Suzette likes to dance 10 hours a week to stay in shape. She tracks the amount of time she dances each week relative to her goal.The table shows the data for the last five weeks.Week12345Dance time (hours)2.4−32140−2What is the average dance time per week for Suzette relative to her goal number of hours?Drag a value to the box to complete the statement.

Answer:

A

Step-by-step explanation:

A

Since it is a right triangle, we can apply trigonometric functions:

Tan a = opposite side / adjacent side

Where:

a= angle = x

Opposite side = 98

Adjacent side = 180

Replacing:

Tan x = 98/180

Solve for x

x = arc tan (98/180)

x= 28.57°

The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Here, we have,

The Taylor series at x=0 for cos(x) is given by:

cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!

Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):

To find the Taylor series for the given function, we'll use power series operations.

We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.

Let's start with cos²((3πx)/2):

cos²((3πx)/2) = (cos((3πx)/2))²

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²

Expanding the square of the series, we get:

cos²((3πx)/2)

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Now, we'll multiply the x term to obtain the Taylor series for the given function:

x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Expanding the multiplication and rearranging the terms, we have:

x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Judging by appearance, it seems reasonable to say that the figures below are similar. They appear to have the same basic shape and size, with similar angles and proportions.

However, to confirm this, we would need to take measurements and compare them to determine if they are mathematically similar. Without precise measurements, it is possible that the figures could have subtle differences that are not immediately apparent to the eye.

To determine if the figures below are similar, we need to examine their proportions and angles. Similar figures have corresponding angles that are equal and corresponding sides that are proportional.

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Answer:

you need a dotted point starting at 3 and going to to the right

Step-by-step explanation:

the dotted point means x < , x > and since it is greater you always go to the right

Answer:

Mia is correct

Step-by-step explanation:

The outer triangle and the inner triangle are similar ( AA postulate )

Then the ratios of corresponding sides are in proportion

\(\frac{2}{2+6} \) = \(\frac{3}{x} \) , that is

\(\frac{2}{8} \) = \(\frac{3}{x} \) ( cross- multiply )

2x = 24 ( divide both sides by 2 )

x = 12

Answer:

4

Step-by-step explanation:

Because you use trial and error to see what x is and it says integet meaning 1,2,3,4,5,6... and their opposites.

Answer:

x ≈ 5 using math and x ≈ 4 using trial and error

Step-by-step explanation:

\(6^x = 3800\)

\(x = log_{6}*3800\)

x ≈ 4.6 ≈ 5

Hope this helped!

-----------------------------------------------------------------------------------------------

Trial and Error:

6 ^ 4 = 1276

6 ^ 5 = 7776

3800 is closer to 1276, so x = 4

It could be D but mathematically it's 3/6=1/2

Answer:

\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)

Answer:

So she has $50–$43.85 = $6.15 in her pocket and $25 in her savings account

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is B.

The correct way of devising a yearly savings plan to pay for college education makes the most sense is,

''Estimate the total cost and divide that by the number of years until you go to college.''

Option B is true.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

To find the way of devising a yearly savings plan to pay for your college education makes the most sense.

Hence, We know that;

The correct way of devising a yearly savings plan to pay for college education makes the most sense is,

Estimate the total cost you have and divide that by the number of years for college time until you go to college.

Thus, correct way of devising a yearly savings plan to pay for college education makes the most sense is,

''Estimate the total cost and divide that by the number of years until you go to college.

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Answer:

24 meters

Step-by-step explanation:

I hope this helps!

Answer:

24 meters

Step-by-step explanation:

you do 6 times 4

The estimated market value of Citrus County's assets, with an average duration of 8 and a market value of $1 million, would be approximately $1,055,284 if the interest rate changes to 4%.

In this case, the assets have an average duration of 8. When the interest rate changes from 5% to 4%, the change in interest rates is 1%. By applying the duration formula, the estimated percentage change in the market value of the assets would be approximately -8% (negative duration multiplied by the change in interest rates).

To calculate the estimated market value, we need to multiply the estimated percentage change (-8%) by the current market value ($1 million) and add it to the current market value. Thus, the estimated market value would be approximately $1,055,284 (1,000,000 + (1,000,000 * -8%)).

Duration is a measure of the sensitivity of an asset's price to changes in interest rates. It provides an estimate of the percentage change in the market value of an asset for a given change in interest rates. The duration formula states that the percentage change in the market value of an asset is approximately equal to the negative duration multiplied by the change in interest rates.

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The empirical formula of a compound is the simplest and lowest whole number ratio of the atoms of each element that makes up a compound.

To find the empirical formula from percentages, you need to first calculate the mass of each element present in the compound, based on the percentage of each element. Once you have the mass of each element, divide each mass by the atomic mass of that element to get the number of moles of each element. Then divide each mole by the smallest number of moles to get the mole ratio. This ratio is the empirical formula for the compound.

