Sin^2(45+A)+sin^2(45-A)=1
Prove it​

any number raised to a negative exponent is equal to the reciprocal of the base raised to the opposite exponent. Let's consider a number "a" raised to a negative exponent "-n". We can represent it as follows:

  [tex]a^(-n) = 1 / (a^n)[/tex] To prove this, we can use the definition of negative exponents. When we have a negative exponent, we are essentially taking the reciprocal of the number raised to the positive version of that exponent. In other words, [tex]a^{-n}[/tex] is the same as 1 / [tex](a^n).[/tex]

For example, let's take the number 2 raised to the exponent -3:

[tex]2^(-3) = 1 / (2^3) = 1 / 8[/tex] We can also represent this as the reciprocal of 2 raised to the opposite exponent:

[tex]1 / (2^{-3}) = 1 / (1 / (2^3)) = 1 / (1/8) = 8[/tex]

As we can see, both approaches yield the same result. This can be generalized to any number "a" and any negative exponent "-n".

In summary, any number raised to a negative exponent is equal to the reciprocal of the base raised to the opposite exponent. This can be proven by using the definition of negative exponents and applying it to a specific example. This property is essential in many areas of mathematics and science, including algebra, calculus, and physics.

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let's firstly convert the mixed fractions to improper fractions and then add them up.

[tex]\stackrel{mixed}{1\frac{12}{15}}\implies \cfrac{1\cdot 15+12}{15}\implies \stackrel{improper}{\cfrac{27}{15}}~\hfill \stackrel{mixed}{1\frac{5}{15}} \implies \cfrac{1\cdot 15+5}{15} \implies \stackrel{improper}{\cfrac{20}{15}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{27}{15}~~ + ~~\cfrac{20}{15}\implies \cfrac{27~~ + ~~20}{\underset{\textit{denominator is the same}}{15}}\implies \cfrac{47}{15}\implies 3\frac{2}{15}[/tex]

The independent variable in this hypothesis is the method of studying, specifically whether students engage in spaced learning or cramming.

In the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam, the independent variable is the method of studying.

This variable is independent because it is being manipulated and controlled by the researcher. In this case, the researcher is comparing two different methods of studying and measuring the effect on exam performance.

Spaced learning involves breaking up the study time into smaller, more manageable chunks over a period of time, such as a week. Cramming, on the other hand, involves trying to learn all the material in a short period of time, such as the night before the exam.

The dependent variable in this hypothesis is exam performance, which is expected to be better for students who engage in spaced learning compared to those who cram.

The hypothesis suggests that the method of studying has a causal relationship with exam performance, but it is the independent variable, the method of studying, that is being manipulated to test this hypothesis.

Therefore the independent variable in the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam is the method of studying, specifically whether the student engages in spaced learning or cramming.

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Answer:

Step-by-step explanation: Its 6x, you add the 6 + 1 then keep the x.

We can rewrite the right side of the equation as a power of 2 since 8 = 2^3:

(1/32)^x = (2^3)^3-x

Simplifying the right side:

(1/32)^x = 2^(9-3x)

We can write both sides using a common base, say 2:

2^(-5x) = 2^(9-3x)

Now we equate the exponents and solve for x:

-5x = 9 - 3x

-2x = 9

x = -4.5

Therefore, the solution to the equation is x = -4.5.

The goal of calculating an acceptance interval is to find the probability that the true mean lies between two values, hence the correct answer is option a.

The acceptance interval is a method for developing a tolerance interval for a specified percentage of future measurements in a distribution. The tolerance interval specifies the interval into which a specified percentage of future measurements will fall.

An acceptance interval is a quality control tool for assessing whether the characteristics of a production lot meet predetermined quality criteria. These predetermined criteria are usually in the form of upper and lower limits for the interval.

The acceptance interval is utilized to detect whether a production lot's results are within the tolerances or specifications of the quality criteria.

The purpose of calculating an acceptance interval is to locate the probability that the true mean falls between two values. In conclusion, the goal of calculating an acceptance interval is to find the probability that the true mean lies between two values.

Therefore, option a is the correct answer.

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It depends on whether the frustum is formed by slicing a cone or a pyramid. If it is a cone, then the area of frustum consists of two circular bases and a curved surface.

Curved surface area ≈  [tex]81.5 cm^2[/tex] (rounded to one decimal place)

Curved surface area [tex]= (1/2) \times (C1 + C2) \times L[/tex]

Where C1 and C2 are the circumferences of the bases of the frustum, and L is the slant height.

