The function f (x) = .85x+3.99 models the total cost of purchasing x key chains from an internet company that charges shipping the function g (x) = 1.10x models the total purchasing of x number of the same key chains from an company that does not charge shipping. Rounding to the nearest whole number what is the best approximation of the number of key chains for which the two companies charge the same amount?

Answer:

51

Step-by-step explanation:

Given

[tex]\mu = 51[/tex]

Required

Where will the mean approach if sample size increase

Using central limit theorem, we have:

[tex]n \to \infty[/tex]

[tex]\mu \to \mu[/tex]

This means that; as n approaches infinity, the mean is almost expected to the [tex]\mu[/tex] i.e. expected to remain unchanged.

Hence, the mean value will approach 51.

Answer:

Volume Original = 471 in³

Volume New = 343.36 in³

Step-by-step explanation:

Radius Original = 5

Radius New = (5) - 0.1(5) = 5 - 0.5 = 4.5

Height original = 6

Height new = (6) - 0.1(6) = 6 - 0.6 = 5.4

Volume original = 3.14 x 25 x 6 = 3.14 x  150 = 471

Volume New = 3.14 x 20.25 x 5.4 = 343.36

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

When we have a function:

f(x)

The average rate of change in the interval a < x < b

is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Now for each of the given intervals, let's find the average rate of changes.

q(x) = (x + 3)^2

1)  -6 ≤ x ≤ -4

[tex]r = \frac{(-4 + 3)^2 - (-6 + 3)^2}{-4 - (-6)} = \frac{1 - 9}{2} = -4[/tex]

here the correct option is F.

2) -3 ≤ x ≤ 0

[tex]r = \frac{(0 + 3)^2 - (-3 + 3)^2}{0 - (-3)} = \frac{9}{-3} = -3[/tex]

Here the correct option is D.

3) -6 ≤ x ≤ -3

[tex]r = \frac{(-3 + 3)^2 - (-6 + 3)^2}{-3 - (-6)} = \frac{9}{3} = 3[/tex]

Here the correct option is C

4)  -3 ≤ x ≤ -2

[tex]r = \frac{(-2 + 3)^2 - (-3 + 3)^2}{-2 - (-3)} = \frac{1}{1} = 1[/tex]

Here the correct option is B.

5) -4 ≤ x ≤ -3

[tex]r = \frac{(-3 + 3)^2 - (-4 + 3)^2}{-3 - (-4)} = -1/1 = -1[/tex]

Here the correct option is A

6)  -6 ≤ x ≤ 0

[tex]r = \frac{(0 + 3)^2 - (-6 + 3)^2}{0 - (-6)} = \frac{9 - 9}{6} = 0[/tex]

Here the correct option is E.

Answer:

x=0

y= x + 8

Step-by-step explanation:

find the oblique asymptotes using long polynomial divison

Answer:

x = √30

Step-by-step explanation:

For an equilateral triangle, the measure of the angle at each vertex is 60 degrees

Thus, the angle 60 faces the side measure x

Also, the given length is adjacent to the angle 60 measure

Mathematically, the trigonometric ratio that links the adjacent and the opposite is the tan

The tan is the ratio of the opposite to the adjacent

Thus;

Tan 60 = x/ root 10

x = root 10 * tan 60

x √(10 * √(3

x = √30

The length of [tex]x[/tex] is required.

The length of [tex]x[/tex] is [tex]\sqrt{30}\ \text{units}[/tex]

In an equilateral triangle the altitude divides the side into halves.

So, the hypotenuse will be [tex]\sqrt{10}+\sqrt{10}=2\sqrt{10}[/tex]

From the Pythagoras theorem we have

[tex]x^2+(\sqrt{10})^2=(2\sqrt{10})^2\\\Rightarrow x=\sqrt{(2\sqrt{10})^2-(\sqrt{10})^2}\\\Rightarrow x=\sqrt{30}[/tex]

The length of [tex]x[/tex] is [tex]\sqrt{30}\ \text{units}[/tex]

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Answer:

is this the full question

Answer:

42.25 feet ³

Step-by-step explanation:

Volume of the box = length × width × height

Length = 6 1/2 feet = 6.5 feet

Width = 3.25 feet

Height = 2 feet

Volume of the box = length × width × height

= 6.5 feet × 3.25 feet × 2 feet

= 42.25 feet ³

Volume of the box = 42.25 cubic foot

Answer:

I think its 132.

The total surface area of the triangular prism is 200 cm².

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

First, find the height of the prism.

Let h is the height of the prism

Use the pythagoras theorem

then

5² = (6/2)² + h²

5² = 3² + h²

25 = 9 + h²

h² = 25 - 9

h² = 16

h =4

Now apply the surface area formula

total surface area = ( 5 + 5 + 6) 11 + 6×4

                             = 16 × 11 + 24

                             = 176 +24

                             = 200 cm²

Hence the surface area is 200 cm²

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Answer:

b.3

Step-by-step explanation:

the initial triangle is small and the final triangle is big so scale factor is grater than 1

the sides of the final triangle got 3 times larger so scale is 3

Answer:

200%

Step-by-step explanation:

.1) Calculate fractions value. 2) Multiply the number by 100. 3) Add rhe percent sign % to the value. 2=2*100/100=(2*100)100=200/100=200%.

Answer:

50%

Step-by-step explanation:

40/80 = 0.5.  We multiply this decimal fraction by 100% to obtain the desired percentage:  0.5(100%) = 50%

Answer:

−7.5. −7. −6.5. −6. −5.5. −5. −4.5.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2} \\[/tex]

13cm is hypotenuse = c

a is an edge = 5cm

b is an edge = 12cm

This is a right angle triangle

Answer:

(goF)(-3)=21

Step-by-step explanation:

Answer:

did somebody already answer?

