explain why 1/6 + 1/3= 1/2

Answer:

x^2 + y^2 = 400

Step-by-step explanation:

the general equation of a circle is,

x^2 +y^2 = r^2

where x, y are the coordinates of the circle

r is the radius

Answer:

The market equilibrium price is approximately $36.43 per barrel.

Step-by-step explanation:

To find the market equilibrium price, we need to set the quantity supplied (QS) equal to the quantity demanded (QD) and solve for the price (P).

Given:

QS = -250 + 7P

QD = 260 - 7P

Setting QS equal to QD:

-250 + 7P = 260 - 7P

Now, let's solve for P:

Add 7P to both sides:

-250 + 7P + 7P = 260 - 7P + 7P

Combine like terms:

14P - 250 = 260

Add 250 to both sides:

14P - 250 + 250 = 260 + 250

Simplify:

14P = 510

Divide both sides by 14:

14P/14 = 510/14

Simplify:

P = 36.43

The market equilibrium price can be found by setting the quantity supplied (QS) equal to the quantity demanded (QD) and solving for the price (P) that satisfies this condition.

In the given scenario, the supply function is QS = -250 + 7P, and the demand function is QD = 260 - 7P. To find the equilibrium price, we set QS equal to QD:

-250 + 7P = 260 - 7P

Simplifying the equation, we get:

14P = 510

Dividing both sides by 14, we find:

P = 36.43

Therefore, the market equilibrium price is approximately $36.43 per barrel. At this price, the quantity supplied and quantity demanded will be equal, resulting in a state of equilibrium in the perfectly competitive domestic crude oil market.

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Answer:

looks proportional to me

Step-by-step explanation:

Answer:

Proportional

Step-by-step explanation:

Direct proportion:

y = kx

1*4 = 4

2*4 = 8

3*4 = 12

Given values in the table satisfy the equation of direct proportion. So, it is a direct proportion.

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Answer: A is 70 B is 45 and C is 50

Step-by-step explanation:

The answer  is that there are 165 ways to distribute eight identical bottles of water to three friends.

We can use the formula for distributing identical objects to distinct groups, which is (n+r-1) choose (r-1), where n is the number of objects and r is the number of groups. In this case, n=8 and r=3.

So the formula becomes (8+3-1) choose (3-1), which simplifies to 10 choose 2. Using the combination formula, 10 choose 2 equals 45. However, this only accounts for cases where all three friends receive at least one bottle of water.

To account for cases where some friends may receive no water, we need to add the number of ways where two friends receive water and one friend receives no water, and the number of ways where one friend receives water and two friends receive no water.

There are three ways to choose which friend receives no water, and then we need to distribute the remaining eight bottles of water among the remaining two friends. Using the formula from earlier, this gives us (8+2-1) choose (2-1) = 9.

So for the case where two friends receive water and one friend receives no water, there are 3 * 9 = 27 ways. Similarly, for the case where one friend receives water and two friends receive no water, there are 3 * 9 = 27 ways.

Adding these cases to the initial case where all three friends receive at least one bottle of water, we get a total of 45 + 27 + 27 = 99 ways. However, we still need to account for cases where all eight bottles of water go to a single friend, which is just 3 ways.

So the final answer is 99 + 3 = 102 ways to distribute eight identical bottles of water to three friends, where some friends may receive no water.

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Yes, we can indeed support the claim that at 0.01 level of significance, the  mean completion time has decreased under new management because  the calculated t-value (-2.64) is less than the critical value (-2.492), hence we reject the null hypothesis that says the mean completion time has not decreased

The p-value is 0.005

There is need to perform a one sample t-test at 0.01 level of significance to test the claim.

The null hypothesis is that the mean completion time has not changed

Alternate hypothesis is that the mean completion time has decreased

The test statistic is given by:

t = (x - μ) / (s / √(n))

where x is the sample mean

μ is the population mean

s is the sample standard deviation

n is the sample size.

by substituting for the the given values, we have;

t = (14.2 - 14.7) / (1.7 / √(80))

t = -2.64

Using a t-distribution table with 79 degrees of freedom (n-1),

the critical value for a one-tailed test with a significance level of 0.01 is -2.492.

Since the calculated t-value (-2.64) is less than the critical value (-2.492), we reject the null hypothesis  and consider the alternative hypothesis as valid.

Therefore, there is sufficient evidence to support the claim that the mean completion time has decreased under new management.

To get the p-value, we can use a t-distribution table.

The p-value for a one-tailed test when df is 79 and calculated t-value is -2.64 is approximately 0.005.

Therefore, the p-value is 0.005 (rounded to at least 3 decimal places).

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The marginal cost function, denoted as C'(x), can be obtained by taking the derivative of the cost function C(x). In this case, the cost function C(x) is given as C(x) = 160 + 3.7x - 0.01x².

