Martin uses 5/8 of a gallon of paint to cover 4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon?
1 7/25of a wall per gallon
1 3/32 walls per gallon
32/25 walls per gallon
1/2 walls per gallon

The value of y in the triangle is 7.5

The given parameter is the triangle

On the triangle, we have the following equivalent ratio

y : 8 = y + 15 : 20

Express as fraction

y/8 = y + 15/20

Cross multiply

20y = 8y + 90

Collect the like terms

20y - 8y = 90

Evaluate

12y = 90

Divide by 12

y = 7.5

Hence, the value of y in the triangle is 7.5

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Answer: 15

Step-by-step explanation: 4+5=15

To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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Answer:

Step-by-step explanation:

(a)

Data Set 1

Data Set 2

Comparison

If we had a polynomial-time algorithm for computing the length of the shortest TSP tour, then we would also have a polynomial-time algorithm for finding the shortest TSP tour by using the following approach: Generate all possible tours, For each tour, compute its length, The shortest tour is the one with the minimum length.

The first step, generating all possible tours, can be done in polynomial time. This is because the number of possible tours is a polynomial function of the number of cities.

The second step, computing the length of each tour, can also be done in polynomial time. This is because the length of a tour is a polynomial function of the distances between the cities.

Therefore, the overall algorithm for finding the shortest TSP tour is polynomial-time.

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(a) There are 40 french mathematics books then non-french books not about mathematics are 210. (b) There are 60 french nonmathematics books then non-french books not about mathematics are 150.

(a) If there are 40 French mathematics books, then the number of French books not about mathematics is 70 - 40 = 30.

Thus, the number of non-French books about mathematics is 100 - 40 = 60.

We can then find the number of non-French books not about mathematics by subtracting the number of French non-mathematics books from the total number of non-mathematics books, which is 300 - 60 - 30 = 210.

(b) If there are 60 French non-mathematics books, then the number of French books about mathematics is 70 - 60 = 10. Thus, the number of non-French books about mathematics is 100 - 10 = 90.

We can then find the number of non-French books not about mathematics by subtracting the number of French non-mathematics books from the total number of non-mathematics books, which is 300 - 60 - 90 = 150.

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Use the drop-down menus to complete the solution to the equation cosine (start fraction pi over 2 end fraction minus x) = start fraction start root 3 end root over 2 end fraction for all possible values of x on the interval [0, 2pi].

Using trigonometric identities, the solution to the equation \(cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2}\) for all possible values of x on the interval [0, 2π].

What are trigonometric identities?

Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.

\(cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2} \\\\cos(x)cos\frac{\pi }{2}+sin(x)sin \frac{\pi }{2} = \frac{\sqrt{3} }{2}\\\\cos(x)(0)+sin(x)(1) = \frac{\sqrt{3} }{2}\\\\sin(x) = \frac{\sqrt{3} }{2}\\\\x = \frac{\pi }{3}, \frac{2\pi }{3}\)

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By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).

The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the greatest power) must be divisible by the fraction's denominator and the constant term (the one without a variable) must be divisible by the fraction's denominator.

It is given that,

x³-5x²-17x+21 = 0x

Factor the left side of the equation,

(x−1)(x−7)(x+3)=0

If any of the factors on the left side of the equation equals 0, the entire expression equals 0.

x−1=0

x−7=0

x+3=0

Set, x−1equal to 0 and solve for x.

x−1 equal to 0.

x−1=0

Add 1 to both sides of the equation.

x=1

Set, x−7 equal to 0 and solve for  x

Set x−7equal to 0.

x−7=0

Add 7 to both sides of the equation.

x=7

Set x+3 equal to 0and solve for x.

Set x+3 equal to 0.

x+3=0

Subtract 3 from both sides of the equation.

x= −3

The final solution is all the values that make (x−1)(x−7)(+3)=0 true.

x=1,7,−3.

Hence, By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).

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The answer of the equation 8(x-3) +7=2x(4-17) is x=1/2.

An equation is a statement that says that the value of two mathematical expressions is equal i.e., it is a mathematical sentence that has two equal sides separated by an equal sign.

We have the equation : 8(x-3) +7=2x(4-17)

Here we are not given Lin's solution so we can not find the error in her solution but we will solve this equation and find the value of x.

            8(x-3) +7= 2x (4-17)    

      ⇒  8x - 24 +7 = 2x(-13)

      ⇒  8x -17= -26x

      ⇒  34x = 17

      ⇒  x= 17/34

      ⇒ x =1/2.

The solution of the above equation is x= 1/2.

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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The approximate probability that the average song length of a sample of 25 songs will last more than 5.25 minutes is 0.012. So, the correct option is b.