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Answer:

125

Step-by-step explanation:

We can graph the system equation

each equation represents a line where the line intercepts each other we find the solution.

the solution of the system is

x=3, y=4

in ordered pair is

(3,4)

we also can solve it

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

The approximate diameter of the sphere with a surface area of 95π inches is approximately 9.74 inches.

The surface area of a sphere is given by the formula:

A = 4πr²

where A is the surface area and r is the radius of the sphere. We can solve this equation for r to get:

r = √(A / 4π)

Substituting A = 95π, we get:

r = √(95π / 4π)

 = √(95/4)

 ≈ 4.87

Therefore, the radius of the sphere is approximately 4.87 inches. The diameter of the sphere is twice the radius, so the approximate diameter of the sphere is:

d ≈ 2r ≈ 2(4.87) ≈ 9.74

Therefore, the approximate diameter of the sphere is approximately 9.74 inches.

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Step 1

Given;

Required; To simplify by combing terms

Step 2

Combine like terms.

Therefore, we will add them together

The full solution will be;

Answer;

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

you stumped me.

Step-by-step explanation:

:/

Answer:

A. is the correct answer

Step-by-step explanation:

I believe don't quote me on this one

The order of values in ascending order will be -4<-2<2<2.64<4<16 as the definition of ascending order says, "When numbers are arranged in ascending order, they are done so from smallest to largest".

When numbers are arranged in ascending order, they are done so from smallest to largest. Climbing down the stairs of numbers starting with their highest value is another way to think of descending. The slide is descended while moving down it. Ascending order, in which the numbers are arranged from lower value to higher value, is the opposite of descending order. A number can be arranged in ascending order by going from smallest to largest from left to right.

Here,

4²=16

-√4=-2

√4²=4

-2√4=-4

6-4=2

√7=2.64

-4<-2<2<2.64<4<16

According to the definition of ascending order, "When numbers are arranged in ascending order, they are done so from smallest to largest," the order of values in ascending order will be -4<-2<2<2.64<4<16.

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Answer: 7.3 inches

Step-by-step explanation: the answer is 7.3 inches because I did 13.7 inches/1000 miles = x inches/100 miles 1000x = 137 x = 7.3 inches. That is how the answer is 7.3 inches.

The type of sampling used in this scenario is A Systematic sampling.

Systematic sampling involves selecting every kth element from a population list after randomly selecting a starting point. In this case, Christopher collects data from all the band members in his class, indicating that he is sampling systematically from a known list of band members.

This method ensures that every band member in the class has an equal chance of being selected, and it simplifies the process by following a predetermined systematic approach rather than relying on random selection or stratification.

Therefore, the type of sampling used in this scenario is A Systematic sampling.

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Complete question is below

To study the sleeping habits of all band members in his school, Christopher collects data from all the band members in his class. Which type of sampling is used? Select the correct answer below:

A Systematic sampling

B Stratified sampling

C Cluster sampling

D Convenience sampling

Answer:

down below

Step-by-step explanation:

The picture is a little blurry so the graph is hard to read. But I believe the answer is 7/8. The rose would be counting up or down the y axis and the run is counting forward or backward on the x axis.

Hope this helps! :)

Answer:

rise = 7, run = 8

slope = rise/run = 7/8

See attached picture for graph in case you have to plot

Step-by-step explanation:

Take two distinguishable points, (x1, y1) and (x2, y2)  on the graph. Find the difference in their y values= y2 - y1. This will be the rise

Find the corresponding difference in the x values, x2 - x1. This will be the run

Divide the y difference by the x difference and you get rise/run which is the slope of the line

Two clear points are (x1 = 0, y1= -7) and (x2=8, y2=0)

(y2 - y1)/(x2 - x1)

= (0 - (-7)/(8 - 0))

= (0+7/(8 - 0)             ==> 2 negatives make a positive

= 7/8  and that is rise/run

Rise = 7, run = 8

Picture shows rise and run if you want to graph it

Answer and Step-by-step explanation:

Yes, the three side lengths could form a triangle.

To find out if the sides can form a triangle, you take the lowest side lengths and add them together. If they are greater than the longest side, then they can form a triangle. If it is equal or less than the longest side, then it CAN NOT form a triangle.

7.8 + 10.4 > 13

18.2 > 13

So, the answer is Yes.

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u have an arithmetic sequence with a common difference of 3

A(n) = -4 + (n-1) * 3

sorry if this isn't the right answer...

i really suck at math

Answer:

c

Step-by-step explanation:

Answer:

it is hard to answer this question because it is not in line, but if I understand corectly then the answer is 20

Step-by-step explanation:

3x=x+40

3x-x=40

2x=40 /:2

x=20