A restaurant bill is $21. You leave a 15% tip. Which of the following represents the amount a customer pays including the tip of 15% if the bill was dollars?

a. 0.15b
b. 15b
c. b + 0.15b
d. 1.15b
e. 1.015b
f. b + 15/100b
g. b + 0.15

Step-by-step explanation: 4d−9=5(2d−3)

im sorry sorry if im wrong pls forgive me :')

also have a blessing day! :)

Answer:

[tex]64(in)^{3} [/tex]

Step-by-step explanation:

The volume of a box is equal to the length l times the width w times the height h.

[tex](lenght) \times (width) \times (height)[/tex]

Substitute the values of the length l=8, the width w=2, and the height h=4 into the formula.

[tex]8 \times 2 \times 4[/tex]

Multiply 8 by 2.

[tex]16 \times 4[/tex]

Multiply 16 by 4.

[tex]64 {in}^{3} [/tex]

Hence, the volume of the rectangle prism is 64(in)³.

Answer:

Step-by-step explanation:

Given dimensions:

Volume of the prism is:

Answer:

$22.05

Step-by-step explanation:

If a product has a sales commission, then one must divide the commission percent by (100) to convert the percent to a decimal. Then multiply the result by the price of the product to find the amount of money that will be given as a commission.

Applying this knowledge to the given problem, one must divide (9%) by (100) to convert to decimal form,

9% / 100 = 0.09

Now multiply the result by the price of the product (245) to find the amount given away in commission,

0.09 * 245 = 22.05

Answer:

A sample size of 385 is needed.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

You feel that a reasonable estimate of the standard deviation is 10.0 hours.

This means that [tex]\sigma = 10[/tex]

What sample size is needed so that the expected margin of error of your estimate is not larger than one hour for 95% confidence?

A sample size of n is needed. n is found when M = 1. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]1 = 1.96\frac{10}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = 1.96*10[/tex]

[tex](\sqrt{n})^2 = (1.96*10)^2[/tex]

[tex]n = 384.16[/tex]

Rounding up:

A sample size of 385 is needed.

Answer:

A- [tex]5.12*10^{-4}[/tex]

Step-by-step explanation:

1.6* 3.2

add the exponents so 10 to the -4

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

)

and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

Short answer (I write nPr = P(n, r) and nCr = C(n, r) ):

P (6, 4) = 6! / (6 - 4)! = 6! / 2! = 720 / 2 = 360

C (6, 4) = P (6, 4) / 4! = 6! / (4! (6 - 4)!) = 360 / 24 = 15

Long answer:

P(n, r) counts the number of permutations of n objects taken r at a time, given by

P(n, r) = n ! / (n - r )!

A permutation is a unique arrangement of objects such that the order in which they are arranged is taken into account. For example, if the objects in question are the numbers in the set {1, 2, 3}, then

• there are 3! = 6 total possible permutations if we take all 3 numbers at once:

123, 132, 213, 231, 312, 321

• there are 3!/(3-2)! = 3!/1! = 6 total permutations if we only take 2 numbers at once:

12, 13, 21, 23, 31, 32

• there are 3!/(3-1)! = 3!/2! = 3 total permutations if we take only 1 number at a time:

1, 2, 3

• and there is 3!/(3-0)! = 3!/3! = 1 way of permuting the 3 numbers without taking any of them:

(the permutation itself is just empty space)

By contrast, C(n, r) counts the combinations of n items taken r at a time, given by

C(n, r) = P(n, r) / r !

A combination is like a permutation, but the order of the objects doesn't matter. Continuing with the previous example of arrangements of the numbers from {1, 2, 3}, we have

• 3! / (3! (3-3)!) = 1 combination taking all 3 numbers at once:

123

(the other 5 permutations listed earlier are made up of the same numbers, so we consider them duplicates)

• 3! / (2! (3-2)!) = 3 combinations taking only 2 numbers at once:

12, 13, 23

• 3! / (1! (3-1)!) = 3 combinations taking only 1 number:

1, 2, 3

• 3! / (0! (3-0)!) = 1 combination taking none of them:

(again, empty space)

The main point is that the order of objects is considered across permutations, while it's ignored across combinations.

Answer:

[tex]y=C_1e^{-x}+C_2xe^{-x}+\frac{1}{5}e^{2x}.[/tex]

Step-by-step explanation:

all the details see in the attached picture.

