The length of a rectangular piece of steel in a bridge in 5 meters less than a triple the width. The perimeter of the piece of steel is 30 meters. Find the length of the piece of steel. Find the width of the piece of steel.

In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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The unknown lengths of the similar figures are:

r = 63 m

x = 45 m

Two figures are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides are also equal.

Using the above concept, we can equate the ratio of the corresponding sides and solve for the unknown lengths. That is:

Quadrilateral:

B/A  = C/B

15/5 = r/21

3 = r/21

r = 3 * 21

r = 63 m

Star:

18/4 = x/10

4.5 = x/10

x = 4.5 * 10

x = 45 m

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Answer:

The value of the test statistic is \(z = 1.78\)

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Sample 1:

\(\mu_1 = 110, s_1 = \frac{7.2}{\sqrt{81}} = 0.8\)

Sample 2:

\(\mu_2 = 108, s_2 = \frac{6.3}{\sqrt{64}} = 0.7875\)

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \(\mu = 0\)

Distribution of the difference:

\(X = \mu_1 - \mu_2 = 110 - 108 = 2\)

\(s = \sqrt{s_1^2+s_2^2} = \sqrt{0.8^2+0.7875^2} = 1.1226\)

What is the value of the test statistic?

\(z = \frac{X - \mu}{s}\)

\(z = \frac{2 - 0}{1.1226}\)

\(z = 1.78\)

The value of the test statistic is \(z = 1.78\)

Answer:

The answer is 80°.

Step-by-step explanation:

360° - 100° = 260°

260° - 100° = 160°

160° / 2 = 80°

* the theorem is m < UTS = 1/2 (m < UTS - m < US)

* m = measure

The measure of m<UTS is 80 degree.

The correct option is D.

An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference.

A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be created by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.

We have,

From the figure we can write

m < UTS = 1/2 (m < UTS - m < US)

As, m <UTS = 360 and arc US = 100

= 1/2(360° - 100° - 100)

= 160° / 2

= 80°

Thus, m< UTS is 80 degree.

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Since the y-intercept of the line is (0,1) and the line passes through the point (2,4) which is also satisfied by the equation of the line, the given equation represents the graph of the line.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation of the line is y = (3/2)x + 1.

To find the y-intercept of the line, substitute x = 0 into the given equation,

y = (3/2)(0) + 1

y = 1

Note that the y-intercept of the graph of the line is also 1.

The graph of the line passes through points (2,4).

To verify whether the equation satisfies the coordinates of (2,4) or not, substitute the coordinates of the point into the given equation:

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

4 =4

The equation is true.

Hence, it can be said that the given equation represents the graph of the line.

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a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

  c, d.  see attached

  e. about 2.96 miles; about $1.63 million

Step-by-step explanation:

e. The x-coordinates of points A and B are 1/3 and 2/3 of the x-coordinate of "Downtown", respectively. The y-coordinates of A and B are 2/3 and 1/3 of the y-coordinate of "Town pool", respectively. Then the distances from A and B to the Mall can be found using the Pythagorean theorem:

  A to Mall = √(4² +(10/3)²) = √(244/9) ≈ 5.20683 . . . miles

  B to Mall = √(8² +(5/3)²) = √(601/9) ≈ 8.17177 . . . miles

The difference in distance is ...

  (BM -AM) = 8.17177 -5.20683 = 2.96493 . . . miles

The mall is about 2.96 miles farther from point B than from point A.

The additional cost is the difference in miles multiplied by the cost per mile:

  (2.96 mi)($0.550 M/mi) = $1.63 M

The additional cost of the longer road is about $1.63 million.

The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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Answer:

Difference, D = 40

Step-by-step explanation:

This question requires options. Since there's none, I'll answer generally.

Represent the distances with d1 and d2

d1 = 527 Meters

d2 = 487 Meters

Required

Determine the absolute difference

The absolute difference (D) of the given distances can be calculated using the following expression

D = |d1 - d2|

Substitute values for d1 and d2

D = |527−487|

D =|40|

D = 40

Hence, Twyla traveled 40 meters.

Answer:

  f(-4) = g(-4) and f(0) = g(0)

Step-by-step explanation:

The x-values where the graphs intersect are -4 and 0. At these points, ...

  f(-4) = g(-4)   and  f(0) = g(0) . . . . . matches the 2nd choice

Answer:

Step-by-step explanation:

Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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MMCMLVII in Hindu-Arabic is 2957

The Hindu-Arabic system uses the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 to count.

