Find the area enclosed by the closed curve obtained by joiningthe ends of the spiralr = 8θ, 0 ≤ θ ≤ 5.2by a straight line segment.

No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.

A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.

When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.

However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.

In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.

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Answer:

4g+8m

Step-by-step explanation:

7m+m=8m 11g-7g=4g

Answer:

㏒e (7.9272)=h

Step-by-step explanation:

have a great day and thx for your inquiry :)

QUESTION 4: m∠A = 53 degrees

QUESTION 7: Area of triangle PQR is 23.6 unit²

QUESTION 8: Using cosine law, JK = 3.1 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

QUESTION 4

tan A = 9.6/7.2

A = arctan(9.6/7.2)

A = 53 degrees

QUESTION 7

Area of ΔPQR = 1/2 * 6 * 8 * sin 80

Area of ΔPQR = 23.6 unit²

QUESTION 8

JK = √(6² + 8² - 2*6*8*cos 20°)    (cosine law)

JK = 3.1 units

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Answer:

1/2 of an answer is zero answer.

Step-by-step explanation:

Answer:

a. Solve for x. x=16

b. The lenght of the missing side is 10 units.

Step-by-step explanation:

a.

        x-6>0      x>6

According to the Pythagorean theorem: a²+b²=c².

Hence,

\((x-6)^2+24^2=26^2\\x^2-2*x*6+6^2+24*24=26*26\\x^2-12x+6*6+576=676\\x^2-12x+36+576-676=676-676\\x^2-12x-64=0\\x^2-12x-4x+4x-64=0\\x^2-16x+4x-64=0\\(x*x-16x)+(4x-64)=0\\x*(x-16)+4*(x-16)=0\\(x-16)*(x+4)=0\\x-16=0\\x_1=16\\x+4=0\\x_2=-4\notin\\\)

b.

\(16-6=\\10\)

Answer:

-1/3

Step-by-step explanation:

The slope an equation is the number that is being multiplied by x. This is known as the coefficient. A coefficient is a number that’s being multiplied by a variable. In this equation, -1/3 is the slope because that’s the coefficient, it’s being multiplied by the variable x.

Hope this helps! :)

Rounded to four decimal places, the p-value is 0.0844.

To determine the p-value for this hypothesis test, we need to follow these steps:

Step 1: State the null and alternative hypotheses.

Null hypothesis: The percentage of readers who own a laptop is 26%.

Alternative hypothesis: The percentage of readers who own a laptop is different from 26%.

Step 2: Determine the test statistic.

We can use a z-test for proportions since we have a large enough sample size and we know the population proportion. The formula for the test statistic is:

z = (p - p) / √(p(1-p) / n)

where p is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

Using the given values, we have:

z = (0.17 - 0.26) / √(0.26(1-0.26) / 100)

z = -1.72

Step 3: Determine the p-value.

Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that corresponds to a z-score of -1.72. Using a table or a calculator, we find that the area in the left tail is 0.0422 and the area in the right tail is also 0.0422.

Therefore, the p-value is the sum of the areas in both tails:

p-value = 0.0422 + 0.0422

p-value = 0.0844

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Answer:

2)vertical angles

3)alternate interior angles

Step-by-step explanation:

yeah thats all i got

The line p || r as, the alternate interior angle are equal.

The basic qualities listed below make it simple to identify parallel lines.

We have to prove that p || r

and, we have given <1 = <5

<4 = <1 by (Vertically Opposite Angle).

and, <4 = <5 (Transitive Property)

So, the line p || r as, the alternate interior angle are equal.

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Answer: A

Step-by-step explanation:

Divide top and bottom by 4

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

The simplest form of the fraction is simply finding a common number to divide both the numerator and denominator by.

4/8 , we can divide both sides by 4 since it's possible to do so.

\(\frac{4/4}{8/4}\)

[\(\frac{1}{2}\)]

A. is the simplest form

Answer:

4(x+2) = 4x + 8

Step-by-step explanation:

because if they are multiplied out it would be 4x+8 = 4x + 8 which means it is infinite because both sides are equal

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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Answer: Line EF Edge GL!

Answer:

Answer above is correct! Option C. Line EF is correct on Edge :D

Step-by-step explanation:

Just answered it correctly on the assignment - hope this helps :P

The solution set is shaded above the boundary lines for inequalities 1, 2, 4, and shaded below the boundary lines for inequalities 3, 5, 6.

