prove that : Cos² (180-x) + 2 CosxCos (90+ x) tan (360-x) = Sin ²x + 1 ​

Answer:

204.8

Step-by-step explanation:

Answer:

The two speeds are equal

Step-by-step explanation:

The speed is the distance divided by the time

100 meters / 9.75 seconds = 10.25641026 meters per second

Rounded to the nearest hundredth  10.26 meters per second

200 meters / 19.5 seconds = 10.25641026 meters per second

Rounded to the nearest hundredth  10.26 meters per second

The two speeds are equal

\(\sf{\bold{\blue{\underline{\underline{Given}}}}}\)

\(\sf{\bold{\red{\underline{\underline{To\:Find}}}}}\)

\(\sf{\bold{\purple{\underline{\underline{Solution}}}}}\)

⠀

we know that,

\(\boxed{\sf{speed=\dfrac{distance}{time}} }\)

In the 100-meter race in the 2012 Olympics he takes 9.75 sec

BUTTT,

he ran the 200-meter race in 19.5 seconds.

According to the question,

we have to compare the speed

⠀⠀⠀

\(\sf{\bold{\green{\underline{\underline{Answer}}}}}\)

The two speeds are equal of Yohan Blake.

The equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

Simplify LHS and RHS?

To verify whether the equation \((sin(x)cos(x))^2 = sin(2x)\) is an identity, we can simplify both sides of the equation and see if they are equivalent.

Starting with the left side of the equation:

\((sin(x)cos(x))^2 = (sin(x))^2(cos(x))^2\)

Now, we can use the trigonometric identity \(sin(2x) = 2sin(x)cos(x)\) to rewrite the right side of the equation:

\(sin(2x) = 2sin(x)cos(x)\)

Substituting this into the equation, we have:

\((sin(x))^2(cos(x))^2 = (2sin(x)cos(x))\)

Next, we can simplify the left side of the equation:

\((sin(x))^2(cos(x))^2 = (sin(x))^2(cos(x))^2\)

Since both sides of the equation are identical, we can conclude that the given equation is indeed an identity:

\((sin(x)cos(x))^2 = sin(2x)\)

Hence, the equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

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Answer:

the answer is (6,9) so the answer for y is 9

Step-by-step explanation:

The 99% confidence interval estimate of the population mean for sugar packed in 10 ounce bags is approximately 9.88 to 10.02 ounces.

To calculate the confidence interval, we use the formula:

Confidence Interval = sample mean ± (critical value * standard deviation / square root of sample size)

Given that the sample mean is 9.95 ounces, the standard deviation is 0.4 ounces, and the sample size is 36, we need to determine the critical value for a 99% confidence level.

Using a t-distribution table or statistical software, we find that the critical value for a 99% confidence level with 35 degrees of freedom is approximately 2.72.

Plugging in the values into the formula, we have:

Confidence Interval = 9.95 ± (2.72 * 0.4 / √36)

Confidence Interval = 9.95 ± (2.72 * 0.0667)

Confidence Interval ≈ 9.95 ± 0.1814

Therefore, the 99% confidence interval estimate of the population mean for sugar packed in 10 ounce bags is approximately 9.88 to 10.02 ounces. This means that we can be 99% confident that the true population mean lies within this range based on the given sample.

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There are 840 ways for NASA to make this selection. Total number of ways melissa and wade can sit together is 96.

We can use the combination formula to solve this problem. The number of ways to choose 2 men from 6 is C(6,2) = 15, and the number of ways to choose 3 women from 8 is C(8,3) = 56. To find the total number of ways to make the selection, we multiply these values together: 15 x 56 = 840.

To solve this problem, we can treat Melissa and Wade as a single unit and then arrange the other 3 people and the Melissa-Wade unit in 4 seats. There are 4 ways to arrange Melissa and Wade (MW, WM, AMW, WMA). After that, we have 4 seats left, and we need to arrange 3 people (Anna, Chris, and Nora) and the Melissa-Wade unit in those seats. There are 4 people to arrange in 4 seats, so there are 4! = 24 ways to do this. Therefore, the total number of ways to seat Melissa and Wade together is 4 x 24 = 96.

