Prove that sin(x) + tan(x) = 1 + sec(x)/csc(x) by using trigonometric identities.

We know that the area of a circle in terms of π will be πr². However the area with respect to the diameter will be a different story. The first step here is to find a function relating the area and diameter of any circle --- ( 1 )

For any circle the diameter is 2 times the radius,

d = 2r

Therefore r = d / 2, which gives us the following formula through substitution.

A = π(d / 2)² = πd² / 4

Hence the area of a circle as the function of it's diameter is A = πd² / 4. You can also say f(d) = πd² / 4.

Now we can substitute " d " as 4, solving for the area ( A ) or f(4) --- ( 2 )

f(4) = π(4)² / 4 = 16π / 4 = 4π - This makes the area of circle present with a diameter of 4 inches, 4π.

Answer:

a

Step-by-step explanation:

Answer:D

there is 5 who pay more then 50$ and there is 15 who pay less then 50$

do the math 75% pay less

Step-by-step explanation:

Complete question :

In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728? 137,982 142,398 292,389 392,097

Answer:

137,982

Step-by-step explanation:

The value of digit 3 in 143, 728

3 in 143,728 is in the 1000 thousand place, hence, digit 3 has a value of :

3 * 1000 = 3000

Therefore, 10 times the value of digit 3 will be :

3000 * 10 = 30000

Feom the options given, we obtain the option where 3 has a value of 30000 if the number is expressed in expanded form:

The answer is 137,982

3 here is in the 10 thousand place = 3 * 10,000 =. 30,000

Answer:

2/3(2)

=(2/3)(2/1)

=(2*2)/(3*1)

=4/3

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

(2/3)2

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

The statement for the congruency of the triangles and the corresponding sides are as follows:

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .

In other words, triangles that have exactly the same size and shape are called congruent triangles.

Let's write a congruency statement for the triangles and identify the pair of congruent corresponding side.

Therefore,

ΔPQR ≅ ΔCBA

Hence,

∠Q = ∠B

∠R = ∠A

∠P = ∠C

PQ = BC

QR = AB

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In linear equation, 4  is the maximum whole number of gigabytes of data he can use while staying within his budget.

What are a definition and an example of a linear equation?

Let the number of gigabyte so f data she can use while staying within her budget then,

we can write the cost equation as following

 4x + 66.50 ) ≤ 85

   85 - 66.50 ≤ 4x

   18.5 ≤ 4x

   x ≤ 18.5/4

   x ≤ 4. 625

   Xmax =  4

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The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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Reciprocal is defined as the inverse of a value or a number.

What is meant by reciprocal?

The reciprocal of any number in mathematics is one divided by that number.

If x is a real number, then \(\frac{1}{x}\) will be x's reciprocal. Hence, we must change the number to its upside-down form.

For instance, 1 divided by 4 is the reciprocal of 4. The result of multiplying a number by its reciprocal now equals one. Inverse multiplicative is another name for it.

The multiplicative inverse is another name for it. It can also be discovered by switching the numerator and denominator. A number's reciprocal and its product are equal to one.

Except for zero, every integer has a reciprocal.

Hence, reciprocal is defined as the inverse of a value or a number.

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Answer:

It's the chemical because they have to work with dangerous stuff.

Answer:

The two ratios are not equivalent

Step-by-step explanation:

If two ratios a/b and a/c are the same and we cross multiply, the left side should equal the right side

In other words if a/b = c/d

a x d = b x c

So if 6/7 = 24/27,

6 x 27 = 7 x 24

6 x 27 = 162

7 x 24 = 168

Since 162 ≠ 168 the two ratios are not equal

Cyphon, this is the solution:

We have to multiply the following fractions:

7/12 * 4/3

7 * 4 / 12 * 3

28/36

Simplifying, we have:

7/9 (Dividing by 4 numerator and denominator)

We have to add the following fractions:

- 1/2 + 4/9

Let's find the lowest common denominator between 2 and 9, as follows:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

9, 18, 27, 36

The lowest common denominator is 18

4: 15 would be The scale factor to size a 12 by 16 photo to a 24 by 30 photo.

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.

Given sizes a 12 by 16 photo to a 24 by 30 photo,

From the general formula of scale factor:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

In our case

Dimension of the new shape = 24 *30

Dimension of the original shape = 12* 16

Thus,

Scale factor = 12*16/24*30

Scale factor = 4/15

Therefore, The scale factor to size a 12 by 16 photo to a 24 by 30 photo, will be 4: 15.

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The error represented in this scenario is an inappropriate task allocation or a mismatch between job responsibilities and the assigned task during the interview process.

The primary role of a customer service representative is to interact with customers, address their concerns, and log calls professionally and efficiently. In contrast, performing a detailed analysis of call-in data falls under the domain of data analysis or business intelligence roles.

