A box of 6 nail polishes cost $10. How much is each nail polish?

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

To learn more about Fraction here,

https://brainly.com/question/10354322

bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

For more such questions on discounts

https://brainly.com/question/28420607

#SPJ8

The joint costs allocated to Product B is $240,000.

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

Read more about Joint cost

brainly.com/question/31392604

#SPJ1

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

For such more questions on function

https://brainly.com/question/11624077

#SPJ8

Answer:

Answer:

P(t) = 10t - 400

Step-by-step explanation:

Selling price of each ticket = $10

Cost of setting up the dance= $400

Profit = Revenue - cost

Revenue = price × quantity

Revenue that will maximize profit = 10t

where t= quantity of tickets that maximises profits

Cost = $400

Profit(t) = Revenue - cost

P(t)= 10t - 400

Step-by-step explanation:

Hope this helps, have a great day!

Answer:

A. Negative correlation

B. Data isn't given

Step-by-step explanation:

A. A positive correlation occurs when variables that are related(not zero correlation)increase together, in other words variable a(independent variable) increases and makes variable b(dependent variable) increase too. There will be a negative correlation if the opposite happens, that is when variables that are related go in opposite directions, one increases while the other decreases. We observe from what we are told that a negative correlation occurs here since death rate from fires has likely(assumed) decreased as smoke detectors have increased.

Answer:

Han's mixture, Claire's mixture

Step-by-step explanation:

I figured out the percentage of orange juice for each person's mixture:

For Claire:

2 1/2 + 1/3 = 2 5/6

2 5/6 as a decimal: about 2.8

Now find what percent of Claire's total mixture was orange juice:

100 * 1/3 / 2.8 = about 11.9%

For Han:

1 2/3 + 1/4 = 1 11/12

1 11/12 as a decimal: about 1.9

Now find what percent of Han's total mixture was orange juice:

100 * 1/4 / 1.9 = 13.2%

So, Han's mixture is stronger, since his has the higher percentage of orange juice concentrate

Answer:

His friend took one from 61 and added it to 39. That made it easy to mentally add 40 and 60 to get 100. Then he mentally added 28 to 100 to get 128.

The height of Stephen is = 1.79 + 0.14 = 1.93 meters

In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple. How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used.

Step: 1

The height of Kobe is 2.07 meters

The height of Marcus is 1.79 meters

The difference between Kobe's height and Marcus's height = 2.07 - 1.79 meters

And its half is = 1/2 * 0.28 = 0.14 meters

Stephen is taller than Marcus by half the difference between Kobe's height and Marcus's height

The height of Stephen is = 1.79 + 0.14 = 1.93 meters

learn more about unitary method here :

brainly.com/question/22056199

#SPJ13

Answer:4

Step-by-step explanation:

A zero-coupon bond  doesn’t make any payments. Instead, investors purchase the zero-coupon bond for less than its face value, and when the bond matures, they receive the face value.

To figure the price you should pay for a zero-coupon bond, you'll follow these steps:

Divide your required rate of return by 100 to convert it to a decimal.

Add 1 to the required rate of return as a decimal.

Raise the result to the power of the number of years until the bond matures.

Divide the face value of the bond to calculate the price to pay for the zero-coupon bond to achieve your desired rate of return.

First, divide 4 percent by 100 to get 0.04. Second, add 1 to 0.04 to get 1.04. Third, raise 1.04 to the sixth power to get 1.2653. Lastly, divide the face value of $1,000 by 1.2653 to find that the price to pay for the zero-coupon bond is $790,32.

The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

More about the number line link is given below.

https://brainly.com/question/13189025

#SPJ1

Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is expressed as a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.

To solve this problem, we can use the formula for the standard deviation of the sample mean:

Standard deviation of sample mean = standard deviation / √(sample size)

Plugging in the given values:

Standard deviation of sample mean = 7 / √(31)

Next, we can calculate the z-score, which is the number of standard deviations the sample mean is below the population mean:

z-score = (sample mean - population mean) / standard deviation of sample mean

Plugging in the given values:

z-score = (141.5 - 145) / (7 / √(31))

Using a calculator, we find that the z-score is approximately -2.22.

Finally, we can use a standard normal distribution table or a calculator to find the probability that a z-score is less than -2.22.

Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

From the circle the value of angle x is 90 degrees

We have to find the value of x

The radius of the circle is 18.5

As we observe the figure the angle x is opposite to the 90 degrees

The angle x and angle 90 degrees are vertical angles

We know that the vertical angles are equal or same

∠x = 90 degrees

Hence, the value of angle x is 90 degrees from the circle

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

The rate of emptying the lake is -1/8.

The rate of filling the lake is 1/15

Let t be the time in weeks to empty the lake,

Now, add the given rate to get the total rate of emptying of -1/t.

Thus,

Therefore, it will take 17 weeks and 1 day to empty the lake.

Answer:

43.6*10⁴

Step-by-step explanation:

4.9 * 10⁵ = 49*10⁴

then:

4.9*10⁵ - 5.9*10⁴ = 49*10⁴ - 5.9*10⁴ = (49-5.4)*10⁴ = 43.6*10⁴

Answer:

4.32 × 10^5

Step-by-step explanation:

First, multiply 4.9 by 10^5=490000 and 5.8 by 10^4=58000. Subtract 58000 from 490000=432000. Then, scientific notation is a number between 1 and 10 being multiplied by a power of ten, so get 432000 down to a number between 1 and 10, which is 4.32 and 4.32 multiplied by 10^5 is 432000.

(hope this helps :P)

The Quotient and remainder of the polynomial is  x² + x -6 and 2 respectively

Synthetic division method is one of the method used to divide the polynomial equations.

The polynomial equation given here is

x³ + 3x² - 4x - 10

We need to divide this polynomial equation with x - 2

Thus by dividing the polynomial x³ + 3x² - 4x - 10 with x - 2, we get

the quotient as x² + x -6 and

     Remainder as 2

Learn more about the synthetic division in

https://brainly.com/question/11850611

#SPJ9

Answer:

Option (4)

Step-by-step explanation:

Jordan spent 5 hours studying for 3 test with equal amount of time studying for each test.

On the number line, there are 3 small segments between each number.

Every small segment will represent time = \(\frac{1}{3}\) hours

Total number of small segments = 15

If Jordan takes 3 equal durations for the study of each test,

Total number of small segments for each test = \(\frac{15}{3}=5\)

Now we can plot these points on the number line.

Further count the segments for the answer ( 1 hour plus 2 small segments)

= 1 + \(2\times \frac{1}{3}\)

= \(1\frac{2}{3}\)

Therefore, time given for studying each test = \(1\frac{2}{3}\) hours

Option (4) will be the answer.

The recursive rule is f(n) = f(n - 1) * 2; f(1) = 9 and the explicit rule is f(n) = 9(2)^n-1

The recursive rule

From the question, we have the following parameters that can be used in our computation:

The table

The table definitions imply that we simply multiply 2 to the previous term to get the current term

This means that

f(n) = f(n - 1) * 2

Where

f(1) = 9

The explicit rule

The table definitions imply that we simply multiply 2 to the previous term to get the current term

a = 9

r = 2

So we have

f(n) = a * r^n-1

This gives

f(n) = 9(2)^n-1

Read more about sequence at

https://brainly.com/question/29431864

#SPJ1

Answer:

(2,0)

Step-by-step explanation:

it is

Answer:

(2,0)

Step-by-step explanation:

Answer: x = 9

Step-by-Step Solution:

Hypotenuse = 15 units

Base = 12 units

Altitude = x units

Using Pythagoras Theorem,

=> Hypotenuse^2 = Base^2 + Altitude^2

(15)^2 = (12)^2 + x^2

225 = 144 + x^2

225 - 144 = x^2

81 = x^2

x^2 = 81

x = √81

=> x = 9

Therefore, Altitude = 9 units

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

Learn more about identities at

https://brainly.com/question/7331447

#SPJ1

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

for such more questions on rational

https://brainly.com/question/30339525

#SPJ8

Answer:

part a) \(x = 2y + 3t\)

Step-by-step explanation:

hope it helps

Answer:

The two numbers are 8&5

Step-by-step explanation:

13 = x + y

y = x-3

13 = x+(x-3)

13=2x-3

16=2x

x=8

y=1(8)-3

y=5

Answer:

-35c+40d

Step-by-step explanation:

distribute -8 through the numbers in the parenthesis by distribute I mean multiply the numbers in the parenthesis by -8

combine the like terms (c)

combine like terms(d)

then you have your answer

Answer:

7.5 sq ft

Step-by-step explanation:

1.5*5=7.5

The design is 1/5 of the actual size, so you just multiply by 5 to get the real size.