the length of the side of a large square is 1 cm less than twice the length of the side of a smaller square. the area of the large square is 33 cm2 more than the area of the small square. find the length of the sides of the two squares. brainly

Answer:

Parallelogram

Step-by-step explanation:

is a polygon that has exactly four sides. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.)

The area enclosed by the ripple is increasing at a rate of  39.2π ft²/s when the radius is 3 feet. To solve this problem, we need to use the formula for the area of a circle: A = πr^2.

We know that the radius is increasing at a constant rate of 2.8 ft/s, so we can write r = 3 + 2.8t, where t is the time elapsed since the stone was dropped.

We want to find how rapidly the area enclosed by the ripple is increasing, which is the same as finding the derivative of the area with respect to time:

dA/dt = d/dt(πr^2)

Using the chain rule, we can simplify this to:

dA/dt = 2πr(dr/dt)

Now we can substitute in the expression we have for r:

dA/dt = 2π(3 + 2.8t)(2.8)

When the radius is 3 feet, we have:

dA/dt = 2π(3 + 2.8t)(2.8)

dA/dt = 39.2π ft^2/s

So the area enclosed by the ripple is increasing at a rate of 39.2π square feet per second when the radius is 3 feet.

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The correct answer is A because this represents discrete categories - ice cream toppings specifically, and not continuous numerical data

The provided data showcases the popular toppings among a random selection of customers and their respective frequency counts.

As this represents discrete categories - ice cream toppings specifically, and not continuous numerical data – it merits presentation via a bar graph which makes a suitable choice for accurate representation.

In contrast, using a histogram is inappropriate in this instance as histograms are intended to exhibit the distribution of frequency for continuous data points.

The relevant chart, Option A displays information using a precisely labeled x-axis ("Topping") along with a y-axis (“Number of Customers”) showcasing labeled bars, each accounting for exact values regarding topping popularity:

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Answer:

8 6/11 is about 8.545, 17/2 = 8.5

From least to greatest: 17/2, 8 6/11, 8.83, 8.838

Step-by-step explanation:

8 6/11 is a mixed fraction

Converting it to improper fraction

Converting it to improper fraction11*8+6=88+6

Converting it to improper fraction11*8+6=88+6=94

Converting it to improper fraction11*8+6=88+6=9417/2 =8.5

8.838 is approximately 8.84

Having simplified all the values

The values to be arranged are 94, 8.838, 8.5 and 8.83

From smallest to biggest you have:

8.83, 8.838, 8.5, 94

I hope I helped

Checking for approximate normality in the population is essential for constructing a valid confidence interval, particularly when dealing with small sample sizes. This ensures the accuracy and reliability of the interval in estimating the true population parameter.

It's important to check whether the population is approximately normal before constructing a confidence interval because the accuracy and validity of the interval depend on the underlying distribution of the population. Here's a step-by-step explanation:

1. A confidence interval is a range of values within which the true population parameter (e.g., mean or proportion) is likely to fall, with a certain level of confidence (e.g., 95% or 99%).

2. The process of constructing a confidence interval relies on the Central Limit Theorem, which states that, for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.

3. However, for small sample sizes, the distribution of the population needs to be approximately normal in order to obtain an accurate confidence interval. This is because the normality assumption is crucial for the proper interpretation of the interval.

4. If the population is not approximately normal, the confidence interval may not provide a reliable estimate of the true population parameter, leading to incorrect conclusions and potentially invalid results.

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The volume of Miriam's container is approximately 58.22 cubic inches

A square prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a square prism is expressed as;

V = l × l × h

Where l is the side length, h is height.

We know that the height of the container is 11.5 inches.

We also know that the side length of the base is 2.25 inches, which means that the length and width of the base are also 2.25 inches.

Therefore, we can plug in the values into the formula and get:

V = 2.25 × 2.25 × 11.5

V = 58.22 cubic inches

Therefore, the volume is approximately 58.22 in³.

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Answer:

Since we are given a straight line on the graph that connects the two endpoints, we can assume that Wilson's scores will follow a linear relationship with the number of hours of science homework done. We can use the equation of the line to estimate Wilson's approximate science score for 6 hours of science homework.

From the graph, we can see that the slope of the line is:

slope = (50 - 14.9) / (5 - 0) = 35.1 / 5 = 7.02

This means that Wilson's science score increases by approximately 7.02 for each additional hour of science homework per week.

To estimate Wilson's score for 6 hours of science homework, we can use the equation of the line:

y = mx + b

where y is Wilson's science score, x is the number of hours of science homework per week, m is the slope of the line, and b is the y-intercept of the line.

