Prove the following:

1 + cos^2 A = 2 ( cos^4A + sin^4A)​

Answer:

infinite

Step-by-step explanation:

\(\\ \sf\longmapsto 4(4x-2)+1=16x-7\)

\(\\ \sf\longmapsto 16x-8+1=16x-7\)

\(\\ \sf\longmapsto 16x-7=16x-7\)

\(\\ \sf\longmapsto 0=0\)

this may help you with your question

Answer:

After 5 hours, they will each have 10 lily pads left..

Step-by-step explanation:

30|25|20|15|10|5|0

38|31|24|17|10|3

After 4 days same number of lily pads remained.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Homer got to the pond, there were 30 lily pads, but he is eating 5 lily pads an hour.

and,  Hungrier Hippo found a better pond with 38 lily pads. She eats 7 lily pads every hour.

let after x days same number of lily pads remained.

So, 30 - 5x = 38 - 7x

30- 38 = -7x + 5x

-8 = -2x

x= 4

Hence, After 4 days same number of lily pads remained.

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The function below is not provided in the question, therefore, I cannot provide a specific linearization method to fit the data to a linear regression model.

However, in general, the correct linearization method for a function to be fit to a data set using linear regression would depend on the functional form of the equation.

For example, if the function is exponential, taking the logarithm of the data may result in a linear relationship that can be fit using linear regression.

The specific linearization method to fit a function to a linear regression model would depend on the functional form of the equation. For an exponential function, taking the logarithm of the data may result in a linear relationship that can be fit using linear regression. However, since the function in question is not provided, I cannot provide a specific linearization method.

The correct linearization method for a function to be fit to a linear regression model depends on the functional form of the equation and cannot be determined without knowledge of the specific function.

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When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

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Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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2,598,960 many different hands consisting of four queens and one king.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

To choose 4 kings, there is only one way, and to choose a queen, there are four.

Thus, there are 4 different methods to draw the 5 cards as instructed.

The probability of drawing cards is taken into account while calculating the number of ways to draw 5 cards from a typical 52-card deck.

= 52!/(47!)(5!) = 2,598,960.

Hence,  2,598,960 many different hands consisting of four queens and one king.

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Answer:

54

Step-by-step explanation: you add 35 and 11 together then subtract 100 by the number you got to get the anwser

Answer:

The answer is $54

Step-by-step explanation:

Since Harry paid $35 for a tie and $11 for a T-shirt,he paid $46, if he gave the cashier $100, then he would get $56 back.

Step 1: Add how much he paid for the tie and T-shirt

$35 + $11 = $46

Step 2:Subtract 100 from the sum of the tie and T-shirt

$100 - $46 = $54

Step 3:Check the solution to make sure it's right

If 100 - 46 = 54, then 54 + 46 = 100

If 35 + 11 = 46, then 46 - 35 = 11

Correct Answer: $54

Answer:

The sum of a rational number and an irrational number is irrational." By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.

Step-by-step explanation:

However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational. "The product of two irrational numbers is SOMETIMES irrational." Each time they assume the sum is rational; however, upon rearranging the terms of their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.

The eigenvalue demonstrated in the lecture notes is given by ₁ = q₁1a + 912aj. The value of 912 depends on whether the eigenvalues are real or complex conjugate pairs. If the eigenvalues are real, then 912 = 0.

In a state-space system, the coefficient matrix represents the dynamics of the system. The eigenvalues of the coefficient matrix provide important information about the stability and behavior of the system. By calculating the eigenvalues, we can determine the response of the system to different inputs and conditions.

The first part of the solution states the specific form of the eigenvalue expression, which includes the parameter "a" and the values of q₁ and 912. The second part explains that the value of 912 depends on the nature of the eigenvalues. If the eigenvalues are real, then the imaginary part of ₁ is zero, and thus 912 equals zero. This distinction is important in determining the behavior and stability of the system.

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the number of cheeseburgers sold was three times the number of hamburgers sold. then (3h)+h=556 solving equation we get 139  hamburgers were sold on monday

The number of cheeseburgers sold is three times the number of hamburgers sold...

c=3h

The total number sold is:

c+h=556, using c found earlier in this equation gives you:

(3h)+h=556

4h=556  divide both sides by 4

h=139

So 139 hamburgers were sold on Monday.

