Prove that:

( sec 4A - 1 ) / ( sec 2A - 1 )

=

tan 4A . cot A

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Answer:

3

Step-by-step explanation:

\(18*\frac{1}{6} \\\\3\)

Answer:

=3x

Step-by-step explanation:

18x^1 / 6

=3x

Answer: answer is 4 multiplied by eleven minus one is fourty three

Step-by-step explanation:

The probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.

The formula (1-p)n-1 represents the probability of having n-1 failures (or successes, depending on which outcome the probability p is associated with) in a Geometric distribution. For example, if p=0.3, then the formula (1-p)n-1 would represent the probability of having two failures before the first success. This would be equal to (1-0.3)2-1, or 0.49. This means that there is a 49% chance of having two failures before the first success in this example. In general, this formula can be used to calculate the probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.

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Complete question:

What does (1-p)n-1 represent in a geometric distribution?

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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Answer:

baaababababbabababab

The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

A = 45 inches!

11 + 7 = 18

12 + 5 = 17

6 + 4 = 10

18 + 17 = 35

35 + 10 = 45

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer:

x=  5

Step-by-step explanation:

Your teacher should have explained it but give me points please

Answer:

900

Step-by-step explanation:

The biker travels 15 m/s and if there are 60 seconds, you multiply 15*60. The answer is 900

Answer:

900 meters

Step-by-step explanation:

The biker can go 15 meters in 1 second.

30 in 2 seconds.... etc etc

To find the length of the street we would multiply his speed (15 m/s) by the amount of seconds (60).

15 * 60 = 900

So, the street was 900 meters

Congruent triangles -Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C.

Concept:

Corresponding angles are two angles that are located at the same relative location of each parallel line and transversal line's intersection. Angles that correspond to one another called congruent.

If two triangles satisfy one of the following conditions, they are congruent: The three corresponding side pairings are all equal. The comparable angles between two pairs of corresponding sides are equal.

An area of a right triangle with rational side lengths can be represented by a congruent number, which is a positive whole number. Because it is the area of a right triangle with sides of 3, 4, and 5, the number 6 is an example of a congruent number. Identifying positive whole numbers that are congruent numbers is the congruent number issue.

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It is false to claim that the concentration of hydronium ions (H₃O⁺) is greater than 1*10⁻⁷ for basic solutions. In fact, for basic solutions, the concentration of hydroxide ions (OH⁻) is greater than the concentration of hydronium ions.

The concentration of hydronium ions ([H3O+]) is a measure of the acidity of a solution. A concentration greater than 1*10⁻⁷ M indicates an acidic solution, not a basic solution. For basic solutions, the concentration of hydroxide ions ([OH-]) is greater than the concentration of hydronium ions ([H3O+]). In basic solutions, the concentration of hydronium ions is less than 1*10⁻⁷ M.

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f(3) means value of y when x = 3

So, the answer is 2

Answer:

I am giving you a short cut formula which gives approximate value of square root

√P = √Q + (P-Q)/2√Q

Where P is the number whose square root is required

Here √P=√3

Q is the nearby perfect square like Q = 4 here

√P = √3 & √Q =√4=2

√P = √Q + (P-Q)/2√Q = 2 + (3-4)/2(√4) = 2 + (-1/4) =2 –(1/4)=2 -.25 = 1.75

This is approximate value

By calculator √3=1.732…

Step-by-step explanation:

Answer:

.86

Step-by-step explanation:

Exponential function formula

\(y = a ( 1 + or - r ) ^t\)

where a = initial value

r = rate of change

and t = number of years

given the equation y = 34000(0.86)^x.

r = .86

Hence the change factor is .86

F=9/5C+32 is the required equation and Greg statement is true

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.

C=5/9(F-32)

We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.

F=9/5C+32

The temperature where John leaves has 77 F.

Let us convert to celsius.

C=5/9(77-32)

C=5/9(45)

C=5(5)

C=25 degrees.

25 degress< 30 degrees.

Hence, F=9/5C+32 is the required equation and Greg statement is true.

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The advantage and disadvantages are sampling.

We have to find the advantages and disadvantages of sampling.

The advantage is:

It provides an opportunity to do data analysis with a lower likelihood of carrying an error.

