Kelly works at her own nail salon. Today, she did 11 manicures and received $55.00 in overall tips. If x represents the cost of each manicure, which of the following equations can be used to find the total amount of money she earned, including tips, for her nail salon today?

Integral setup The following equation can be used to determine the volume of a solid of revolution:

V = ∫[a, b] A(x) dx where A(x) is the area of the cross-sections and dx is the thickness of each cross-section.

To determine the volume V generated by rotating the region bounded by y = x³, y = 0, and x = 4 around the y-axis,

For the region bounded by y = x³, y = 0, and x = 4, the cross-sections are perpendicular to the y-axis and they take the shape of washers.  

The washer's area can be determined by taking the difference between the area of the larger circle (with radius 4) and the area of the smaller circle (with radius x³) which is:

A(x) = π(4² - x⁶) dx

To determine V, integrate A(x) over the limits of x = 0 to x = 4 which gives:

V = ∫[0,4] π(4² - x⁶) dx = π[4³x - 1/7x⁷][0,4]V = π[(64 × 4) - (1/7 × 4⁷)] = π[256 - (16384/7)] = 780.189 cubic units

Therefore, the integral set up to determine the volume V generated by rotating the region bounded by y = x³, y = 0, and x = 4 around the y-axis is:

V = ∫[0,4] π(4² - x⁶) dx where A(x) is the area of the cross-sections and dx is the thickness of each cross-section.

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Answer:

5

Step-by-step explanation:

We can see a pattern of 1/2 as the week progresses. 1/2 of 80 is 40, 1/2 of 40 is 20, 1/2 of 20 is 10, so for the fourth week 1/2 of 10 is 5.

Answer:

use symbolab

Step-by-step explanation:

To draw a curve in the horizontal alignment for an area in 12D, you can follow these steps: Open the 12D software or any other software specifically designed for civil engineering and surveying purposes.

Create a new project or open an existing project that contains the desired area where you want to draw the curve.

Ensure that you have the necessary data, such as survey measurements or design specifications, to accurately depict the curve.

Access the alignment tools within the software. These tools allow you to define the horizontal alignment of the road or area.

Select the curve tool from the alignment menu. This tool is typically represented by an icon that resembles a curved line.

Specify the properties of the curve, such as the radius, length, and degree of curvature. These values will depend on the design requirements for the area you are working on.

Click on the starting point of the curve and then click on the endpoint to create the curve. The software will automatically calculate the necessary curve parameters based on the values you provided.

Review and adjust the curve if necessary. The software will display the curve visually, allowing you to make any modifications or refinements.

Save your project to preserve the curve you created.

To draw a curve in the horizontal alignment for an area in 12D, you need to use specialized civil engineering and surveying software. By accessing the alignment tools, selecting the curve tool, specifying the curve properties, and creating the curve between the desired points, you can accurately depict the curve in the software. Remember to review and adjust the curve as needed before saving your project.

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To find the water-level height (feet) as a function of time (hours), we need to know the volume of the pool and how much water is being pumped in per hour.

The volume of the rectangular pool can be found by multiplying its length, width, and height:

Volume = Length x Width x Height

Since we know the dimensions of the pool are 20 feet by 10 feet, we can assume the height is 5 feet (half the length of the pool).

Volume = 20 ft x 10 ft x 5 ft = 1000 cubic feet

This means the pool can hold 1000 cubic feet of water.

If 50 cubic feet of water is pumped into the pool per hour, we can write the water-level height (h) as a function of time (t) as follows:

h(t) = (50t) / 1000

where t is the time in hours.

For example, after 1 hour, the water-level height would be:

h(1) = (50 x 1) / 1000 = 0.05 feet

After 2 hours, the water-level height would be:

h(2) = (50 x 2) / 1000 = 0.1 feet

And so on.

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Answer:

yes it is safe.

Step-by-step explanation:

Tan^-1 (5.8/1.5)

theta = 75.5

yes, it is safe

The angle is between 70° to 80°.

Yes, the ladder is safe.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

tan Θ = 5.8 / 1.5

Θ = tan (5.8 / 1.5)

Θ = 75.5°

The angle is between 70° and 80°.

