A diet is to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200 calories.
Two foods, Food A and Food B are to be purchased. Each unit of Food A provides 50 units of
vitamins, 30 units of minerals, and 10 calories. Each unit of Food B provides 20 units of vitamins,
20 units of minerals, and 40 calories. Food A costs $2 per unit and Food B cost $1 per unit.
How many units of each food should be purchased to keep costs at a minimum?

[tex]x^{2} y^{4}[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can solve this 2 ways:

1) just count the number of units from one point to the other

2) calculate it using the coordinates of the points and the distance between 2 points formula:  d = √(x2-x1)²+(y2-y1)²

A(-7, 6)     B(7, 6)     C(7, -5)     D(-7, -5)

AB = √(7--7)²+(6-6)² = √14² = 14

BC = √(7-7)²+(-5-6)² = √-11² = 11

CD = √(-7-7)²+(-5--5)² = √-14² = 14

AD = √(-7--7)²+(-5-6)² = √-11² = 11

Let's call the rectangle's length x and its width, x - 6.

Since a rectangle has 4 sides and the perimeter of the rectangle

is just the distance around the outside of the figure,

we can create an equation.

This equation will be x + x + x - 6 + x - 6 = 72.

Simplifying on the left gives us 4x - 12 = 72.

Add 12 to both sides to get 4x = 84.

Now divide both sides by 4 to get x = 21.

Since x represents our length, we know that the length is 21 inches.

Answer:

N=8

Step-by-step explanation:

61 + 4n = 3.1n + 68.2

        .9n = 7.2

          n = 8

The distance between the diamond and the circle is approximately 5.83 units.

What is the distance between two points?

[tex]d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

Where [tex](x_1,y_1) and (x_2,y_2)[/tex] are two co-ordinates.

Here we want to find the distance between the diamond and the circle.

We need to use the distance formula.

Here position of diamond is (2,3) and circle is (5,8)

Substituting the values into the formula, we get:

[tex]d = √((5 - 2)^2 + (8 - 3)^2) \\ = √(3^2 + 5^2) \\ = √34 \\ ≈ 5.83 units[/tex]

Therefore, the distance between the diamond and the circle is approximately 5.83 units.

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Correct question is "Position of a diamond in the point (2,3) and a circle in (5,8). How many units are between the diamond and the circle?"

The distance between the diamond and the circle is approximately 5.83 units.

Here we want to find the distance between the diamond and the circle.

Here position of diamond is (2,3) and circle is (5,8)

Substituting the values into the formula, we get:

d²= ([tex]x_{2} -x[/tex]₁)²+(y₂-y₁)²

Therefore, the distance between the diamond and the circle is approximately 5.83 units.

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The cοrrect equatiοn that shοws the relatiοnship between the values is |7| < |-7|

An inequality is a relatiοn that cοmpares twο numbers οr οther mathematical expressiοns in an unequal way.

The absοlute value οf a number represents its distance frοm zerο οn the number line. The absοlute value οf 7 and -7 are bοth 7, sο |7| = |-7|.

The inequality |7| < |-7| means that the absοlute value οf 7 is less than the absοlute value οf -7. This is true because the absοlute value οf -7 is alsο 7, but negative, sο it is farther frοm zerο οn the number line than the absοlute value οf 7.

The cοrrect equatiοn that shοws the relatiοnship between the values is:

|7| < |-7|

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The phrase that describes the probability that Claire reaches in without looking and pulls out a strawberry or a cherry chew is "an equal chance" or "50-50 chance".

Chance is represented by probability. The study of the occurrence of random events is the subject of this mathematical subfield. The value is expressed as a number from 0 to 1. Mathematicians have begun to use the concept of probability to predict the likelihood of certain events.

This is because there are 5 strawberry chews and 15 cherry chews in the bag, so

the probability of drawing a strawberry chew is 5/20 or 1/4, and

the probability of drawing a cherry chew is 15/20 or 3/4.

Despite the fact that neither of the outcomes has the same probability, there are only two possible outcomes

Therefore, the probability of Claire drawing either a strawberry or a cherry chew is an equal chance or 50-50.

