Can you help solve and explain how to solve this problem

Answer:

  9.5 square units

Step-by-step explanation:

You want the area of the shaded shape bounded by diagonals in a figure composed of two squares.

When a shape is bounded by lines on a grid, the area of the shape can be found by counting boundary grid points (b) and interior grid points (i). The area is ...

  A = i + b/2 -1

In the attached figure, the 11 boundary points are identified by the larger blue dots, and the 5 interior points are identified by the smaller red dots. Using these numbers, the area is found to be ...

  A = 5 +11/2 -1 = 9.5 . . . . square units

(Blue points marked A and E are not counted in the boundary of the shaded shape.)

We can also find the area of the shaded shape by subtracting the unshaded areas from the total area of the two squares.

The 3×3 square and the 5×5 square have a total area of ...

  3·3 +5·5 = 9 +25 = 34 . . . . square units.

The upper unshaded triangle has an area of ...

  A = 1/2bh = 1/2(5)(5) = 12.5 . . . . square units

The lower unshaded triangle has an area of ...

  A = 1/2bh = 1/2(8)(3) = 12 . . . . square units

The area of the shaded figure is the total area less the unshaded area:

  A = 34 - 12.5 -12 = 9.5 . . . . square units

The area of the shaded shape is 9.5 square units.

Suppose that 2 of the 24 randomly selected golf balls are found to exceed, Based on the given information, it is not possible to make a definitive conclusion about the claim that no more than 3 percent of the brand of golf balls exceed 1.62 oz. in weight.

In order to assess the claim, we would need to conduct a hypothesis test. The claim states that no more than 3 percent of the golf balls exceed 1.62 oz. in weight. We would set up the null hypothesis as the proportion of golf balls exceeding 1.62 oz. is less than or equal to 0.03 (3 percent).

To test this hypothesis, we would need to calculate the sample proportion based on the 24 randomly selected golf balls and compare it to the hypothesized proportion of 0.03. Then, using statistical techniques, such as a one-sample proportion test, we can determine if the observed proportion is significantly different from the hypothesized proportion.

Without the specific values or calculations, it is not possible to conclude whether the claim is supported or not. The hypothesis test would provide the necessary statistical evidence to make a decision about the claim.

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Answer:

There is a slight problem with this question

Do numbers starting with "0" count as a digit position

I would say no, thus the answer is 4...

if you are allowed to use 0 then the answer is 8

in other words if the question was using only 4's and 1's then the answer would be 8  

Step-by-step explanation:

000

004

040

044

400

404

440

444

Answer:

(6,-3)

Step-by-step explanation:

;-;

Answer:

\(\sf 3^{-3x}=3^{(-4x+6)}\)

\(\sf x=6\)

Step-by-step explanation:

\(\sf Given \ equation: \left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}\)

\(\sf As \ \dfrac{1}{27}=\dfrac{1}{3^3} \ and \ \dfrac{1}{a^b}=a^{-b} \ then \ \dfrac{1}{27}=3^{-3}\)

Therefore, we can rewrite the given equation with base 3:

\(\implies \sf (3^{-3})^x=3^{(-4x+6)}\)

Apply the exponent rule \(\sf (a^b)^c=a^{bc}\) :

\(\implies \sf 3^{-3x}=3^{(-4x+6)}\)

\(\sf If \ a^{f(x)}=a^{g(x)} \ then \ f(x)=g(x)\)

\(\implies -3x=-4x+6\)

Add 4x to both sides to solve for x:

\(\implies \sf x=6\)

a. The number of graks after 1.5 years are given as follows: 707.

b. The same amount of graks and of sprogs is after 18 years.

The definition of an exponential function is presented as follows:

\(y = a(b)^{\frac{x}{n}}\)

In which the terms of the function are listed as follows:

Then the functions are given as follows for this problem:

After 1.5 years, the number of graks is given as follows:

y = 500 x 2^(0.5) = 707 graks.

The amounts will be the same when:

\(4000(2)^{\frac{x}{6}} = 500(2)^{\frac{x}{3}}\)

\(\frac{(2)^{\frac{x}{3}}}{(2)^{\frac{x}{6}}} = \frac{4000}{500}\)

\(2^{\left(\frac{x}{3} - \frac{x}{6}\right)} = 8\)

\(2^{\left(\frac{x}{3} - \frac{x}{6}\right)} = 2^3\)

Hence:

x/3 - x/6 = 3

x/6 = 3.

x = 18 years.

In the first question, it is after 1.5 years.

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The state-space equations for the undamped two-story building system can be written using the given value of k/m = 270.

The state-space representation describes the dynamic behavior of the system in terms of state variables and their derivatives. In this case, the state variables can represent the displacements and velocities of the two-story building.