I'm asking because I'm about to answer

Answer:

24

Step-by-step explanation:

h(x) = [tex]\frac{1}{2}[/tex]x - 5, x < 0   This formula would be used for h(-30). Since -30 is less than 0.

h(x) = [tex]\frac{1}{2}[/tex]x - 5, x < 0 ← You can now ignore the x<0.

h(-30) = [tex]\frac{1}{2}[/tex](-30) - 5      Input the -30 as x.

h(-30) = [tex]\frac{-30}{2}[/tex] - 5         Simplify

h(-30) = -15 - 5          Simplify further

h(-30) = -20

Next

h(x) = [tex]\frac{1}{5}[/tex]x - 2, x < 0   This formula would be used for h(30). Since 30 is greater than 0.

h(x) = [tex]\frac{1}{5}[/tex]x - 2, x ≥ 0  ← You can ignore the x≥0.

h(30) = [tex]\frac{1}{5}[/tex](30) - 2         Input the 30 as x.

h(30) = [tex]\frac{30}{5}[/tex] - 2              Simplify

h(30) = 6 - 2               Simplify further

h(30) = 4

Finally the problem is asking for h(30) - h(-30) = ?

h(30) - h(-30)    

(4) - (-20)   Substitute the value of h(30) and the value of h(-30).

4 + 20       You distribute the - sign into the parentheses. A negative times a

24             negative is a positive. That is how the equation had become 4 + 20 towards the end. Which is equal to 24.

So the answer is 24.

Answer:

It would be the fourth one

Step-by-step explanation:

Answer:

 ^^

Step-by-step explanation:

Answer:

You didn't add the range. I'll use (0<x<2π)

cosx = -1/2

x=-cos-¹(1/2)

x= -60°

Cosine is negative in the second and 3rd quadrants

180-x ---- Second quadrant

x+180 ----- 3rd quadrant

So

Our answer

180-(-60)=240° or 4π/3 second quad

180+(-60) = 120° or 2π/3---- 3rd quad

Answer:

37.1

Step-by-step explanation:

12²=144

39²= 1521

1521-144 =1377

Then find the square root of 1377

=37.1

Answer:

C. 110

Step-by-step explanation:

It decrease each time by 30

230-30=200

200-30=170

170-30=140

So

140-30=110

110 is the correct answer.

Hope this helps!!

Answer:

$15.70 an hour

Step-by-step explanation:

$251.20/16= $15.70

Answer:

25.13

Step-by-step explanation:

C = 2πr

C = 2π(4)

C = 25.13

Hope this helps!

The value of QR in the triangle is 16 units

Recall that Congruence of triangles represents the similarity of triangles. Two triangles are congruent if their corresponding sides and angles are congruent

The question states that  ΔPML≅ΔTRQ

This implies that ML/QR = PM/TR

⇒(7x-9)/2x+2  = 35/14

Cross and multiplying we have

14(7x-9) = 35(2x+2)

=98x-126 = 70x +70

98x-70x = 70+126

⇒28x = 196

Making x the subject of the formula

x= 196/28 = 7

Recall that the side QR = 2x+2

Then by substitution,

2(7) +2

14+2 =16

This therefore keeps the side QR as 16 units.

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Answer:

total balls 5+4 = 9

Probability of getting blue ball in the first try

                                                                   =[tex]\frac{5}{9}[/tex]

After replacing, total number of balls  = 9

Probability of getting blue ball in the second try

                                                                  [tex]= \frac{5}{9}[/tex]

Therefore probabilty of getting 2 blue balls

                                                               =[tex]\frac{5}{9}*\frac{5}{9} =\frac{25}{81}[/tex]

Answer:

a) 2.188

b) John's rent is not an outlier

c) His rent has to be higher than $1,235 to be an outlier

Step-by-step explanation:

The mean monthly rent of students at Oxnard University is $780 with a standard deviation of $208.

(a) John’s rent is $1,235. What is his standardized z-score?

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = $1235

μ is the population mean = $780

σ is the population standard deviation = $208

Hence,

z = 1235 - 780/208

z = 2.1875

Approximately to 3 decimal place = 2.188

(b) Is John’s rent an outlier?

No it isn't

(c) How high would the rent have to be to qualify as an outlier?

John’s rent would have to be higher than $1235

Answer:

A) f^5

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

50 - 40 + c

50 - 40 + 4

10 + 4

14

9514 1404 393

Answer:

  3√3 square units

Step-by-step explanation:

The area of a regular n-sided polygon with radius r is given by the formula ...

  A = (n/2)r²·sin(360°/n)

For n=3 and r=2, the area is ...

  A = (3/2)(2²)·sin(360°/3) = 6·sin(120°) = 6(√3/2)

  A = 3√3 . . . . square units

_____

Alternate solution

The center of this polygon is the centroid, which divides each median into parts with the ratio 2:1. This means the given radius is 2/3 of the height of the triangle. The base of the triangle is 2/√3 times the height, so is ...

  b = (2/√3)(3) = 2√3

The area using these dimensions is calculated as ...

  A = 1/2bh

  A = 1/2(2√3)(3) = 3√3 . . . . square units

Answer:

Infinitely many solutions.

Step-by-step explanation:

2 (n - 1) + 4n = 2 (3n - 1) Let's simplify this to solve it.

2n - 2 + 4n = 6n - 2 Distribute 2(n-1) and 2(3n-1)

2n + 4n - 2 = 6n - 2 Rearrange the left side of the equation.

6n - 2 = 6n - 2 Add 2n + 4n.

-6n        -6n Subtract 6n from both sides.

-2 = -2

the answer is infinitely many solutions, meaning that n can be any real number.