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.

The set of months having 31 days will be S = { January, March, May, July, August, October, December }.

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

We know that there are 12 months in a year.

From these months, we get that the months that have 31 days are:

January

March

May

July

August

October

December

The set of months having 31 days will be:

S = { January, March, May, July, August, October, December }

Therefore, we get that, the set of months having 31 days will be S = { January, March, May, July, August, October, December }.

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The perimeter of the equilateral triangle will be 27x - 48.

It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.

Therefore, the perimeter of the equilateral triangle will be:

= 3(9x - 16)

= 27x - 48

Therefore, the perimeter of the equilateral triangle will be 27x - 48.

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Find the perimeter of the equilateral triangle.

9x - 16

Answer:

  {-2}

Step-by-step explanation:

You want the solution set for the inequality 4(x +2)² ≤ 0.

The expression on the left cannot be negative, but it can be zero when ...

  x +2 = 0   ⇒   x = -2

The only solution to this inequality is x = -2.

Expressed as a set of solutions, we have ...

  x ∈ {-2}

Answer:

D. F

Step-by-step explanation:

Both F and G are not on plane P

Answer:

  1000

Step-by-step explanation:

You want the next number after 222 in base 3.

In any useful number base, the counting at any given integer position is ...

  0, 1, 2, 3, ..., (base -1), 0 and add 1 to the next number position

For base 3, this is ...

  0, 1, 2, 10

When the digit in the next higher position is also (base -1), then it gets incremented to 0 and the carry is propagated to the left.

In base 10, the equivalent is ...

  999 +1 = 99(9+1) = 99(10) = 9(9+1)0 = 9(10)0 = (9+1)00 = 1000

In base 3, your incremented value is ...

  222 +1 = 22(2+1) = 22(10) = 2(2+1)0 = 2(10)0 = (2+1)00 = 1000

The next whole base 3 number after 222 is 1000.

The circle has an area of 28.26 ft².

It is assumed that the circle's radius is 3 feet.

The circle's area must be determined.

What is radius of a circle ?

A line segment from a circle's center to its perimeter is known as the radius.

As per the question ;

Radius of circle , r = 3 ft

Area of the circle is given by ;

A = πr²

A = π × 3²

A = 9π

or

A = 9 × 3.14

or

A = 28.26 ft²

Thus , the area of the circle will be 28.26 ft².

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Answer:

Step-by-step explanation:

97

Answer:

$97 per/tire

Step-by-step explanation:

         [tex]Borrow\:8\\4 \cdot 9 = 36\\= 38 - 36\\= 2\\4 \cdot 7 = 28\\28 - 28 = 0\\\\= 97\:\mathrm{R0}[/tex]

Using integrals, the desired probabilities and measures are given as follows:

a) P(X < 6) = 0.84375 = 84.375%.

b) P(X < 13) = 1 = 100%.

c) P(6 < X < 8) = 0.15625 = 15.625%.

d) P(X > 5) = 0.31641 = 31.641%.

e) x = 6.434.

The distribution is given as follows, simplifying the operations:

f(x) = 0.09375x - 0.01171875x², 0 ≤ x ≤ 8.

Hence the density function is:

[tex]\int_{a}^{b} f(x) dx[/tex]

[tex]\int_{a}^{b} (0.09375x - 0.01171875x^2) dx[/tex]

[tex]0.046875x^2 - 0.00390625x^3|_{x=a}^{x = b}[/tex]

Applying the Fundamental Theorem of Calculus:

P(a < X < b) = 0.046875b² - 0.00390625b³ - 0.046875a² + 0.00390625a³

Hence, for item a:

P(X < 6) = 0.046875(6)² - 0.00390625(6)³.

P(X < 6) = 0.84375 = 84.375%.

For item b, the entire distribution is below 13, hence:

P(X < 13) = 1 = 100%.

For item c:

P(6 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(6)² + 0.00390625(6)³.