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Answer: Y =183

Step-by-step explanation:

The price after the discount but before tax, to the nearest dollar and cent, is $18.4.

Given Information:

Price on the tag = $23

Amount of Discount =20%

A % or Percentage is a figure or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred").  A % lacks dimensions and has no associated unit of measurement.

Percentage Formula =\(\frac{value}{Total value} *100\)

Calculating the discount,

There is a 20 % discount on the camera

So, the amount of discount by using the percentage formula = \(\frac{20*23}{100} = 4.6\)

Hence, the amount of discount is $4.6

Subtracting the discount to calculate the price after the discount =

Initial Price - Discount amount = $23-$4.6 = $18.4

Thus, the price after the discount is $18.4

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Me too, your not alone

Answer:

i feel that lol

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The incenter is the intersection of the angle bisectors, the distances from the incenter to the sides are proportional to the lengths of the adjacent sides, which gives the desired proportionality.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

To sketch the segments representing the distance from the incenter to the sides of a triangle, we draw perpendiculars from the incenter to each of the sides, as shown in the attached image.

The segments representing the distances from the incenter P to the sides of the triangle are the inradii.

Let r1, r2, and r3 be the lengths of the inradii corresponding to sides AB, BC, and AC, respectively.

Then, we have:

r1 = distance from P to AB

r2 = distance from P to BC

r3 = distance from P to AC

To compare these distances, we use the fact that the incenter is the intersection of the angle bisectors of the triangle.

Therefore, the distance from the incenter to each side is proportional to the length of the corresponding side. More precisely, we have:

r1 : r2 : r3 = AB : BC : AC

This proportionality can be proved using the angle bisector theorem, which states that the length of the segment of an angle bisector in a triangle is proportional to the lengths of the adjacent sides.

Hence, the incenter is the intersection of the angle bisectors, the distances from the incenter to the sides are proportional to the lengths of the adjacent sides, which gives the desired proportionality.

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Based on the given information, when x equals 9, the regression line predicts that log(y) will equal 3.992. To find the predicted value of y when x is 9, you will need to apply the inverse transformation to the logarithmic value.  

The inverse transformation of log(y) is achieved by using the exponential function. Specifically, you can use the formula:

y = 10^(log(y))

In this case, since log(y) = 3.992, you can plug this value into the formula:

y = 10^(3.992)

When you calculate this, you will find that y ≈ 9762.97. Rounded to the nearest whole number, the regression line predicts that y will equal 9763 when x equals 9.

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The Wald test is a statistical test that can be used to test the significance of a group of coefficients in a multiple regression model.

The test statistic is calculated as the ratio of the estimated coefficient to its standard error. If the test statistic is significant, then the null hypothesis that the coefficient is equal to zero can be rejected.

Suppose we have a multiple regression model with three independent variables: age, gender, and education. We want to test the hypothesis that the coefficients for age and education are both equal to zero. The Wald test statistic would be calculated as follows:

Test statistic = (Estimated coefficient for age) / (Standard error of estimated coefficient for age) + (Estimated coefficient for education) / (Standard error of estimated coefficient for education)

If the test statistic is significant, then we can reject the null hypothesis that the coefficients for age and education are both equal to zero. This would mean that there is evidence that age and education are both associated with the dependent variable.

The Wald test is a powerful tool that can be used to test the significance of a group of coefficients in a multiple regression model. However, it is important to note that the test statistic is only valid if the assumptions of the multiple regression model are met. If the assumptions are not met, then the p-value of the Wald test may be inaccurate.

Here are some of the assumptions of the multiple regression model:

* The independent variables are independent of each other.

* The dependent variable is normally distributed.

* The errors are normally distributed.

* The errors have constant variance.

If any of these assumptions are not met, then the Wald test may not be accurate.

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Answer:

y equals -2x - 3

Step-by-step explanation:

hope it helps

(would appreciate mark brainliest)

the discount rate is 3.5% (rounded to one decimal place).

