re us"

The phrase "re" is the error word in this sentence.

The three types of sentence errors we have are run-on sentences, sentence fragments and overloaded sentence.

In this problem, the type of sentence error that occurs when a sentence is missing a subject of predicate is a sentence fragment

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The number of bows Lulu can make  from the remaining ribbon is 13 bows.

To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.

10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.

She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:

(26/3) * 12 = 104 inches of ribbon remaining.

Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:

104 / 8 = 13 bows.

Lulu can make 13 bows with the remaining ribbon.

Learn more about improper fraction here: https://brainly.com/question/19318336

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