To make rice in a factory, Lois mixes rice and water in the ratio 2 : 3. If she uses 10 cups of rice, how many
cups of water does she need?

Answer:

7+(5 3/10+ 2 2/10) = 12 5/10

The mathematical expression will be;

⇒ 7 + (5 3/10 + 2 2/10)

⇒ 145/10

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''Seven plus the sum of five and three tenths and two and two tenths​.''

Now,

Since, The algebraic expression is,

''Seven plus the sum of five and three tenths and two and two tenths​.''

Hence, We can formulate;

The mathematical expression as;

⇒ 7 + (5 3/10 + 2 2/10)

⇒ 7 + (53/10 + 22/10)

⇒ 7 + (75/10)

⇒ (70 + 75) / 10

⇒ 145/10

Thus, The value of the expression is,

⇒ 145/10

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Answer:

A. 3x+2=14. 3×+2-2=14-2. 3×=12

B. 12(×+10)=24. (12)(×)+(12)(10)=24. 12+120=24. 12×+120-120=24-120

C. 12×= -96. 12×/12. -95/12 x= -8

The speed of the boat was 36 miles per hour when going downstream and 30 miles per hour.The speed of the current was 6 miles per hour.

The speed of the boat can be calculated using the equation Speed = Distance/Time. The boat traveled 180 miles downstream in 5 hours, so the speed of the boat downstream was 180/5 = 36 miles per hour. The speed of the boat upstream was 180/6 = 30 miles per hour.The speed of the current can be calculated by subtracting the speed of the boat upstream from the speed of the boat downstream. The speed of the current is 36 - 30 = 6 miles per hour. The speed of the current is the same in both directions, so the boat was traveling 6 miles per hour faster when going downstream than when going upstream .In conclusion, the speed of the boat was 36 miles per hour when going downstream and 30 miles per hour when going upstream. The speed of the current was 6 miles per hour.

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Answer:

-11

Step-by-step explanation:

f(x) = 5x + 11

g(x) = x^2 + 4x - 11

g(f(-3)) = ?

f(-3) = 5(-3) + 11

= -15 + 11 = -4

g(f(-3)) = g(-4) = -(4)^2 + 4(-4) - 11

= 16 - 16 - 11 = -11

A function assigns the value of each element of one set to the other specific element of another set. The value of g(f(-3)) is -11.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x)=5x+11 and g(x)=x²+4x-11, therefore, we can write the value of g(f(x)) as,

g(f(x)) = (5x + 11)² + 4(5x + 11) - 11

         = 25x² + 121 + 110x + 20x + 44 - 11

         = 25x² + 130x + 154

Now, substitute the value of x as -3 in the function g(f(x)), therefore, we can write,

g(f(-3)) = 25x² + 130x + 154

          = 25(3)² + 130(-3) + 154

          = 225 - 390 + 154

          = -11

Hence, the value of g(f(-3)) is -11.

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Answer: 4x10²

Step-by-step explanation:

Answer: 5 hours per mile

We can find the perimeter of a rectangle by means of the formula:

Where a and b are the length of the sides of the rectangle

To find the area of the rectangle, we can use the formula:

Then for each rectangle, we have:

First rectangle, sides: 5ft and 12.5 ft

-Perimeter:

Then, the perimeter of the first rectangle equals 35 feet

-Area:

Then, the area of the rectangle equals 62.5 ft^2

Second rectangle, sides: 15m and 8.2m

-Perimeter:

Then, the perimeter of the rectangle equals 46.4 m

-Area:

Then, the area of this rectangle equals 123 m^2

The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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The solution for R2 is:

R2 = (R1*R)/(R1+R)

We can begin by multiplying both sides of the equation by the product of R2 and R1 to eliminate the denominators:

1/R = 1/R1 + 1/R2

Multiplying both sides by R1*R2:

R1R2(1/R) = R1R2(1/R1) + R1R2(1/R2)

Simplifying:

R2 = (R1*R)/((R1+R))

Therefore, the solution for R2 is:

R2 = (R1*R)/(R1+R)

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The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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Answer: x+ 2x -3 = 12

Step-by-step explanation:

x represents Michael's laps. 2x -3 represents Braden's laps. Added together for a total of 12

One step further would be to combine the x terms, so the equation becomes 3x - 3 = 12

Answer:

IM SLOWWWWWWWWWWWWWWWWWWWWWw

Step-by-step explanation:

Answer:

The correct answer is 12.8 J.

