Megan cuts pieces of colored felt to
create a logo of a sun behind a
mountain peak. Determine the
approximate total amount of felt used
in the logo.

Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

Answer:

Least no of packs = 120

Step-by-step explanation:

Given that,

Plastic plates come in packs of 8, plastic utensils come in packs of 12, and plastic cups come in packs of 20.

We need to find least numbers of packs you should buy in order to have the same number of plates, utensils, and cups.

It means we need to find the LCM of 8,12,20

Prime factorisation of 8 = 2×2×2

Prime factorisation of 12 = 2×3×2

Prime factorisation of 20=2×5×2

LCM = 120

Hence, there are 120 least number of packs you should buy in order to have the same number of plates, utensils, and cups

Answer:

\( {9x}^{2} - 30x + 25\)

\(\huge\underline\bold\blue{ƛƝƧƜЄƦ}\)

(3x + 5)(3x - 5)

By using identity

(a + b)(a - b) = a² - b²

3x² - 5²

9x² - 25

To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:6

Step-by-step explanation:

42/7.

Answer:

Percent of people satisfied with the​ car  = 70%

Step-by-step explanation:

Given:

Total number of people survey = 1,400

Number of people satisfied with the​ car = 980

Find:

Percent of people satisfied with the​ car

Computation:

Percent of people satisfied with the​ car  = [Number of people satisfied with the​ car / Total number of people survey]100

Percent of people satisfied with the​ car  = [980 / 1400]100

Percent of people satisfied with the​ car  = 70%

The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.

It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.

By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).

So,

5/6 × 6/5

= 30/30

= 1

Hence, 6/5 is the multiplicative inverse of 5/6

Read more on multiplicative inverse:

https://brainly.com/question/21973802

#SPJ1

Answer:

20 men

Step-by-step explanation:

1. 4:9 = 20:45

men to women

a. 45 divided by 9 = 5

b. 4 x 5 = 20

Answer:

There is no insufficient sufficient evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.

The flow chart to prove m∠3≅m∠4 is given below.

What is the vertical angle theorem?

The Vertical Angle Theorem states that when two straight lines cross, they create two linear pairs. Due to the fact that their angles add up to 180 degrees, the adjacent angles created when two lines intersect are known as supplementary angles.

Given, m∠1≅m∠2

Then, m∠1≅m∠3 ( vertical angles theorem)

m∠2≅m∠3 (Given)

Then, m∠2≅m∠4 (vertical angle theorem)

Hence, m∠3≅m∠4 (transitive property of congruence) proved

To learn more about the vertical angle theorem

https://brainly.com/question/1673457

#SPJ4

Exact form: 14/9

Decimal:1.555555…

Mixed number: 1 5/9

The values of z in the regular polygon  is 21.

A regular polygon is a polygon with congruent sides and equal angles.

To calculate the value of z in the regular polygon, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for z

Hence, the values of z is 21.

Learn more about regular polygon here: https://brainly.com/question/1592456

#SPJ1

Answer:

{a, e, i, o, u}

Step-by-step explanation:

Since U is the universal set of all the letters in the English alphabet = {a, b, c, ......, x, y, z}

and A is the subset containing all the consonants,

Ac which is the complement of set A must be all the letters that are not consonants.

This would be the set of all vowels

a, e, i , o, u

No distinction made between upper and lowercase letters

Given that U is the Universal set and we are to find the subset that is not the consonants then the values that we would have would be the vowels {a, e, i, o, u}

This is the term that is used to refer to the collection of different elements in the field of mathematics and statistics.

The Universal set here would be all of the alphabets

This would be

U= {a, b, c ,d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}

The consonant is a subset of the universal set U.

This would be

A= {b, c ,d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}

The we have another subset that is defined as Ac, these are the values that are not contained in the set A.

Hence the value would be {A, e, i, o, u} That is the vowels in the alphabet.

Read more on sets here:

https://brainly.com/question/2166579

#SPJ1

Answer:

In geometry symmetry has to measure to the same but in real life if they are close enough it is good enough

The specified scale factor of the dilation from S to M is 3/2 therefore, the scale factor of the dilation transformation from M to S is 2/3

A dilation is a transformation in which the lengths of the sides of the image are increased or decreased in the proportion, specified by a scale factor to the dimensions of the pre-image.

The specified scale factor from triangle S to triangle M = 3/2

3/2 = 1.5

Therefore, the length of the sides of triangle M are 1.5 times the lengths of the sides of triangle S

Let L represent the length of a side of triangle S, we get;

The length of the corresponding side on triangle M = 1.5 × L

The scale factor from triangle M to triangle S is found by taking the ratio of the corresponding sides of triangle S and M as follows;

Scale factor, SF, from M to S  = Length of a side on triangle S ÷ Length of the corresponding side on triangle

Therefore;

\(SF = \dfrac{L}{1.5\cdot L} = \dfrac{1}{1.5}\)

1.5 = 3/2, therefore;

\(SF = \dfrac{1}{1.5} = \dfrac{1}{\frac{3}{2} } =\dfrac{2}{3}\)

Therefore, the scale factor from M to S is 2/3

Learn more about scale factor of a dilation here:

https://brainly.com/question/13005407

#SPJ1

Answer:the answer is 1/16

so none of the above

Step-by-step explanation:

Step-by-step explanation:

Square root of

784 / 1225

28 / 35

In simplest form

4/5

Answer:

I do not understand the question please ask a question before sending that

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

for more search question  function

https://brainly.com/question/25638609

#SPJ8

Answer:

Step-by-step explanation:

Answer: 2

Step-by-step explanation:            

A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

Learn more about theory here:

brainly.com/question/18996125

#SPJ2

Answer: the graph is incorrect

Step-by-step explanation:

The graph should be headed towards the left (the negative x side) because x is negative

Answer:

The graph is not correct, because it is a positive graph. It answers the equation y= x, and Franco said it was y= -x. His line would be negative, and this graph is positive.

Step-by-step explanation:

By trigonometric functions, the missing sides of the right triangles are:

Case 7: AC = 9.725, BC = 10.071

Case 8: AB = 21.301, BC = 18.807

Case 9: BC = 4.585, AC = 8.999

Case 10: AB = 10.461, BC = 7.774

In this problem we have four cases of right triangles, each of which has a known side and a known angle and we must determine all the missing lengths by trigonometric functions:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Where:

Now we proceed to determine the values of the missing lengths:

Case 7

AC = 14 · sin 44°

AC = 9.725

BC = 14 · cos 44°

BC = 10.071

Case 8

AB = 10 / cos 62°

AB = 21.301

BC = 10 · tan 62°

BC = 18.807

Case 9

BC = 10.1 · sin 27°

BC = 4.585

AC = 10.1 · cos 27°

AC = 8.999

Case 10

AB = 7 / cos 48°

AB = 10.461

BC = 7 · tan 48°

BC = 7.774

To learn more on trigonometric functions and right triangles: https://brainly.com/question/28984437

#SPJ1

The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

Read more about Area of shaded portion at: https://brainly.com/question/1297097

#SPJ1

The value of x is 65°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:
Angle PQR is a right angle.

The measure of angle SQR is 25 degrees.

The measure of PQS is x degrees.

The angle addition postulates:

∠PQR = ∠SQR  + ∠PQS

90° = 25° + x

x = 90° - 25°

x = 65°

Hence, ∠PQS = 65°.

To learn more about the angle addition postulate;

https://brainly.com/question/14957499

#SPJ1

Answer:

9x - 6

Hope this helps! <3

(If you need a step by step lmk)

Answer:

6x+3(x-2)

6x+3x-6

9x-6