((sec x -1) / x sec x) = (1 - cos x) / x. Verify

Answer:

−4x + 10 < 26

Step 1: Subtract 10 from both sides.

−4x + 10 − 10 < 26 − 10

−4x < 16

Step 2: Divide both sides by -4.

-4x/−4  <  16 /−4

x > −4

Answer:

x > −4

assuming you're solving for x:

solve using pemdas backwards, so basically sadmep :)

first subtract 10, and you end up with the equation -4x < 16.

Next is dividing the -4. Remember dividing by a negative number switches the sign direction, so the < becomes a >. So, your answer would be x > -4

Therefore, the linear convolution of the two sequences is \( y(n) = \{0, 1, 3, 8\} \). Therefore, the periodic convolution of the two sequences is \( y_p(n) = \{0, 1, 3, 0\} \).

To determine the linear convolution of two sequences, we convolve the two sequences by taking the sum of the products of corresponding elements. For the given sequences \( x_1(n) = \{0, 1, 2, 3\} \) and \( x_2(n) = \{1, 1, 2, 2\} \), the linear convolution can be calculated as follows:

\( y(n) = x_1(n) * x_2(n) \)

\( y(0) = 0 \cdot 1 = 0 \)

\( y(1) = (0 \cdot 1) + (1 \cdot 1) = 1 \)

\( y(2) = (0 \cdot 2) + (1 \cdot 1) + (2 \cdot 1) = 3 \)

\( y(3) = (0 \cdot 2) + (1 \cdot 2) + (2 \cdot 1) + (3 \cdot 1) = 8 \)

To determine the periodic convolution, we need to consider the periodicity of the sequences. Since both sequences have a length of 4, their periods are also 4. We calculate the periodic convolution by performing the linear convolution modulo 4.

\( y_p(n) = (x_1(n) * x_2(n)) \mod 4 \)

\( y_p(0) = 0 \)

\( y_p(1) = 1 \)

\( y_p(2) = 3 \)

\( y_p(3) = 0 \)

The output sequence depends on the specific application or context in which the convolution is used. The linear convolution and periodic convolution represent the relationships between the input sequences, but the output sequence may have different interpretations based on the system being analyzed.

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A) The 96% confidence interval for the proportion of defective items in the whole shipment is (0.064, 0.176).

B) We have sufficient evidence to disprove the manufacturer's claim at the 15% level of significance, but not at the 4% level.

a) The point estimate for the proportion of defective items in the whole shipment is 0.12 (24/200). Using a 96% confidence level and the normal distribution, the margin of error is 0.056. Therefore, the 96% confidence interval for the proportion of defective items in the whole shipment is (0.064, 0.176).

b) The null hypothesis is that the true proportion of defective items in the shipment is at most 0.1, while the alternative hypothesis is that it is greater than 0.1. Using the sample proportion of 0.12, the test statistic is z = (0.12-0.1)/√(0.1*0.9/200) = 1.33.

At the 4% level of significance, the critical value for a one-tailed test is 1.645. Since 1.33 < 1.645, we fail to reject the null hypothesis. At the 15% level of significance, the critical value for a one-tailed test is 1.036. Since 1.33 > 1.036, we reject the null hypothesis in favor of the alternative hypothesis at the 15% level of significance.

Therefore, we have sufficient evidence to disprove the manufacturer's claim at the 15% level of significance, but not at the 4% level.

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Answer:

The first one is

\(x=\frac{3}{a }\)

The second one is

\(x=- \frac{a }{6 }\)

The third is

\(x=-\frac{6}{a}\)

Hope this helps, it's just simple rearrangement for x!

Answer:

I think it should be like this:

|8/7|, -1, 0.05, 0.1, 2/3

Step-by-step explanation:

because the absolute value of 8/7 is -8/7 which is -1.142857143

Answer:

3/8

Step-by-step explanation:

Total = 8

Probability of blue: 1/8

Probabiity of white: 2/8

Probbility of blue AND white:

1/8 + 2/8

3/8

Answer:

3/8

Step-by-step explanation:

because there are 3 possbile places the spinner can go, and that there are 8 sections, the answer is 3/8

The angle of depression should be 26.57 degrees so the security camera should be directed downwards from the wall.

To find the angle of depression, we can use the tangent function. Let's call the angle of depression "θ". The tangent of an angle is equal to the opposite side (the difference in height between the camera and the spot) divided by the adjacent side (the horizontal distance between the camera and the spot). So, in this case:

tan(θ) = 6/12 = 1/2

Now that we have the tangent value, we can use the inverse tangent function (arctan) to find the actual angle:

θ = arctan(1/2)

Using a calculator, we can find that the angle of depression is approximately 26.57 degrees. So the security camera should be directed downward at an angle of 26.57 degrees to be directed at the spot 6 feet above the floor and 12 feet from the wall.

