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If central angle is 360° then Arc length is circumference.

An angle with the circle's center as its vertex is referred to as a central angle. The radius refers to each side of the angle that extends outward from the center to a particular point on the circle.

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.

Since, when considering the circle's central angle we consider 360° which is the central angle of the whole circle.

So, when considering the arc length of a sector, we consider the arc length of the whole circle which is the circumference.

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9514 1404 393

Answer:

  B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5

Step-by-step explanation:

Replacing x by x/5 in a function causes its graph to be stretched horizontally by a factor of 5. This is because x must be 5 times as large in order for the function argument to be the same.

Given:

The term is [tex]5^x[/tex].

To find:

The differentiation of [tex]5^x[/tex] with respect to x.

Solution:

Formula used:

[tex]\dfrac{d}{dx}a^x=a^x\log(a)[/tex]

Let the given function is:

[tex]f(x)=5^x[/tex]

Here, a=5.

Differentiate the given function with respect to x.

[tex]f'(x)=5^x\log(5)[/tex]

Therefore, the derivative of [tex]5^x[/tex] with respect to x is [tex]5^x\log(5)[/tex].

Answer:

option A

Step-by-step explanation:

∠WPS +∠OPW  = 180   {straight line}

∠WPS +110 = 180

∠WPS = 180 - 110

∠WPS = 70°

∠RWQ + ∠QWT +∠TWU = 180   {straight line}

∠RWQ + 60 + 50 = 180

∠RWQ + 110 = 180

∠RWQ = 180 - 110

∠RWQ= 70°

∠PWU +  ∠USP + ∠ WPS = 180  {angle sum property of triangle}

∠PWU + 40 + 70 = 180

∠PWU + 110 = 180

∠PWU = 180 - 110  

∠PWU = 70°

Answer:

A

Step-by-step explanation:

∠WPS +∠OPW  = 180 (adj angles on a str line)

       ∠WPS +110 = 180

                ∠WPS = 180 - 110

                            = 70°

∠RWQ + ∠QWT +∠TWU = 180 (adj angles on a str line)

            ∠RWQ + 60 + 50 = 180

                   ∠RWQ + 110 = 180

                             ∠RWQ = 180 - 110

                                         = 70°

∠PWU +  ∠USP + ∠ WPS = 180 (adj angles on a str line)  

            ∠PWU + 40 + 70 = 180

                     ∠PWU + 110 = 180

                              ∠PWU = 180 - 110  

                                          = 70°

Answer:

d.156.

x+24=180 ( being staright angle)

The answer is 48 notepads.

Given:

A figure of right triangle with terminal angle [tex]\theta[/tex], base u, perpendicular v and hypotenuse r.

To find:

The value of [tex]\sin \theta[/tex].

Solution:

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

Substituting Perpendicular = v and hypotenuse = r in the above formula, we get

[tex]\sin \theta=\dfrac{v}{r}[/tex]

The value of [tex]\sin \theta[/tex] is [tex]\dfrac{v}{r}[/tex].

Therefore, the correct option is B.

Answer:

35

All angles of a triangle = 180 degrees subtract 40 from 180 and you get 140

180-40=140 because the other angles are equal with the same equation to get them divide 140 by 2 140/2=70  then you have to get h alone so you divide by the other 2 in the equation 70/2=35  h=35

Answer:

55

Step-by-step explanation:

In triangle ABC (LET'S SAY TRIANGLE IS ABC)

Angle A=40

Angle B = Angle C = x (since 2h is beside B and C both)

40+x+x=180 (Angle sum property)

40+2x=180

2x=140

x=70

2h+70=180 (Angle in a straight line=180)

2h=110

h=55

Answer:

3/2

Step-by-step explanation:We know that,

Slope of the straight line passing through the points (x1,y1) and (x2,y2) is

m=y2-y1/x2-x1

Here,

Given, x1= 3,x2= 1

    and y1= 2,y2= -4

so, the slope of the straight line is,

m= -4-2/-1-3

   =3/2

Answer:

11.4pounds

Step-by-step explanation:

(5.58+4.68)÷0.90

＝11.4(pounds)

Step-by-step explanation:

the answer is in the above image

Answer:  0.0766

Step-by-step explanation:

Let x be the random team scores.

Given: Mean = 76

Standard deviation = 8.4

We assume that x follows normal distribution.

