6. Answer the following questions given the following infinite geometric series:

8 + 12 + 18 + 27 + ...

Using the normal distribution, it is found that 55.7% of response times are between 4 and 6 minutes.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 4.5, \sigma = 1.2[/tex]

The proportion between 4 and 6 minutes is the p-value of Z when X = 6 subtracted by the p-value of Z when X = 4, hence:

X = 6:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (6 - 4.5)/1.2

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

X = 4:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (4 - 4.5)/1.2

Z = -0.42

Z = -0.42 has a p-value of 0.3372.

0.8944 - 0.3372 = 0.5572 = 55.72%.

Hence:

55.7% of response times are between 4 and 6 minutes.

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Answer:

Second equation Answer: [tex]y=-\frac{1}{2}x-1[/tex]

First equation Answer: [tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]

Step-by-step explanation:

Concept:

The general equation of a line in slope-intercept form is given below as

[tex]y=mx+c[/tex]

where

[tex]m=slope[/tex]

[tex]c=intercept[/tex]

The first equation is given below as

[tex]4x+3y=7[/tex]

We will make y the subject of the formula to change the equation in slope-intercept form

[tex]4x+3y=7[/tex]

subtract 4x from both sides

[tex]4x-4x+3y=7=-4x[/tex]

[tex]3y=-4+7[/tex]

divide both sides by 3

[tex]\frac{3}{y} =\frac{-4x}{3} +\frac{7}{3}[/tex]

[tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]

Hence,

The equation of 4x+3y=7 in slope intercept form is given below as

The second equation is given below as

Hence,

The equation of x+2y=-2 in slope-intercept form is

AshTheNeko

[tex]y(\pi/3)=1 \implies 1=C-2\cos(\pi/3) \\ \\ 1=C-1 \\ \\ C=0 \\ \\ \therefore y=\boxed{-2\cos x}[/tex]

Answer:

Step-by-step explanation:

16/4

The amount that he owes will be $6610.54.

From the information, the base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.

Therefore the amount that will be paid will be:

= ($30.45 × 2) + (15.75 × 415.85 miles)

= $60.90 + $6549.64

= $6610.54

The cost is $6610.54.

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Answer:

4410

Step-by-step explanation:

45 x 98 = 4410

Answer:

-3/2

Step-by-step explanation:

x < -3/2

The distance between any two point is 5 unit.

What is distance?

The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors.

As per the question

Triangle xyz is translated = 4units

And triangle xyz left to yield=3 unit

The distance between the corresponding is hypotenuse of the triangle is-

Buy applying Pythagorus theorem we can get C^2=a^2+b^2

As we know a,b=legs

                       c=hypotenus

C^2=a^2+b^2C^2

      =3^2+4^2

     =9+16  

     =25C =√25 =5 unit

Therefore, the distance between any two point is 5 unit.

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Answer:

i don't known the question you are asking

Answer: Domain {-4,-2,2}

Range{4,6}

Step-by-step explanation:

The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x

The domain is x >= 0 and the range is c(x) >= 9.99

The given parameters are:

One topping = 9.99

Additional topping = 1.25 each

We have x to represent the number of toppings

This means that

C(x) = One topping + Additional topping  * x

So, we have

C(x) = 9.99 + 1.25x

We have

C(x) = 9.99 + 1.25x

The smallest number of topping is 0

So, the domain is x >= 0

Substitute 0 for x in C(x) = 9.99 + 1.25x

C(0) = 9.99 + 1.25(0)

This gives

C(0) = 9.99

So, the range is c(x) >= 9.99

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Answer:
C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]

Step-by-step explanation:

a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.

We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.

So the equation is C(x) = 9.99 + 1.25x right?

Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!

So the new equation is:

    C(x) = 9.99 +1.25(x - 1)

or, C(x) = 9.99 + 1.25x - 1.25

or, C(x) = 1.25x + 8.74  

b) We need to find the Domain of C(x).

We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.

So we can choose up to 10 different toppings. And we need at least 1 topping.

∴ Domain is 1 ≤ x ≤ 10.

b) We need to find the Range of C(x).

We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.

Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.

    C(10) = 1.25(10) + 8.74

or, C(10) = 12.50 + 8.74

or, C(10) = 21.24

∴ Range of C(x) = [9.99, 21.24]

Answer:

C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]

Answer:

16

Step-by-step explanation:

16: 16=4^2 and is even. 16/2=8

30: 30 is even, 30/2=15. However, the square root of 30 is between 5 and 6([tex]\sqrt{25}[/tex]and [tex]\sqrt{36}[/tex]).

81: 81=9^2, but 81 is not even. 81/2=40.5.

99: 99 is not even and doesn't have a square root. The square root of 100 is 10, so the square root of 99 is around 9.9, slightly less than 10.

Answer:

Step-by-step explanation:

-20

a. 3h = -12 + 5s

b. Speed = 51. 6 miles per hour

c. Height = 76 feet

Given the function;

5s - 3h = 12

Where;

a. To solve for 3h

We have;

- 3h = 12 - 5s

3h = -12 + 5s

b. If the height is 82 feet , then

5s - 3(82) = 12

5s - 246 = 12

collect like terms

5s = 12 + 246

5s = 258

Make 's' the subject

s = 258/ 5

s = 51. 6 miles per hour

c. If the speed is 48 miles per hour, we have;

5(48) - 3h = 12

240 - 3h = 12

collect like terms

-3h = 12 - 240

-3h = -228

Make 'h' the subject

h = -228/ -3

h = 76 feet

Thus, the speed and height are 51. 6 miles per hour and 76 feet respectively.