We can use the point (0, 14.9) on the line to find the value of b:

14.9 = 7.02(0) + b

b = 14.9

Now we can use the equation of the line to estimate Wilson's score for 6 hours of science homework:

y = 7.02(6) + 14.9

y = 42.12 + 14.9

y = 57.02

Therefore, Wilson's approximate science score if he does science homework for 6 hours a week would be around 57.02.

Step-by-step explanation:

Answer:

Let c = number of calories.

[tex] \frac{120}{ \frac{3}{4} } = \frac{c}{2} [/tex]

[tex] \frac{3}{4} c = 240[/tex]

[tex]c = 320[/tex]

Ans 960

Step-by-step explanation:

120/3/4 = x/6 Cross multiply: 0.75x = 720 Divide each side of the equation by 0.75 x = 960.

Answer: x = 19/9.

Step-by-step explanation:

Answer:

d-29.05

Step-by-step explanation:

tan^1(5/9) in the calculator which then gives you 29.05

The statement 6 is not more than z can be written in inequality as,

6 < z and 6 = z.

Given statement is that,

6 is not more than z.

We have to find the correct statement related to this.

6 is not greater than z.

So there are two options for inequalities.

6 can be less than z or 6 can be equal to z.

Hence the correct options are 6 < z and 6 = z.

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The formula for calculating the volume of an octagonal pyramid is

V = 1/3(Bh)

From the question, we are to determine the formula that can be used to determine the volume of octagonal pyramid.

An octagonal pyramid is a pyramid that has a bottom that's the shape of an octagon and has triangles as sides. It has a total of nine faces. The octagonal base and eight connecting triangles.

The formula for calculating the volume of an octagonal pyramid is

V = 1/3(Bh)

Where V is the volume of the octagonal pyramid

B is the area of the base

and his the perpendicular height

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To estimate this variance, we can use the formula Var(ß) = MSE(X'X)^(-1) where MSE is the mean squared error obtained from the OLS regression.

If E[e|X] = 0, then we know that the OLS estimator of ß is unbiased.

The variance of e|X is denoted as Var(e|X) and is equal to σ² where σ is the standard deviation of the error term.

The asymptotic variance of the OLS estimator of ß is denoted as Var(ß) and is given by the formula Var(ß) = σ²(X'X)^(-1) where X is the matrix of predictors and (X'X)^(-1) is the inverse of the matrix X'X.

 Alternatively, we can use the residual standard error (RSE) to estimate σ and then use the formula Var(ß) = RSE²(X'X)^(-1).

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The forecast for t=11 is 90.76.

a) To construct a time series plot in Excel, you can follow these steps:

Enter the time period (t) in column A, starting from cell A2 and continuing down to A11.

Enter the corresponding values of the time series (yt) in column B, starting from cell B2 and continuing down to B11.

Select the range of cells containing the time period and the time series values (A1:B11).

Click on the "Insert" tab in the Excel ribbon.

Click on the "Line" chart type and select the first option (2-D Line).

Your time series plot should now appear on the worksheet.

Based on the plot, it appears that there is a downward linear trend in the data.

b) To develop the linear trend equation, we can use Excel's LINEST function. Follow these steps:

In cell D2, enter the formula "=LINEST(B2:B11,A2:A11)"

Press CTRL+SHIFT+ENTER to enter the formula as an array formula. The slope and intercept values should appear in cells D2 and D3, respectively.

The linear trend equation is: yt = -3.04t + 123.6

The slope is -3.04 and the intercept is 123.6.

c) To find the forecast for t=11, we can use the linear trend equation and substitute t=11.

Therefore, yt = -3.04(11) + 123.6 = 90.76.

So the forecast for t=11 is 90.76.

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True. Pooled variance is the weighted average of the variances of two or more groups or samples, and it is used in calculating the estimated standard error of the difference in sample means.

The estimated standard error of the difference in sample means, on the other hand, is a measure of the variability of the differences between two sample means, and it takes into account the sample sizes and variances of the two groups being compared. Therefore, these two terms are related, but they represent different concepts in statistics.
The difference between pooled variance and the estimated standard error of the difference in sample means lies in their purpose and calculation. Pooled variance is a weighted average of the variances from two or more independent samples, while the estimated standard error of the difference in sample means measures the variability of the difference between the means of two samples.

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Boolean expressions are mathematical equations that are used to represent logic in digital circuits.

These expressions are made up of Boolean operators such as AND, OR, and NOT, and are used to determine how digital circuits should behave in response to various inputs.
It is important for Boolean expressions to be minimized in the design of digital circuits for several reasons. First, minimizing these expressions can reduce the complexity of the circuit, making it easier to design and maintain. This is because smaller expressions require fewer components and are less likely to result in errors.
Additionally, minimizing Boolean expressions can improve the efficiency and speed of the circuit. This is because smaller expressions require less processing power to execute, which can reduce the overall time it takes for the circuit to respond to inputs.
Overall, minimizing Boolean expressions is an important part of designing efficient and effective digital circuits. By reducing complexity and improving efficiency, circuits can perform more reliably and efficiently, which is essential for many applications.