To find the marginal cost function C'(x), we need to differentiate the cost function C(x) with respect to x. Taking the derivative of each term in C(x), we have:

C'(x) = d/dx (160) + d/dx (3.7x) - d/dx (0.01x²).

Since the derivative of a constant is zero, the first term becomes 0. The derivative of 3.7x is simply 3.7, and the derivative of 0.01x² is 0.01(2x) = 0.02x. Therefore, we can rewrite the marginal cost function as:

C'(x) = 3.7 - 0.02x.

This is the expression for the marginal cost at any given level of production x. It represents the rate at which the cost changes with respect to the level of production. For each additional unit produced, the cost increases by 3.7 units but decreases by 0.02 units per unit of production.

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Answer:2 tablespoons of milk

Step-by-step explanation:

If nolan divides 6 by 2 he gets 3 cups of shredded cheese and to get the same results he would have to divide the milk portion too. 4/2 is 2 so he would need 2 tablespoons of milk.

Answer:

length • width = area

expression:

area • height = (result) • 1/3 = volume

Example:

x (area) • 6 (height) = 6x

6x • 1/3 = 2x(inches)³ or 6x ÷ 3 = 2x(inches)³

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Side AC is computed s by applying similar triangles to give 12

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

From the description, pair of equivalent sides are

AB and BD, AC and CE

The solution is worked out using sides AB and BD, AC and CE

AB / BD = AC / CE

where

AB = 8

BD = 10

CE = 15

AC = ?

8 / 10 = AC / 15

cross multiplying

8 * 15 = 10 * AC

AC = 8 * 15 / 10

AC = 12

hence  AC is 12

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Answer:

1/6 chance

Step-by-step explanation:

there are six sides of a dice with only one side being 2. that means there's a one in six chance that a roll of the dice will give the cube landing on a 2

Answer:

c

Step-by-step explanation:

becasue it would have a 3/8 chance of landing on silver , 8 goes into 240 30 times. so if we multiply 3 by 30 it gives us 90.

Answer:

the brain performs at its optimum level

Step-by-step explanation:

answer on edg 2020

The brain performs at its optimum level. Option B is correct.

Given that,
Complete the statement by choosing the appropriate option.

A healthy and balanced diet is what nutrition is all about. Food and drink supply the energy and nutrients required for good health. Understanding this nutrition terminology may help you make smarter meal choices.

Here,
The most crucial reason to have a nutritious meal the morning of a test is to guarantee that the brain operates at peak performance. So, the correct statment among the option is "the brain performs at its optimum level.."

Thus, the most important reason to have a nutritious breakfast on the morning of a test is to ensure that the brain performs at its optimum level.

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The ratio is 2 : 3 and the value that completes the table is 15

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

Table of values

The entries on the table of values are

Red and Green

Using one of the entries, we have

Red : Green = 2 : 3

To complete the table, we have

10 : Green = 2 : 3

Multiply by 5

10 : Green = 10 : 15

So, we have

Green = 15

Hence, the required entry on the table is 15

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Answer:

The test  has 10 3-point questions and 14 5-point questions.

Step-by-step explanation:

x + y = 24

3x + 5y = 100

From the first equation:

3x + 3y = 72

Subtracting:

3x - 3x + 5y - 3y = 100 -72

2y = 28

so y = 14

x + 14 = 24 so x = 10.

10*3 + 5*14

= 30 + 70 = 100 points.

Answer:

\(y=11*3^x\)

Here is the graph showing this function.

Answer:

\(\sf y = 11(3)^x\)

given points: ( 0, 11) , (2,99)

solve for 1st

\(\sf y = ab^x\)

\(\sf 11 = ab^0\)

since we know \(\sf b^0 = 1\)

\(\sf 11 =a\)

solve for 2nd

\(\sf y = ab^x\)

\(\sf 99 = ab^2\)

\(\sf \dfrac{99}{b^2} = a\)

solve simultaneously:

\(\sf 11 = \sf \dfrac{99}{b^2}\)

\(\sf 11 b^2= \sf 99}\)

\(\sf b^2= 9\)

\(\sf b = 3\)

Therefore equation:  \(\sf y = 11(3)^x\)

Answer:

The first pic is for 2x +3y = 12 and the second is for x=7

The local grocery store mixed 13 oz of planters mixed nuts with 19.5 oz of emerald mixed nuts to get 32.5 oz bags of mixed nuts that contain 56% peanuts.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of planters mixed nuts and y represent the amount of emerald mixed nuts, hence:

x + y = 32.5   (1)

Also:

0.5x + 0.6y = 0.56(32.5)       (2)

From both equations:

x = 13, y = 19.5

The local grocery store mixed 13 oz of planters mixed nuts with 19.5 oz of emerald mixed nuts to get 32.5 oz bags of mixed nuts that contain 56% peanuts.

