I’m a bit confused on how to solve this problem, and could use some help!

The lengths of the diagonals or "hips" of the trapezoid are:

d1 = 10 cm

d2 = 4 cm

In an inscribed trapezoid, the opposite angles are supplementary, meaning they add up to 180 degrees. Since one of the angles in the trapezoid is 120 degrees, the opposite angle will be 180 - 120 = 60 degrees.

Now, let's label the trapezoid. Let A and B be the endpoints of the longer base, with AB = 10 cm, and let C and D be the endpoints of the shorter base, with CD = 4 cm. Let E be the intersection point of the diagonals, creating two triangles within the trapezoid.

Since the opposite angles at the intersection point of the diagonals are equal, we have angle AEC = angle BDE = 60 degrees.

Since the sum of the angles in a triangle is 180 degrees, we can find angle AED by subtracting the sum of angles AEC and BDE from 180 degrees:

angle AED = 180 - (angle AEC + angle BDE)

angle AED = 180 - (60 + 60)

angle AED = 60 degrees

Now, let's consider triangle AED. It is an isosceles triangle since AE = ED (both are radii of the circle). Thus, angle ADE = angle AED = 60 degrees.

We have angle AED = angle ADE = 60 degrees, and angle AEB = 120 degrees. Therefore, angle ABE = 180 - (angle AED + angle AEB) = 180 - (60 + 120) = 0 degrees.

Angle ABE being 0 degrees means that line AB is parallel to line CD. Hence, the trapezoid is actually a rectangle.

In a rectangle, the diagonals are equal in length. Let's denote the length of the diagonals as d1 and d2.

Since AB and CD are the bases of the trapezoid, d1 is equal to the longer base AB, and d2 is equal to the shorter base CD:

d1 = 10 cm

d2 = 4 cm

Therefore, the lengths of the diagonals or "hips" of the trapezoid are:

d1 = 10 cm

d2 = 4 cm

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Answer:

180 degrees

Step-by-step explanation:

Given

\(Time = 5:00pm\)

Required

The measure of the major arc, 30 minutes after

First, we calculate the time after 30 minutes

\(Time = 5:00pm +30\ mins\)

\(Time = 5:30pm\)

At 5:30pm, the hour and the minute hand will be directly opposite each other.

In other words, the hands divide the time into two equal parts (180 degrees each)

At this point, there is no major or minor arc as both sides have the same measurement

Hence, the measure of the arcs is 180 degrees

Answer: 20°  &  70°

Step-by-step explanation:

We know complementary angles will add up to 90° and we also know we can divide the total by 9 parts because our ratio is 2 parts to every 7 parts.

To find each individual part size...

9x=90

x=10

so use our ratio...

2x10=20  for first angle

7x10=70 for second angle

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30. (False)

To determine if a point is feasible for a constraint, we need to substitute the values of the point into the constraint equation and check if the resulting inequality holds true.

In this case, the constraint is 2x1 + 6x2 ≤ 30. Substituting x1 = 3 and x2 = 2 into the equation, we get 2(3) + 6(2) = 6 + 12 = 18. Since 18 is not less than or equal to 30, the inequality is not satisfied.

Therefore, the point (3, 2) is not feasible for the given constraint. Feasible points satisfy the constraint, while infeasible points do not. In this case, any point that lies below the line represented by the constraint equation would be feasible, while points above the line would be infeasible.

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To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Answer:

c. 412.5 cm^2

Step-by-step explanation:

first triangle: 5 x 15 = 75

75/2 = 37.5

rectangle:  15 x 19 = 285

triangle 2: 15 x 12 = 180

180/2 = 90

37.5 + 285 + 90 = 412.5

Answer:

READ  BELOW

Step-by-step explanation:

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Determined by various factors such as sample size, statistical significance, and the chosen level of confidence. the probability that the test will fail to decide that the true value is 72.5 when it is indeed 72.5.  

In order to calculate the probability of a Type II error, one would need to know the specific details of the test being used, such as the sample size, the statistical power of the test, and the chosen level of significance.

In general, the probability of a Type II error increases as the sample size decreases and the level of significance decreases. This means that if the test being used is not sufficiently powered or if the level of confidence is too low, there is a higher probability of failing to detect a true effect.

If the test is not able to accurately determine if the statement is true or not when the actual value is 72.5, then there is a possibility that a Type II error has occurred. The probability of this error depends on the specific details of the test being used and cannot be determined without further information.