Researchers can analyze the data that is collected with a smaller margin of error thanks to random sampling. This is permitted since the sampling procedure is governed by predetermined boundaries. The fact that the entire procedure is random ensures that the random sample accurately represents the complete population, which enables the data to offer precise insights into particular topic matters.

The disadvantage is:

No extra information is taken into account.

Although unconscious bias is eliminated by random sampling, deliberate bias remains in the process. Researchers can select areas for random sampling in which they think particular outcomes can be attained to confirm their own bias. The random sampling does not take into account any other information, however sometimes the data collector's supplementary information is retained.

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The particular solution to the differential equation with the initial condition y(7) = 0 is:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:

Step 1: Write the given differential equation in the form dy/dx = f(x, y).

  In this case, dy/dx = y² - 4.

Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:

  dy / (y² - 4) = dx.

Step 3: Integrate both sides of the equation:

  ∫ dy / (y² - 4) = ∫ dx.

Let's solve each integral separately:

For the left-hand side integral:

Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).

Using partial fractions, we can decompose the left-hand side integral:

1 / (y² - 4) = A / (y - 2) + B / (y + 2).

Multiply both sides by (y - 2)(y + 2):

1 = A(y + 2) + B(y - 2).

Expanding the equation:

1 = (A + B)y + 2A - 2B.

By equating the coefficients of the like terms on both sides:

A + B = 0, and

2A - 2B = 1.

Solving these equations simultaneously:

From the first equation, A = -B.

Substituting A = -B in the second equation:

2(-B) - 2B = 1,

-4B = 1,

B = -1/4.

Substituting the value of B in the first equation:

A + (-1/4) = 0,

A = 1/4.

Therefore, the decomposition of the left-hand side integral becomes:

1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).

Integrating both sides:

∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.

Integrating the right-hand side:

∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy

= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,

where C₁ is the constant of integration.

For the right-hand side integral:

∫ dx = x + C₂,

where C₂ is the constant of integration.

Combining the results:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.

Simplifying the equation:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).

Combining the constants of integration:

C = C₂ - C₁, where C is a new constant.

Finally, we have the solution to the differential equation that satisfies the initial condition:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.

To find the value of the constant C, we use the initial condition y(7) = 0:

(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.

Simplifying the equation:

(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,

(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,

0 = 7 + C,

C = -7.

Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

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Answer:

24

Step-by-step explanation:

subtract 48 from 36 and that equals 12 than add 12=24

The correct statement is: "These Graphs do not have horizontal asymptotes."

Based on the given options, the correct statement is: "These graphs do not have horizontal asymptotes."

An asymptote is a line that a graph approaches but does not intersect. In the context of these graphs, a horizontal asymptote represents a horizontal line that the graph approaches as the x-values increase or decrease without bound.

To determine if the graphs have horizontal asymptotes, we need to analyze their behavior as x-values become very large or very small.

From the given information, it is not clear what the graphs represent or how they behave for large or small x-values. Therefore, we cannot make definitive statements about their horizontal asymptotes.

Without additional information about the equations, functions, or behavior of the graphs, it is not possible to determine if they have horizontal asymptotes or compare the heights of their asymptotes.

Hence, the correct statement is: "These graphs do not have horizontal asymptotes."

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The integral 6 ∫ |3x - 3| dx can be interpreted as the area between the curve y = |3x - 3| and the x-axis, multiplied by 6.

The integral [\(\int\limits(5 + \sqrt{(49 - 2z^2)} )\) dz can be interpreted as the area between the curve \(y = 5 + \sqrt{(49 - 2z^2)}\) and the z-axis.

Now let's calculate the integrals in detail:

For the integral 6 ∫ |3x - 3| dx, we can split the integral into two parts based on the absolute value function:

6 ∫ |3x - 3| dx = 6 ∫ (3x - 3) dx for x ≤ 1 + 6 ∫ (3 - 3x) dx for x > 1

Simplifying each part, we have:

\(6 \int\limits (3x - 3) dx = 6 [x^2/2 - 3x] + C for x \leq 1\\6 \int\limits (3 - 3x) dx = 6 [3x - x^2/2] + C for x \geq 1\)

Combining the results, the final integral is:

\(6 \int\limits |3x - 3| dx = 6 [x^2/2 - 3x] for x \leq 1 + 6 [3x - x^2/2] for x > 1 + C\)