P(6 < X < 8) = 0.15625 = 15.625%.

For item d:

P(5 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(5)² + 0.00390625(5)³.

P(X > 5) = 0.31641 = 31.641%.

For item e:

We have to find b when a = 0 and P(X < b) = 0.9, hence:

0.046875b² - 0.00390625b³ = 0.9.

Using a calculator, the solution in the range of the distribution is given by:

b = x = 6.434.

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Answer:

See explanation

Step-by-step explanation:

Selected theme park admission prices has the lower standard deviation.

Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.

specific home stereo system: 3.99/59=0.0676.

selected theme park admission prices: 4/1499=0.002668

0.0676>0.002668

Answer:

The theme park ahs the lower standard deviation

The value of the integer number is -1

The statement is given as:

The sum of an integer and 7 times the next consecutive odd integer is 6

Let the integer value be x

So, the next consecutive odd integer is x + 2

When represented as an equation, we have

x + 7(x + 2) = 6

Open the bracket

x + 7x + 14 = 6

Evaluate the like terms

8x = -8

Divide both sides by 8

x = -1

Hence, the value of the integer number is -1

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A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex] kg and the earth has a mass of 5.972 x [tex]10^{24}[/tex] kg,26x[tex]10^{5}[/tex] earths would it take to equal the mass of the sun.

A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex]kg

earth has a mass of 5.972 x [tex]10^{24}[/tex]kg

Let x number of earths equal the mass of the sun

x (5.972 x [tex]10^{24}[/tex]) =  1.55272 x [tex]10^{31}[/tex]

x=  1.55272 x [tex]10^{31}[/tex] / 5.972 x [tex]10^{24}[/tex]

x= 26x[tex]10^{5}[/tex]

The wavelength of light emitted by a far-off galaxy extends and is "redshifted" toward the infrared region of the electromagnetic spectrum as it moves away from us. This means that by the time the light from a very distant galaxy that emits mostly visible or ultraviolet light reaches Earth, it will appear as infrared light.

Webb's ability to detect infrared light and the cosmos' expansion, which extends light to redder wavelengths, make it a good tool for identifying galaxies that originated at the beginning of the Universe's existence.

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Answer:

7/10

Step-by-step explanation:

Rewriting 0.7 as a fraction would be 7/10. 0.7 can also be 0.70, and 70/100

3 houseplants will weigh 15 kg (Refer to the tape diagram below).

The weight of 3 household plants will be about 15 kg.

Therefore, the weight of 3 household plants will be about 15 kg (Refer to the tape diagram below).

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Answer:

This point would affect the mean more because the median is less sensitive to outliers.

Step-by-step explanation:

Hope this helps!

Answer: I'm pretty sure its a verb

Step-by-step explanation:

4 × 10 then put a 6 by the 10 as an exponent.

The sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11

(6.9 × 10^6) and (5.9 × 10^5)

Sum

= (6.9 × 10^6) + (5.9 × 10^5)

= (6.9 + 5.9) × 10^(6+5)

= 12.8 × 10^11

Therefore, the sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11

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Answer:

c) 1

Step-by-step explanation:

Solving for the value of s,

→ 3s - 12 = -9

→ 3s = -9 + 12

→ s = 3/3

→ [ s = 1 ]

Thus, option (c) is correct.

There is no number which is satisfying the given conditions.

The first condition is that the number has seven digits.

The second condition is that the number lies between 1000 and 10000.

From these two conditions, we can conclude that there is no number which satisfies all the given conditions. Because there is no seven-digit number which is less than 10000.

Let us assume that the second condition is the number lies between 1000000 and 10000000.

And let the required number be "abcdefg".

The third condition is the digit in the tenth place is 150% of the digit in the thousandth place.

⇒ f = 150 × (d) / 100 = 1.5 × d

The fourth condition is the digit in the hundredth place is the sum of the digit in the tenth place and the digit in the thousandth place.