To analyze the linear inequalities and determine if the solution set is the shaded region above or below the boundary line, let's examine each inequality one by one:

y > -1.4x + 7

The inequality represents a line with a slope of -1.4 and a y-intercept of 7. Since the inequality is "greater than," the solution set is the shaded region above the boundary line.

y > 3x - 2

Similar to the previous inequality, this one represents a line with a slope of 3 and a y-intercept of -2.

Since the inequality is "greater than," the solution set is the shaded region above the boundary line.

y < 19 - 5x

This inequality represents a line with a slope of -5 and a y-intercept of 19. Since the inequality is "less than," the solution set is the shaded region below the boundary line.

y > -x - 42

The inequality represents a line with a slope of -1 and a y-intercept of -42. Since the inequality is "greater than," the solution set is the shaded region above the boundary line.

y < 3x

This inequality represents a line with a slope of 3 and a y-intercept of 0. Since the inequality is "less than," the solution set is the shaded region below the boundary line.

y < -3.5x + 2.8

This inequality represents a line with a slope of -3.5 and a y-intercept of 2.8.

Since the inequality is "less than," the solution set is the shaded region below the boundary line.

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Answer:

√178 = 13.3416640641

:-))

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....

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Answer:

wow Johnny is going to be a million-are by the end of the year :) lol

Step-by-step explanation:

Have a nice night mate

:)

mark brainliest please :)

Answer:

I.d.k wut the question is asking but...

Step-by-step explanation:

30 cents a day then for every day he adds on so day 1 = 30 cents

Day 2 will be 60 cents day 3 would be 90 cents and so on just keep adding 30 cents per day Hope this helps if i didnt answer wut you were asking comment wut you were looking for and i will gladly help :D

The total differential of z = xy + y² is dz = (y + x)dx + (2y + 1)dy.

To find the total differential of z = xy + y², we differentiate each term with respect to its corresponding variable.

Differentiating xy with respect to x gives us y dx, and differentiating y² with respect to y gives us 2y dy. Therefore, the total differential is dz = y dx + 2y dy.

However, we need to consider the chain rule since the variables x and y depend on another variable. Using the chain rule, we have dx = ∂x/∂x dx + ∂x/∂y dy and dy = ∂y/∂x dx + ∂y/∂y dy.

Simplifying these expressions, we get dx = dx + 0 dy and dy = 0 dx + dy.

Substituting these values into dz = y dx + 2y dy, we obtain dz = (y + x)dx + (2y + 1)dy.

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The number of weeks that they cat treats will train out is 27 weeks.

From the information given, the total grams will be:

= 200 + (2.5 × 1000)

= 200 + 2500

= 2700 grams.

Then he uses about 100 grams of cat treats every week, the number of weeks will be:

= 2700 / 100

= 27

There'll be 27 weeks.

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Answer:

the answers are C,D,E

Step-by-step explanation:

hope this helps luis!

Step-by-step explanation:

Right triangles obey Pythagorean theorem :

?^2  = 2^2 + 9^2

?^2 = 85

? = sqrt 85  ft

Answer:

85ft

Step-by-step explanation:

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

6.5

Step-by-step explanation:

The vertices A, B and C belongs to a right triangle whose area is equal to 24 square units.

According to geometry, two sides are perpendicular when their common angle is equal to 90°, as cos 90° = 0. This can be found by proving this result from linear algebra:

\(\overrightarrow {BC} \,\bullet \,\overrightarrow{BA} = \|\overrightarrow{BC}\|\cdot \|\overrightarrow {BA}\|\cdot \cos \theta = 0\)

Where:

The triangle is a right triangle if and only if the dot product of the two sides adjacent to the angle is equal to zero. First, we determine each vector associated to the two sides of the triangle:

Side BC

\(\overrightarrow{BC}\) = C(x, y) - B(x, y)

\(\overrightarrow {BC}\) = (- 4, 2) - (2, - 4)

\(\overrightarrow{BC}\) = (- 6, 6)

Side BA

\(\overrightarrow{BA}\) = A(x, y) - B(x, y)

\(\overrightarrow {BA}\) = (6, 0) - (2, - 4)

\(\overrightarrow{BA}\) = (4, 4)

Second, determine the dot product of the two sides:

(- 6, 6) • (4, 4) = (- 6) · 4 + 6 · 4 = - 24 + 24 = 0

Then, the sides BC and BA represent the base and the height of the triangle, respectively. The area of the right triangle (A) is equal to:

A = (1 / 2) · BC · BA

Where:

BA = √(4² + 4²)

BA = √32

BA = 4√2

BC = √[(- 6)² + 6²]

BC = √72

BC = 6√2

A = (1 / 2) · 4√2 · 6√2

A = (1 / 2) · 24 · 2

A = 24

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The probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

To solve this problem, we need to use the Poisson process and the exponential distribution.