To determine the discount rate, we need to compare the present value of Option A (one-time payment) with the present value of Option B (equal annual payments). The winner is indifferent between the two options when their present values are equal.

Option A: The one-time payment is $471 million.

Option B: The winner will receive 30 equal annual payments, with the first payment made in 2020. The total amount of payments is $768.4 million, so each payment is $768.4 million / 30 = $25.613 million.

Now, we can calculate the present value of Option B using the formula for the present value of an annuity:

\(PV = PMT / (1 + r)^n\)

Where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

Plugging in the values, we have:

$471 million = $25.613 million / \((1 + r)^{30}\)

Simplifying the equation and solving for r, we find:

\((1 + r)^{30}\) = $25.613 million / $471 million

\((1 + r)^{30}\) = 0.054427

Taking the 30th root of both sides, we get:

1 + r = (0.054427)^(1/30)

r = (0.054427)^(1/30) - 1

Calculating the value, we find that r is approximately 0.035 or 3.5%.

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Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

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Answer:

= − 56

Step-by-step explanation:

:D If you want me to explain it I can

Answer:

6 x 4 = 24

24 x 15.3 = 367.2

half of 4 is = 2

2^2 = 4

4 x 3.14 = 12.56

12.56 divided by 2 = 6.28

6.28 x 15.3 = 96.084

367.2 + 96.084 =

463.284 ft3 is your answer.

Answer:

\(5 \sqrt{5} - 2 \sqrt{5} = 3 \sqrt{5} \\ 8 \sqrt{7} + 3 \sqrt{7} = 11 \sqrt{7} \)

hope this helps.

Answer:

\(11 \sqrt{7} \)

Step-by-step explanation:

\(8 \sqrt{7} + 3 \sqrt{7} \)

\( \sqrt{7} (8 + 3) \)

\(11 \sqrt{7} \)

The perimeter of the parallelogram is 28 cm.

Let's first recall that the area of a parallelogram is given by the formula:

Area = base x height

where the base is any of the sides of the parallelogram and the height is the perpendicular distance between the base and its opposite side.

In this case, we are given the heights drawn from P and R, which are 6 cm and 8 cm respectively. Since PQRS is a parallelogram, we know that opposite sides are parallel and have the same length, so we can assume that the base is equal to PQ or RS.

Let's use the height drawn from P to find the base:

Area = base x height

48 cm² = base x 6 cm

base = 8 cm

Now we can use the height drawn from R to find the other side:

Area = base x height

48 cm² = base x 8 cm

base = 6 cm

We can see that both bases have the same length of 8 cm.

Therefore, the perimeter of the parallelogram is the sum of the four sides, which is:

Perimeter = 2PQ + 2RS

Perimeter = 2(8 cm) + 2(6 cm)

Perimeter = 16 cm + 12 cm

Perimeter = 28 cm

Therefore, the perimeter of the parallelogram is 28 cm.

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Answer:

555/1000

Step-by-step explanation:

I guess it is the answer.

5 km = 5000 meters

66 minutes = 3960 seconds

Meters per second = 5000/3960 = 1.26

The answer is A.1.26

When continuous data points such as age or GPA are divided into groups, they have been reduced to discrete data.

This process of dividing continuous data into discrete categories is called "discretization" or "binning". Discretization can be useful in some cases, such as when we want to simplify data analysis or make data more understandable to non-experts. However, it can also lead to information loss, as we are losing some of the detailed information contained in the original continuous data.

Continuous data is a type of data that can take on any value within a given range. For example, age can be any value between 0 and infinity, and GPA can be any value between 0 and 4.0 (or higher, in some cases). These types of data are typically measured using numerical scales, such as inches, centimeters, or percentages.

However, when we divide continuous data points into groups, we are creating categories that can only take on certain values. For example, if we divide ages into groups of 10 years (e.g., 0-9, 10-19, 20-29, etc.), we are reducing the continuous data to a set of discrete categories. Similarly, if we divide GPAs into categories (e.g., 0-1.0, 1.1-2.0, 2.1-3.0, etc.), we are also reducing the continuous data to a set of discrete categories.

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