To represent the system in state-space form, we can define the state vector x as [x1, x2, v1, v2], where x1 and x2 are the displacements of the first and second floors respectively, and v1 and v2 are their corresponding velocities. The state derivatives can be represented as ẋ = [ẋ1, ẋ2, ẋv1, ẋv2].

The matrices A, B, C, and D can be determined as follows:

A is the system matrix and relates the state vector to its derivatives. In this case, A is a 4x4 matrix and can be written as:

A = [[0, 0, 1, 0],

    [0, 0, 0, 1],

    [-270, 270, 0, 0],

    [270, -270, 0, 0]]

B is the input matrix and relates the control inputs to the state derivatives. Since there are no control inputs in this system, B is a 4x0 matrix, i.e., B = []

C is the output matrix and relates the state vector to the system outputs. In this case, the outputs can be the displacements of the first and second floors. Thus, C is a 2x4 matrix and can be written as:

C = [[1, 0, 0, 0],

    [0, 1, 0, 0]]

D is the feedthrough matrix and relates the control inputs directly to the system outputs. Since there are no control inputs, D is a 2x0 matrix, i.e., D = []

In summary, for the undamped two-story building system with a k/m value of 270, the state-space representation can be written as:

ẋ = Ax

y = Cx

where A is a 4x4 matrix with the values specified above, B is a 4x0 matrix, C is a 2x4 matrix, and D is a 2x0 matrix.

Explanation:

The state-space representation is a mathematical model commonly used to describe the behavior of dynamic systems. It consists of a set of first-order differential equations that relate the derivatives of the state variables to the state variables themselves.

In this problem, we are dealing with an undamped two-story building system, which means there is no damping present in the system. The value of k/m = 270 indicates the stiffness of the system. Stiffness is a measure of how much force is required to produce a given displacement.

To derive the state-space equations, we define the state vector x, which includes the displacements and velocities of the two-story building. The state derivatives are represented as ẋ.

The matrix A relates the state vector to its derivatives and captures the dynamics of the system. In this case, the matrix A is a 4x4 matrix with specific values determined by the problem. The first two rows of A are zeros because the derivatives of the displacements are velocities. The next two rows represent the equations of motion for the two floors, which involve the stiffness term k/m = 270.

The matrices B, C, and D are related to control inputs and system outputs. Since there are no control inputs in this system, B and D are empty matrices. The matrix C defines the output variables, which in this case are

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Step-by-step explanation:

42086

14

12

10+

4

2

422

+ 9

2 4 6

8 10 12 14 16 x

42595

The measure of angle ∠C is 75 degrees.

Given is a cyclic quadrilateral ABCD with ∠B opposite to ∠D and ∠A opposite of ∠C and angles ∠B = x+67, ∠C = 3x and ∠D = 3x+13,

We need to find the measure of angle ∠C,

To find the measure of angle ∠C in the given cyclic quadrilateral ABCD, we can use the property that the opposite angles in a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees.

We are given that ∠B is opposite ∠D, so we have:

∠B + ∠D = 180 degrees

Substituting the given values, we have:

(x + 67) + (3x + 13) = 180

Simplifying the equation:

4x + 80 = 180

Subtracting 80 from both sides:

4x = 100

Dividing both sides by 4:

x = 25

Now that we have found the value of x, we can substitute it into the expression for ∠C:

∠C = 3x = 3(25) = 75

Therefore, the measure of angle ∠C is 75 degrees.

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If a continuous function f is such that the integral of its partial derivative over any rectangle R in the unit disc is zero, then the function satisfies f(z)d = 0 for every triangle 7 in the unit disc.

The statement can be proven by applying Green's theorem, which relates the integral of a function over a region to the integral of its partial derivatives over the boundary of that region. If the integral of the partial derivative of f over any rectangle R in the unit disc is zero, it implies that the circulation of f around any closed curve in the unit disc is zero. By applying Green's theorem to a triangle 7 in the unit disc, which can be divided into two rectangles, we can show that the integral of f(z)d over the triangle is zero. This is because the circulation around the boundary of the triangle is zero due to the circulation being zero for each rectangle. Thus, if the integral of the partial derivative over rectangles is zero, it implies that f(z)d = 0 for every triangle in the unit disc.

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The pair of lines perpendicular to RS are EA and FG.

A flat surface on which a straight line joining any two points on it would wholly lie is known as a plane.

What is plane?

A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.

Main Body:

Given

E,F and G are on plane X. R and S are in both planes X and Y. EA and FG are parallel. AE and FG are vertical lines and are present on plane X. RS is present at the intersection of the 2 planes.

Explanation:

The lines which together could be perpendicular to RS are EA and FG.

We have to first draw both the planes according to the given information in question.

X is a vertical plane so draw a plane vertical on the horizontal plane that is Y plane. Now plot A and F And G in X plane and R,S in such a way that they  are in both plane so they will be at the intersection of both the planes. Now draw lines from A and F to form lines EA and FG.