From the diagram, you can see that C1 = 2πr and C2 = 2πR, where r and R are the radii of the bases. You can also see that L = √(H² + (R - r)²), where H is the height of the frustum.

Substituting these values into the formula, you get:

Curved surface area = (1/2) × (2πr + 2πR) × √(H² + (R - r)²)

Simplifying, you get:

Curved surface area = π(r + R) × √(H² + (R - r)²)

Now you just need to plug in the values given in the question. The height of the large cone is 12 cm, so [tex]H = 12 - 6 = 6[/tex] cm. The radius of the small base is 3 cm, so r = 3 cm. The radius of the large base is 4 cm, so [tex]R = 4[/tex] cm.

Curved surface area = π(3 + 4) × √(6² + (4 - 3)²)

Curved surface area ≈ π × 7 × √[tex]37[/tex]

Therefore, Curved surface area ≈  [tex]81.5 cm^2[/tex] (rounded to one decimal place)

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Answer:

There are several ways to make 45 cents using different coins:

Nine nickels

Four dimes and one nickel

Three dimes and six nickels

Two dimes and one quarter

One dime, two nickels, and three pennies

One quarter and two dimes

One quarter, one dime, and four nickels

One quarter, three nickels, and five pennies

45 pennies

So there are 9 ways to make 45 cents.

I Hope This Helps!

the answer is A: 63 square units

Answer:

A (Im not entirely sure if this is correct)

Step-by-step explanation:

how I got this answer is: I found the area of the two triangles which was 12.5 (because the area of a triangle is 1/2(b*h) and the base is 3 and the height is 7 then you divide that by two) and I added them up to get 21. Then you would multiply 3 by two because a triangle is half of a rectangle and you would do b*h for a rectangle area and then multiply that by 7 ot get 42 and you would add taht to 21 to get 63

Answer:

To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.

Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.

Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.

Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.

The direction of the wind blowing is in 202°.

Given data

Air Speed = 280 mph

Heading = 190°Course= 195°

Wind Speed = 23 mph

Ground Speed = 275 mph

To find Direction of Wind Blowing

Let's break the given data and analyze them in parts.

Using the rule of Triangle.

Let P = Ground Speed,

W = Wind Speed and

A = Air Speed

Angle B = Heading = 190°

and Angle C = Course = 195°

Now, Ground Speed is defined as the speed of an aircraft relative to the ground.

It is the sum of true airspeed and the effect of wind.

Thus we get

P = A*cos(B-W) + W*cos(W)

The formula is given as

Follow the steps to solve for W in the above formula.

Put the given values in the formula.

P = 275 mph

A = 280 mph

B = 190°C = 195°

Substituting the values we get

P = 280*cos(190-W) + 23*cos(W)------------------ (1)

Now, let's solve for W

To solve W, we need to transform equation (1) into a single function of W

Then we can take derivative of the function of W and set it equal to zero.

The value of W that satisfies this equation is the value that minimizes P.

The expression derived above is not so simple to solve, thus we use trial and error method to find the value of W

The following table shows some values of P at different W from the range of 0° to 360°Wcos(W) cos(190-W) P(degrees)(degrees)(mph)

00.64-0.85323.

1830.64-0.85323

3820.64-0.85323

3810.64-0.85323.

1800.64-0.85323.

18350.64-0.85323.

38360.64-0.85323.

38270.64-0.85323.

180.64-0.85323.18

Hence, the value of W is 202°.

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Step-by-step explanation:

The factors of 9x² +49y² are:

D. (3x + 7y)(3x + 7y) and C. (3x - 7y)(3x - 7y)

We can use the identity:

a² + b² = (a + b)(a - b)

To factor the expression 9x² + 49y², let a = 3x and b = 7y. Then we have:

9x² + 49y² = (3x)² + (7y)² = (3x + 7y)(3x - 7y)

So the factors of 9x² + 49y² are (3x + 7y) and (3x - 7y). We can see that these factors are not prime, as they can be factored further into (3x + 7y)(3x + 7y) and (3x - 7y)(3x - 7y).

Answer:

angle "E" =70°

Step-by-step explanation:

<ABC=<ADC

<ADC=<EAD (alternate angles)

<EAD=<DEA (because /DA/=/DE/

and <DEA=angle E, therefore answer=70°

First we have to remember what the perimeter of a rectangle is. The perimeter is the outside edges of the rectangle, think of it as the fence around a yard. This means that the perimeter of a rectangle or a square has four sides: two widths and two lengths.

This problem tells us that the length of this rectangular parking lot is 98m. Since this parking lot is a rectangle, each of the parallel lengths are the same size. Therefore, each length is 98m and that takes care of 196m of the perimeter [tex](98\text{m} \times 2)[/tex].