⇒ e = f + d = 1.5d + d = 2.5d

The fifth condition is the sum of all the digits in the number is 17.

⇒ a + b + c + d + e + f + g = 17

⇒ a + b + c + d + 2.5d + 1.5d + g = 17

⇒ a + b + c + 5d + g = 17

And the last condition is none of the digits is zero.

Using the last condition the possible values for d are either 1 or 2.

Because, if d is 3, then if we take the least possible digit(1) for others, the sum on the LHS is 19, which is greater than 17.

And d can not be 1. Because, if d is 1, then f and e are 1.5 and 2.5 respectively. 1.5 and 2.5 are not valid digits.

Therefore, the value of d = 2.

f = 1.5d = 3

e = 2.5d = 5

If d = 2, then we get a + b + c + g + 10 = 17

⇒ a + b + c + g = 17 - 10

⇒ a + b + c + g = 7

⇒ The possible values for (a, b, c, g) are (4, 1, 1, 1), (1, 4, 1, 1), (1, 1, 4, 1), (1, 1, 1, 4), (2, 2, 2, 1), (2, 2, 1, 2), (2, 1, 2, 2), (1, 2, 2, 2), (2, 3, 1, 1), (3, 2, 1, 1), (1, 1, 2, 3), and (1, 1, 3, 2)...

Therefore there are more than 12 possible answers that satisfy the assumption made.

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Answer:

[tex]x = \frac{2a}{a - 2} [/tex]

Answer: ann is 69 and beth is 138

Step-by-step explanation:

Answer: f(x^2) = x^2 - 5

Answer:

39 is the sum of their ages

Step-by-step explanation:

Hope this helps :)

Yes; The construction demonstrates how to bisect an angle correctly using technology because Circles D & E have the same radius

How to properly bisect an angle?

In construction of angles and lines, bisection means dividing either a given angle or line segment into two equal parts. This means after the construction, the two parts must have equal measure.

The steps to bisect a line segment are as follows;

1. Draw the required length of the line segment AB.

2. With point A and radius of the compass greater than half of AB, describe arcs above and below the segment.

3. With the same radius as in step 2 and point B, describe two arcs above and below the segment. These would intersect that of step 2 at C and D.

4. Join the points of intersection of the arcs with a straight line CD.

Now, in this given question with the circle, we can see that line AG is the line that bisects the angle EAD.

Now, we see that circles C and D have the same radius and as such the construction demonstrated is correct for that very reason.

Answer: yes

Step-by-step explanation: the construction correctly shows how to bisect an angle using technology because circles D and E have the same radius. 

Answer:

3

Step-by-step explanation:

i think its 3 because 28 divided by 9 is 3

Answer: 2.1606

Step-by-step explanation:

36.01 x 0.06 =

3601/100 x 6/100=

3601 x 6/(100 x 100)=

21606/10000=2.1606

If the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019

The given parameters are:

Year Millionaire Households

2015 9,200,000

2016 9,350,000

2017 9,620,000

2018 9,970,000

From the question, we have

The percentage increase between 2017 and 2018 continued for 2018 and 2019

The percentage increase between 2017 and 2018 is calculated as

Percentage = (2018 - 2017)/2017 * 100%

So, we have

Percentage = (9,970,000 - 9,620,000)/9,620,000 * 100%

Evaluate

Percentage = 3.64%

The number of millionaire households in 2019 is calculated as

2019 = 2018 * (1 + percentage)

So, we have

Households = 9,970,000 * (1 + 3.64%)

Evaluate

Households = 10332908

Hence, if the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019

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Check the picture below.

Answer:

below

Step-by-step explanation:

25)-ab

=-(-1/2)(3/4)

=3/8

26)b÷c

=(3/4)×1/-6

=3/-24

=-1/8

27)c÷a

=-6÷-1/2

=6×2/1

=12