Answer:

I rhink the answer would be 273°

Step-by-step explanation:

57+180=237°

Answer:

∠ BAC = 28.5°

Step-by-step explanation:

∠ AOB = 180° - 57° = 123° ( straight angle )

OA and OB are congruent ( radii of the circle ) , then Δ AOB is isosceles with base angles congruent, that is

∠ BAC = ∠ ABO , then

∠ BAC = [tex]\frac{180-123}{2}[/tex] = [tex]\frac{57}{2}[/tex] = 28.5°

Answer:

15x9 is 130 but, what u mean by divided by 2 fraction?

Step-by-step explanation:

135/ 2 this is correct unless you want a mixed fraction which is 67 and 1/2

Answer:

1

Step-by-step explanation:

Take an arbitrary interval [a, b], where a < b.

Compute the arc length L of y = f(x) over [a, b] :

[tex]L=\displaystyle\int_a^b\sqrt{1+\left(f'(x)\right)^2}\,\mathrm dx[/tex]

Now comptue the area A under the curve y = f(x) over [a, b] :

[tex]A=\displaystyle\int_a^bf(x)\,\mathrm dx[/tex]

We have

f (x) = 1/4 e ⁻ˣ + e ˣ   →   f ' (x) = -1/4 e ⁻ˣ + e ˣ

Then

√(1 + (f ' (x))²) = √(1 + (-1/4 e ⁻ˣ + e ˣ)²)

… = √(1 + 1/16 e ⁻²ˣ - 1/2 + e ²ˣ)

… = √(1/16 e ⁻²ˣ + 1/2 + e ²ˣ)

… = 1/4 √(e ⁻²ˣ + 8 + 16e ²ˣ)

… = 1/4 √((e ⁻ˣ + 4 e ˣ)²)

… = 1/4 (e ⁻ˣ + 4 e ˣ)

… = 1/4 e ⁻ˣ + e ˣ

… = f (x)

so both A = L for any choice of interval [a, b].

It is true that the arc length on any interval has the same value as the area under the curve.

The function is given as:

[tex]f(x) = \frac 14e^{-x} + e^x[/tex]

Differentiate the function

[tex]f'(x) = -\frac 14e^{-x} + e^x[/tex]

On any interval, the following must be true

[tex]f(x) =f'(x)[/tex]

and

[tex]f(x) = \sqrt{1 + (f'(x))^2}[/tex]

So, we have:

[tex]f(x) = \sqrt{1 + (-\frac 14e^{-x} + e^x)^2}[/tex]

Expand the exponents

[tex]f(x) = \sqrt{1 + (\frac{1}{16}e^{-2x} - \frac 12 + e^{2x})}[/tex]

Remove the bracket

[tex]f(x) = \sqrt{1 + \frac{1}{16}e^{-2x} - \frac 12 + e^{2x}}[/tex]

Evaluate the like terms

[tex]f(x) = \sqrt{\frac{1}{16}e^{-2x} + \frac 12 + e^{2x}}[/tex]

Multiply by 16/16

[tex]f(x) = \sqrt{\frac{16}{16}(\frac{1}{16}e^{-2x} + \frac 12 + e^{2x})}[/tex]

So, we have:

[tex]f(x) = \sqrt{\frac{1}{16}(e^{-2x} + 8 + 16e^{2x})}[/tex]

Take the square root of 1/16

[tex]f(x) = \frac{1}{4}\sqrt{e^{-2x} + 8 + 16e^{2x}}[/tex]

Express the radical as a perfect square

[tex]f(x) = \frac{1}{4}\sqrt{(e^{-x} + 4e^{x})^2}[/tex]

Evaluate the exponents

[tex]f(x) = \frac{1}{4} * (e^{-x} + 4e^{x})[/tex]

Evaluate the products

[tex]f(x) = \frac{1}{4}e^{-x} + e^{x}[/tex]

Hence, it has been proved that  the arc length on any interval has the same value as the area under the curve.

Read more about areas at:

https://brainly.com/question/24487155

Answer:

6 hours.

Step-by-step explanation:

To find how many hours it would take to drive a 240 mile distance at a constant speed of 40 miles per hour, you'd divide 240 by 40 and the result of that is 6.

Answer:

6 hours

Explanation:

240/40= 6

Answer:

1

3814697265625

Decimal Form:

2.62144 ⋅ 10 / 13

Step-by-step explanation:

Answer:

40 square meters

Step-by-step explanation:

Perimeter means to add up all sides.

area means one side times one side

10 times 10 makes 100 so i am guessing each side is 10

10 + 10 + 10 + 10 = 40

Answer:

b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

When multiplying exponents, you would add the degrees.