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The answer is B, which is to find the common denominator.

In solving a rational equation, the first step is usually to find a common denominator for all the fractions in the equation. This allows us to combine the fractions into a single fraction and simplify the equation.

To find the common denominator, we need to identify the factors of the denominators and determine the least common multiple (LCM) of these factors. Then, we multiply each fraction by the appropriate factor(s) to get the common denominator. For example, if we have the equation:

(3/x) + (4/2x) = 1/4

The denominators are x and 2x, which have factors of x and 2. The LCM of these factors is 2x, so we need to multiply the first fraction by 2 and the second fraction by 1 to get:

(6/2x) + (4/2x) = 1/4

Then we can combine the fractions and simplify the equation to get:

(10/2x) = 1/4

From here, we can continue to solve for x by cross multiplying and manipulating the equation.

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Answer:

D: 63

Step-by-step explanation:

The value of ∠BAD would be as follows:

D). 63

Given that,

The measure of ∠ABC \(= 114\)

We know that,

BD bisects the ║gm ABCD

So,

∠ABD \(= 57\)

Since opposite angles of a ║gm give equal

∠ABC = ∠ADC

So,

∠ ADB \(= 57\)

Since the sum of all the angles of a ║gm is 360.

∠BAD can be found using this.

∵ ∠BAD \(= 63\)

Thus, option D is the correct answer.

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Given:

The area of a square garden = 100 sq. ft

To find:

The perimeter of the garden.

Solution:

Let the side of the square garden be a.

Area of a square = \(a^2\)

So, \(a^2=100\).

Taking square root on both sides.

\(a=\pm \sqrt{100}\)

\(a=\pm 10\)

Length of side cannot be negative. So, a=10. It means, side length of the garden is 10 ft.

Perimeter of square = 4a.

Perimeter of square garden is

\(4(10)=40\)

Therefore, the perimeter of the square garden is 40 ft.

a. When evaluating a model, we use R2 as a parameter for performance assessment.

b. If model A has a higher MAPE but model B has a higher R2, we choose the model with the higher R2 for better overall performance.

c. For accuracy measures, we typically use MAPE (Mean Absolute Percentage Error) due to its interpretability and ability to capture relative errors.

When evaluating a model's performance, it is crucial to choose the appropriate parameters to assess its accuracy and reliability. In the case of MAPE (Mean Absolute Percentage Error) and R2 (Coefficient of Determination), the choice between them depends on the specific evaluation goals.

The R2 parameter is commonly used for evaluating models because it measures the proportion of the dependent variable's variance that can be explained by the independent variables. R2 provides insights into how well the model fits the data and captures the relationship between the input features and the target variable. Therefore, R2 is a suitable parameter to use when evaluating a model.

When comparing two models, if model A has a higher MAPE but model B has a higher R2, it is advisable to choose the model with the higher R2 value. This is because R2 indicates the proportion of variance explained, suggesting that model B performs better in capturing the underlying patterns and predicting the target variable.

Although model A may have a lower relative error (MAPE), it is crucial to prioritize the model's ability to explain and predict the target variable accurately.

Among MAPE, MAD (Mean Absolute Deviation), and MSD (Mean Squared Deviation), MAPE is commonly preferred as a parameter for accuracy measures. MAPE calculates the average percentage difference between the predicted and actual values, making it interpretable and easily understandable.

It captures relative errors and enables comparisons across different scales and datasets. MAD and MSD, on the other hand, measure absolute and squared errors, respectively, but they do not account for the relative magnitude of the errors. Hence, MAPE is a more suitable parameter for accuracy measures.

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Answer:

The answer is B. rectangle

Step-by-step explanation:

Hope this helps:)....if not then sorry for wasting your time and may God bless you:)

The surface area of the given cylinder is 112π cm².

Given is a cylinder.

Radius of the base = 4 cm

Height of the cylinder = 10 cm

Here there are two circular bases and a lateral face.

Area of the bases = 2 × (πr²)

                             = 2 × π (4)²

                             = 32π cm²

Area of the lateral face = 2π rh

                                      = 2π (4)(10)

                                      = 80π

Total area = 112π cm²

Hence the total surface area of the cylinder is 112π cm².

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Answer:

Step-by-step explanation:

5(x-3)<20

5x-15<20

5x<35

x<7

Answer:

-3 - 16b

Step-by-step explanation:

by simply doing the multiplication and then add combinable terms.