By asking the candidate to perform a task unrelated to their potential job responsibilities, the company may not accurately assess the candidate's aptitude for customer service tasks. This error could lead to selecting a candidate who may excel in data analysis but may not possess the necessary communication and problem-solving skills required for a customer service representative position.

To avoid this error, the company should focus on evaluating candidates based on their skills, experience, and performance in tasks directly relevant to the customer service role.

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a) The truth table for the compound proposition is shown below.

b) The English sentence would be "If it is raining today, then either I took an umbrella or my clothing did not remain dry."

(a) Here is the truth table for the compound proposition p → (q ˅ ¬r):

p q r ¬r q ˅ ¬r p → (q ˅ ¬r)

T T T  F     T               T

T T F  T     T               T

T F T  F     F               F

T F F  T     T               T

F T T  F     T               T

F T F  T     T               T

F F T  F     F               T

F F F  T     T               T

(b) The compound proposition p → (q ˅ ¬r) can be expressed as the following English sentence: "If it is raining today, then either I took an umbrella or my clothing did not remain dry."

This sentence captures the logical relationship between the propositions p, q, and r. It states that if it is raining today (p is true), then there are two possibilities. The first possibility is that I took an umbrella (q is true), which would be a reasonable action to take when it's raining. The second possibility is that my clothing did not remain dry (¬r is true), indicating that despite my efforts to stay dry, the rain managed to make my clothes wet.

In summary, the compound proposition conveys a conditional statement where the occurrence of rain (p) has implications for the actions taken (q) and the outcome of keeping clothing dry (r).

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Compound Interest

The final value of an investment P deposited at an interest rate r for t years is:

Where m is the number of times the investment earns interest in a year (compounding times per year).

In the problem, P = $16,000, r = 10% = 0.1, t = 8, and m = 4 (there are 4 quarters in a year).

Applying the formula:

Now we can calculate the amount of interest earned by subtracting:

I = FV - P

I = $35,260.11 - $16,000

I = $19,260.11

Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( \(\frac{x-\mu }{\sigma}\)  > \(\frac{2.3-\mu }{\sigma}\) )

P (z  > \(\frac{2.3-1.9 }{0.3}\)  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( \(\frac{x-\mu }{\sigma }\) <  \(\frac{a-\mu }{\sigma }\) )

\(\frac{a-1.9 }{0.3 } = -1.55\)

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

The sample size is needed so that the 95% confidence interval will have a margin of error of no more than 3% is 1067.11

In medical research, it is essential to determine the effectiveness of a drug on a certain disease or disorder. Scientists often use statistical methods to estimate the proportion of patients who would benefit from taking the drug. In this case, the scientists want to estimate the proportion of patients who would benefit from a new drug for a certain blood disorder.

To estimate the proportion of patients who would benefit from the drug, the scientists need to create a confidence interval. A confidence interval is a range of values that is likely to contain the true value of the proportion of patients who would benefit from the drug. The margin of error is the maximum amount by which the confidence interval is expected to differ from the true value of the proportion.

To determine the sample size needed to create a confidence interval with a margin of error of no more than 3%, the scientists need to use a formula. The formula is:

n = (Z² * p * q) / E²

Where:

n = sample size

Z = the Z-score for the desired confidence level (in this case, a 95% confidence interval corresponds to a Z-score of 1.96)

p = the proportion of patients who would benefit from the drug (unknown)

q = 1 - p

E = the desired margin of error (in this case, 0.03 or 3%)

The scientists know that they want a margin of error of no more than 3%, which means that E = 0.03. They also know that they want a 95% confidence interval, which corresponds to a Z-score of 1.96. The only unknown in the formula is the proportion of patients who would benefit from the drug (p).

The scientists estimate that about half of all people with the blood disorder would benefit from the drug. Therefore, they assume that p = 0.5. They plug in the values into the formula:

n = (1.96² x 0.5 x 0.5) / 0.03²

n = 1067.11

They round up to the nearest whole number and determine that they need a sample size of at least 1068 patients to create a 95% confidence interval with a margin of error of no more than 3%.

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The correct option is D. 400% \(>\) the cube root of 63

The comparison form is:  ∛63 \(<\) 400%

A mathematical operation known as the cube root yields the number that, when multiplied by itself three times, yields the initial number.

To compare the ∛63 and 400%, we need to first evaluate their values.

The ∛63 is approximately 3.97 because 3.97³ = 63.007 which is very close to 63.

To find 400%, we need to convert it to a decimal by dividing by 100.

400% ÷ 100 = 4

So, 400% is equal to 4.

Now we can compare them:  3.97 < 4

Therefore, the  ∛63  is less than 400%, or equivalently, 400% is greater than the cube root of 63.

