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Explain why systems of measurement are defined and provide an example to support your answer.​

Answer:

Step-by-step explanation:

Let X denote the first step

Let Y denote the second step

Then

E(X) = 0.2

E (Y) = 0.3

V (X) = 0.04

V (Y) = 0.09

Now,

E(X,Y) = E[X] + E{Y}

0.2 + 0.3 = 0.5

And since X and Y are independent

Therefore,

V(X , Y) = V(X) + V(Y)

= 0.04 + 0.09

= 0.13

Now required probability is

\(P\{ \sum X_i+\sum Y_i<8 \}=P\{ \frac{\sum X_i + \sum Y_i-nE[X+Y]}{\sqrt{Var(X+Y)n} } <\frac{8-20\times0.5}{\sqrt{0.13\times20} } \}\\\\=P\{Z_n<\frac{8-10}{\sqrt{2.6} } \}\\\\=P\{Z_n<-1.24\}\)

= Φ(-1.24)

= 1 - Φ (1.24)

= 1 - 0.8925

= 0.1075

The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

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The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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Answer:

The answer is Ahope this helps

Answer: 1

Step-by-step explanation:

16⁰ = 1

Anything to the power of zero is 1.

Answer:

8

Step-by-step explanation:

y = 4 and n = 3

5y - 4n = 5(4) - 4(3)

= 12

Answer:

−4n+5y

Step-by-step explanation:

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer:

it is a x= 40 degrees

Step-by-step explanation:

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

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The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².

The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;

P(x) = (x-3) (x-3) (x) (x) (x+1)

The expanded form is therefore;

P(x) = x^5 - 5x⁴- 6x³+ 18x².

Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².

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Answer:

50

Step-by-step explanation:

3/10 of x is 15, which means that 1/10 of x must be 5 because 15/3 = 5.

Now we can multiply 5 x 10, which is 50, so we know that x is equal to fifty

Answer:

=15

Step-by-step explanation:

Furthermore, you can convert "three" to "3" and "tenths" to "10" and then the equation and answer is:

3/10 x 15 = 4.50

Answer:25.3

Step-by-step explanation:

Because your adding 25 to 0 and leaving the decimal point and taking away 0 from 30

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Given statement solution is :-  For the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.

Regular Pay:

Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:

Regular Pay = Regular Hours x Hourly Rate

Regular Pay = 40 hours x $11.90/hour

Regular Pay = $476

Overtime Pay:

Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.

Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)

Overtime Pay = 13 hours x ($11.90/hour x 1.5)

Overtime Pay = 13 hours x $17.85/hour

Overtime Pay = $231.45

Gross Pay:

Gross Pay is the sum of Regular Pay and Overtime Pay.

Gross Pay = Regular Pay + Overtime Pay

Gross Pay = $476 + $231.45

Gross Pay = $707.45

Therefore, for the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

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Answer:

hope this helps u llllllllllllll

Answer:

5/18

Step-by-step explanation:

We assume they share equally.

5/6 ÷ 3 = 5/6 × 1/3 = 5/18

Answer:

They'll be on page 72

Step-by-step explanation:

Kaylee:

Current page = 24

Page per day = 16

Page, K, Kaylee is on at end of t days

K = current page + (page per day * Number of days)

K = 24 + 16t

Josiah:

Current page = 50

Page per day = 14

Page, J, Josiah is in at the end of t days

J = current page + (page per day * Number of days)

J = 50 + 14t

To be on the same page ;

K = J

24 + 16t = 50 + 14t

24 - 50 = 14t - 16t

- 26 = - 2t

t = 13

After 13 days, they'll be on same page :

K = 24 + 16(13)

K = 24 + 48

K =72

They'll be on page 72

The standard deviation of the number of toys donated by juniors is greater than that of seniors.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.

\(\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}\)

For the seniors, the mean is given as,

Mean = (5 x 2 + 35 x 2 + .... + 15 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 5)² + (26 - 5)² + (26 - 15)²] / 10

σ = 14.28

For the juniors, the mean is given as,

Mean = (40 x 2 + 25 x 2 + ....... + 40 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 40)² + (26 - 25)² + (26 - 40)²] / 10

σ = 13.19

The standard deviation of the number of toys donated by juniors is greater than that of seniors.

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The complete question is given below.

Answer:

one 10$ bill

1×10$ = 10$

10× 1$ = 10$

Answer:

One $10 bill

Step-by-step explanation:

1 x 10 = 10

10 x 1 = 10

10 = 10

The bell-shaped curve, also known as a Gaussian curve or a symmetrical distribution , showcases a central peak with data symmetrically distributed around it .

Revered for its iconic shape, the bell curve enchants the discerning observer with its symmetrical countenance, reminiscent of a resonant chime.

This majestic distribution unveils its true essence through its discernible apex, a testament to central tendency , where the mean, median, and mode converge, bestowing upon it an air of distinction .

The rough sketch of the curve having the bell shape is shown attached to the question.

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Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

$2.4 is the discount used to purchase a pair of sunglasses

percentage, a relative value indicating hundredth parts of any quantity.

Given that Alexandra bought a pair of sunglasses online for $24.

She used a coupon code to get a 20% discount.

The website also applied a 10% processing fee to the price after the discount.

20%-10%=10%

Now 10% of price is 24

10/100×24=x

2.4=x

24+2.4=26.4 is the actual price.

Hence, $2.4 is the discount used to purchase a pair of sunglasses

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Answer:

One Answer

Step-by-step explanation:

Take two points like (8,2) and (12,4) and do y2-y1/x2-x1.

4-2/12-8 = 4/2 = 2.

Then that another point and plug it in to the equation, y = 2x + b.

i will use (8,2). 2 = 2(8)+b. solve this and you get b= -14.

now you found your answer. y=2x + -14.

Answer:

1) What is the average score of the student surveyed?

b. 52.5

2) What is the median of the student's surveyed?

52.5

3) How many students were surveyed?

20 students

Step-by-step explanation:

1) What is the average score of the student surveyed?

Average score of the student's been surveyed means we should calculate the mean of the above scores

The formula for Mean = Sum of the number of terms/ Number of terms

Number of terms = 20

Average(Mean score) =

25 + 30 + 35 + 40 + 40 + 45 + 45 + 50 + 50 + 50 + 55 + 55 + 55 + 60 + 60 + 65 + 65 + 70 + 75 + 80/20

= 1050/20

= 52.5

2) What is the median of the student's surveyed?

25, 30, 35, 40, 40, 45, 45, 50, 50, 50, 55, 55, 55, 60, 60, 65, 65, 70, 75, 80

From the above data, we can see that 20 students were surveyed. To find the Median, we find the sum of the 10th value and the 11th value and we divide by 2

Hence,

25, 30, 35, 40, 40, 45, 45, 50, 50,) 50, 55, (55, 55, 60, 60, 65, 65, 70, 75, 80

10th value = 50

11th value = 55

Median = 50 + 55/2

= 105/2

= 52.5

3) How many students were surveyed?

Counting the results of the survey, the number of students that were surveyed = 20 students

Answer:

3/2 im oretty sure thats the answer

Answer:

7/2

3 as a whole number = 6/2

6/2 + 1/2 = 7/2

Step-by-step explanation:

Answer:

\(5 \times 10^4\)

Step-by-step explanation:

Let the number of grains of rice be g.

\(\frac{g}{1}=\frac{1}{2 \times 10^{-5}} \\ \\ g=\frac{1}{2} \times 10^5 \\ \\ =5 \times 10^4\)

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4