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The number that makes the equation 0.54 + 17/100 = x/100 + 17/100 true is 54.

To solve this equation, we want to isolate x on one side of the equation.

Starting with:

0.54 + 17/100 = x/100 + 17/100

We can first simplify the left side by finding a common denominator for 0.54 and 17/100:

0.54 = 54/100

54/100 + 17/100 = 71/100

Now, we can simplify the right side by combining like terms:

x/100 + 17/100 = (x + 17)/100

Substituting these simplifications back into the original equation, we get:

71/100 = (x + 17)/100

To isolate x, we can multiply both sides by 100:

71 = x + 17

Subtracting 17 from both sides, we get:

x = 54

Therefore, the number that makes the equation true is 54.

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The question is -

Enter the number that makes the equation true.

0.54 + 17/100 = x/100 + 17/100

To find the magnitude of r prime of quantity pi over 3 end quantity, we first need to take the derivative of r of t. r prime of t = a vector with two components, sec^2(t) and 2csc(2t) .Then, we can evaluate r prime of pi/3 using these components: r prime of pi/3 = a vector with two components, sec^2(pi/3) and 2csc(2(pi/3)).
Using the fact that sec^2(pi/3) = 4 and csc(2(pi/3)) = -2sqrt(3)/3, we can simplify the vector to: r prime of pi/3 = a vector with two components, 4 and -4sqrt(3)/3
Now, we can find the magnitude of this vector using the formula:

magnitude of a vector = square root of (sum of squares of its components)

magnitude of r prime of pi/3 = square root of (4^2 + (-4sqrt(3)/3)^2)

= square root of (16 + 16/3)

= square root of (64/3)

= 4/square root of 3

Multiplying this by the given constants (1/3 square root of thirty four, 1/2 square root of nineteen, 2 square root of thirteen over three, 4/3 square root of ten), we get the final answer:

magnitude of r prime of quantity pi over 3 end quantity = (4/square root of 3) * (1/3 square root of thirty four) * (1/2 square root of nineteen) * (2 square root of thirteen over three) * (4/3 square root of ten)

= 16/square root of (3 * 34 * 19 * 13 * 10/9)

= 16/square root of 2,583.49

= 16/50.83

= 0.3147 (rounded to four decimal point)

To find the magnitude of r'(π/3), we need to take the square root of the sum of the squared components:

Magnitude of r'(π/3) = √[sec^4(π/3) + (2*cot(2(π/3))*csc^2(2(π/3)))^2]

Once you evaluate the trigonometric functions at π/3 and simplify the expression, you will have the magnitude of r'(π/3).

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Using differentials, we can approximate the quantity sqrt(5.05^2 3.1^2) - sqrt(5^2 3^2) as approximately 0.1555.

To use differentials to approximate the quantity sqrt(5.05^2 3.1^2) - sqrt(5^2 3^2), we need to first find a function z that represents this quantity.

Let z = f(x,y) = sqrt(x^2 y^2) = xy. Then, we have:

z(5.05, 3.1) - z(5, 3) = f(5.05, 3.1) - f(5, 3)

We want to approximate this difference using differentials. To do this, we can use the formula:

Δz ≈ dz = ∂f/∂x dx + ∂f/∂y dy

where Δz is the change in z, dz is the differential of z, ∂f/∂x and ∂f/∂y are the partial derivatives of f with respect to x and y, and dx and dy are small changes in x and y.

Taking partial derivatives of f(x,y) = xy with respect to x and y, we have:

∂f/∂x = y and ∂f/∂y = x

Substituting these into the formula for dz, we get:

dz = y dx + x dy

We can now use this differential to approximate the original quantity as follows:

z(5.05, 3.1) - z(5, 3) ≈ dz = y dx + x dy

Substituting the given values, we have:

z(5.05, 3.1) - z(5, 3) ≈ (3.1)(0.05) + (5.05)(0.01)

Simplifying, we get:

z(5.05, 3.1) - z(5, 3) ≈ 0.1555

Therefore, using differentials, we can approximate the quantity sqrt(5.05^2 3.1^2) - sqrt(5^2 3^2) as approximately 0.1555.

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An equation for which the solution is the speed of this automobile is 200 = 0.5v + v²/51.2.

In Mathematics and Science, stopping distance can be defined as a measure of the distance between the time when a brake is applied by a driver to stop a vehicle that is in motion and the time when the vehicle comes to a complete stop (halt).

Based on the information provided above, the speed of this car is represented by the following equation;

d = vs + v²/64m

Where:

By substituting the given parameters, we have:

200 = 0.5v + v²/64(0.8)

200 = 0.5v + v²/51.2

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The constant c that makes f(x,y) a joint pmf for X and Y is c = 1/18.

