An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 31 feet up. The ladder makes an angle of 78
with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

The range of name lengths is equal to 8.

In Mathematics and Statistics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

From the given data set, we have:

Highest number = 10.

Lowest number = 2.

By substituting, we have:

Range = 10 - 2

Range = 8.

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Answer:

see explanation

Step-by-step explanation:

f(x) = - (x + 1)(x - 3)(x + 2)

to find the zeros let f(x) = 0 , that is

- (x + 1)(x - 3)(x + 2) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

x + 2 = 0 ⇒ x = - 2

the zeros are x = -1, 3 and x = - 2

to find the y- intercept let x = 0

f(0) = - (0 + 1)(0 - 3)(0 + 2) = - (1)(- 3)(2) = - (- 6) = 6

y- intercept is located at (0, 6 )

Answer:

by o of u 999987ui87 u ko9h u kgnnh b mjuokkwuij

The solution to the given equation in the real number system is x = 2 or x = -4 or x = -3/2

A real number system comprises rational numbers, irrational numbers, integers, and whole numbers. When solving a polynomial in a real number system, we need to first factor the polynomial by grouping;

i.e.

= 2x³ + 7x ² - 10x - 24

= 2x³ + 11x² + 12x - 4x² - 22x - 24

= x(2x² + 11x + 12) - 2(2x² + 11x + 12)

= (x - 2) (2x² + 11x + 12)

= (x - 2) (2x² + 8x + 3x + 12)

= (x - 2) (2 (x² + 4x) + 3(x + 4))

= (x - 2) (2x (x + 4) + 3(x + 4) )

= (x - 2) (x + 4) (2x + 3)

In a real number system;

x = 2 or x = -4 or x = -3/2

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Simplifying and expressing each term in standard and polar form are respectively; 49/2 and  -512 - 512i√3

1) We are given the expression;

[7 cos (45)]²

We know that cos (45) in standard form is 1/√2. Thus;

[7 cos (45)]² = (7 * 1/√2)² = 49/2

2) We are given the expression;

(-2 + 2i√3)⁵

Using binomial theorem, we have;

(−2)⁵ + 5(−2)⁴ (2i√3) + 10(−2)³(2i√3)² + 10(−2)²(2i√3)³ + 5 * −2(2i√3)⁴ + (2i√3)⁵

Simplifying each term gives;

−32 + 160i√3 + 960 − 960i√3 −1440 + 288i√3

⇒ -512 - 512i√3

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The correct match of the inequalities will be given as:-

A   ( x - 51 ≤ 43

B   ( x -99 ≤ -104

C  ( 75 <  69 - x )

D  ( 150+x ≤ 144 )

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The correct pair of the inequality will be calculated as:-

A   ( x - 51 ≤ 43)            x ≤ 8

B   ( x -99 ≤ -104          x  ≤ -5

C  ( 75 <  69 - x )         x < -6

D  ( 150+x ≤ 144 )         x ≤ -6

Hence the correct order is explained above.

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Answer:

B. g(x) = -4(x - 3)²

Step-by-step explanation:

Given :

On shifting 3 units right :

On stretching vertically by a factor of 4 :

On reflecting over the x-axis :

Vertically strech by 4 means it's should be multiplied with -a and a =4

So

Shifted 3 units right means change in x

So

it should be

Option B

Answer:

69.53

Step-by-step explanation:

I did it on my calculator.

Answer:

=1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We are asked to find the amount of interest earned on $16,500 than $15,000 with APYs of 4.1% for a year.

We will use simple interest formula to solve our given problem.

I= prt

i= amount of interest

p=principal amount

r= interest rate in decimal form

t= time in years

4.1%=  41/100= 0.041

$16,500 times 0.041 -  $15,000 times 0.041

(16,500- 15,000) times 0.041

(1,500) times 0.041

So the answer is $61.50

I hope this is right, have a nice day.

Answer:

Every fraction can be written as a decimal that will be either a decimal number or a decimal number

Hehe hope its helpful :-P

The relative frequency of female mathematics majors will be 0.5142.

The proportion of the examined subgroup's value to the overall account is known as relative frequency.

A sample of 317 students at a university is surveyed.

The students are classified according to gender (“female” or “male”).

The table is given below.