Hence we can observe that lines EA and FD are perpendicular on line RS.

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Answer:

B) 65 sq in

Step-by-step explanation:

SA = area of base + 1/2(perimeter of base)(slant height)

= 5² + 1/2(20)(4)

= 25 + 40

The estimate of the following weight, length and capacity are:

Weight: The quantity of matter which a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms.

Length: This is the distance measured along the longest dimension of an object.

Capacity: This is the ability to hold, receive or absorb something.

In conclusion, the units of weight are milligram, gram and kilograms. The units of length are millimeter, centimeter and meter. The units of capacity are milliliter, liter.

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The matching of the first row of expressions with the second row of expressions are;

1) 2√(3x²y) → x√(12y)

2) 2x√(6xy²) → y√(24x³)

3) 2y√(2x⁴) → x²√(8y²)

4) 3x²√(2y⁴) → xy√(18x²y²)

1) 2√(3x²y)

This can be broken down into the expression;

2x√(3y)

2) 2x√(6xy²)

This can broken down into;

2xy√(6x)

3) 2y√(2x⁴)

This can be simplified into;

2x²y√2

4) 3x²√(2y⁴)

This can be simplified into;

3x²y²√2

The second row of expressions are simplified as;

xy√(18x²y²)

= 3x²y²√2

x√(12y)

= 2x√3y

x²√(8y²)

= 2x²y√2

y√(24x³)

= 2xy√6x

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Answer:

See figure below.

Step-by-step explanation:

Since the dilation is 1/5 with respect to the origin, divide each x- and y-coordinate by 5 to find the new points. Then plot them. See figure below.

The probability distribution of X is 0.5, 0.25, 0.25, and 0.125. Mean value ∑ X × P (X) = 1.875. Standard Deviation of X = 1.0533

a) For a fair coin,

P(H) = P(T) = 0.5

Outcome  X                            Probability

T                  1                                  0.5

HT              2                       0.5×0.5 = 0.25

HHT          3                       0.5×0.5×0.5 = 0.125

HHHT          4                           0.5×0.5×0.5×0.5 = 0.0625

HHHH          4                           0.5×0.5×0.5×0.5 = 0.0625

So, probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X     P(X)    X×P(X)         X2×P(X)

1     0.5     0.5          0.5

2     0.25      0.5               1

3     0.125    0.375         1.125

4     0.125       0.5            2

sum 1     E(X) = 1.87

c) Variance = E(X²) - E(X)²

= 4.625 - 1.875²

= 1.1094

Standard Deviation of X = √ Variance

= √1.1094

= 1.0533

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fractional number equivalent of 2.888 is

Answer:

\(\frac{26}{9}\) or \(2 \frac{8}{9}\)

Step-by-step explanation:

Let x equal the decimal. Set up two equations such that the digits after the decimal point are identical.

10x = 28.8888...

x = 2.8888...

Subtracting the two equations, we have:

9x = 26

Answer:

Salena is incorrect. I would advise her to try reversing the question to check her work. Please see below to check it.

Step-by-step explanation:

38 ÷ 5 = 7

Try reversing to check.

7*5=35

38 divided by 5 does not equal to 7.

Hope this helps!

Please mark as brainliest if correct!

Answer:

x-intercept(s):  ( \(\frac{5}{2}\) , 0 )

y-intercept(s):  ( 0 , 5 )

the actual calculations will require numerical values for \(f(0.5)\), \(f'(0.5)\), \(f''(0.5)\), \(f(0.8)\), and the subsequent evaluations.

To find the second Taylor polynomial for \(f(x)\) expanded about \(x_0\), we need to calculate the first and second derivatives of \(f(x)\) and evaluate them at \(x = x_0\).

(i) First, let's find the derivatives:

\(f'(x) = 3x^2 + e^{-x} - xe^{-x}\)

\(f''(x) = 6x - e^{-x} + xe^{-x}\)

Next, evaluate the derivatives at \(x = x_0 = 0.5\):

\(f'(0.5) = 3(0.5)^2 + e^{-0.5} - 0.5e^{-0.5}\)

\(f''(0.5) = 6(0.5) - e^{-0.5} + 0.5e^{-0.5}\)

Now, let's find the second Taylor polynomial, denoted as \(P_2(x)\), which is given by:

\(P_2(x) = f(x_0) + f'(x_0)(x - x_0) + \frac{f''(x_0)}{2!}(x - x_0)^2\)

Substituting the values we found:

\(P_2(x) = f(0.5) + f'(0.5)(x - 0.5) + \frac{f''(0.5)}{2!}(x - 0.5)^2\)

(ii) To evaluate \(P_2(0.8)\), substitute \(x = 0.8\) into the polynomial:

\(P_2(0.8) = f(0.5) + f'(0.5)(0.8 - 0.5) + \frac{f''(0.5)}{2!}(0.8 - 0.5)^2\)

Finally, to compute the actual error, \(f(0.8) - P_2(0.8)\), substitute \(x = 0.8\) into \(f(x)\) and subtract \(P_2(0.8)\).

