The height of a building is proportional to the number of floors. The figure shows the height of a building with 8 floors. Complete parts a and b.

The distance across the lake is 552.98 ft

Define Cosine Rule.

According to the Cosine Rule, the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle that separates them. Law of cosines and Cosine Formula are other names for the cosine rule.

We have,

a = 217 ft

b = 347 ft

y = 53°

We have cosine formula,

c² = a² + b² – 2ab cos ∠z

Here, ∠z =  53°

let, c = distance across the lake

Now, plug in the values like that

c² = (217)² + (347)²  - 2 * 217 * 347 cos 53

   = (217)² + (347)²  - 2 * 217 * 347 * (-0.91828278621)

   = (217)² + (347)² - (-138291.551037654)

   = 47,089 + 120409 + 138291.551037654

   = 167498 + 138291.551037654

c² = 305789.551037654

c = 552.982414763 or 552.98 ft

Therefore, the distance across the lake is  552.98 ft

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The equation is x = 4f - 148 and value of f is 62 degree Fahrenheit.

Given,

In the question:

The number of snowy tree cricket chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.

The equation x= 4f - 148 relates the number of chirps per minute x and the outside temperature in degrees Fahrenheit f.

Now, According to the question:

Let x = number of Chirps.

f = temperature in Fahrenheit

Equation Connecting the two is

x = 4f -148

When, x = 100

100 = 4f - 148

100 + 148 = 4f

248 = 4f

f = 248/4

f = 62

Hence, The equation is x = 4f - 148 and value of f is 62 degree Fahrenheit.

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The nth term rule of linear sequence is aₙ = aₙ₋₁ + 3

Linear sequence is a sequence of number in order with same difference .or same ratio.

when fixed number is added to any term of a sequence to get next term . That Fixed number is known as common difference.

The sequence in the given question

-5 , -2 , 1 , 4 , 7, . . . .

The first term of sequence : a₁ = -5

The second term : a₂ = -2

Common difference : d = a₂ - a₁

=> d = -2 - (-5)

=> d = -2 + 5

=> d = 3

The nth rule of linear sequence is aₙ = aₙ₋₁ + d

replacing the value of d

aₙ = aₙ₋₁ + 3 is nth rule of the linear sequence.

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i) Angle 5 and 7 - Adjacent angles are supplementary

ii) Angle 3 and 5 - Same side interior angles are supplementary

iii) Angle 1 and 7 - Same side exterior angles are supplementary

Adjacent Supplementary Angles

Same side interior angles are supplementary

Same side exterior angles are supplementary

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The volume of the sphere can be calculated using the formula V = 4/3πr³

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. It is a perfectly-round 3D shape with one continuous curved surface

We have a sphere.

Since the dimensions of a sphere are not given, we will assume it. Assume the radius of sphere be [r]. Then the approximate value of the volume of the sphere can be calculated using the formula -

V = 4/3πr³

Where -

[r] is the radius of sphere

Therefore, the volume of the sphere can be calculated using the formula V = 4/3πr³

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5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.

Let x be the number of pints of the first fruit juice (i.e., 30%) and y be the number of pints of the second fruit juice (i.e., 80%).

Since the total number of pints to make the 75% pure fruit juice is 50, it can be represented using the equation:

x + y = 50 -----(1)

Also, x pints of the first juice = 0.30x, y pints of the second juice = 0.80y and 50 pints of the mixture to be produced = 50(0.75)= 37.5. Therefore:

This is represented as ;

30% × x + 80% × y = 50 of 75%

Make x in the subject x + y = 50

Substitute:

x = 50 - y in 30% × x + 80% × y = 50 of 75%

0.30 (50 - y) + 0.8 × y = 50 of 0.75

15 - 0.3y + 0.8y = 37.5

Collect like terms :

-0.3y + 0.8y = 37.5 - 15

0.5y = 22.5

y = 45

Recall that :

x = 50 - y

x = 50 - 45

x = 5

Hence, 5 and 45 pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 75% pure fruit juice.