So the correct option is D. 400% \(>\) the cube root of 63

The comparison is: ∛63 < 400%

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Answer:

d)  400% > the cube root of 63

Step-by-step explanation:

To approximate the cube root of 63, find the two perfect cubes that are either side of 63.

Therefore, the perfect cubes that are either side of 63 are 27 and 64:

\(27 < 63 < 64\)

Cube root the numbers:

\(\sqrt[3]{27} < \sqrt[3]{63} < \sqrt[3]{64}\)

\(3 < \sqrt[3]{63} < 4\)

Therefore, the cube root of 63 is more than 3 but less than 4.

\(\hrulefill\)

The percent sign (%) is used to represent a quantity as a fraction of 100.

Therefore:

\(400\% = \dfrac{400}{100}= 4\)

\(\hrulefill\)

Since 400% equals 4, and the cube root of 63 is less than 4, the correct inequality is:

There are 200 more houses with an area between 150 and 200 square meters than between 250 and 300 square meters.

To find out how many more houses have an area between 150 and 200 square meters than between 250 and 300 square meters, we need to subtract the number of houses in the larger range from the number in the smaller range. Let's assume we have a data set that tells us the number of houses in each range.

Let's say there are 500 houses in the 150-200 square meter range and 300 houses in the 250-300 square meter range. To find out how many more houses are in the smaller range, we can subtract the number in the larger range from the number in the smaller range:

500 - 300 = 200

Therefore, we can state that there are 200 more houses with an area between 150 and 200 square meters than between 250 and 300 square meters.

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x-intercept:

(−3,0)

y-intercept:

(0,118098)

The total amount you have paid from May 2014 to July 2022 is $75,319.86

= 96 + 2

= 98 months

Total amount paid from May 2014 to July 2022 = $768.57 × 98 months

= $75,319.86

The total amount paid so far from May 2014 to July 2022 is $75,319.86

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Answer:

2/6 < 7/9 < 9/10

Step-by-step explanation:

Answer: look at the picture i attached!

Answer:

\(\frac{2(a+4b)}{a^2 -b^2 }\)

Step-by-step explanation:

\(\frac{3}{a-b} -\frac{1}{a+b} +\frac{4b}{(a-b)(a+b)}\) =

\(\frac{3(a+b)}{(a-b)(a+b)} -\frac{a-b}{(a-b)(a+b)} +\frac{4b}{(a-b)(a+b)}\) =

\(\frac{3a + 3b -a + b + 4b}{(a-b)(a+b)}\) =

\(\frac{2(a+4b)}{a^2 -b^2 }\)

To determine the amount of wrapping paper needed to wrap a cylindrical gift with a diameter of 8 meters and a height three times the radius, we need to find the surface area of the cylinder.

The diameter is 8 meters, so the radius (r) is half of that, which is 4 meters. The height (h) is three times the radius, so it is 3 * 4 = 12 meters.

The surface area of a cylinder is given by the formula: A = 2πr(h + r)

Plugging in the values, we get: A = 2 * π * 4 * (12 + 4) = 2 * π * 4 * 16 = 128π square meters.

So, it would take approximately 128π square meters of wrapping paper to wrap the cylindrical gift.

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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What problems will two decimal places have in the product? Select all that apply.

A 7.5 × 10

B 6.3 × 3

C 3.2 × 4.7

D 5 × 0.85

E 5.47 × 100

Answer:Both A and C

Step-by-step explanation:

Four friends want to take a vacation together, so each one gets a part-time job. Each person has 8 weeks to save $720 for the vacation. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $720 for vacation.

Friend A: Works 13 hours per week at $6.95 per hour.

Friend B: Works 15 hours per week at $5.85 per hour.

Friend C: Works 18 hours per week at $5.25 per hour.

Friend D: Works 11 hours per week at $7.80 per hour.  there!

Area of the rectangle is 15\(x^{11}\) - 27\(x^{7}\) - 21\(x^{5}\) + 6\(x^{4}\).

To find the area of the rectangle, we need to multiply its length by its width. In this case, the width is given as 3x^4, and the length is given as 5\(x^{7}\)-9\(x^{3}\)-7x+2. Therefore, the area of the rectangle can be calculated as:

Area = width x length

Area = 3\(x^{4}\)(5\(x^{7}\)-9\(x^{3}\)-7x+2)

To simplify this expression, we need to distribute the 3x^4 term into the parentheses:

Area = 15\(x^{11}\) - 27\(x^{7}\) - 21\(x^{5}\) + 6\(x^{4}\)

This is the final expression for the area of the rectangle in terms of x. We can see that the degree of the polynomial is 11, which means that the area of the rectangle is a high-degree polynomial. The area also contains both positive and negative terms, which means that it can take on both positive and negative values depending on the value of x.

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