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ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information.

In the given figure, we are provided with the lengths of various line segments. Using this information, we can determine the length of ZW. Given that XY = 15 and ZX = 52, we can subtract the length of XY from ZX to find the length of ZW. Therefore, ZW = ZX - XY = 52 - 15 = 37.

Now let's provide a detailed explanation of each length:

ZY = 37

To find the length of ZY, we need to subtract the length of WY from ZW. From the previous calculation, we know that ZW = 37. However, the length of WY is not given directly. To find it, we can use the fact that WX = 22 and WT = 23. Since WY is a part of WX and WT, we can subtract WT from WX to get WY. Therefore, WY = WX - WT = 22 - 23 = -1.

Now, we can substitute the value of WY into the equation for ZY: ZY = ZW - WY = 37 - (-1) = 38. Thus, ZY is equal to 38.

TX = 15

To find the length of TX, we need to subtract the length of WT from XY. We know that XY = 15 and WT = 23. Therefore, TX = XY - WT = 15 - 23 = -8. However, it is important to note that lengths cannot be negative, so TX cannot be -8. This indicates that there might be an error in the given information or measurements.

WY = -1

As calculated earlier, the length of WY is -1. However, it is important to note that lengths cannot be negative in a geometrical context. Therefore, we can conclude that there might be an error in the given information or measurements. It is advisable to double-check the given lengths or clarify any inconsistencies before proceeding with further calculations.

In summary, using the given information, we determined that ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information. It is recommended to verify the measurements to ensure accurate results.

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The numbers of questions answered correctly by various students on a 10 question quiz are an example of discrete data.

Discrete data is the type of data that has clear spaces between values.

As a result, the test-scores are discrete data. Although most discrete data, refers to things we can count easily, it does not have to be numeric. Non-numeric categories could be described as discrete data.

Discrete data is a count that involves integers — only a limited number of values is possible. This type of data cannot be subdivided into different parts. Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers.

Discrete data is a type of quantitative data that includes figures and statistics of non divisible, single points of data that you can count. You typically write discrete data points as numbers that represent exact values, and discrete data usually represents single events that have already occurred. When reviewing discrete data, companies analyze exact figures like units that were sold on a given day or the hours that an employee worked during a certain week.

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Answer:

b

Step-by-step explanation:

An alpha particle with a charge of +2e and a mass of 6.64 × 10^-27 kg enters an electric field of 1.2 × 10^3 N/C. The alpha particle is accelerated from rest through a distance of 3.7 cm.

Find the speed of the alpha particle when it emerges from the electric field and the time taken to travel the distance.   More than 100 words.Electric fields accelerate charged particles. Alpha particles have a charge of +2e and a mass of 6.64 × 10^-27 kg, where e is the fundamental unit of charge.

The electric field that is responsible for the acceleration of the alpha particle can be calculated as follows:F = EqWhere F is the electric force, E is the electric field, and q is the charge of the particle.

The electric field can, therefore, be calculated as:E = F/qE = (2 × 1.6 × 10^-19) / (6.64 × 10^-27)E = 1.2 × 10^3 N/CThe alpha particle is accelerated from rest, meaning that its initial velocity is zero.  

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Answer:

The value of home when bought was $913,780.

Step-by-step explanation:

Given that:

Current worth of the house = $1,553,426

This is 70% more than the original worth of the house.

Let,

100 be the original percent and x be the original worth

Percent increase = (100+70)% = 170%

170% of x = $1,553,426

\(\frac{170}{100}x=1553426\)

1.7x = 1553426

Dividing both sides by 1.7

\(\frac{1.7x}{1.7}=\frac{1553426}{1.7}\\x= 913780\)

Hence,

The value of home when bought was $913,780.

Yes, if "a" is an uncountable set and "zb" is a countable set, then "a-b" must be uncountable.

To prove this statement, we first need to understand what it means for a set to be countable or uncountable. A set is countable if its elements can be put in one-to-one correspondence with the natural numbers (1, 2, 3, ...). On the other hand, a set is uncountable if it cannot be put in one-to-one correspondence with the natural numbers.

Now, suppose "a" is an uncountable set and "zb" is a countable set. Let "b" be the subset of "zb" that is contained in "a". Then, since "zb" is countable, "b" is also countable. Now, consider the set "a-b". This set consists of all the elements in "a" that are not in "b". Since "a" is uncountable and "b" is countable, it follows that "a-b" must be uncountable.

Therefore, we can conclude that if "a" is an uncountable set and "zb" is a countable set, then "a-b" must be uncountable.

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