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Answer:

Step-by-step explanation:

Fraction=2/100

Decimal=0.02

Percent=2%

Answer: 0.02 as a decimal and 2%

Step-by-step explanation:

its correct!

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

now, to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}} \implies \cfrac{-4}{-3 +6} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{4 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{4 }{ 3 }}(x-\stackrel{x_1}{(-6)}) \implies y -6 = - \cfrac{4 }{ 3 } ( x +6) \\\\\\ \stackrel{\textit{multiplying both sides by}\stackrel{LCD}{3}}{3(y-6)=3\left( - \cfrac{4 }{ 3 } ( x +6) \right)} \implies 3y-18=-4(x+6) \\\\\\ 3y-18=-4x-24\implies 3y=-4x-6\implies {\Large \begin{array}{llll} 4x+3y=-6 \end{array}}[/tex]

Step-by-step explanation:

We know rhat

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 - \cos(x) }{2} } [/tex]

whenever x lies from 90 to 180.

If

[tex] \csc(x) = 9[/tex]

Using Reciprocal Identities

[tex] \sin(x) = \frac{1}{9} [/tex]

Using Pythagorean Identity,

[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]

[tex]( \frac{1}{9} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]

[tex] \cos {}^{2} (x) = \frac{80}{81} [/tex]

[tex] \cos(x) = \frac{4 \sqrt{5} }{9} [/tex]

Cosine is negative in when x lies between 90 and 180 so

[tex] \cos(x) = - \frac{4 \sqrt{5} }{9} [/tex]

So

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{2} } [/tex]

[tex] \sin( \frac{x}{2} ) = \sqrt{ \frac{9 + 4 \sqrt{5} }{18} } [/tex]

For cosine remember

[tex] \cos( \frac{x}{2} ) = \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]

Cosine is negative in second quadrant so

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 + \cos(x) }{2} } [/tex]

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{1 - \frac{4 \sqrt{5} }{9} }{2} } [/tex]

[tex] \cos( \frac{x}{2} ) = - \sqrt{ \frac{9 - 4 \sqrt{5} }{18} } [/tex]

For tangent,

[tex] \tan( \frac{x}{2} ) = \frac{ \sin( \frac{x}{2} ) }{ \cos( \frac{x}{2} ) } [/tex]

[tex] \frac{ \sqrt{ \frac{1 - \cos(x) }{2} } }{ \sqrt{ \frac{1 + \cos(x) }{2} } } [/tex]

[tex] = \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]

Tangent is negative over 90<x<180 so

[tex] - \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]

[tex] - \sqrt{ \frac{1 + \frac{4 \sqrt{5} }{9} }{1 - \frac{4 \sqrt{5} }{9} } } [/tex]

[tex] - \sqrt{ \frac{ \frac{9 + 4 \sqrt{5} }{9} }{ \frac{9 - 4 \sqrt{5} }{9} } } [/tex]

[tex] - \sqrt{ \frac{9 + 4 \sqrt{5} }{9 - 4 \sqrt{5} } } [/tex]

[tex] - \sqrt{ \frac{1}{(9 - 4 \sqrt{5) {}^{2} } } } [/tex]

[tex] - \frac{1}{9 - 4 \sqrt{5} } [/tex]

so

[tex] \tan( \frac{x}{2} ) = - \frac{1}{ 9 + 4 \sqrt{5} } [/tex]

or

[tex] \tan( \frac{x}{2} ) = - 9 + 4 \sqrt{5} [/tex]

Answer: 2 < x < 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: true

Step-by-step explanation:

In the scientific notation, the total population of Brazil and Lithuania is 2.02255 x 10⁸

Scientific notation

A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10 is known as Scientific notation.

Given,

In 2010, the population of Brazil was about 1.987 x 10⁸ people. The population of Lithuania was about 3.555 x 10⁶ people.