The probability of a test failing to decide a certain hypothesis is true, when it is actually true, can be determined using the concept of Type II error or false negative rate. In statistical hypothesis testing, Type II error (β) refers to the probability of failing to reject a false null hypothesis. These factors influence the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false. The power of the test (1 - β) is complementary to the probability of making a Type II error.

In this case, the null hypothesis (H0) could be that the value is not equal to 72.5,

while the alternative hypothesis (H1) states that the value is equal to 72.5.

The probability you are looking for is the Type II error rate when the true value is 72.5.

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A)

b)

The value of the given expression -1 5/6 x 6 1/2 is equal to  -11 11/12.

As given in the question,

Given expression is equal to :

-1 5/6 x 6 1/2

Simplify the given expression -1 5/6 x 6 1/2 to get the value of the expression:

-1 5/6 x 6 1/2

Convert mixed fraction to proper fraction we have :

-1 5/6 = -11 /6

6 1/2 = 13 /2

-11/6 × 13 /2

= -(11 ×13) / (6×2)

= -143 /12

Convert the proper fraction into mixed fraction we get,

= -11  11/12

Therefore, the value of the given expression -1 5/6 x 6 1/2 is equal to  -11 11/12.

The complete question is:

Find the value of the given expression:

-1 5/6 x 6 1/2

please explain now!

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Answer:

the answer is = a) 480 cm³

Answer:

25.55

Step-by-step explanation:

Let us take the number he thinked of be x .

On doubling it :-

→ N = 2x

On adding 19 :-

→ N = 2x + 19

According to Question :-

→ 2x + 19 = 70.1

→ 2x = 70.1 - 19

→ 2x = 51.1

→ x = 51.1/2

→ x = 25.55

The sum of the fractions 1/3 and 2/5 is 11/15.

How can we add two fractional numbers?

For the addition of fractions with the same denominator, we just add the numerators of two fractions, keeping the denominator common. We can then simplify the fraction to the lowest form.

For the addition of fractions with different denominators, we first find the LCM of the denominators and rationalise them. Then we add the numerators and simplify the fraction.

Following the above rules, we can add 1/3 and 2/5.

Now they have different denominators.

LCM of 3 and 5 is 15.

So we rationalise them.

\(\frac{1*5}{3*5} +\frac{2*3}{5*3} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}\)

Therefore the sum of the given fractions is 11/15.

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The process of describing the steps necessary for finding a solution to a problem in programming is commonly referred to as algorithm design.

Algorithm design is an essential aspect of programming, as it allows programmers to devise a systematic approach to problem-solving. When faced with a programming problem, the first step is to analyze and understand the problem requirements thoroughly.

Once the problem is understood, the next step is to design an algorithm that outlines the sequence of steps needed to solve the problem.

In algorithm design, programmers typically consider factors such as efficiency, correctness, and maintainability. They aim to devise algorithms that produce accurate results, optimize resource usage, and are easy to understand and maintain.

The process involves selecting appropriate data structures, determining control flow, and defining the specific operations or computations required at each step.

By describing the steps in an algorithm, programmers can effectively communicate their approach to solving a problem and provide a roadmap for implementing the solution in code.

Well-designed algorithms help streamline the programming process, improve code quality, and facilitate the development of reliable and efficient software systems.

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Answer:

Equation of the  parabola    x² = -12.56 y

Step-by-step explanation:

Explanation:-

Given Y- intercept ( 0, -3.14)

Given Focus is ( 0 , -a) = ( 0, -3.14)

So  a = 3.14 center C(0,0)

The graph of the parabola is downwards and the axis of the parabola is Y-axis.

Equation of the standard parabola    x² = -4 a y

                                                              x² = -4 (3.14) y

                                                              x² = -  12.56 y

Conclusion:-

Equation of the  parabola    x² = -12.56 y

Answer:

10.3

Step-by-step explanation:

7.5+2.8=10.3

You reverse the equation. :)

The mean of samples 10, 10, 10, 10, 10, and 16 will be 11.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16.

Then the data set will be given below.

10, 10, 10, 10, 10, 16

Then the mean of the data set will be

Mean = (10 + 10 + 10 + 10 + 10 + 16) / 6

Mean = 66/6

Mean = 11

Thus, the mean of the sample will be 11.

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5.30 % rate of return would you expect on a 5-year treasury security, assuming the pure expectations theory is valid.