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3 and 17

7 and 13

Step-by-step explanation:

........

The 21% of taxes and annual percentage decrease of 0.32, using arithmetic progression gives;

The percentage of tax that comes from corporate income tax = 21%

Amount by which the percentage decreased each year = 0.32

Period during which the tax reduced = Between 1960 and 2010

Required;

The year corporations pay zero taxes.

Solution;

The amount of tax paid each year can be given by the arithmetic progression formula,

[tex] a_{n} = a + (n - 1) \cdot d[/tex]

Where;

a = The first term = 21

[tex] a_{n} = value \: on \: the \: nth \: year[/tex]

d = The common difference = -0.32

When [tex] a_{n} = 0 [/tex], we have;

[tex] 0 = 21 + (n - 1) \times (-0.32) [/tex]

0.32•(n - 1) = 21

n - 1 = 21/0.32 = 65.625

n = 65.625 - 1 = 64.625 ≈ 65

The year the corporations will pay no taxes is 1960 + 65 = 2025

Corporations will pay no taxes in the year 2025

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Answer: Ok

Step-by-step explanation:

9-0-0

Answer: 450 miles

Step-by-step explanation: we can put the info we got from the question into an equation. since the car was only rented for a day, the daily rate that was paid was $26. and $0.10 for every mile the car was driven. So we can put into the equation 71 = 26 +0.10m, where m represents miles. Now subtract 26 from both sides and we get 45 = 0.10m. Divide both sides by 0.10 and we get m= 450

Answer:

I'm pretty sure the answer is 6.

Step-by-step explanation:

Labeling the rooms A, B, and C makes it easier.

Room A - All BUT 4

Room B - All BUT 4

Room C - All BUT 4

Since you can see each room is all but four, you can split the 4 into 2 into 2 OTHER rooms than the one stated. For example, Room A is all but 4, so 2 go to Room B and the other 2 go to Room C because each room is all BUT 4.

Basically, 2+2+2 = 6

The company's profit will start to decline if it only produces one bag.

Given f(x) = 2x⁴ ₋ 4x³ ₊ 7

Differentiate it with respect to x.

therefore, f'x) = 8x³ ₋ 12x²

= 4x²(2x ₋ 3)

For decreasing, f'(x) ≤ 0

⇒ 4x²(2x ₋ 3) ≤ 0

⇒ 2x ₋ 3  ≤  0

⇒ x  ≤ 3/2

Since the number of bags are represented by x.

Hence, x ∈ N

Therefore, x = 1 is only possibility.

Therefore, if the company only produces one bag, its profit begins to decline.

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Your question was incomplete. Please find the missing the content here.

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson's eventual profit function is given as: pi = 2x⁴ ₋ 4x³ ₊ 7 where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson's profit start decreasing?

Answer:.......................

When the market price is $20, the number of cars that Denny will be willing to repair is 5 cars.

It should be noted that the total revenue will be:

= price × quantity

= 20 × s

= 20s

where s = number of cars

The marginal revenue will be 20.

The total cost is given as:

= 2s² + 10

The marginal cost will be 4s

We will equate the marginal. This will be:

4s = 20

Divide

s = 20/4

s = 5

Therefore, the number is 5.

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The apprοpriate dοmain fοr this situatiοn is t ≥ 0.

In mathematics, a functiοn is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput. It can be thοught οf as a rule οr a machine that takes inputs and prοduces οutputs accοrding tο a specific set οf instructiοns οr οperatiοns.

The dοmain οf a functiοn represents the set οf all pοssible input values fοr which the functiοn is defined. In this case, the functiοn h(t) represents the height οf the rοcket as a functiοn οf time t after launch.

Since time cannοt be negative in this cοntext (we can't have negative secοnds), the apprοpriate dοmain fοr this situatiοn is t ≥ 0, which means the functiοn is defined fοr all nοn-negative values οf t after the rοcket is launched.

Therefοre, the apprοpriate dοmain fοr this situatiοn is t ≥ 0.

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Based on the filing status of Brock and Erin, their itemized deductions, and their income from their salaries, their income tax liability is $4,250.

First, find the taxable income:

= Adjusted gross income - larger of Itemized deductions or standard deductions

= (50,000 + 8,000 + 5,000 + 3,000 - 2,500) - 24,800

= $38,700

The tax rate is 10 % for income between $0 and $19,750 and 12% for salaries between $19,751 and $80,250.

Brock and Erin therefore have a tax liability of:

= (10% x 19,750) + (12% x (38,700 - 19,750))

= $4,252

Rest of the question is:

Find the Income tax liability before any credits

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By evaluating following logarithm equation and we we get the value of required expression is -0.54.

What is logarithm?

The logarithm is the opposite of exponentiation as a function. This indicates that the base b of another fixed number, the logarithm of a given number x, is the exponent that must be raised in order to obtain the given number x.

As per the question

we have to assume x

log x=0.27

log by=0.81

We have to calculate log bx/y by following expression

We know loge (a/b)= log_e a-log_e b

We know (x)= logb y

=0.27-0.81

= -0.54

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The proportion of users that park bike on the trail is 0.1728

The table represents the given parameters

From the table, we have the following parameters

Suburban total = 243

Users that park bike on the trail = 42

The proportion of users that park bike on the trail is then calculated as

P = Users that park bike on the trail/Suburban total

This gives

P = 42/243

Evaluate

P = 0.1728

Hence, the proportion of users that park bike on the trail is 0.1728

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