Here we need to find the total population of Brazil and Lithuania and expression the value in scientific terms.

Here we know that,

Population of Brazil = 1.987 x 10⁸

Population of Lithuania = 3.555 x 10⁶

In order to find the total population, first we have to make the exponent of the two value as equal,

For that we have to rewrite the population of Brazil as,

Population of Brazil = 198.7 x 10⁶

Now, we have to add the two population count in order to find the total population,

=> (198.7 x 10⁶) + (3.555 x 10⁶)

Take the exponent term as common,

=> (198.7 + 3.555) x 10⁶

=> 202.255 x 10⁶

Now, we have to move the two decimal point to simplify this one, then we get,

=> 2.02255 x 10⁸

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Answer:

1

Step-by-step explanation:

1) substitute z with 4 in the equation

(m^3)^4

2) multiply the index

m^3*4

=m^12

3) m^12≠ m^7

therefore, 1 is a lie

The statements above which is a lie is number 1

Statement 1 :

(m^3)^z = m^7

m^3z = m^7

3z = 7

z = 7/3 (False)

Statement 3 :

(4^5)^z = 4^20

4^5z = 4^20

5z = 20

z = 4 (True)

Statement 2 :

(12^3)^2 = 12^6

(12^y)^x = 12^6

12^6 = 12^6

(True)

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Answer:

A ................................

24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.

Let x ounces of 15% alcohol must be mixed with the 16 ounces of 20% alcohol.

The amount of alcohol in 16 ounces solution is = (20/100) * 16 ounces

                                                                              = 3.2 ounces

The amount of alcohol in x ounces  solution is = (15/100) * x

                                                                              = 0.15x ounces

Total amount of alcohol is = (16 + x) ounces

According to the problem we get an equation,

(3.2 + 0.15x)/(16 + x) = 17/100

100(3.2 + 0.15x) = 17(16 + x)

320 + 15x = 272 + 17x

320 - 272 = 17x - 15x

48 = 2x

x = 48/2

x = 24

Therefore, 24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.

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6.25 more students received a B than that received a grade of A.

Total students = 30

No. of students received grade B = 1/3 of 30

                                                        = (1/3)*30

                                                        = 10

No. of students received grade C = 1/4 of 30

                                                        = (1/4)*30

                                                        = 7.5

No. of students received grade D = 1/6 of 30

                                                        = (1/6)*30

                                                        = 5

No. of students who failed = 1/8 of 30

                                            = (1/8)*30

                                            = 3.75

Total students with grade B,C,D or fail = 10 + 7.5 + 5 + 3.75

                                                                = 26.25

No. of students received grade A = 30 - 26.25

                                                        = 3.75

Difference between grade B and grade A = 10 - 3.75

                                                                      = 6.25

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Answer:

6(y-2) would be 6y-12

Step-by-step explanation:

Answer:

$25940

Step-by-step explanation:

Future value of an Investment at r% for n years is given by:

Future Value = Initial Investment (1 + r/100)n

If r = 10% and n = 10 years

Future Value = 10000(1 + 10/100)10

= 10000(1.1)10

= 10000(2.594)

= $ 25940

Hence the required value is $ 25940.

Answer:

[tex]\huge\boxed{\sf 1 \frac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\displaystyle =\frac{2}{3} + \frac{4}{6} \\\\Equalize \ the \ denominator \\\\= \frac{2 \times 2}{3 \times 2} + \frac{4}{6} \\\\= \frac{4}{6} + \frac{4}{6} \\\\Add \\\\=\frac{4+4}{6} \\\\= \frac{8}{6} \\\\Simplify\\\\= \frac{4}{3} \\\\Convert \ into \ mixed \ fraction\\\\= 1 \frac{1}{3} \\\\\rule[225]{225}{2}[/tex]

The surface area of a square pyramid is 192 cm²

What is the surface area of a square pyramid?

