Use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Answer:

first option is the correct answer.

Step-by-step explanation:

Answer: [tex]32.36\ ft[/tex]

Step-by-step explanation:

Given

Ladder is leaned and make an angle of [tex]68^{\circ}[/tex]

Electric box is 30 ft up the ground.

Suppose x is the length of ladder

From the figure, we can write

[tex]\Rightarrow \sin 68^{\circ}=\dfrac{30}{x}\\\\\Rightarrow x=\dfrac{30}{\sin 68^{\circ}}\\\\\Rightarrow x=32.36\ ft[/tex]

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The length of the ladder is 32.356 feet.

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

As it is given that the height of the electric box from the bottom is 30 feet, while the ladder makes an angle of 68° with the ground.

The length of the ladder can be found using the trigonometric functions, therefore, the length of the ladder can be written as,

[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\\\Sine(\angle C) = \dfrac{AB}{\text{Length of the ladder}}\\\\\\{\text{Length of the ladder}}= \dfrac{AB}{Sine(\angle C) }\\\\\\{\text{Length of the ladder}}= \dfrac{30}{Sine(68^o) }\\\\\\{\text{Length of the ladder}}= 32.356\ feet[/tex]

Hence, the length of the ladder is 32.356 feet.

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Answer:

0.28 = 28% probability that a randomly selected driver will come to complete stop

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Recording of 75 drivers.

Of those, 21 came to a complete stop.

Then

21/75 = 0.28

0.28 = 28% probability that a randomly selected driver will come to complete stop

Answer:

y=1/4x - 1

Step-by-step explanation:

going off of the picture, I'd say this is your answer

Answer:

Step-by-step explanation:

7*(4) - 2(-3) - (-3)^2

28 +  6 - 9

34 - 9 = 25

Answer:

i velo you

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

a) The third interior angle of this triangle is 180 - 20 x.  

The three interior angles must sum up to 180 degrees.

Therefore,  60 + 7x + 5 + 180 - 20x = 180, or

                       65  + 180 - 13x = 180, or

                               65 -  13x     = 0

Finally, 13x = 65, and so x = 5

9514 1404 393

Answer:

  3/(√(3(x+h)) +√(3x))

Step-by-step explanation:

The conjugate of a binomial is the same sum, but with the sign changed. That is (a +b) and (a -b) are a conjugate pair: each is the conjugate of the other.

The purpose of multiplying expressions involving roots or complex numbers by their conjugate is to take advantage of the relation ...

  (a +b)(a -b) = a² -b²

Here. you want to eliminate the h from under the radical, so squaring the radical containing h is useful for the purpose. Hence the conjugate gets involved.

"Multiply by the conjugate" means multiply both the numerator and the denominator by the conjugate. (Effectively, multiply by 1.)

__

  [tex]\displaystyle\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{3(x+h)}-\sqrt{3x}}{h}\\\\=\frac{(\sqrt{3(x+h)}-\sqrt{3x})(\sqrt{3(x+h)}+\sqrt{3x})}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\frac{3(x+h)-3x}{h(\sqrt{3(x+h)}+\sqrt{3x})}\\\\=\frac{3h}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\boxed{\frac{3}{\sqrt{3(x+h)}+\sqrt{3x}}}[/tex]

_____

Additional comment

In the end, you will want the limit as h → 0, which will be 3/(2√(3x)). You will notice that h=0 no longer makes the denominator zero, so the limit is found by simple evaluation.

When the "binomial" is a complex number of the form a+bi, its conjugate is a-bi, regardless of the sign of b. That is, the conjugate of a complex number is found by negating its imaginary part. The sign of the real part is left alone.

Step-by-step explanation:

Hey there!

The given function is; f(x) = 2x-4.

To find: f'(X)

Let f(X) be y, then;

y = 2x - 4

Interchanging"X" and "y" we get;

x = 2y - 4

or, X+4 = 2y

or, y = (X+4)/ 2

Therefore, f'(X) = (X+4)/2.

Hope it helps!

Answer:

Law of Sines, two angles and an opposite side are known

Step-by-step explanation:

Law of Sines, two angles and an opposite side are known

q/sinQ = p/sinP

q = p/sinP * sinQ

Answer:

The correct answer is -

monthly payment = 521.99

total pain intrest = 4319.14

Step-by-step explanation:

Given:

a or the borrowed amount = 27000

r or the interest rate = 6%

n = 5 years or 60 months

Monthly payment = ?

total intreset = ?

Formula:

The formula for the monthly payment is -

[tex]\frac{a}{\frac{{[(1+r)^n]-1}}{[r(1+r)^n]}} = P[/tex]

or, [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex] = P

Where, the amount of the loan = a

r = 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)

n = 60 months

Solution:

Putting all the values in the either of the following formula will give monthly payments:

[tex]\frac{27000}{\frac{{[(1+0.005)^{60}]-1}}{[0.005(1+0.005)^{60}]}} = P[/tex] or  [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex]

= 521.9856 or to the nearest cent 521.99.

The total intrest would be -

= (monthly payment*number of month) - amount borrowed

= 521.99*12-27000

= 31319.14-27000

= 4319.14

Step-by-step explanation:

6/5 this is the answer hopes this help

C.(f-g)(x) = 4x^3 +5x²-7x-1

Step-by-step explanation:

Given information :

[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]

Find :

[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]

Open bracket and Simplify

[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]

Given:

The frequency distribution table is:

Values of variable X        Frequency

              32                                2    

              37                                5

              46                                3

              48                                9

To find:

The mode of the given data set.            