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Answer: 66 yards of fence

Step-by-step explanation:

This is a circular enclosure so the length of the fence must be the circumference of the circular enclosure.

The fence was built 10.5 yards from the centre which would mean that 10.5 yards is the radius of the circle.

The circumference will therefore be:

= 2 * Pie * radius

= 2 * 22/7 * 10.5

= 66 yards of fence

An estimate of DEF Company's cost of equity is 7.14%.

To estimate the cost of equity, we can use the dividend growth model. The formula for the cost of equity (Ke) is: Ke = (Dividend per share / Current share price) + Growth rate

Given data:

The cost of equity iss:

Ke = ($0.55 / $16) + 0.037

Ke ≈ 0.034375 + 0.037

Ke ≈ 0.071375.

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Both the cost of equity and the cost of preferred stock play important roles in determining a company's overall cost of capital and the required return on investment for different types of investors.

To estimate DEF Company's cost of equity, we need to calculate the dividend growth rate and use the dividend discount model (DDM). The cost of preferred stock can be found by dividing the fixed dividend by the current price of the preferred stock.

The calculations will provide the cost of equity and cost of preferred stock as percentages.

To estimate DEF Company's cost of equity, we use the dividend growth model. First, we calculate the expected dividend for the next year, which is given as $0.55 per share.

Then, we calculate the dividend growth rate by taking the expected growth rate of 3.7% and converting it to a decimal (0.037). Using these values, we can apply the dividend discount model:

Cost of Equity = (Dividend / Current Share Price) + Growth Rate

Plugging in the values, we get:

Cost of Equity = ($0.55 / $16) + 0.037

Calculating this expression will give us the estimated cost of equity for DEF Company as a percentage.

To calculate the cost of preferred stock, we divide the fixed dividend per share ($1.8) by the current price per share ($27.6). Then, we multiply the result by 100 to convert it to a percentage.

Cost of Preferred Stock = (Fixed Dividend / Current Price) * 100

By performing this calculation, we can determine DEF Company's cost of preferred stock as a percentage.

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If the sample correlation coefficient of x and y is r = 0, x and y are independent. Thus, option C is the answer.

The coefficient of correlation measures the statistical relationship between two variables. It is denoted by "r". The value lies between - 1 and + 1.

When r is 1 it means there is a perfect positive correlation. When r is -1 it means there is a perfect negative correlation. When r is 0 it means there is no correlation.

Thus, the two variables are independent. There is no linear relationship between the two variables. Change in one variable has no impact on another variable.

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Probability of selecting a female student from the given number of students is equal to 0.5217.

As given in the question,

Number of female students in algebra class = 48

Number of male students in algebra class = 44

Total Number of students in algebra class = 48 + 44

                                                                  = 92

Total number of outcomes = ⁹²C₁

Number of favourable outcomes = ⁴⁸C₁

Probability of selecting a female student

= (Number of favourable outcomes) / (Total number of outcomes )

= ⁴⁸C₁ /  ⁹²C₁

= 48 / 92

= 12/23

= 0.5217

Therefore, the probability of selecting a female students from the given number of male and female students is equal to 0.5217.

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The calculated expectation of X is 0.1

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

P{X = -1}=0.2, P{X = 0} = 0.5, P{X = 1}=0.3

The expectation of X is calculated as

E(x) = ∑xp(x)

So, we have

E(x) = -1 * 0.2 + 0 * 0.5 + 1 * 0.3

Evaluate

E(x) = 0.1

Hence, the expectation of X is 0.1

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Answer:

(-2, 2).

Step-by-step explanation:

y = x + 4

y = - 2x - 2

Substitute y = x + 4 in the second equation:

x + 4 = -2x - 2

x + 2x = -2 - 4

3x = -6

x = -2.

Now substitute x = -2 in the first equation:

y = -2 + 4 = 2.

Check the results by substituting for x and y in equation 2:

2 = -2*-2 - 2 = 4 - 2 = 2.  - this checks out.

Answer:

(-2, 2).

Step-by-step explanation:

d

Answer: 3.03 Miles, 20,000 yards, and 16,000 feet

Step-by-step explanation:

Not sure if my last answer was correct because I am not sure what you are trying to ask.

Answer:

124858

Step-by-step explanation:

The first 4 digits are simple, you multiply the first digit of the equation by the 2nd digit and then for the other 2 you multiply the first digit of the equation by the 3rd digit.

6 + 2 + 8

6 * 2 = 12

6 * 8 = 48

Then the last 2 digits are the sum of the products of the 1 and 2 and 1 and 3 and subtract it by the 2

12 + 48 = 60

60 - 2 = 58

Put them together