Then the relative frequency of female mathematics majors will be

⇒ 36 / (36 + 34)

⇒ 36 / 70

⇒ 0.5142

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Answer:

The reason why this may be happening is because the expenses may be higher than the amount of revenue that the business is making, the cost of rent, paying the employees and running the business may be higher than the revenue that is being made. The inflows may be higher than the outflows, in which case the profit is lower than the loss and may be the reason why the owner is having trouble keeping the business running.

The two congruent triangles that share the side AC are (c) △ADC and △CFA

For two triangles to share the sides AC, then the points A and C must appear on the names of the triangles

In option (c), we have A and C in the names of the triangles ADC and CFA

Hence, the two congruent triangles that share the side AC are (c) △ADC and △CFA

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Answer:

63,750

Step-by-step explanation:

1. Simplify the expression

625*192-625*90

120000-625*90

120000-56250

63750

Why learn this:

Terms and topics

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\large\textbf{Assuming that you meant}\bf\downarrow[/tex]

[tex]\mathbf{625\times129 - 625\times90}[/tex]

[tex]\large\textbf{If so, let's solve for the answer, shall we?}[/tex]

[tex]\mathbf{= \boxed{\bf 80,625} - 625\times90}[/tex]

[tex]\mathsf{= \bf 80,625 - \boxed{\bf 56,250}}[/tex]

[tex]\mathbf{= 80,625 - 56,250}[/tex]

[tex]\large\textbf{We have met your answer to this question.}[/tex]

[tex]\huge\textbf{Therefore, your answer is: \boxed{\mathsf{24,375}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}[/tex]

Answer:

36.

Step-by-step explanation:

There were 10 elephants that were marked.  Only 4 of those were counted.  The other 26 were new elephants.  Because of this, we know that there were 6 other elephants that were not counted.  There were the 30 counted, and the other 6.  Add those and you get 36.

Answer:

  75 elephants

Step-by-step explanation:

This sort of population study assumes that the probability of catching any particular elephant is the same as for any other.

__

We are given that there is a population of 10 painted elephants, of which 4 of them are caught in a sample of 30 elephants. We know the total population of painted elephants is 10/4 = 2.5 times the number caught in the sample. This suggests the total population of elephants is 2.5 times the sample size.

  estimated population = 2.5 × 30 = 75 . . . elephants

Answer:B

Step-by-step explanation: it's because you're choosing random peoplepeoplepeople

Answer:

First you start with what is in the ( ). 15- 14 is 1. then you do multiplication next. 1* 6. is 6. now you do addition. 6 + 4 = 10

Answer:

The highest is 1 but i cannot work out the rest

Step-by-step explanation:

Bidmas

A) the equation that models the situation is 8000 x 0.9635 ^ Years = Value, B) the value of the stock today is $5515.78, so I lost $2484.22, and C) it will take more than 18 years for the stock to decrease by half.

Given that ten years ago, you invested most of the money you made during that summer into an Energy drink stock, and you purchased $8,000 dollars worth of stock and it was initially projected to continuously compound by 2%, but, however, the Energy drink stock consistently declined by 3.65% each year until the present, for a) Write an equation to model this situation, b) Estimate the value of the stock today and how much did you gain/lose, and c) Assuming the stock rate of decline remains the same, approximate the number of years it will take for the value of the stock to decrease by half, the following calculations must be made:

Therefore, A) the equation that models the situation is 8000 x 0.9635 ^ Years = Value, B) the value of the stock today is $5515.78, so I lost $2484.22, and C) it will take more than 18 years for the stock to decrease by half.

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Answer:

A) the equation that models the situation is 8000 x 0.9635 ^ Years = Value, B) the value of the stock today is $5515.78, so I lost $2484.22, and C) it will take more than 18 years for the stock to decrease by half.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

First put all the numbers in order. Like this,

1,2,3,4,5,7,7,7,8,8

Then subtract (take away) the lowest number from the highest. Like this,

8-1=7

The answer to the questions are given below.

The triangles which do not have same side length or angles but are similar in appearance are called similar Triangles .

It is given in the question that

If triangle abc and triangle def are similar, then their corresponding sides are proportional.

The hypothesis is

if the triangle abc and def are similar

The conclusion is

that the triangle abc and def are similar and the sides corresponding are proportional.