To reflect the true cost and purchasing power of money that is borrowed or invested, an interest rate is called a real interest rate that has been adjusted for inflation. The nominal interest rate depicts the cost of money and reflects the state of the market. A good's nominal value is its price in terms of money. Its value in relation to another good, service, or collection of goods is what determines its true worth. Given that it is the current interest rate in the economy, it is frequently referred to as the market interest rate (usually charged by banks and other institutions). Depending on the bank or the type of loans or deposits, this nominal interest rate may be 8%, 10%, or 12%.

Nominal interest rate = Real interest rate + Inflation rate

= 2.5% + 2.8%

= 5.30%

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The function f(x) should be shifted 4 units to the right to obtain g(x). To shift f(x) to obtain g(x), we need to find the horizontal shift or translation.

In g(x), the function is shifted 4 units to the right compared to f(x). This means that the vertex of g(x) is at x = 4, while the vertex of f(x) is at x = 0.To calculate the shift, we compare the vertex positions. The vertex form of a parabola is given by f(x) = a(x-h)^2 + k, where (h,k) represents the vertex coordinates. For f(x), the vertex is at (0, 0), and for g(x), the vertex is at (4, 0). The shift can be determined by finding the difference in x-coordinates of the two vertices, which is 4.

To obtain g(x) from f(x), we need to shift f(x) 4 units to the right. The resulting function g(x) will have its vertex at x = 4, matching the vertex of g(x) = (x - 4)^2.

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Two lines that intersect in one point are always coplanar, and two lines that never intersect are sometimes coplanar

From the question, we have the following parameters that can be used in our computation:

The statements

Explaining each statement, we have

Statement 1

Two lines that intersect in one point are always coplanar,

This is becase they both lie in the same plane that contains the intersection point.

Satement 2

Two lines that never intersect are sometimes coplanar

This is because, two skew lines are not coplanar, but two parallel lines are coplanar.

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Answer:

Yes, because when the side lengths of a triangle are in the ratio 3: 4: 5, then it is a right triangle. These sides are 6: 8: 10, then the triangle is a right one.

Step-by-step explanation:

Answer:

Absolute Value measures the distance a number is from zero on the number line. ... 20) 2 - 5 = -3 21) -7+4 = -3 22) 20 - 15 = 5 23) -11 - 20 = -31

Step-by-step explanation:

To find the area between the curves x = -5, x = 1, y = 2x, and\(y = x^2 - 3\), we need to determine the points of intersection of the curves and then integrate the difference between the two curves over the interval.  we find that the area between the curves is \(\(A = \frac{109}{3}\)\)or approximately 36.33 square units.

To find the points of intersection, we set the two equations equal to each other: \(\[2x = x^2 - 3\]\)

Rearranging, we get \(\(x^2 - 2x - 3 = 0\)\). Factoring, we have\(\((x - 3)(x + 1) = 0\)\), so the points of intersection are x = 3 and x = -1.

Next, we integrate the difference between the two curves over the interval from x = -5 to x = 1:

\(\[A = \int_{-5}^{1} [(2x) - (x^2 - 3)] \, dx\]\)

Simplifying, we have \(\(A = \int_{-5}^{1} (-x^2 + 2x + 3) \, dx\).\)

Evaluating the integral, we get:

\(\[A = \left[-\frac{x^3}{3} + x^2 + 3x\right]_{-5}^{1}\]\[A = \left[-\frac{1}{3} + 1 + 3 - \left(\frac{-125}{3} + 25 - 15\right)\right]\]\)

Simplifying the expression further, we find that the area between the curves is \(\(A = \frac{109}{3}\)\) or approximately 36.33 square units.

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Answer: The smallest two-digit prime number such that reversing the digits of the number produces a composite number is 19

Step-by-step explanation:

11, which is the smallest two-digit prime number, 11 remains the same number when the digits are reversed, and it is a prime number, of course.

The next two-digit prime number is 13. 13 becomes the prime number 31 when the digits are reversed.

17 is the following two-digit prime number. The result of flipping the digits of 17 is 71, a prime number.

19 is the following two-digit prime number. Reversing the digits of 19 results in 91, which is composite because 7*13= 91

Thus, 19 is the answer.

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Answer:

1402 tiles

Step-by-step explanation:

so in order to find the amount of glass tiles we will first need to find the surface area of the box

so the surface area formula for a rectangular prism is

2 (wl * hw* hl)

w- width

h- height

l- length

so the width would be 18centimeters

the height would be 7 cm

and the length would be 23 cm

therefore if we plug in the measurements into the equation it will give us a total surface area of

1402cm^2

therefore if Dimitri wants to cover the box with 1cm glass tiles then we take the 1402cm and divide it by 1cm leaving us with the same answer of

1402 tiles

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1