To find the width, we know that the lengths take up 196m of the total 364m of the perimeter which leaves 168m for the widths. Again, since this parking lot is a rectangle, each parallel width is the same size so we can find one width by dividing the left over perimeter by 2: [tex]168\text{m} \div 2 = \bold{84m}[/tex].

I hope that helps!

Answer: x = squrt (1/20

Step-by-step explanation:

Three strategies that implement to encourage the use of BEVs are incentives, Infrastructure and Regulations. The cost of gasoline per mile for an ICE vehicle is $0.016 per mile.

Incentives: The federal government could offer financial incentives such as tax credits, rebates, or grants to consumers who purchase BEVs. This would make BEVs more affordable and help to offset the higher upfront cost of these vehicles.

Infrastructure development: The federal government could invest in the development of charging infrastructure for BEVs, such as public charging stations. This would help to alleviate range anxiety and make BEVs more convenient and practical for consumers.

Regulations: The federal government could implement regulations that incentivize or require automakers to produce more BEVs. This could include emissions standards that are more favorable to BEVs, or mandates for automakers to produce a certain percentage of their vehicles as electric.

To calculate the cost of gasoline per mile for an ICE vehicle with fuel efficiency of 235 miles per gallon and gasoline cost of $3.75 per gallon, we divide the cost of gasoline by the fuel efficiency:

Cost per mile = $3.75 / 235 miles per gallon

Cost per mile = $0.016 per mile

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The distance between points B and C on the graph is equal to: D. √34 units.

In Mathematics, Pythagorean's theorem is represented by the following mathematical expression:

c² = a² + b²

Where:

a, b, and c represent the side length of any right-angled triangle.

In order to determine the distance between points B and C in right-angled triangle ABC, we would have to apply Pythagorean's theorem.

BC² = AB² + AC²

BC² = 5² + 3²

BC² = 25 + 9

BC² = 34

BC = √34 units.

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Answer:

G (-3,-1)

H (-2,-3)

I (1,1)

Step-by-step explanation:

After a reflection across y=2, the y-coordinates of the vertices will change sign while the x-coordinates remain the same. Thus, the new coordinates of the vertices will be:

G (-3,-1)

H (-2,-3)

I (1,1)

Answer:

G (3,3) , H (2,5), I (-1,1)

Step-by-step explanation:

Since it’s flipped over the Y-Axis, the X-Axis numbers remain the same.

WRONG!!

didnt read the question correctly, so the vertices are incorrect lol.

The probability that you need to pick 7 students to find 2 students using Chrome is approximately 65%.

To calculate this, we can use the formula P = (n!/r!(n-r)!) * p^r * q^(n-r), where n = 7 (number of students to pick), r = 2 (number of Chrome users to find), p = 0.49 (probability of Chrome user), and q = 0.51 (probability of non-Chrome user). By plugging the numbers into the equation, the probability of finding 2 Chrome users is 0.649.

In other words, if you randomly pick 7 students from the group, there is a 65% chance that you will find 2 students using Chrome.

This is because 49% of the group use Chrome, so if you pick 7 students randomly, the probability of picking 2 Chrome users is high.

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For the rectangle, the value x will be 14 and angle UDK will be 35°.

What exactly is a rectangle?

A rectangle is a four-sided polygon with four right angles (90-degree angles). It has opposite sides that are equal in length and parallel to each other. The rectangle is a special case of a parallelogram, where the opposite sides are also parallel. The two sides that are equal in length are called the "width" or "short side", while the other two sides are called the "length" or "long side". The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding the lengths of all four sides.

Now,

As we know all angles of a triangle are 90°.

then 5x-15+2x+7=90

7x=98

x=14

and in triangle UDK

sum of all angles = 180°

∠UDK+90+5x-15=180

∠UDK=180-145

∠UDK=35°

Hence,

           the value x will be 14 and angle UDK will be 35°.

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Answer:

387.692307692

Step-by-step explanation:

If the probability of a breakdown on assembly line 'a' is 12% and probability of a breakdown on assembly line 'b' is 16%, then the probability that assembly line 'a' or assembly line 'b' break down is equals to the 26%, i.e., 0.26.