Step-by-step explanation:

To solve this problem, we must remember how to calculate the kinetic energy of an object.

The kinetic energy is represented by the formula K = 1/2 * m * v^2, where m represents the mass of the object and v represents the speed or velocity of the object.  If we plug in the given values into the formula, we get:

K = 1/2 * m * v^2

K = (1/2) * (0.40) * (8.0)^2

Our first step is to square the velocity.  After doing this step, we get the following:

K = (1/2) * (0.40) * (64)

Finally, we can perform the multiplication, to get:

K = 12.8

The unit for kinetic energy is joules, so the correct answer is 12.8 J.

Hope this helps!

Kinetic energy is the energy due to motion of an object

The kinetic energy of the bird is 12.5 joules

Reason:

The known parameter are;

The mass of the bird, m = 0.50 kg

The speed of the bird, v = 8.0 m/s

Required:

To find the kinetic energy of the bird

Solution:

\(Kinetic \ energy = \dfrac{1}{2} \cdot m \cdot v^2\)

Therefore;

\(The \ kinetic \ energy \ of \ the \ bird = \dfrac{1}{2} \times 0.40 \ kg \times (8.0 \ m/s)^2 = 12.8 \ J\)

The kinetic energy of the bird is 12.8 J

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Answer:

P= 2L+2W+2H

P=2(3)+2(3)+2(3)

=18ft

Answer:

4:3 because 20 divided by 5 is 4 and 15 divided by 5 is 3.

The expectation value of \(\(r^{\wedge} 2\)\) is equal to \(\(r_{32}^2\)\).

To find the expectation value of \(\(r^{\wedge} 2\)\) for an electron in the hydrogen state described by the wave function \(\(\psi=\frac{1}{\sqrt{3}}\left(\psi_{322}+\Psi_{32-2}+\Psi_{321}\right)\)\), we need to calculate the integral\(\(\langle r^{\wedge} 2 \rangle = \langle \psi | r^{\wedge} 2 | \psi \rangle\)\), where\(\(r^{\wedge} 2\)\) is the operator corresponds to the square of the radial distance.

The expectation value can be expressed as \(\(\langle r^{\wedge} 2 \rangle = \int \psi^* r^{\wedge} 2 \psi \, dV\)\), where \(\(\psi^*\)\) is the complex conjugate of \(\(\psi\)\) and\(\(dV\)\) represents the volume element.

Since \(\(\psi\\)) is a linear combination of hydrogen wave functions\(\(\psi_{n l m}\)\), we can express\(\(\langle r^{\wedge} 2 \rangle\)\) as a sum of individual expectation values for each hydrogen wave function component. Let's calculate the expectation value for each component and then sum them up.

For a given hydrogen wave function \(\(\psi_{n l m}\)\), the expectation value of\(\(r^{\wedge} 2\)\) is given by\(\(\langle r^{\wedge} 2 \rangle_{n l m} = \langle \psi_{n l m} | r^{\wedge} 2 | \psi_{n l m} \rangle\).\)

Using the reduced matrix element\(\(r_{n l} = \langle n l | r | \psi \rangle\)\)(where \(| \psi \rangle\) represents the electron state), we can express \(\(\langle r^{\wedge} 2 \rangle_{n l m}\)\) as \(\(\langle r^{\wedge} 2 \rangle_{n l m} = r_{n l}^2\) since \(r^{\wedge} 2\)\) acts only on the radial part of the wave function.

