My friend needs help with her homework. The problem she is on is: There is 11 sandwiches. 2 children shares each sandwich. How many children share the sandwiches?

The approximation sin (x) = x - x^3/6 has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].

In mathematics, the alternating series is an infinite series of a term in the form of

[tex]{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}} \\{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}[/tex]

The expansion series of sin(x)

[tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!} +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +..[/tex]  (a)

the given approximation [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex]     (b)

So, the approximation error term =(b)-(a)

       [tex]\rm = -[ +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +\frac{x^{9} }{9!}-....]\\\rm = -\frac{x^{5} }{5!} +\frac{x^{7} }{7!} -\frac{x^{9} }{9!}+....[/tex]

The alternative series theorem states that we need to ensure that the absolute value of the first term [tex]\rm \frac{x^{5} }{5!}[/tex]less than the error limit, For that the sum will be below the error limit, which means

[tex]\rm \frac{x^{5} }{5!}[/tex] <  0.000001

Solving for x, we get

x [tex]\rm x^{5} = 5! \times 0.000001\\ = 0.000120\\\rm = 0.000120^{1/5} \\ = 0.164375[/tex]

Therefore, the approximation   [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex] has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].

by checking

[tex]\rm sin(0.164375)-(0.164375)^{3/3!} \\= 9.993513\times10^{-7} < 0.000001[/tex]

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Answer:

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Step-by-step explanation:

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

we have

[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}[/tex]

we know that

[tex](x+a)^{2}=x^{2}+2ax+a^{2}[/tex]

in this problem

[tex]2ax=\frac{1}{2}x[/tex] ------> [tex]a=\frac{1}{4}[/tex]

[tex]a^{2}=\frac{1}{16}[/tex] -----> [tex]a=\frac{1}{4}[/tex]

so

[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=(x+\frac{1}{4})^{2}[/tex]

the missing number in the left side is [tex]\frac{1}{4}[/tex]

A diameter is a line segment that has endpoints on a circle and passes through the center of the circle. The correct option is: diameter

A diameter is a line segment that has endpoints on a circle and passes through the center of the circle. It is a crucial geometric element in the study of circles and plays a fundamental role in various geometric properties.

Key points about the diameter:

Definition: As mentioned, a diameter is a line segment that connects any two points on the circle's circumference and passes through the center of the circle. It is the longest chord of the circle.

Length: The length of the diameter is exactly twice the length of the radius. If "r" represents the radius, then the length of the diameter is "2r."

Properties: The diameter divides the circle into two equal halves, each known as a semicircle. It is also the largest possible chord of a circle.

In summary, a diameter is a significant geometric concept related to circles, and it is characterized by its property of passing through the center of the circle and being twice the length of the radius.

The correct option is: diameter

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Answer:

The correct answer is a triangle will be formed.

Step-by-step explanation:

If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex, the resulting figure will have 3 sides or vertices. Hence, this shape will be a triangle. The triangle only forms if it does pass through the top vertex.

So, triangle is the answer.

u - v = <6 - 1, -9 - (-4)> = <5, -5> . . . . . . . matches selection A)

_____

The sum or difference of vectors is simply the sum or difference of corresponding coordinates.

The answer is 17.8° C

In order to Convert Fahrenheit to centigrade scale we use the formula

°C = (°F - 32) × 5/9

So putting the values in the equation we get

(64°F − 32) × 5/9 = 17.778°C

The line segments AC and CE break this quadrilateral into three triangles.  The area of a triangle is given by A=1/2bh.  The base of ΔADC is 6 and the height is 4.5; A=1/2(6)(4.5)=13.5m².  

To find the area of ΔACE, we must first find the length of segment AE.  To do this, we will need to know both EC, which we are given, and AC, which we are not.  We will use the Pythagorean theorem for ΔADC to find the length of AC.

6²+(4.5)²=(AC)²

36+20.25=(AC)²

56.25=(AC)²

√56.25=√(AC)²

7.5=AC

Now that we know the length of AC, we will use the Pythagorean theorem on ΔACE to find the length of AE:

7²+(AE)²=(7.5)²

49+(AE)²=56.25

49+(AE)²-49=56.25-49

(AE)²=7.25

√(AE)²=√7.25

AE≈2.69

Now we can find the area of ΔACE:  A=1/2(7)(2.69)=9.415m²

To find the area of ΔBCE, we need to find the length of EB.  We know that AB=9 and AE=2.69.  Subtracting those two, we find the length of EB to be 6.31m.  Therefore the area of ΔBCE=1/2(6.31)(7)=22.085m²

The total area is given by adding these three together:

13.5+9.415+22.985=45m².