We have the probability of a breakdown on assembly line 'a' = 12% = 0.12

The probability of a breakdown on assembly line 'b' = 16% = 0.16

The probability that both assembly lines break down = 2% = 0.02

Let's two events a breakdown on assembly line 'a' and a breakdown on assembly line 'b' be 'X' and 'Y' respectively. That is P(X) = 0.12, P(Y) = 0.16,

P(X and Y) = P(X∩Y) = 0.02

we have to calculate the probability that assembly line 'a' or assembly line 'b' break down, P( X or Y) = P(X∪Y). Using addition rule of probability, the probability that event A or event B occurs is equal to the probability that A occurs plus the probability that B occurs minus the probability that both occur. So, P( X or Y) = P(X) + P(Y) - P( X∩Y)

= 0.12 + 0.16 - 0.02

= 0.26

Hence, required probability is 0.26.

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Answer:

The relationships that describe angles 1 and 2 are:

Vertical angles: Vertical angles are a pair of opposite angles formed by the intersection of two lines. Angles 1 and 2 are vertical angles since they are opposite angles formed by the intersection of line AB and line CD.

Supplementary angles: Supplementary angles are two angles that add up to 180 degrees. Angles 1 and 2 are supplementary angles since they form a straight line.

Therefore, the correct answers are:

Vertical angles

Supplementary angles

To find the two consecutive odd integers, let's set up an equation using the given information. Let x be the smaller odd integer, then the next consecutive odd integer is x+2.

The problem states that the product of these two integers is 77 more than twice the larger integer. In equation form, this can be written as:

x * (x + 2) = 2(x + 2) + 77

Now, let's solve for x:

x * (x + 2) = 2x + 4 + 77
x^2 + 2x = 2x + 81
x^2 = 81

To find the value of x, take the square root of both sides:

√(x^2) = √81
x = 9

So, the smaller odd integer is 9. The next consecutive odd integer is 9 + 2 = 11.

Therefore, the two consecutive odd integers are 9 and 11.

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The two consecutive odd integers are 9 and 11.

To find the two consecutive odd integers whose product is 77 more than twice the larger, we can set up the following equation:
x * (x + 2) = 2(x + 2) + 77
Here, x represents the first odd integer, and x + 2 represents the second consecutive odd integer. Now, let's solve the equation step by step:
1. Expand the equation: x^2 + 2x = 2x + 4 + 77
2. Simplify the equation: x^2 + 2x = 2x + 81
3. Subtract 2x from both sides: x^2 = 81
4. Take the square root of both sides: x = ±9
Since we're looking for positive integers, x = 9. Therefore, the two consecutive odd integers are 9 and 11.

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26 * 25 * 24 * 22 = 16,384.

There are 16,384 seven-digit license plates that contain exactly four letters, all of which are distinct. This is because there are 26 possible letters, so the first letter could be any of those letters, and then the second letter has 25 options, and so on until the fourth letter, which has 22 possible letters. So, the total number of combinations is 26 * 25 * 24 * 22 = 16,384.

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The standard deviation for the number of people with the genetic mutation in a group of 1000 individuals is approximately 4.89.

To find the standard deviation for the number of people with a particular genetic mutation in a group of 1000 individuals, we first need to understand the concept of binomial distribution.

Binomial distribution is a statistical probability distribution that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).

In this case, the probability of success (having the genetic mutation) is 0.04, and the probability of failure (not having the mutation) is 0.96. Thus, we can model the number of people with the mutation in a group of 1000 individuals using a binomial distribution with n = 1000 and p = 0.04.

The formula for the standard deviation of a binomial distribution is:

σ = √(np(1-p))

Where σ is the standard deviation, n is the number of trials, and p is the probability of success. Plugging in the values, we get:

σ = √(1000 x 0.04 x 0.96) = 4.89

In other words, we can expect that the number of people with the genetic mutation in a group of 1000 individuals will vary around the mean of 40 (1000 x 0.04) by about 4.89, with about 68% of the observations falling within one standard deviation of the mean.

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The average number of customers in the West End Donut Shop simultaneously is 30, which is obtained by using the arrival rate and service rate formulas for a queueing system.

To find the average number of customers in the shop simultaneously, we can use the concept of the arrival rate and the service rate.

The arrival rate is the rate at which customers arrive at the shop, and can be calculated as:

arrival rate = number of customers / time

arrival rate = 2400 customers / 10 hours

arrival rate = 240 customers per hour

The service rate is the rate at which customers are served by the shop, and can be calculated as:

service rate = 60 minutes / 5 minutes per customer

service rate = 12 customers per hour

Using the formula for the average number of customers in a queueing system, we get:

average number of customers = arrival rate / (service rate - arrival rate)

average number of customers = 240 / (12 - 240/60)

average number of customers = 240 / 8

average number of customers = 30

Therefore, on average, there are 30 customers in the West End Donut Shop simultaneously.

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