Analysis:

MM = 2000

+

CM = 900

+

L = 50

+

VII = 7

MMCMLVII = 2957

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Answer:

1.B

2.A

Step-by-step explanation:

Answer:

The answer is

1 B

2 A

Step-by-step explanation:

I did it on khan academy :)

Answer:

2

Step-by-step explanation:

F(2)=2×2+1=5

g(1)=3×1+1=4 so

(f(2)-g(1))=5-4=1×2=2

The break even of a company is when cost equals selling function. The break even of xyz company is 500000 units.

Given that:

\(c=500000+5q\) --- cost function

\(s = 6q\) --- selling function

The break even is when the functions are equal

i.e.

\(s = q\)

So, we have:

\(6q=500000+5q\)

Collect like terms

\(6q - 5q=500000\)

\(q=500000\)

The break even is at 500000 units

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Answer:

In50=3.912023005

Step-by-step explanation:

press it on your calculator

Using the information given, it is found that:

a) 0.39

b) z = 1.96

c) s = 0.0218

d) M = 0.0428

e)

f) The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more  safety regulations is (0.3472, 0.4328).

Item a:

The point estimate is the sample proportion, hence:

\(\pi = \frac{195}{500} = 0.39\)

Item b:

95% confidence level, hence \(\alpha = 0.95\), the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so \(z = 1.96\).

Item c:

The standard error is:

\(s = \sqrt{\frac{\pi(1-\pi)}{n}}\)

For this problem, \(\pi = 0.39, n = 500\), hence:

\(s = \sqrt{\frac{\pi(1-\pi)}{n}}\)

\(s = \sqrt{\frac{0.39(0.61)}{500}}\)

\(s = 0.0218\)

Item d:

The margin of error is:

\(M = zs\)

In this problem, \(z = 1.96, s = 0.0218\), hence:

\(M = zs = 1.96(0.0218) = 0.0428\)

Item e:

The lower bound is:

\(\pi - M = 0.39 - 0.0428 = 0.3472\)

The upper bound is:

\(\pi + M = 0.39 + 0.0428 = 0.4328\)

The lower bound is 0.3472.

The upper bound is 0.4328.

Item f:

The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more  safety regulations is (0.3472, 0.4328).

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Answer:

d -3

Step-by-step explanation:

Answer:

3f+6

Step-by-step explanation:

To solve this, we combine like terms which are in this case 4f and f.  4f-9-f+15 is (4f-f)+(-9+15), which we simplify to 3f+6.

Answer:

0.46

Step-by-step explanation:

42.78/m = 93

=> m = 42.78/93

=> m = 0.46

Hope my answer helps :)

Answer:

the answers D

Step-by-step explanation:

just times the bottom and top number together and to re check divide the value by any number already given in question

Step-by-step explanation:

f(x) = (x-3)-16

g(x) =3x + 7

X= - 7

3

Answer:

-5

Step-by-step explanation:

y = -0.5x + [?]

The equation is put in slope intercept form

slope intercept form: y = mx + b

where m = slope and b = y intercept

We want to find the y intercept.

the y intercept is the value of y when x = 0

looking at the table when x = 0, y = -5 so the y intercept is -5.

In other words -5 belongs in [?]

Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

Answer:

56

Step-by-step explanation:

ttcggdlhziyzyitzpsr5

The corresponding element in the range of the function F when 7 is in the domain is 4.6.

The expression for the given function F following as:

F(x) = 6(x) - 19 / 5

The corresponding element in the range of the function F is the output of the function when 7 is input into the function.

To find this output, we can substitute 7 for X in the expression for the function F:

F(7) = 6(7) - 19 / 5

F(7) = 42 - 19 / 5

F(7) = 23 / 5

F(7) = 4.6

Thus, when 7 is in the domain, the equivalent element in the range of the function F is 4.6.

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Answer:

3/10 in fractions, 0.3 in decimals.

Step-by-step explanation:

I dont know how to explain for decimal, but for fractions, just divide by 10, and you will get 3, and since 10 can fit in 100 10 times, you just put 3/10 which means 30/100. for decimals, just move the percent two parts backwards, and it should be 0.3 or .30. hopefully it helped (for fraction).