For the integral [ ∫ (5 + √(49 - 2z^2)) dz, we can simplify the square root expression and integrate as follows:

\([ \int\limits (5 + \sqrt{(49 - 2z^2)}dz = [5z + (1/3) * (49 - 2z^2)^{3/2}] + C\)

Therefore, the final result of the integral is:

\([ \int\limits (5 + \sqrt{(49 - 2z^2)}dz = [5z + (1/3) * (49 - 2z^2)^{3/2}] + C\)

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Answer:

skew right;

most of the data is on the left (the start)

Step-by-step explanation:

Observing the data distribution in the leaf plot given, we would see that most of the data are occuring at the start. This can be referred to as a positively skewed data. The tail of the distribution (the thin side) is to the right.

Therefore, the shape can be described as SKEW RIGHT.

As given by the question

There are given that the roll of die.

Now,

In the die, there are total outcomes is 6.

And,

The value in die which is odd number is:

1, 3, 5,

The number that an odd number or a number greater than 2

So, the succesfull outcomes is:

1, 3, 4, 5, 6.

Then,

The probability will be:

Hence, the correct option is B

The trigonometric relations from the triangles are

a) tan A = 5/12

b) sin C = 3/5

c) cos X = 3/5

d) sin Z = 4/5

e) tan Z = 4/3

f) tan X = 12/5

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

a)

The triangle is ΔABC

tan A = opposite side / adjacent side

Substituting the values in the equation , we get

tan A = 10/24

tan A = 5/12

b)

The triangle is ΔABC

sin C = opposite side / hypotenuse

Substituting the values in the equation , we get

sin C = 24/40

sin C = 3/5

c)

The triangle is ΔXYZ

cos X = adjacent side / hypotenuse

Substituting the values in the equation , we get

cos X =21/35

cos X = 3/5

d)

The triangle is ΔXYZ

sin Z = opposite side / hypotenuse

Substituting the values in the equation , we get

sin Z = 32/40

sin Z = 4/5

e)

The triangle is ΔXYZ

tan Z = opposite side / adjacent side

Substituting the values in the equation , we get

tan Z = 28/21

tan Z = 4/3

f)

The triangle is ΔXYZ

tan X = opposite side / adjacent side

Substituting the values in the equation , we get

tan X = 12/5

Hence , the trigonometric relations are solved from the triangles

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The probability that exactly 6 individuals in the sample favor this president candidate is 0.2068.

The area of mathematics known as probability deals with the outcomes of random events. Probability refers to a result's chance or potential. It clarifies the likelihood that a specific occurrence will take place. We frequently say things like, "He will probably pass the test," "There is very little chance of receiving a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for every instance of chance, uncertainty, maybe, likely, etc. in these statements. In essence, probability is the ability to anticipate an outcome based on the variety and quantity of potential possibilities or the analysis of historical data.

Given,

P( favor president) = 0.4

P( does not favor president) = 0.6

P( x = 6)

= ¹⁵C₆ (0.4)⁶(0.6)⁶⁻³

= 15!/6!9! (0.6)³(0.4)⁶

= 0.2068916

= 0.2068

The probability that exactly 6 individuals in the sample favor this president candidate is 0.2068.

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The length of x is 4.1.

Given:

Base = 9 + 4.5 = 13.5

From figure:

= \(\sqrt{9^{2}+5^{2} }\)

= \(\sqrt{81+25}\)

= \(\sqrt{96}\)

= 9.797

4.5 opposite is equal to 4.5.

5 opposite equal to 5 and remaining to x - 5.

According to pythagorean theorem:

= \(\sqrt{4.5^{2}+(x-5)^{2} }\)

\(13.5^{2} +x^{2} =(\sqrt{96}+\sqrt{4.5^{2} +(x-5)^{2} })^{2}\)

\(\sqrt{13.5^{2} +x^{2} }\) - \(\sqrt{96} = \sqrt{20.25+x^{2} +25 -10x}\)

squaring on both sides

182.25 + \(x^{2}\) - 96 = \(x^{2}\) - 10x + 45.25

10x = 45.25 + 96 - 182.25

10x = 41

x = 4.1.

Therefore the value of x is 4.1.

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