The term "surface" refers to the "outer or exterior part of an object or body." As a result, the total surface area of a square pyramid is the sum of its lateral face and base areas.

To find the surface area of the square pyramid, we'll use the mathematical formula.  

Mathematically, the formula for calculating the surface area A  of a square pyramid is :

S.A. = s² + sl

where,

s is the pyramid height,

l is the base length.

S.A. = (8)² + 8 * 16

S.A. = 64 + 128

S.A. = 192 cm²

Hence, the surface area of a square pyramid is 192 cm².

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Answer:

2

Step-by-step explanation:

The sum of interior angles of a tray that is of pentagon shape is 540°

Given,

There is a tray which is of pentagon shape.

We have to find the sum of interior angles of the tray.

We have to find the sum of interior angles of pentagon.

That is,

Sum of interior angle of polygon formula = (n - 2) × 180°

Where, n is the number of sides in a polygon.

Here,

Pentagon has 5 sides.

Then,

Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°

That is,

The sum of interior angles of a tray that is of pentagon shape is 540°

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The question is incomplete. Completed question is given below;

Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon. The sum of the interior angles of the tray will be

Answer:

Step-by-step explanation:

a) Translation rule has been used in first image.

b) Reflection rule has been used in second image.

Transformations can be divided into four categories: translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognise which ones have already been done. A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given,

Transformations used:

a) Translation rule has been used in first image.

b) Reflection rule has been used in second image.

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Answer:

Don't be a secret agent. You never know what's going to happen.

Step-by-step explanation:

Until he slipped on a puddle of goose poop. His hat flew off, revealing a shiny, bald head, which he immediately grabbed his scarf to cover. In his rush, he failed to notice a goose prodding at the secret package in his pocket. With a flurry of wingbeats, the goose flew off with the secret package in its beak. The secret agent suddenly realized that the goose was a spy in disguise from a rival organization.

The equation of the line q that is perpendicular to line p is  y = - 3 / 5 x - 9.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, p has an equation of y = 5 / 3 x - 4 Line q includes the point (-10,-3) and is perpendicular to line p.  The equation of line q can be found as follows:

The product of the slope of perpendicular lines is equals to negative one.

Therefore, let's find the slope of line q.

m₁m₂ = -1

5 / 3m₂ = - 1

m₂ = - 3 / 5

Hence, the equation of line q is y = - 3 / 5x + b.

Let's find the y-intercept using (-10, -3)

-3 = - 3 / 5(-10) + b

-3 = 6 + b

-3  - 6 = b

b = -9

Therefore, the equation of line q is y = - 3 / 5 x - 9

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Since the area of this kite is 5 times the shorter diagonal, the length of the longer diagonal is 10 cm and the area is equal to 30 cm².

In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:

A = ½ × d₁ × d₂

Where:

For the longer diagonal, we have:

d₁ = d₂ + 4

For the area of kite, we have:

Area = 5d₂ = 5(6) = 30 cm²

Substituting the given parameters into the formula, we have;

30 = ½ × d₁ × 6

60 = 6d₁

d₁ = 60/6

d₁ = 10 cm.

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The probability that the mean battery life would be greater than 636.4 minutes if in a sample of 152 batteries having a variance of, 6724 and a mean life of 645 minutes is 0.0968.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 6724,

The mean life of a battery, m = 645,

The total number of samples, n = 152

Calculate the probability of a mean battery life of lower than 636.4 minutes by the following formula,

z = m - x / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 645 - 636.4  / (82 / √ 152)         [σ = √ variance = √6724 = 82]

z = 1.29

Consult the cumulative standard normal table

P (z < 636.4) = 0.9032,

But we know that

P (z > 636.4) = 1 - P (z < 636.4)

P (z > 636.4) = 1 - 0.9032 = 0.0968

Therefore, the probability that the mean battery life would be greater than 636.4 minutes if in a sample of 152 batteries having a variance of, 6724 and a mean life of 645 minutes is 0.0968.

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