A, B, and D's degrees add up to [tex]5^{-2}[/tex] , which is equal to 1/25.

C adds up to [tex]5^{2}[/tex], which is 25, therefore making it C

Answer:

The graph shows a proportional relationship because t=50, and that pattern follows.

Step-by-step explanation:

The graph shows a proportional relationship because t=50, and that pattern follows.

The graph represent a proportional relationship between the variables d and t as distance in miles, d a car travels is proportional to the time in hours t.

The speed of a body is the rate at which it covers the total distance in the time taken. The speed of the body is given as,

[tex]s=\dfrac{d}{t}[/tex]

Here, (d) is the distance travelled by the body and (t) is the time taken by the body to cover that distance.

The graph shows the distance in miles, d, a car travels in hours. Rewrite the above formula, ​considering it for the car,

[tex]s=\dfrac{d}{t}\\t\times s={d}[/tex]

In this formula, distance in miles, d, is directly proportional to the time taken by car in hours.

It is because as the car moves, the time start to pass and so the distance car start to cover the distance. In more time, the car will cover more distance with same speed.

Thus, the graph represent a proportional relationship between the variables d and t as distance in miles, d a car travels is proportional to the time in hours t.

Learn more about the speed here:

https://brainly.com/question/359790

#SPJ2

Answer:

260,000

Step-by-step explanation:

The value decreases by 40,000 per year (500000-42000/2 years) the value will decrease by 240000 in six (4 years plus 2 years already passed) years. 6 x 40,000 =240000

So, the value should be 260,000 (500000-240000)

Or

year 1 500000-40000=460000

year 2 460000-40000=420000

year 3 420000-40000=380000

year 4 380000-40000=340000

year 5 340000-40000=300000

year 6 300000-40000=260000

The machine's resale value Garland Mills purchased in 4 years from now will be; $353,049

We are told that the machines present resale value is $420000. Now formula for future value is;

Future value = present value * exp(cx)

Thus;

$420,000 = $500,000 * exp(2c)

420000/500000 = exp(4c)

2c = In(420000/500000)

c = -0.087

Future value = present value * exp(cx)

Future value = $500,000 * exp(-0.087 * 4)

Future value = $353,049

Therefore, the machine's resale value in 4 years from now will be  $353,049

Read more about future value amount at; https://brainly.com/question/13961729

Step-by-step explanation:

We need to find the area of the shaded region. We see that the region next to that has a central angle of 120°. Also we know that angle in a straight line is 180° . So the measure of central angle of that shaded region will be 180° - 120° = 60° . Now we can use the formula of area of sector to find out the area of the shaded region.

[tex]\tt\to Area = \dfrac{\Theta}{360^o}\times \pi r^2 \\\\\tt\to Area = \dfrac{60^o}{360^o}\times \pi (8cm)^2 \\\\\tt\to Area =\dfrac{\pi \times 64}{6}cm^2\\\\\to\boxed{\orange{\tt Area_{(Shaded)}= 10.66\pi cm^2}}[/tex]

Answer:

m<2=60

Step-by-step explanation:

52+68=120+60=180

The calculated quadratic function for the height of the rocket is "[tex]h = 64t - 16.085t^2[/tex]" and the further calculation of the given points can be defined as follows:

For point A):

Rocket Initial velocity (u) [tex]= 64 \ \frac{feet}{sec}[/tex]

Considering gravity's acceleration of 32.17 feet/sec2

The rocket's height can be expressed as follows:

[tex]h = ut - \frac{1}{2} \times 32.17 \times t^2 \\\\h = 64 - 16.085 \times t^2 \\\\h = 64t - 16.085t^2[/tex]

For point B):

A y-axis indicates its rocket's height in feet, whereas the x-axis represents the duration in seconds.

Please find the attached file.

For point C):

Find out more information about the velocity here:

brainly.com/question/25749514

Answer:

1320

Step-by-step explanation:

i am

Answer:

y=0x+6

Step-by-step explanation:

slope intercept form is: y=mx+b

Answer:

1/26

Step-by-step explanation:

There is only one 6 of hearts and only one ace of diamonds.

The probability of selecting the 6 of hearts is thus 1/52, and that of selecting the ace of diamonds is also 1/52.

The probability of selecting the 6 of hearts or the ace of diamonds is the SUM of these two results:  1/52 + 1/52 = 2/52 = 1/26.

Answer:

whts the question??

Step-by-step explanation:

Answer:

1/3, 3/8 are closer to 0

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

dont know i just remeberd