To find the approximate probability that the average song length of a sample of 25 songs will last more than 5.25 minutes, we will use the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases. In this case, we have:

1. Population mean (μ) = 4.75 minutes
2. Standard deviation (σ) = 1.10 minutes
3. Sample size (n) = 25 songs

Now, we will calculate the standard error (SE) using the formula:

SE = σ / √n
SE = 1.10 / √25
SE = 1.10 / 5
SE = 0.22

Next, we will find the z-score using the formula:

z = (x - μ) / SE
z = (5.25 - 4.75) / 0.22
z = 0.50 / 0.22
z ≈ 2.27

Now, we will use a z-table to find the probability that the z-score is greater than 2.27. Looking up the value in the table, we find the area to the left of the z-score is approximately 0.988. Since we want the probability to the right of the z-score, we subtract the area from 1:

P(Z > 2.27) = 1 - 0.988 = 0.012

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Answer:

0; one real roots

* the answer is C

In a binomial experiment, there are only two possible outcomes for each of the n trials. True statement.

These outcomes are typically labeled as "success" and "failure," and they are mutually exclusive (meaning that only one outcome can occur per trial) and collectively exhaustive (meaning that one of the two outcomes must occur per trial).

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Comparing the value of 1 lbs of the candy we observe that, store A sells the candy at a much cheaper price and hence it has the better buy.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Given the number of candies the store sells for a given amount:

Store A:

2 1/4 lbs candy = $13.50

1 lbs candy = x

\(x = \frac{13.50}{\frac{9}{4} } \\\\x = \frac{(13.50)(4)}{9}\\ \\x=6\)

Hence, store A sells 1 lbs of candy for $6.

Store B:

1 1/2 lbs candy = $15.75

1 lbs candy = y

\(y = \frac{15.75}{\frac{3}{2} } \\\\y = \frac{(15.75)(2)}{3}\\ \\y = 10.5\)

Store B sells 1 lbs of candy for $ 10,5.

Comparing the value of 1 lbs of the candy we observe that, store A sells the candy at a much cheaper price and hence it has the best buy.

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Answer: Try this:

Step-by-step explanation:

798 rounded to one sig. fig. = 800.

8 is already just one sig. fig.

41 rounded to one sig fig. Is 40.

800/8x40

800/320 = 2.5.......

Rounded to one sig fig. =3

Or if you left the entire equation as is and just rounded the answer to 1 sig. fig.

798/(8x41) = 2.4329.......

rounded to one sig fig =2

Without knowing what specifically the question wants estimated to one significant figure, there could be multiple answers.

The estimate of the equation to one significant figure is 2.

Significant figures are the digits in a number that is significant and required to denote a value and also add to the correctness of that value.

The way we will solve this equation is to first determine the final value and then approximate it to 1 significant figure.

\(\mathbf{= \dfrac{798}{8 \times 41}}\)

= 2.4329

≅ 2 (to one significant figure)

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The two Caroline's marbles are hence blue.

Adding a whole number to the numerator multiplies it. No change is made to the denominator. In the simplest possible way, simplify the product. The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.

The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.

Adding a whole number to the numerator multiplies it. No change is made to the denominator. In the simplest possible way, simplify the product. The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.

3 Caroline's marbles are blue.

In line with the assertion made:

16 marbles total, 1/8 of which are blue belong to Caroline.

16 marbles are included in the total.

Blue portions of them

calculate the proportion of blue marbles in Caroline's collection.

marbles that are blue in number =1/8 * 16 = 2.

The two Caroline's marbles are hence blue.

The complete question is,

Caroline has sixteen marbles. eight of them are blue. what proportion of Caroline's marbles are blue?

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Answer:

1) 25x + 15y = 750

2) 25. On a graph it would look like : (25,0)

3) 15.  On a graph it would look like : (15,0)

4) 25x - 750 = 15y or 15y - 750 = 25x

Step-by-step explanation:

Consider the function fx) 20x^2 e^-3x on the domain 0, [infinity]) On its domain, the curve y = f(x) attains its maximum value at x = 2/3 and attains its minimum value at value x=0. minimum value at x = and attains its minimum value at x = 0. So, the correct answer is D).

To find the maximum and minimum values of the function f(x) = 20x^2 e^(-3x) on the domain [0, ∞), we need to find the critical points and the endpoints.

Taking the derivative of f(x), we get

f'(x) = 40xe^(-3x) - 60x^2 e^(-3x)

= 40x e^(-3x) (1 - 1.5x)

Setting f'(x) = 0, we get critical points at x = 0 and x = 2/3. We can verify that f''(0) < 0 and f''(2/3) > 0, so x = 0 gives a maximum value and x = 2/3 gives a minimum value.

To check the endpoints, we calculate

lim x→0+ f(x) = 0

lim x→∞ f(x) = 0

So the maximum value of f(x) on the domain [0, ∞) is attained at x = 0 and the minimum value is attained at x = 2/3. Therefore, the correct option is D.