Thus,

The ladder is safe.

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The standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

Given, the chance that a certain type of thumbtack lands point up when you toss it in the air is 80%.

we have to find the standard deviation of the proportion of the given data that it lands point up out of 100 tosses.

Number of trials be, 100

probability of success be, 80/100 = 0.8

On using the formula of Standard deviation, we get

standard deviation = n×p×(1 - p)

standard deviation = 100×0.8×(1 - 0.8)

standard deviation = 100×0.8×0.2

standard deviation = 16

So, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

Hence, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

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Answer:

Aonnalin, great name  :)  answer as below

Step-by-step explanation:

They tell us to use slope-intercept form.   This is something you will just have to remember  y = mx+b    

It is confusing b/c there is the other one, the point-slope formula too.  but just remember both and know that the point-slope one is to get to the slope-intercept one.    y-y1 = m(x-x1)  

m= slope

m = (y2-y1) / (x2-x1)

P1= (0,7)  in the form (x1,y1)

P2 =(8,-2) in the form (x2,y2)

m = -2-7 / 8-0

m = -9 / 8

now that we have the slope, just use either point with the point-slope

y-7 = (-9/8)(x-0)

y-7 = -9x/8

y = -9x/8 + 7

y = \(\frac{-9}{8}\) X + 7

slope-intercept form  :)

a) The expected value of a random variable is given by the formula: E(X) = np, where n is the size of the population and p is the probability of the event occurring.

In this case, n = 100 and p = 0.15 (since 15% of the population is left-handed). Therefore, E(X) = 100(0.15) = 15. So, we expect 15 students to be left-handed in this class.b)

The probability of exactly x successes in n independent trials, each with probability of success p, is given by the formula: P(X = x) = (nCx)(p^x)(1-p)^(n-x)where nCx = n!/(x!(n-x)!) represents the number of combinations of x elements that can be selected from a set of n elements.

In this case, n = 100, p = 0.15 and we want to find P(X = 12). So, P(X = 12) = (100C12)(0.15^12)(0.85^88) ≈ 0.147c) The probability of at least x successes in n independent trials, each with probability of success p, is given by the formula:P(X ≥ x) = Σ(nCx)(p^x)(1-p)^(n-x) from x to n.

In this case, n = 100, p = 0.15 and we want to find P(X ≥ 10). So, P(X ≥ 10) = Σ(100Ck)(0.15^k)(0.85^(100-k)) from k = 10 to k = 100. Using a calculator, we find that P(X ≥ 10) ≈ 0.972.

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Answer:

75 cents

Step-by-step explanation:

3 dollars divided by 4 lemons would equal 75 cent per lemon.

In decimal form it is 0.75 dollars :)

a and b must be on opposite sides of zero​ (option D)

Explanation:

if a × b = c

and c is less than zero.

c can be less than zero if a < 0 and b > 0

c can be less than zero if b < 0 and a > 0

From the above, we can say a nd b must be on opposite sides this is because the left hand side of 0 shows > 0. While the right side of 0 shows > 0.

Hence, for a × b = c where c < 0,

a and b must be on opposite sides of zero​ (option D)

Answer:

13

11

Step-by-step explanation:

The value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

The expression is given as:

(3x^5 + y^2)^2

Expand the expression

So, we have

(3x^5 + y^2)^2 = (3x^5 + y^2)(3x^5 + y^2)

Expand the bracket

(3x^5 + y^2)^2 = 9x^10 + 3x^5y^2 + 3x^5y^2 + y^4

Evaluate the sum

(3x^5 + y^2)^2 = 9x^10 + 6x^5y^2 + y^4

Hence, the value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

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Answer:

The answer should be C

The only option that describes the given histogram is; D.) Numerical and univariate.

A histogram is defined as a graphical representation representing data points that are organized into user-specified ranges.

Now, we see that from the given histogram that it shows how much water is used in a household in a given day.

Since it is dealing with amount of water, then we can call this a numerical data set since it is only one and doesn't categorize anything.