The converse is

If the sides of two triangles are proportional then two triangles are similar

Yes it is true

Inverse is if the two triangles are not similar then the sides corresponding are not proportional.

Contrapositive statement is if the sides are not proportional then the two triangles are not similar.

Yes , it is true.

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The graphs with no solutions are the ones with no intercepts between the curves. These are the first one and the last one.

If we have an equation like:

f(x) = g(x).

One way of finding the solutions is to graph:

y = f(x) and y = g(x) and see where the two curves intercept.

From that, the graphs where the curves do not intercept are the graphs that indicate that the equations have no solutions.

The two graphs with no intercepts are the first one (top left) and the last one (bottom right), so these are the correct options.

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Answer:

kid named finger

Step-by-step explanation:

I simply just used a form of alien math solving and I got my answers but I'm not willing to share

Answer:

12

Step-by-step explanation:

you divide 120 by 10 since dimes are equal to ten cents

To determine how many dimes are in dollars:

  ⇒ must know the rate of conversion

     ⇒ for every dollar, there are 10 dimes

         ⇒  [tex]\frac{1_. dollar}{10_. dimes}[/tex]

Let's solve:

   [tex]120_. dimes * \frac{1_.dollar}{10_.dimes} = \frac{120}{10} *\frac{dimes}{dimes} *dollar=12_.dollars[/tex]

Thus you would get 12 dollars

Answer: 12 dollars

Hope that helps!

The combination that denotes the empty set{∅} is motor ∩ bicycle.

Set theory is the mathematical study of well-defined groups of things called elements of the set.

In the given Venn diagram, the elements in the set of Motor, Manual, and Bicycle are as follows:

The combination that represents an empty set {∅} is the intersection that occurred between motor and bicycle and can be expressed as:

= motor ∩ bicycle

This is because there are no set elements overlapping between motor and bicycle, this makes it an empty set{∅}.

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Answer: motor U bicycle

Step-by-step explanation:

The statement that is true about the given dot plot is: A. Exactly 2 goals was never scored by the team in a single game.

A dot plot is a graphical representation of data using dots to denote the frequency of one data point in a distribution.

In the dot plot given, for number of goals scored per game, the data point 2 has no dot. Therefore, the statement that is true about the dot plot is: A. Exactly 2 goals was never scored by the team in a single game.

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Answer:

[tex]D) ~ 14.066[/tex]

Step-by-step explanation:

[tex]~~~~87e^{0.3x} = 5918\\\\\implies e^{0.3x} = \dfrac{5918}{87}\\\\\implies \ln\left(e^{0.3x} \right)=\ln \left( \dfrac{5918}{87} \right)\\\\\implies 0.3x \ln e = \ln \left( \dfrac{5918}{87} \right)\\\\\implies 0.3x = \ln \left( \dfrac{5918}{87} \right)\\\\\implies x = \dfrac{\ln \left( \dfrac{5918}{87} \right)}{0.3}\\\\\implies x \approx14.066[/tex]

The equation of the parabola in standard form whose focus is (2, 5) and directrix is y = 3 is equal to the quadratic equation y = 0.25 · x² - x + 5. (Correct answer: C)

Since the directrix is a horizontal line, then we have a parabola with a vertical axis of symmetry. The standard equation of the parabola is described below:

y - k = [1/(4 · p)] · (x - h)²     (1)

Where:

By analytical geometry we understand that the least distance between the focus and the directrix is twice as the distance between the vertex and the focus. First, we find the coordinates of the vertex:

V(x, y) = 0.5 · F(x, y) + 0.5 · D(x, y)

V(x, y) = 0.5 · (2, 5) + 0.5 · (2, 3)

V(x, y) = (1, 2.5) + (1, 1.5)

V(x, y) = (2, 4)

By Pythagorean theorem we find that the distance between vertex and focus is 1. Then, the equation of the parabola in standard form is:

y - 4 = 0.25 · (x - 2)²

y - 4 = 0.25 · (x² - 4 · x + 4)

y - 4 = 0.25 · x² - x + 1

y = 0.25 · x² - x + 5

The equation of the parabola in standard form whose focus is (2, 5) and directrix is y = 3 is equal to the quadratic equation y = 0.25 · x² - x + 5. (Correct answer: C)

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