Let X be the number of arrivals in a 3-minute interval. Since customers arrive at a rate of 25 per hour, the expected number of arrivals in a 3-minute interval is:

λ = (25/60) x 3 = 1.25

Thus, X is Poisson distributed with parameter λ = 1.25.

Let Y be the service time for a customer. Since Linda serves a customer, on average, in 1.5 minutes, Y is exponentially distributed with parameter μ = 1/1.5 = 0.6667.

Let Z be the waiting time for a customer in the line. Z is the sum of X independent service times, so Z is gamma distributed with parameters X and μ.

We want to find the probability that Z is between 3 and 6 minutes:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

where f(x,y) is the joint probability density function of X and Y:

f(x,y) = (λ^x / x!) e^(-λ) μ e^(-μy) = (1.25^x / x!) e^(-1.9167) e^(-0.6667y)

Now we can evaluate the double integral:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

= ∫∫ (1.25^x / x!) e^(-1.9167) e^(-0.6667y) dx dy

= ∫ e^(-0.6667y) e^(-1.9167) ∑ (1.25^x / x!) dx dy (x=0 to ∞)

= e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

The sum in the integral is the Taylor series expansion of e^1.25, which is equal to e^1.25 = 3.4903.

Using a table of integrals or a computer software, we can evaluate the integral:

∫ e^(-0.6667y) e^(1.25) dy = (1/0.6667) (e^(1.25) - e^(-0.6667(6))) = 3.7225

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is:

P(3 ≤ Z ≤ 6) = e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

= e^(-1.9167) (3.7225) (3.4903) = 0.1658 or about 16.58% (rounded to four decimal places).

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

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Answer: The equation x^2+3x+4 is a quadratic equation.

A quadratic equation is a second-degree polynomial equation in one variable (usually x), where the highest power of the variable is squared (x^2).

In this case, x^2+3x+4 is a second-degree polynomial with the variable x raised to the power of 2. Therefore, it is a quadratic equation.

Linear equations, on the other hand, are first-degree polynomial equations in one variable, where the variable is not raised to any power higher than 1.

Step-by-step explanation:

The angle of elevation, θ, can be found using the formula: tan(θ) = H / L. Therefore, the angle of elevation of the sun to the nearest degree is 75 degrees.

To find the angle of elevation of the sun, we can use the tangent function. Let's call the height of the tower "h" and the length of the shadow "s". Then, we have:

tan θ = h/s

Plugging in the values given, we get:

tan θ = h/s = (feet tall)/(feet long) =

Now we can use a calculator to find the inverse tangent of this value:

θ ≈ 74.5 degrees

Therefore, the angle of elevation of the sun to the nearest degree is 75 degrees.

To find the angle of elevation of the sun, you can use the tangent function from trigonometry. Let the height of the tower be H feet, and the length of the shadow be L feet. The angle of elevation, θ, can be found using the formula:

tan(θ) = H / L

To find θ, you can use the arctangent (inverse tangent) function:

θ = arctan(H / L)

Using a calculator, input the values for H and L, and find the arctan of the result to get θ. Make sure your calculator is in degree mode. Finally, round θ to the nearest degree to get the angle of elevation of the sun.

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To calculate the salary in the sixth year, we need to apply the annual increase of 6% to the initial salary of $32,000 for five consecutive years.

Year 1: $32,000

Year 2: $32,000 + 6% increase = $32,000 + (0.06 * $32,000) = $32,000 + $1,920 = $33,920

Year 3: $33,920 + 6% increase = $33,920 + (0.06 * $33,920) = $33,920 + $2,035.2 = $35,955.20

Year 4: $35,955.20 + 6% increase = $35,955.20 + (0.06 * $35,955.20) = $35,955.20 + $2,157.31 = $38,112.51

Year 5: $38,112.51 + 6% increase = $38,112.51 + (0.06 * $38,112.51) = $38,112.51 + $2,286.75 = $40,399.26

Year 6: $40,399.26 + 6% increase = $40,399.26 + (0.06 * $40,399.26) = $40,399.26 + $2,423.95 = $42,823.21

Therefore, the salary in the sixth year is approximately $42,823.

Total Salary = $32,000 + $33,920 + $35,955.20 + $38,112.51 + $40,399.26 + $42,823.21

Total Salary ≈ $223,210

The total salary paid over the six-year period is approximately $223,210.

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Answer: 6x

Step-by-step explanation:

so consider x as the number,

twice of x= 2x

2x tripled= 2x*3

               = (2*3)x

               = 6x