Consider the following function:
f(3) = log2(x + 3)
Which interval has the smallest average rate of change in the given function?
O (0,2
O 4,6]
O [2,4
O (6,8)

Answers

Answer 1

In the function f(x) = log2(x + 3)), the smallest average rate of change in the  function is in the interval,  (6,8)

What is a logarithmic function ?

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.

Formulae for logarithmic function are,

LogAB = LogA + LogB

Logₐaᵇ = b

Given that,

A logarithmic function,

f(x) = = log2(x + 3)

Rate of change = Change in values of function/change in x

                          =  [F(b) - F(a)]/ b-a

For the interval, (0, 2)

f(0) = Log2(0 + 3)  = Log(6)

f(2) = Log2(2 + 3)  = Log(10)

Rate of change =   Log(10) -  Log(6) /2

                          =  0.11

Similarly, for the intervals,    (4, 6),   (2, 4),   (6,8)

Hence, the smallest average rate is for the interval, (6, 8)

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Related Questions

Joe has 23 carnival ride tickets and it takes 3 tickets to ride the roller coaster how many times can he ride the coaster how many tickets will he have left over

Answers

Answer:

JIKA ANDA YANG

Step-by-step explanation:

yang bales anak yang

[tex]5 { \frac{3 \frac{ + > }{?} }{?} }^{?} [/tex]

Answer:

20

Step-by-step explanation:

He has 23 carnival ride tickets and it takes 3 tickets to ride a roller coaster

so 23 - 3 = 20

Find the Area of the Shaded Region.
Round to the nearest tenth if necessary.
14 cm
25 cm
11 cm

Answers

Answer:

[tex]Shaded = 212.5cm^2[/tex]

Step-by-step explanation:

Given

See attachment

Required

The shaded region

First, calculate the area of the complete rectangle

[tex]Area =Length * Width[/tex]

[tex]Area = 14cm * 25cm[/tex]

[tex]Area = 350cm^2[/tex]

Next, calculate the area of the triangle

[tex]Area = \frac{1}{2} * Base * Height[/tex]

[tex]Area = \frac{1}{2} *25cm * 11cm[/tex]

[tex]Area = 137.5cm^2[/tex]

Subtract the area to calculate the shaded region area

[tex]Shaded = 350cm^2 - 137.5cm^2[/tex]

[tex]Shaded = 212.5cm^2[/tex]

Explain why the sum of the interior angles in a regular pentagon is 540?

Answers

Answer:

Step-by-step explanation:

formula to find the sum of interior angle of a regular pentagon is

(n-2)*180 degree

here n means no of sides .since pentagon has 5 sides replace it by 5

=(5-2)*180

=3*180

=540 degree

In order to safely land, the angle that a plane approaches the runway should be no more than 15°. A plane is approaching Ottawa Macdonald–Cartier International Airport to land. It is at an altitude of 500 m and a horizontal distance of 3 km from the start of the runway. At what angle is the plane approaching and is it safe for the plane to land?

Answers

9514 1404 393

Answer:

  9.5°, yes

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

The distance opposite the angle of elevation is the plane's height, 500 m. The distance adjacent to the angle of elevation is the horizontal distance to the plane, 3 km = 3000 m. Then the angle is found from ...

  tan(α) = 500/3000 = 1/6

  α = arctan(1/6) ≈ 9.46°

The plane is approaching at an angle of 9.46°. It is safe to land, since that angle is less than 15°.

_____

Additional comment

The usual descent angle for most commercial air traffic is 3°. Some airport geography demands it be different (steeper). A higher descent angle can put undue stress on the landing gear.

ASAP PlS First answer mark as Brainlist.​

Answers

Answer:

9 servings

Step-by-step explanation:

Can someone please answer this question for me with explanation bc im kinda having a hard time

Answers

Answer:

Step-by-step explanation:

First we find out the area of circle, and then subtract the area of triangle from it to find the area of the shaded region

Area of Circle

Here, r=radius

area of circle= π×r²

                     = π × 5²     (radius=half of diameter)

                     = 25π

                     = 78.54cm²

Area of Triangle

Here, b=base, h=height

area of triangle = [tex]\frac{1}{2\\}[/tex]×b×h

                          = [tex]\frac{1}{2}[/tex]×8×6

                          = 24cm²

Area of shaded region= area of circle - area of triangle

                                     = 78.54 - 24

                                     = 54.54

                                     ≈ 54.5cm² [Ans]

Which figure can be formed from the net?
6 cm
4 cm
4 cm
6 cm
4 cm
4 cm
6 cm
6 cm

Answers

Answer:

It's the fourth option, the bottom right one

The last one is the answer to the right. look at the base you can understand it from there, the net that shows from the question is a square base pyramid so that means you have to look for square base and that will give you the correct answer.