For f(x,y) to be a joint pmf, it must satisfy the following two conditions:

The sum of f(x,y) over all possible values of x and y must be equal to 1.

f(x,y) must be non-negative for all possible values of x and y.

Let's first find the value of c that satisfies condition 2:

Since Sx=(1,2) and Sy=(1,2,3), the possible values of (x,y) are:

(1,1), (1,2), (1,3), (2,1), (2,2), (2,3)

We need to ensure that f(x,y) is non-negative for all of these possible values. This means that:

c(x+2y) ≥ 0

Since x and y are both non-negative integers, the expression inside the parentheses can never be negative. Therefore, we just need to make sure that c is non-negative. If c is negative, then f(x,y) will be negative for some values of x and y, which violates condition 2.

Now let's find the value of c that satisfies condition 1:

We need to find the sum of f(x,y) over all possible values of x and y, and set it equal to 1:

ΣΣ f(x,y) = 1

Σx=1,2 Σy=1,2,3 c(x+2y) = 1

cΣx=1,2 Σy=1,2,3 (x+2y) = 1

c(1+2+3+2+4+6) = 1

c(18) = 1

c = 1/18

Therefore, the constant c that makes f(x,y) a joint pmf for X and Y is c = 1/18.

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Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

We have,

Carl Friedrich Gauss, known as the "Prince of Mathematicians," made significant contributions to number theory, geometry, physics, and statistics.

He formulated the fundamental theorem of arithmetic, developed concepts in differential geometry such as intrinsic curvature and Gaussian curvature, and formulated Gauss's law for electric fields.

Gauss's work laid the foundation for modern mathematics and his emphasis on rigor and precision influenced subsequent generations of mathematicians.

His legacy as one of the greatest mathematicians of all time is based on his profound theorems, laws, and concepts that continue to shape the field.

Thus,

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

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Answer:

3.04

Step-by-step explanation:

df/7.6=4.4/11

11df=4.4×7.6

df=4.4×7.6/11

df=3.04

The graph of {(x, y)} : x3 } and { ( x, y ) : y-3} is shown in image.

We have to given that;

Expression is,

⇒ {(x, y)} : x3 } and { ( x, y ) : y-3}

Now, We can find that;

Point (1.672, 4.672) is a solution of the give expression.

Hence, We get;

The graph of {(x, y)} : x3 } and { ( x, y ) : y-3} is shown in image.

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The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.

This principle states that if there are more items than the number of spaces available to place them in, at least two items must occupy the same space. In this case, there are six classes and only five weekdays available for each class to meet on. Therefore, at least two classes must meet on the same day.

Correct answer: b. The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.

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The remaining volume of the cone will be 4247 cubic units.

Let's assume that the base of the square pyramid has side lengths, and let's also assume that the height of the pyramid is h. Then, the volume of the pyramid is:

V(Pyramid)= (1/3) x s² x h

Now, let's consider the inscribed cone. Since the cone is inscribed in the pyramid, the base of the cone must lie at the base of the pyramid, and the vertex of the cone must lie at the apex of the pyramid.

Let's assume that the radius of the base of the cone is r, and let's also assume that the height of the cone is also h. Then, the volume of the cone is:

V( cone)= (1/3) x π x r² x h

Since the cone is inscribed in the pyramid, the base of the cone has the same side length as the base of the pyramid. Therefore, the diameter of the base of the cone is equal to the side length of the square pyramid. Since the radius of the cone is half of the diameter, we can write:

r = (1/2) x s

Substituting this into the formula for the volume of the cone, we get:

V(cone) = (1/3) x π x (1/4) x s² x h

= (1/12) x π x s² x h

Now, we can find the volume of the remaining solid by subtracting the volume of the cone from the volume of the pyramid:

V(remaining) = V(pyramid) - V(cone)

= (1/3) x s² * h - (1/12) x π x s² x h

= (1/3) x s² x h x (1 - (1/4) x π)

So, the volume remaining is approximate:

V(remaining) ≈ 0.79 x s² x h

V(remaining) = 0.79 x (16)² x 21

V(remaining) = 4247 cubic unit

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A plane intersects a cylinder perpendicular to its bases this cross section can be described as a rectangle. Therefore, the correct answer is option 1).

The cross section of a plane intersecting a cylinder perpendicular to its bases is a rectangle. This is because when a plane intersects a cylinder perpendicularly (at right angles) the cross-section area has the shape of a rectangle. The base of the rectangle is determined by the diameter of the cylinder and the height is determined by the length of the cylinder.

A parabola, triangle, and circle are not possible when the plane intersects the cylinder perpendicularly since their shapes cannot accurately represent the intersection of two geometric shapes.

Therefore, the correct answer is option 1).

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