The probability that a random team scores less than 64 points = P(x<60)

[tex]=P(\frac{x-\mu}{\sigma}<\frac{64-76}{8.4})\\\\=P(z<-1.4286) \ \ \ [Z=\frac{x-\mu}{\sigma}]\\\\= 1-P(z<1.4286)\\\\=1-0.9234\\\\=0.0766[/tex]

Hence, the probability that a random team scores less than 64 points =0.0766

Answer:

A

Step-by-step explanation:

The others are exterior

Answer:

x = 2

Step-by-step explanation:

The denominator of the rational function cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

5x - 10 = 0 ⇒ 5x = 10 ⇒ x = 2 ← excluded value

Thus x = 2 is the vertical asymptote

I = $ 1,200,000.00

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year,

then, solving our equation

I = 1000000 × 0.03 × 40 = 1200000

I = $ 1,200,000.00

The simple interest accumulated

on a principal of $ 1,000,000.00

at a rate of 3% per year

for 40 years is $ 1,200,000.00.

If s=side, then each side is 12m.

It got cut off but

12mx12m=144m^2 because mxm=m^2.

heart if helpful

Answer:

2 y x

Step-by-step explanation:

Answer:

500 -100 = 400

la respuesta es 400

Answer:

120 - 4.5t= 75

t = 10 minutes

Step-by-step explanation:

the equation :

120 - 4.5t= 75

the solution:

-4.5 t = 75-120

-4.5t = -45

t = -45/(-4.5) = 10 minutes

The equation to model the given situation is 120 - 4.5t= 75 and the  solution to the equation is 10 minutes.

Given that, a hot air balloon is cruising at an altitude of 120 meters above the ground when it begins its descent.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The balloon will reach an altitude of 75 meters above the ground.

Now, 120-75 =45 meters

Let t be the time to descends 45 meters

So, 120 - 4.5t= 75

⇒ -4.5 t = 75-120

⇒ -4.5t = -45

⇒ t = -45/(-4.5)

⇒ t = 10 minutes

Hence, the equation to model the given situation is 120 - 4.5t= 75 and the  solution to the equation is 10 minutes.

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Answer:

  84 adult tickets

Step-by-step explanation:

Let 'a' represent the number of adult tickets sold. Then (135-a) is the number of child tickets sold, and total revenue is ...

  5.70(135 -a) +9.40(a) = 1080.30

  3.70a = 310.80 . . . . . . . . subtract 769.50 and simplify

  a = 310.80/3.70 = 84

84 adult tickets were sold on Sunday.

Answer:

56л

Step-by-step explanation:

area of a pizza of 18 in=  лr²

                                         r=18/2=9

                                          area= л×9²

                                          =81л

area of a pizza of 10in=

                                      r=10/2=5

                                       area=л×5²

                                       =25л

difference=81л-25л

                =56л

Answer:

A sample of 752 should be taken.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

No preliminary sample is taken

This means that [tex]\pi = 0.5[/tex]

How large should the sample be to be 90% sure that the estimate is within .03 of the population proportion?

This is n for which M = 0.03. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645*0.5[/tex]

[tex]\sqrt{n} = \frac{1.645*0.5}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2[/tex]

[tex]n = 751.7[/tex]

Rounding up:

A sample of 752 should be taken.

Answer:

-4(5)+1(-2*-5+5*3)

Step-by-step explanation:

-20+1(10+15)

-19(25)

-475

Answer:

5

Step-by-step explanation:

Given :- a = -2 , b = 5 , c = -5 & d = 3

Solution :-

Answer:

832.6lbs

Step-by-step explanation:

Answer:

This triangle is a right triangle

Hi there!  

»»————-　★　————-««

I believe your answer is:  

C) x = 16

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\\frac{x}{2}=8\\-------\\\rightarrow{\frac{x}{2}=8}\\\\\rightarrow(\frac{x}{2}})*2=8*2\\\\\rightarrow\boxed{x=16}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

x = 16

Step-by-step explanation:

х/2 = 8

Multiply each side by 2

x/2*2 = 8*2

x = 16

Answer:

10.5 is the answer

Step-by-step explanation:

i hope it helps u

Answer:

is the answer y=7? if correct its ok but if the answer didn't match then plesse let me know

Answer:

[tex]\frac{x2}{a} - \frac{y2}{b2} = 1[/tex]

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

[tex]\frac{X2}{16} - \frac{b}{4} = 1[/tex]

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

I don't feel like explaining so...

a. = 4

The foci c is at +/-2√5, using c² = a² + b²:

B = 2

Substituting the value of a and b to get the equation of the hyperbola:

[tex]\frac{x2}{a2} - \frac{y2}{b2} = 1[/tex]  

[tex]\frac{x2}{16} - \frac{b2}{4} = 1[/tex]