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Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:

y = f(0) = 1.

Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:

y = g(0) = -1.

From the information provided above, we have the following function:

g(x) = f(x) + k

g(0) = f(0) + k

Making k the subject of formula, we have:

k = g(0) - f(0)

k = -1 - 1

k = -2.

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Answer:

The answer is plant B will exceed plant A in two months at the height of 12 centimeters long.

Step-by-step explanation:

Rewrite plant A and B as a linear function

y=3x + 5

y=4x + 4

Then, let x represent the # of months

Next, try to increase the amount by one in both equations until plant B will exceed plant A

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Answer:

3 + x

Step-by-step explanation:

Sum means to add, so you would just add 3 and x (since they haven't given an actual number and only a variable).

The sum of the number 3 and the variable x will be (x + 3).

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

In the linear expression, the degree of the variable is one.

The sum of 3 and a number x.

Then the expression will be

⇒ 3 + x

The number 3 is a constant number and the term x is a variable.

The expression (x + 3) is a linear expression because the degree of the expression is one.

The number of the variable is one, then the expression is linear expression of one variable.

Thus, the sum of the number 3 and the variable x will be (x + 3).

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We need to know about rate of change to solve the problem. The flower was 16.5 cm tall on 13th April.

Rate of change is the rate at which a quantity changes over time, the rate of change might be increasing or decreasing. We know that the flower was 15 cm tall on 8th April and it grew to become 17.4 cm tall on 16th April, we can find the rate of growth of flower from this information. We need to use the rate of change to find out in how many days the flower will be 16.5 cm tall.

rate of growth= 17.4-15/16-8=0.3 cm

number of days to grow by 1.5 cm =1.5/0.3=5

Therefore the flower becomes 16.5 cm tall on 13th April.

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The approximate percentage of bulb replacement requests between 57 and 73 is 95%.

The empirical rule, also known as the 68-95-99.7 rule, is used to determine the percentage of observations that lie within a specified number of standard deviations of the means in a normal distribution. The rule states that approximately:

68% of the observations are within one standard deviation of the means

95% of the observations are within two standard deviations of the mean

99.7% of the observations are within three standard deviations of the mean

The given problem states that the distribution of the number of daily requests for fluorescent light bulbs at a university is bell-shaped and has a mean of 57 and a standard deviation of 8. Therefore, to find the approximate percentage of light bulb replacement requests between 57 and 73, we need to find the number of standard deviations of the means that are 73 and 57.

\(z-score = (x - \mu) / \sigma\)

Where

For x = 73,

\(z-score = (73 - 57) / 8\\z-score = 2\)

For x = 57,

\(z-score = (57 - 57) / 8\\z-score = 0\)

Therefore, observations 57 and 73 are separated by two standard deviations.

Using the empirical rule, we can say that approximately 95% of the observations lie within two standard deviations of the mean. Therefore, approximately 95% of the daily requests for replacement of fluorescent bulbs in the university are between 57 and 73.

Thus, the approximate percentage of bulb replacement requests between 57 and 73 is 95%.

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For Felipe and Helena's final grades, the solution is option C, [74 71].

Using the given values for Q, T, and P weights and Felipe and Helena's grades, calculate their final grades as follows:

Felipe's final grade:

0.40 x 80 + 0.50 x 60 + 0.10 x 90 = 32 + 30 + 9 = 71

Helena's final grade:

0.40 x 70 + 0.50 x 80 + 0.10 x 60 = 28 + 40 + 6 = 74

To represent the final grades for Felipe and Helena in a matrix F, given formula F = WG, where W = matrix of weights and G = matrix of grades:

[0.40 0.50 0.10]   [80 70]

F = WG = [0.40 0.50 0.10] x [60 80]

[0.40 0.50 0.10] [90 60]

Performing matrix multiplication:

[32 + 30 + 9  28 + 40 + 6]

F = WG = [32 + 40 + 6 28 + 40 + 3]

[36 + 25 + 6 36 + 20 + 3]

Simplifying:

[71 74]

F = WG = [78 71]

[67 59]

Therefore, [74 71] for Felipe and Helena's final grades, respectively.