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The solutions to the differential equations depend on the equation itself. Depending on the equation, there could be a variety of solutions, including linear solutions, constant solutions, polynomial solutions, exponential solutions, and trigonometric solutions.
Linear solution: A linear solution is of the form\(y=mx+b\). This is the solution to a first-order linear differential equation.
Constant solution: A constant solution is when the differential equation has a solution of the form y=c, where c is a constant.
Polynomial solution: A polynomial solution is when the differential equation has a solution of the form

\(y=a_nx^n+a_(n-1)x^(n-1)+…+a_0,\)

where a_n, a_(n-1),…,a_0 are constants.
Exponential solution: An exponential solution is when the differential equation has a solution of the form\(y=Ae^(kx),\)where A and k are constants.
Trigonometric solution: A trigonometric solution is when the differential equation has a solution of the form \(y=a_ncos(nx)+b_nsin(nx),\) where a_n and b_n are constants.
Therefore, it is important to carefully analyze the equation in order to determine the type of solution needed.

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The x-intercept and the y intercept of the graph of 6x - 3y = 36 are x = 6 and y = -12

How to determine the x-intercept and the y intercept of the graph?

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

6x - 3y = 36

Set y to 0 to determine the x-intercept

So, we have the following representation

6x = 36

Divide by 6

x = 6

Set x to 0 to determine the y-intercept

-3y = 36

Divide by -3

y = -12

hence, the intercepts are x = 6 and y = -12

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The measure of the angle x in the isosceles triangles are;

x = 44°

1) x = 80°

An isosceles triangle is a triangle that has a pair of congruent sides and a pair of congruent angles.

The measure of the specified angle are found as follows;

The isosceles triangle that has 92° as the exterior angle, indicates that we get;

Base angles of the isosceles triangle = (180° - 92°)/2 = 44°

Vertical angles theorem, indicates that the vertical angle and the base angles of the second isosceles triangle are congruent.

Base angles of the second isosceles triangle = 44°

1) The angle adjacent to the angle x is a base angle of the isosceles triangle that has a base angle of 70°

The vertex angle of the isosceles triangle = 180° - 2 × 70° = 40°

The measure of the section of the indicated 90° angle that is a part of the isosceles triangle that has angle x as the vertex angle = 90° - 40° = 50°

The measure of angle x found using the relationship between the angles in an isosceles is; x = 180° - 2 × 50° = 80°

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Answer:

26 i believe 66 - 40 = 26 hope this helps

The McKinsey GE Matrix, also known as the General Electric Matrix, is a strategic management tool used to assess and prioritize a company's portfolio of business units.

The McKinsey GE Matrix evaluates business units based on two key dimensions: market attractiveness and competitive strength.

1. Market Attractiveness: This dimension assesses the attractiveness of the market in which the business unit operates. Factors considered may include market size, growth rate, profitability, industry trends, competitive dynamics, and regulatory environment. The market attractiveness score helps identify the potential for growth and profitability in a particular market.

2. Competitive Strength: This dimension evaluates the competitive strength of the business unit within its market. It takes into account factors such as market share, brand reputation, technological capabilities, distribution channels, product quality, cost structure, and customer loyalty. The competitive strength score helps assess the business unit's ability to outperform competitors and achieve sustainable competitive advantage.

The McKinsey GE Matrix consists of a 9-cell grid, with market attractiveness on the y-axis and competitive strength on the x-axis. Each business unit is plotted on the matrix based on its scores in these dimensions. The matrix is divided into three zones: Invest/Grow, Select/Earn, and Harvest/Divest.

- Invest/Grow: Business units located in this zone have high market attractiveness and strong competitive strength. They are considered promising opportunities for growth and investment. Companies should allocate resources to these units to capitalize on their potential and drive market expansion.

- Select/Earn: Units in this zone have moderate market attractiveness and competitive strength. Companies need to carefully evaluate and decide whether to selectively invest in these units to enhance their performance or maintain their current level of earnings.

- Harvest/Divest: Units in this zone have low market attractiveness and weak competitive strength. They may be in declining markets or face strong competition. Companies should consider divestment or strategic restructuring to minimize losses and reallocate resources to more promising areas.

The McKinsey GE Matrix provides a visual representation of a company's business unit portfolio and helps prioritize resource allocation based on market attractiveness and competitive strength. It assists in identifying growth opportunities, managing risks, and making strategic decisions to enhance overall business performance.

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Answer:

D

Step-by-step explanation:

I'll try to be brief

Let's plug in our 'y' variable (2x)

2x + (2x) = 20

4x = 20

x = 5

Now, plug in our 'x' variable to get our 'y' variable:

y = 2(5)

y = 10

So, our answer in (5, 10)

Or, D

The ratio of c:d:e is 1:3:2.

To find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.

A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.

You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.

It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.

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