In the figure below, YZA and YZX are right angles, XYZ and AYZ are
congruent, and XZ = 10. What is the length of ZA ?

Answers

Answer:

10

Step-by-step explanation:

Triangles AYZ and XYZ are congrunt, therefore AZ = XZ = 10

Alexandra plays poker with seven friends. Each of the eight players starts with 60 chips, but players take chips from one another as play progresses. The goal of the game is to win all of the chips. A player drops out of the game if she loses all her chips to other players in the game. After five players have dropped out of the game, what is the average number of chips each of the remaining players has

Answers

Answer:

160 chips

Step-by-step explanation:

Given

[tex]n = 8[/tex] --- players

[tex]c = 60[/tex] --- chips per player

First, calculate the total chips

[tex]Total = n * c[/tex]

[tex]Total = 8 * 60[/tex]

[tex]Total = 480[/tex]

After 5 players are out; there are 3 players remaining in the game

So, the average number of chip with each of the remaining player is:

[tex]Average = \frac{Total}{n-5}[/tex]

[tex]Average = \frac{480}{8-5}[/tex]

[tex]Average = \frac{480}{3}[/tex]

[tex]Average = 160[/tex]

Please check my function,
Tell my function right or not, And if not please tell me how to correct

Answers

Answer:

yes, i think it is correct :)

Step-by-step explanation:

Which is an equation for the line that passes through (0, 2) and (-2, 0)?

Answers

Answer:

Step-by-step explanation:

(0,2). y=mx+b or 2=-2 × 0+b, or solving for b: b=2-(-2)(0).

Answer:

the required equqtion is x-y=2

A public health organization reports that 30% of baby boys 6 - 8 months old in the United States weigh more than 20 pounds. A sample of 15 babies is studied. Round the answers to three decimal places. Part 1 of 4 (a) What is the probability that exactly 5 of them weigh more than 20 pounds

Answers

Answer:

0.206 = 20.6% probability that exactly 5 of them weigh more than 20 pounds.

Step-by-step explanation:

For each baby, there are only two possible outcomes. Either they weigh more than 20 pounds, or they do not. The probability of a baby weighing more than 20 pounds is independent of any other baby, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A public health organization reports that 30% of baby boys 6 - 8 months old in the United States weigh more than 20 pounds.

This means that [tex]p = 0.3[/tex]

A sample of 15 babies is studied.

This means that [tex]n = 15[/tex]

What is the probability that exactly 5 of them weigh more than 20 pounds

This is P(X = 5). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{15,5}.(0.3)^{5}.(0.7)^{10} = 0.206[/tex]

0.206 = 20.6% probability that exactly 5 of them weigh more than 20 pounds.

Solve rational equations 5/6+3/b=1/3

Answers

5/6+3/b = 1/3
B = -6

Choose the pair of sets which is equivalent.



Answer and I will give you brainiliest ​

Answers

I think it’s c i hope im correct

NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.

The fence around a circular garden is 18 feet long.What is the area of the garden to the nearest square foot?Use 3.14 for pi.

Type the answer in the box

________ square feet​

Answers

A= 26ft squared

lmk if this helped :)

Determine whether the triangles are similar. If so, write a similarity
statement.

Answers

Answer:

[tex]\triangle FED\sim \triangle JEH[/tex]

Step-by-step explanation:

Both pairs of vertical angles formed at point E are equal. Therefore, the two triangles share two angles. If two triangles share two angles, they must also share the third angle, since the sum of the interior angles of a triangle add up to 180 degrees. Therefore, all three angles of the two triangles are equal, which is a proof of similarity. [tex]\implies \boxed{\triangle FED\sim \triangle JEH}[/tex]

9514 1404 393

Answer:

  ΔDEF ~ ΔHEJ

Step-by-step explanation:

The vertical angles at E are congruent, and the marked angles at F and J are congruent. The two triangles are similar by the AA postulate.

The given portion of the similarity statement names the angles in the order "unspecified", "vertical", and "50°". If we name those angles in the same order in the other triangle, the similarity statement becomes ...

  ΔDEF ~ ΔHEJ

What is the value of log E 100

Answers

Answer:

4.605170185988091

Step-by-step explanation:

ln 100 = 4.605170185988091

e^4.605170185988091 = 100

Step-by-step explanation:

100=1 log 10(1)=0

I hope this is helpful for you

10. Fill in the blank to make an equal problem 2,165 + ______ + 1,678 = 6,414

Answers

Answer:

2,165 + 2571 + 1,678 = 6,414

Step-by-step explanation:

We can say;

=> 2,165 + unknown number + 1,678 = 6,414

So let's add like terms first;

=> 3,843 + unknown number = 6,414

=> unknown number = 6,414 - 3,843

=> unknown number = 2571

Hope this helps!

