A circle has a diameter of 9 inches. What is the approximate ratio of the circumference of the circle to its diameter?


A) 22/7
B)7/22
C)1/2
D)2/1

Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller

AND OR

Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

Explicit Formula: an = a1 · dn-1

a1 = 64, d = 0.5

an = 64 · 0.5n-1

The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.

To find the expected number of books a customer will purchase,

use the formula for the expected value (also known as the mean) of a random variable:

Expected Value (μ) = Σ (x × P(x))

Where:

μ is the expected value.

x represents the possible values of the random variable (in this case, 0, 1, and 2).

P(x) is the probability associated with each value of x.

Probability of purchasing 0 books (P(0)) = 0.2

Probability of purchasing 1 book (P(1)) = 0.4

Probability of purchasing 2 books (P(2)) = 0.4

Now, calculate the expected value:

μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)

μ = 0 + 0.4 + 0.8

μ = 1.2

To find the standard deviation (σ) of the customer's book purchases,

use the formula for the standard deviation of a discrete random variable:

Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]

Where:

σ is the standard deviation.

x represents the possible values of the random variable.

μ is the expected value.

P(x) is the probability associated with each value of x.

In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).

Now, calculate the standard deviation:

σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]

σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]

σ = √[0.288 + 0.064 + 0.256]

σ = √0.608

σ ≈ 0.78

Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.

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Answer:

Jerome noticed the following house numbers on his street:

Answer 292 +13n

A polynomial expression is shown below. What is the value of m?

Answer -3

What is the domain of the function shown below

Answer −8 ≤ x <3and 4 ≤ x <8

The description relates to an isosceles right triangle.

An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.

In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.

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Answer:

For 5 songs the monthly charge be the same for both clubs.

It will cost $ 24.

Step-by-step explanation:

Let, for x songs, the monthly charges are same for both clubs,

Given,

For Treys online music club,

Monthly rate = $ 20,

Additional Charges for a song = $ 0.80,

⇒ Additional Charges for x song = $ 0.80x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 20 + 0.80x

Now, for Debs online music club,

Monthly rate = $ 21,

Additional Charges for a song = $ 0.60,

⇒ Additional Charges for x song = $ 0.60x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 21 + 0.60x

Hence, we can write,

[tex]20 + 0.80x = 21 + 0.60x[/tex]

[tex]0.80x - 0.60x = 21 - 20[/tex]

[tex]0.20x = 1[/tex]

[tex]\implies x = \frac{1}{0.20}=5[/tex]

Hence, for 5 songs the monthly charge be the same for both clubs.

Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24

The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.

We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).

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The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).

If a company bought 28 tickets and x of these tickets were for adults, then:

a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.

b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.

c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).

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Answer:

A

Step-by-step explanation:

⎡−25 26 −33⎤

⎥  4   −4    5  ⎥

⎥  3   −3    4  ⎦

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

Given :

The equation of the curve is [tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9[/tex]

Given tangent line is horizontal . Tangent line is horizontal when slope =0

Slope is nothing but the derivative.

So we find out x values where derivative =0

Lets take derivative for the given curve y

[tex]y=2x^3+3x^2-12x+9\\y'=2(3x^2)+3(2x)-12\\y'=6x^2+6x-12[/tex]

Now we set the derivative =0 and solve for

[tex]6x^2+6x-12=0\\Divide\; whole \; equation \; by \; 6\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0, x=-2\\\\x-1=0, x=1[/tex]

So , the slope =0 when x=1 and x=-2

Now we find out the points . Use the original function

[tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9\\x=-2\\2\left(-2\right)^3+3\left(-2\right)^2-12\left(-2\right)+9=29\\(-2,29)\\\\x=1\\2\left(1\right)^3+3\left(1\right)^2-12\left(1\right)+9=2\\(1,2)[/tex]

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

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Answer:

The answer is A: Quadrant 1

Step-by-step explanation:

On Edge :)

The probability that the number selected is the square of a natural number will be 0.20.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Robin randomly selects a number between 1 and 20.

Then the total number of the events will be

Total events = 20 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

The probability that the number selected is the square of a natural number will be

We know that natural numbers 1, 2, 3, 4, 5, and so on.

Then the square of the natural  numbers will be

1, 4, 9, 16, 25, ....

Favorable event = 3 {1, 4, 9, 16}

Then the probability will be

P = 4 / 20

P = 1/5

P = 0.20

The probability that the number selected is the square of a natural number will be 0.20.

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Answer:

√3

Step-by-step explanation:

got 100%

The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.

Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that   (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.

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Final answer:

The volume of the parallelepiped with sides of lengths a = 3.9 units, b = 5.7 units, and c = 3 units is given by the formula V = a × b × c. After performing the calculation, the volume comes out to be 66.87 cubic units.

Explanation:

To find the volume of the parallelepiped with edges of lengths a, b, and c, you can multiply the length of each edge together. The volume (V) of a parallelepiped (a three-dimensional figure formed by six parallelograms) is given by the product of the lengths of its three dimensions. In this case, the formula to calculate the volume is V = a × b × c.

By plugging in the values provided:

a = 3.9 units

b = 5.7 units

c = 3 units

We get:

V = 3.9 units × 5.7 units × 3 units

Doing the multiplication:

V = 66.87 cubic units

Therefore, the volume of the figure is 66.87 cubic units.

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the height of cylinder is h and radius of base is r.

The volume of cylinder will be : [tex]\pi r^2h[/tex]

The cone is of same height means h and same base means radius will be r.

The formula of volume of cone is : [tex]\frac{1}{3} \pi r^2h[/tex]

It means the volume of cone is one third of the volume of cylinder.

The volume of cylinder is given as π.

So, the volume of cone will be : [tex]\frac{\pi }{3}[/tex]   :   Answer

Hope it will help :)

Answer:  The correct option is (B).  It is not possible to determine if the triangles are congruent.

Step-by-step explanation:  We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.

As shown in the figure,

In ∆ABD and ∆ACD, we have

∠ADB = ∠ADC = 90°,

AD is the common side.

So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.

That is, to prove that the two triangles are congruent, we need one of the following two conditions:

(i)  BD = CD

or

(ii) ∠BAD = ∠CAD.

Since none of these two are given, so we cannot determine the congruence of the two triangles.

Therefore, it is not possible to determine if the triangles are congruent.

Thus, option (B) is correct.

While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.

The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.

The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

Given an integral expression:

[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

This can be written as:

[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

It is required to find the integral value.

Let u = 5 + (ln (x))²

Differentiate.

[tex]du=2ln(x)*\frac{1}{x} dx[/tex]

Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]

Substitute the values.

[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]

[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]

[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]

Substitute back the value of u.

[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]

Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

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