It would take 15 rows of 20 tiles each to cover the rectangular portion of this patio (4.5m*100 =450cm; 450cm/30-cm tiles = 15 rows of tiles; 6m*100=600cm; 600cm/30-cm tiles = 20 tiles per row) which comes out to 300 tiles.  However, adding an extra 10% to that:

300*0.1+300=30+300=330 tiles.

To determine the affected area by an asteroid impact, calculate the radius from the circumference of the crater and then the area of the circle. The estimated crater area from a 79.5-mile circumference is approximately 506.7 square miles, indicating the surface area affected.

To estimate how much of the Earth's surface has been affected by the asteroid impact that resulted in a crater with a measured circumference of 79.5 miles, we need to recognize that this measurement refers to the circumference of a circle (the crater). We use the circumference to find the radius of that circle, and then calculate the area of the circle to understand the extent of the impact.

First, we calculate the radius (r) of the crater using the circumference (C): C = 2πr. Plugging in the known circumference, r = C / (2π), so r = 79.5 miles / (2 × 3.14), which approximates to 12.7 miles. Moving forward, we can now find the area (A) of the crater using A = πr². Squaring the radius gives us [tex](12.7)^2[/tex] and then multiplying by π gives us approximately 506.7 square miles.

The actual crater area accounting for the circular shape is approximately 506.7 square miles, which roughly indicates the immediate surface area affected by the impact. It's noteworthy that the surrounding ecosystem and earth's surface may also experience indirect effects extending beyond this area.

Answer:

Step-by-step explanation:

A geometric sequence or geometric progression is a sequence where each term after the first one can be found by multiplying a certain factor.

So, basically, to find the geometric sequence, we just need to divide the second term by the first term and observe if it results a constant factor.

By doing that, we observe that the second equence is a geometric sequence with a reasonf of 1/2, let's demonstrate it

[tex]8\times \frac{1}{2}= 4 (second \ term)\\4 \times \frac{1}{2}=2 (third \ term)\\ 2 \times \frac{1}{2}= 1 (fourth \ term)\\ 1 \times \frac{1}{2}= \frac{1}{2} (fiftg \ term)\\ \frac{1}{2} \times \frac{1}{2}= \frac{1}{4} (sixth \ term)[/tex]

As you can observe, we perfectly built the sequence is its ratio or factor.

Therefore, choice B is a geometric sequence.

The standard deviation for the given binomial distribution is 1.449.

A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution.

σ = [tex]\sqrt{nP(1 -P)}[/tex]

where,

σ is the standard deviation

n is the number of trials in the binomial experiment.

P is the probability of success on an individual.

According to the given question we have,

The number of trials in the binomial experiment, n = 10

The probability of success on an individual, p = 0.70

Therefore, the standard deviation is given by

σ = [tex]\sqrt{10(0.70)(1 -0.70)} = \sqrt{7(0.3)}=\sqrt{2.1} =1.449[/tex]

Hence, the standard deviation for the given binomial distribution is 1.449.

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To calculate the cash option payout, we need to discount the annual payment at a rate of 44% over 2222 years using the present value formula. The cash option payout would be approximately $2,938,624.13.

To determine the cash option payout, we need to calculate the present value of the annuity. The annual payment is the total amount of the lottery prize divided by the number of years, which is $33 million / 2222 = $14,808.81. To discount this amount at a rate of 44% over 2222 years, we can use the formula:

PV = Payment / ((1 + r)^n - 1) * (1 - (1 / (1 + r))^n)

where PV is the present value, Payment is the annual payment, r is the discount rate (0.44), and n is the number of years (2222). Plugging in the values, we get:

PV = $14,808.81 / ((1 + 0.44)^2222 - 1) * (1 - (1 / (1 + 0.44))^2222)

Solving this equation gives us the cash option payout, which is approximately $2,938,624.13.

Number of assistants required to make 13 flower arrangements = 2

Let us use unitary method here.

Number of assistants required to make 1 flower arrangements = 2/13

Number of assistants required to make 195 flower arrangements = 2/13 *195 =30

Answer : So 30 assistants are required to make 195 flower arrangements.