Now, we can substitute the wave function \(\(\psi=\frac{1}{\sqrt{3}}\left(\psi_{322}+\Psi_{32-2}+\Psi_{321}\right)\)\) into the expectation value expression and calculate the sum of the individual expectation values:

\(\(\langle r^{\wedge} 2 \rangle = \frac{1}{3} \left( \langle r^{\wedge} 2 \rangle_{322} + \langle r^{\wedge} 2 \rangle_{32-2} + \langle r^{\wedge} 2 \rangle_{321} \right)\)\)

Substituting \(\(\langle r^{\wedge} 2 \rangle_{n l m} = r_{n l}^2\)\) for each component, we have:

\(\(\langle r^{\wedge} 2 \rangle = \frac{1}{3} \left( r_{32}^2 + r_{32}^2 + r_{32}^2 \right)\)\)

Since the reduced matrix element \(\(r_{n l}\)\) is the same for all components, we can simplify the expression to:

\(\(\langle r^{\wedge} 2 \rangle = r_{32}^2\)\)

Therefore, the expectation value of \(\(r^{\wedge} 2\)\) for the given electron state is equal to \(\(r_{32}^2\)\).

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Answer:

1,9

Step-by-step explanation:

The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from CHANCE .

The word "chance" describes unpredictability or the unexpected in relation to things like events that happen without a clear reason why and without human intention.

The conclusion is that chance is the tendency of people to recognize different kinds of significant patterns in a random order or sequence in addition to evaluating any kind of outcome. Because chance can also result in an underestimating of a system's conclusion or result, it is crucial to consider it when conducting an investigation.

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Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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We can use the trigonometric tangent identity, this is:

Where z = 60°

opposite side = x

adjacente side = 50ft

Then:

And the tower height is:

Answer: 93.6 ft

Answer:

Step-by-step explanation: 3,-1?

Answer:

You need at least 101 cans of food in order to meet or surpass the goal.

Step-by-step explanation:

a.

135+89=224

224+c>=325

b.

224-224+x>=325-224

x>=101

You need at least 101 cans of food in order to meet or surpass the goal.

Answer:

what do you need help with

Step-by-step explanation:

Answer:

Look in the file, I've drew it there!

The dimensions of the rectangular corral:

length = 75 ft and width = 5 ft

Let m be the length of the rectangular corral and n be the width of the rectangular corral.

The perimeter of the rectangular corral,

P = 2m + 2n

The rectangular corral split into 2 pens of the same size.

So, P = 2m + 3n

The 2 pens producing the greatest possible enclosed area given 300 feet of fencing.

300 = 2m + 3n

n = (300 - 2m)/3

Area of the rectangular corral,

A = m * n

A(n) = m * (300 - 2m)/3

A(m) = (300/3)*m - (2/3)*m

Taking derivatives on both sides of the equation:

A'(m) = 100 - (4/3)*m

for A'(m) = 0,

100 - (4/3)*m = 0

m = 100 * (3/4)

m = 75

So, n = (300 - 2(75))/3

n = 50

Therefore, the length of the rectangular corral = 75 ft and width = 5 ft

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The values of x and y using the concept of similar figures are:

y = 166 and x = 3.33 units

Two triangles are said to be similar if their corresponding side proportions are the same and their corresponding pairs of angles are the same. When two or more figures have the same shape but different sizes, such objects are called similar figures.  

We are told that Polygon ABCD is similar to Polygon EFGH and as such applying the similar figure definition above, we can say that:

∠B = ∠F

Thus:

∠B = 360 - (61 + 116 + 90)

∠B = 360 - 267

∠B = 93°

Thus:

y - 73 = 93

y = 166

Using the concept of similar figures, then:

6/4 = 5/x

x = 20/6

x = 3.33 units

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