Solution:

We know that mode is the most frequent value of the data set.

In the given data set highest frequency is 9 that is corresponding to the value 48.

Therefore, the mode of the given data set is 48. Hence, the correct option is (b).

Cosine(angle) = adjacent leg/ hypotenuse

Cosine( angle ) = 18/20

Angle = arccos(18/20)

Angle = 26 degrees

Answer:

26°

Step-by-step explanation:

For a right triangle, we can use trigonometry equations :-

In this case we need to use cosine equation .

cos A = adjacent side / hypotenuse

cos A = 18 / 20

A = cos × 18/20

A = arccos × 18/20

A = 26°

27 is the answer

gbu...

Answer:

- 9 × - 3 = 27

Step-by-step explanation:

when we multiply two negative numbers then the sign of the product convert to positive sign

I.e( - )×( - )= (+) product

Answer:

(5a+3b)(5a+3b) or SQ(5a+3b)

Step-by-step explanation:

Now you can plot by referring to the above factors

Answer:

NQ : Summary

CodeNQOne-letter codeXMolecule name2-HYDROXYNAPHTHOQUINONESynonyms2-HYDROXY-1,4-NAPHTHOQUINONESystematic namesProgram Version Name ACDLabs 10.04 2-hydroxynaphthalene-1,4-dione OpenEye OEToolkits 1.5.0 2-hydroxynaphthalene-1,4-dione

cos 36 × cos 72 = 0.25

cos 36 × cos 72 =

0.309 x 0.809 = 0.249 = 0.25

ko  iê ế t???????????????    t

Answer:

Because this gravity of. The earth

Answer:

15 days

+

Step-by-step explanation:

A

200 pages / (8 pages / day) =

= 200 pages days / 8 pages =

= 200 days / 8 = 25 days

B

200 pages / (5 pages / day) =

= 200 pages days / 5 pages =

= 200 days / 5 = 40 days

40-25 = 15 days

A will finish 15 days sooner than B.

A will finish her report 15 days sooner than B.

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Writer A averages 8 pages a day,

Number of pages per day written by writer A = 8 per day

Writer A will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (8 pages / day)

⇒ 200 pages days / 8 pages

⇒ 200 days / 8

⇒ 25 days

Writer B averages 5 pages a day

Number of pages per day written by writer B = 5 per day

Writer B will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (5 pages / day)

⇒  200 pages days / 5 pages

⇒  200 days / 5

⇒  40 days

Difference between both of time when they finished their report = 40-25 = 15 days

Hence, A will finish her report 15 days sooner than B.

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Answer:

(x-3) * (x-2

Step-by-step explanation:

Answer:

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Step-by-step explanation:

Tem.Before    Tem.After       diff.      

103.7                   102.6            1.1

103.7                   102.7             1

100.7                     98.8             1.9

102.7                    103.5            -0.8

100.7                      99.4             1.3

102.4                      101.41           (Mean)

1.4                             1.9              0.9       Std. Dev.

n =  6

df  =  6  -  1  =  5

CI we propose to be 95 %

Then  α  = 5 %  α = 0.05    

The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever

Hypothesis test

Null Hypothesis                      H₀         μd  = 0

Alternative Hypothesis          Hₐ         μd > 0

(NOTE:)   μd (average) = Temp Before  -  Temp. after

Therefore if   μd >  0   means that there is a statistical difference between values before ( bigger ) and after  or that the aspirin will reduce a child´s fever

To find t(c)  from t-student table  df = 5  and α = 0.05

t(c)  =  2.015

To compute  t(s)

t(s)  =  μd/ sd/√n      t(s)  =  0.98/ 0.9/√6

t(s)  =  2.66

Comparing  t(s) and  t(c)

t(s) > t(c)    

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Answer:

Prat two of e) 6/12 Both the numerator and denominator were multipled by three, the number of boxes we split each box into.

F) we can multiply both the numerator and denominator without changing the values, so 2a/2b or 10a/10b

Answer:

The numbers of ways to permute letters of the word Illinois if the two Ls must be consecutive is 7.

The word ILLINOIS contains 7 letters.

To estimate the number of different permutations, consider the total number of letters factorial and divide by the frequency of each letter factorial. The little n's exist the frequencies of each various (different) letter.

We will use the formula for the number of permutations with imperceptible objects. Since the two L's must be consecutive, we consider them to be a single letter LL. Then the word ILLINOIS contains n = 7 letters: 3 I's, 1 LL, 1 N, 1 O, and 1S.

Hence the number of methods to permute letters of the word ILLINOIS if the two L's must be consecutive exists:

[tex]$\frac{7 !}{3 ! 1 ! 1 ! 1 ! 1 !}=7 \cdot 6 \cdot 5 \cdot 4=840 \text {. }$$[/tex]

The word ILLINOIS contains 7 letters.

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Answer:

[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]

Step-by-step explanation:

Given

See attachment for parallelogram

Required

Proof that ABCD is a parallelogram

We know that opposite sides are equal and parallel.

First, we calculate the slope of BC

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{q - r}{m- n}[/tex]

Next, the slope of AD using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{p - s}{m - n}[/tex]

For ABCD to be a parallelogram; then:

[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]