Answer:

2571

Step-by-step explanation:

Let x be the blank.

2165 + x + 1678 = 6414

3843 + x = 6414 (combine like terms)

x = 2571

The atmosphere of a certain planet is made up of many
elements. What part of the atmosphere is made up of Element
2?

I’ll make you a brilliant answer plsss help

Answers

I think is element 2? I’m not sure but I think is 2

I don’t get this one but the question was something about finding the equation.

Answers

9514 1404 393

Answer:

  y = -(x -3)^2 +2

Step-by-step explanation:

The vertex form of the equation for a parabola is ...

  y = a(x -h)^2 +k

where the vertex is (h, k) and the value 'a' is a vertical scale factor.

The value of 'a' can be found by looking at the y-value of points ±1 either side of the vertex relative to the vertex. Here, the vertex y-value is +2 at x=3, and either side goes down 1 unit (to y=1) for 1 unit to the right or left. So, a = -1.

Using the values we've read from the graph for the vertex (h, k) = (3, 2) and the scale factor a = -1, we can write the equation as ...

  y = -(x -3)^2 +2

Which of the following represents the factorization of the trinomial below?
x2 - 17x+ 30
A. (x-3)(x-10)
B. (x-2)(x+15)
C. (x-2)(x-15)
D. (x-3)(x +10)

Answers

this is c! you can always just expand the answer choices.

Write the equivalent of the fraction using a dominator of 35 4/14​

Answers

Answer:

10/35

Step-by-step explanation:

4*2.5=10

14*2.5=35

4/14=10/35

HELP ASAP 35 POINTS

Answers

Answer:

Given function:

y = -x² + 6

Fill in the table by substituting the value of x:

x = 0 ⇒ y = - 0² + 6 = 6x = 1 ⇒ y = - 1² + 6 = 5x = -1 ⇒ y = -(-1)² + 6 = 5x = 2 ⇒ y = -2² + 6 = 2x = -2 ⇒ y = -(-2)² + 6 = 2

The graph is attached

PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!

Answers

Answer:

216

Step-by-step explanation:

outcome of one die is 1 out of 6 and if you roll 3 dices, the outcome is 216 possible outcomes because 6 times 6 times 6 is 6 cubed or 216

From her eye, which stands 1,61 meters above the ground, Savannah measures the
angle of elevation to the top of a prominent skyscraper to be 24°. If she is standing at
a horizontal distance of 340 meters from the base of the skyscraper, what is the
height of the skyscraper? Round your answer to the nearest hundredth of a meter if
necessary

Answers

Answer:

152.99 m

Step-by-step explanation:

Using the solution diagram attached below :

We can obtain the height, h of skyscraper to the position of her eye level using trigonometry ;

Tan θ = opposite / Adjacent

Tan 24 = h / 340

h = tan 24 * 340

h = 151.37775

Hence, the height will be (h + distance from eyelevel to ground)

151.37775 + 1.61

= 152.98775

= 152.99 m

Answer:

132.6 meters tall

Step-by-step explanation:

it gave me the answer

Integers help me with this question

Answers

9514 1404 393

Answer:

  5196 m

Step-by-step explanation:

The difference in elevation is found by subtracting one elevation from the other. Usually, we're interested in the positive difference, so we subtract the smaller number from the larger.

  5040 -(-156) = 5040 +156 = 5196

The difference in elevation is 5196 meters.

The circle below has a radius of 10 centimeters. What is the area of the shaded
region?
10 cm
120
A. 10 square centimeters
B. 50 square centimeters
C. 3 square centimeters
D. 100 3 square centimeters

Answers

D I think
Explanation

The area of the shaded segment is 100/3π square centimeter

What is a area?

Area is nothing but the surface bounded by the object in 2D.

What is a segment?

A part of a line or curve between two points In circle we can say segment is nothing but a region or area cutoff from the circle by chord.

What is a segment area?

Area bounded by a segment. Area of segment has a formula (θ/360°)πr²

According to the question

θ=120°

radius =10cm

area of segment = (120°/360°)π(10²)

120°/360° =0.333

10²=100

0.333×π×100

33.3π or (100/3)π

Thus area of the shaded segment is 33.3π or (100/3)π square centimeters

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Help me solve this please !

Answers

Answer:

The answer is D, 14. This is because those bars are asking for absolute value, meaning you simply change any negative to a positive and give its value in general instead of as a negative or positive

what is equivalent to 4 to the power of 3

Answers

Answer:

64

Step-by-step explanation:

because you multiply 4 by it self

4•4•4
when using exponents the number above is how many times you multiply the number by itself
4^3=64

What is the probability of the spinner landing on 1 or 3

Answers

Answer:

Assuming there are 3 possibilities for the spinner, the answer is [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

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