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To convert 4 hours and 45 minutes to a fraction, we need to first convert the minutes to hours by dividing by 60 and then add the result to the 4 hours.

4 hours and 45 minutes = 4 + 45/60 hours = 4 + 0.75 hours

Now, we can write this as a fraction by expressing the decimal part as a fraction:

4 + 0.75 = 4 + 3/4 = (4*4 + 3)/4 = 19/4

Therefore, 4 hours and 45 minutes is equal to 19/4 when expressed as a fraction in simplest form.

The answer is (B) 4 3/4.

The probability of x ≤ 65.60 is 0.9205, given a mean of 50 and standard deviation of 8.

First, calculate the z-score of 65.60 by subtracting the mean (50) from the value (65.60) and then dividing the result by the standard deviation (8). This gives a z-score of 1.45.

Second, use the z-score to look up the appropriate probability in a table of the standard normal distribution. The probability associated with a z-score of 1.45 is 0.9205.

Therefore, the probability that x is less than or equal to 65.60 is 0.9205.

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Answer:

2,3 is the paired fraction

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

the reason being is that when you multiply 15(2x+2) it would equal 30x+30, but on the other side 10(3x+4) it equals 30x+40. so that is the reasoning of no solution they don't equal together.

Answer: A = P + 0.2P

Step-by-step explanation:

r = 0.04, t = 5

Original equation:

A = P + Prt

A = P + P(0.04)(5)

A = P + P(0.2)

The statement A line of symmetry divides a figure into two equal halves in all aspects is true.

A line of symmetry does indeed divide a figure into two equal halves in all aspects. When a figure has a line of symmetry, it means that if you were to fold the figure along that line, both halves would match exactly. This implies that the two halves of the figure are mirror images of each other, and they are congruent in terms of shape, size, and all other aspects.

The concept of symmetry is widely used in various fields, including mathematics, art, and design. Figures that possess symmetry often have an aesthetically pleasing and harmonious appearance.

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since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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The lateral surface area of the cone is:

A = 84.3 in²

We know that for a cone of height H and a radius R, the lateral surface area is given by the formula:

A = pi*R*( √(H² + R²))

Where pi = 3.14

Here the height is 12 inches, and the diameter is 4.4 inches, then the radius is:

R = 4.4i/2 = 2.2 in

Then the lateral surface area is:

A = 3.14*2.2in*( √((12in)² + (2.2in)²))

A = 84.3 in²

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Answer:

27

Step-by-step explanation:

6x3=18, which means the bottom half of the shape is 18. The top half is a triangle, and triangles are half a square or rectangle. So again, 6x3=18. 18/2=9. So 18+9=27. So the ANSWER IS 27

Answer:

c

Step-by-step explanation:

\(a\div 3 +11 = -5\\\\\implies a\div 3 = -5 -11\\\\\implies a \cdot \dfrac 13 =-16\\\\\implies a = -16 \cdot 3\\\\\implies a = -48\)

Answer:-5 it's already given you the answer its only asking how you got it it's simply asking for the work

Step-by-step explanation: First off you're solving for A, (-5 x 14) which is -70 so now all you need is to do the work for (-70 by 14) and there you have it (probably)

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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  By using triangle sum theorem in triangle EFG, measure of the unknown angle ∠G will be 68°.

Measures of the angles in a triangle has been given as,

m∠E = 97°

m∠F = 15°

By triangle sum theorem,

m∠E + m∠F + m∠G = 180° (Sum of interior angles of a triangle is 180°)

97° + 15° + m∠G = 180°

m∠G = 180 - 112

m∠G = 68°

  Therefore, measure of the third angle (∠G) of ΔEFG will be 68°.

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Answer:

I believe that the answer is 'C. 9d+2c+3t'.

Step-by-step explanation:

I hope this was helpful, have a blessed day.

Answer:10

Step-by-step explanation:

so lets say 4 is 100 then you are decreasing it by 1/4 so it is 3/4 with is 10 :)

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Answer:

the answer would be 15 books

Step-by-step explanation:

.