9 - 4(3 + 4b) = 9 - 12 - 16b = -3 - 16b

Explanation:

Let's simplify step-by-step:

9-4(3 + 4b)

Distribute:

= 9 + (-4)(3) + (-4)(4b)

= 9 + (-12) + (-16b)

Combine Like Terms:

= 9 + (-12) + (-16b)

= (-16b) +(9 + (–12) )

= -16b + (-3)

Answer:

-16b + (-3)

Answer:

3x - 10 = 13 would be the verbal expression where x = a number

Hope this helps!

Step-by-step explanation:

For first triangle,

sin 45 = 3 / d

1 / root 2 = 3 / d

d = 3 root 2

For second triangle,

tan 60 = 7 / a

root 3 = 7 / a

a = 7 / root 3

The correct answer is option  c. Interval. The level of measurement for the data set described is Interval.

This is so because the data set calculates each student's enrollment in classes during the course of a semester at a particular college.

Numerical information that is measured on a scale with evenly spaced intervals but lacks an absolute zero point is called interval data.

The numerical values themselves do not reflect quantities or have any absolute value, but the intervals between them all have the same size.

The interval between 3 classes and 4 classes, for instance, would be the same as the interval between 8 classes and 9 classes if the data set were measuring the number of classes each student took in a semester, but 3 classes and 8 classes do not have any such absolute value.

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Answer:

elsa can do 150 in 3 minutes.

so together they can do 450 in 3 minutes, or 150 in 1 minute

they would need two minutes

Answer:

4.5 minutes long to do their job.

R = 2x + 9y [ Given ]

When,

★ Substituting the values in the above equation

=> 13 = 2x + 9 × 3

=> 13 = 2x + 27

=> 13 - 27 = 2x

=> -14 = 2x

=> x = -14/2

=> x = -7

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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sin O = 1/2 = p/h

p=1, h = 2.

by pythagoras tgeorem,

b =

\( \sqrt{3} \)

tan0= p/b

\(1 \div \sqrt{3} \)

The expression 12x + 8 can be Witten as product as 4(3x +2)

In this question we have to write the value into the product.

Firstly, we have to write it as twelve 'x' plus eight. Then we have to check in which table both numbers in common.

The common between both is four hence we multiply the common values from the two into 'x'  in order to find the product of the equation.  

12x + 8

3*4= 12 and 4*2 = 8

Hence, we take 4 as common

We just take the common value and write numbers as product form like multiplication,

Therefore, the answer is 4(3x+2).

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C.

Step-by-step explanation:

To calculate the total distance Tyson traveled, we need to use the formula: distance = speed x time. First, we calculate the distance traveled during the first segment at 60 mph for 1.5 hours: distance = 60 x 1.5 = 90 miles. Then, we calculate the distance traveled during the second segment at 70 mph for 2.5 hours: distance = 70 x 2.5 = 175 miles. Adding these two distances together, we get: 90 + 175 = 265 miles. Therefore, the answer is C, 265 miles.

The winner of the treasure hunt calculates the resultant displacement by using vector addition. They add the three given displacements together to determine the net displacement needed to find the buried keys to the Porsche. This involves both magnitude and direction calculations.

In the first contest, the winner calculates the magnitude of the resultant displacement by adding the magnitudes of the three given displacements: 72.4 m, 57.3 m, and 17.8 m. The sum of these magnitudes gives the total distance that needs to be covered to reach the buried keys.

In the second contest, the winner calculates the direction of the resultant displacement by considering the angles associated with each given displacement. They take into account the directions mentioned, such as east, north, south, and west. By using trigonometric principles and vector addition, the winner determines the overall direction in which they should proceed to locate the buried keys.

By calculating both the magnitude and direction of the resultant displacement, the winner maximizes their chances of reaching the treasure efficiently and accurately.

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Answer:

angle FXG is congruent to angle IXJ or JXI. GHI is 81°

Step-by-step explanation:

Angle FXG is congruent to angle IXJ because the two are vertical angles. (Vertical angle theorem)

FXG + GXH = FXH

Substitute the given values given:

49 ° + GXH = 130°

Subtract 49 both sides

49 - 49 + GXH = 130 - 49

GXH = 81°

Answer:

x = 4\(\sqrt{3}\) , y = 4

Step-by-step explanation:

using the cosine and sine ratios in the right triangle and the exact values

cos30° = \(\frac{\sqrt{3} }{2}\) , sin30° = \(\frac{1}{2}\) , then

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{8}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2x = 8\(\sqrt{3}\) ( divide both sides by 2 )

x = 4\(\sqrt{3}\)

and

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{y}{8}\) = \(\frac{1}{2}\) ( cross- multiply )

2y = 8 ( divide both sides by 2 )

y = 4