Secondly, since it gives only one information which is the amount of water for each household, then we can call this a univariate data set.

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complete question:

The display shows how much water is used in a household in a given day. Which of the following describes this data set

A.) Categorical and bivariate

B.) Categorical and univariate

C.) Numerical and bivariate

D.) Numerical and univariate

Step-by-step explanation:

the initial salary is $52,365

increment = $57,128

Raise = $57,128 - $52,365 = $4,763

%raise = $4,763/$52,365 × 100

= 9.1%

Answer:

x = 9

Step-by-step explanation:

(7x + 7) + 60 = 13x + 13 (exterior angle)

7x + 67 = 13x + 13

6x = 54

x = 9

Answer: 23

Step-by-step explanation:

23 is the next prime number. 20 is divisible by 2, 4, 5, etc. 21 divisible by 3, 22 is divisible by 2, so 23 is the next prime number.

23 will come next in the given sequence of prime numbers.

Looking at the sequence, we observe that each subsequent number is either an increment of 2 or an increment of 4 from the previous number. In other words, we can see that the sequence alternates between adding 2 and adding 4.

Applying this pattern to the last number in the given sequence, which is 19, we add 2 to it, resulting in 21.

However, 21 is not a prime number since it is divisible by 3.

Now, applying this pattern to the last number in the given sequence, which we add 4 to it, resulting in 23.

Therefore the next number of the sequence will be 23.

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Answer:

First blank is 15, second blank is 4

Step-by-step explanation:

\(\frac{1}{5}=\frac{1*3}{5*3}=\frac{3}{15}\)

\(\frac{1}{5}=\frac{1*4}{5*4}=\frac{4}{20}\)

The required measure of side y = 8

Given : Triangle TUV and triangle XWV are similar

Thus \(\frac{UV}{VW} = \frac{6}{21}\)

this is further equal to \(\frac{2}{7}\)

Thus the ratio UV : VW = 2 : 7

this implies that the ratio TV : VX should also be equal to the ratio of UV : VW = 2 : 7 because of cpst or also called corresponding parts of similar triangles.

Given  UV : VW = 2 : 7

thus TV : VX = \(\frac{y}{28 }\) which on equation will give y as 8

because \(\frac{8}{28}\) when divided by 4 will give us the required ratio that is 2 : 7

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\( \bf\implies \: 18y \: - 12\)

\( \bf \implies15(y - 4) - 2(y - 9) + 5(y + 6)\) \(\bf \implies \: (15 \times y )+ (15 \times - 4 )- (2 \times y )+ ( - 2 \times - 9) + (5 \times y )+ (5 \times 6)\) \(\bf \implies (15y) + ( - 60) - (2y) + (18) + (5y) + (30)\) \(\bf \implies 15y - 60 - 2y + 18 + 5y + 30\) \(\bf \implies (15y - 2y + 5y) - (60 + 18 + 30)\) \(\bf \implies 18y - 12 \: \underline{ \red{Ans.}}\)

Answer: Parallel

Step-by-step explanation:

if two secanys of a circle are made them they cut off congruent arcs

Answer:

+60

Step-by-step explanation:

This is the answer because you multiply -15 x -4 =60

because negative and negative make positive and =60

Hope this helps:)

pls mark brainly

Answer:

y=1/2x-3

Step-by-step explanation:

Hope this helps :) Have a great day!!!

Step-by-step explanation:

check the pic. I just sent

the answer is $1500

The originally invested price will be;

⇒ $1,500

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Money is invested in a saving account at 12% simple interest.

And, After  one year there is $1680 in the account.

Now,

Let the original invested amount = x

So, We can formulate;

⇒ x + 12% of x = 1680

⇒ x + 12x/100 = 1680

⇒ 112x = 1680 × 100

⇒ 112x = 1,68,000

⇒ x = 1,68,000/112

⇒ x = $1,500

Thus, The original invested amount = $1,500

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Answer:kepler's 3rd law

Step-by-step explanation:

Answer:

5^6

Step-by-step explanation:

When dividing numbers with exponents that have the same base, you can subtract the exponents.

5^9-3 = 5^6