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Volume of the ellipsoid using cylindrical coordinates is 12.56unit³.

A three-dimensional symmetrical ellipsoid is one in which all of the plane sections are ellipses and all of the plane sections normal to one of the three perpendicular axes are circles.

Given equation,

x² + y² + 9z² = 64.

We can write the equation as:

x² + y² + (3z) ² = 8².

Now the axes of the ellipsoid are as follows:

a = 1

b = 1

c = 3

Volume of ellipsoid = 4/3 × π × 1 × 1 × 3

= 4 × π

= 4 × 3.14

= 12.56 units³.

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Answer: 11

Step-by-step explanation: Based on the given conditions, formulate::

Calculate the sum or difference:

Simplify fraction(s): 11

The value of {-4,6} is -4.

The braces {} create a set.

The elements in a set are written inside the braces.

When a set contains only two elements, it is considered a set with two elements or a pair of elements.

In this case, the braces {-4,6} contain two elements: -4 and 6.

Thus, the value of this set is the union of these two elements, which in this case is the sum of the two elements: -4 + 6 = 2

Answer:

210 minutes

Step-by-step explanation:

We know that 1 hour = 60 minutes.

3 hours = 3 * 60 = 180 minutes

1/2 hour = 1/2 * 60 minutes = 30 minutes

3 1/2 hours = 180+30 = 210 minutes

Answer:

210 minutes

Step-by-step explanation:

To convert from hours to minutes, we can multiply by a conversion ratio:

[tex]\left(3 \dfrac{1}{2} \text{ hr}\right)\left(\dfrac{60 \text{ min}}{1 \text{ hr}}\right)[/tex]

↓ converting the mixed number to a fraction

[tex]\left(\dfrac{7}{2} \text{ hr}\right)\left(\dfrac{60 \text{ min}}{1 \text{ hr}}\right)[/tex]

↓ canceling the hours unit

[tex]\dfrac{7}{2} \cdot 60 \text{ min}[/tex]

↓ multiplying

[tex]\boxed{210\text{ min}}[/tex]

__

Note: When we multiply something by a conversion ratio, we are not changing the value of it, but rather changing its form. In other words, a conversion ratios has a value of 1, and anything multiplied by 1 is itself. To illustrate this:

[tex]\dfrac{60 \text{ min}}{1 \text{ hr}} = \dfrac{60 \text{ min}}{60\text{ min}} = \dfrac{1}{1} = 1[/tex]

because

[tex]1 \text{ hr} = 60 \text{ min}[/tex].

Answer:

Hope this helps

Step-by-step explanation:

△ABC - Find the ratios and simplify them if necessary

[tex]\frac{8}{10} =\frac{4}{5}\\\\\frac{8}{6}= \frac{4}{3} \\\\\frac{10}{6}= \frac{5}{3}[/tex]

△DEF - Find the ratios (they can't be simplified)

[tex]\frac{4}{5}\\\\\frac{4}{3} \\\\\frac{5}{3}[/tex]

Answer:

Step-by-step explanation:

2,800,000,000

Answer:9

Step-by-step explanation:

0

according to the question the volume of the right rectangular prism is 67.5 cubic inches.

Volume is characterized as the space involved inside the limits of an article in three-layered space. The capacity of the object is another name for it.

A right rectangular prism's volume can be calculated by multiplying its lengths, width, and height. The prism's measurements are 3, 3/4, 5, & 4 1/2 inches.

First, we need to convert 4 1/2 to an improper fraction:

4 1/2 = (4 x 2 + 1)/2 = 9/2

Now, we can multiply the dimensions together to find the volume:

Volume = length x width x height

Volume = 3 x 3/4 x 5 x 9/2

Volume = 67.5 cubic inches

Hence, the bottom rectangular prism has a 67.5 cubic inch volume.

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Answer:

Step-by-step explanation:

If it takes him one hour to get dressed and make his bed

then another to eat breakfast + brush his teeth

that's two hours total because

1hr+1hr=2hrs

Using chain rule, the derivative of the function is 1 / [4x^(3/4) (1 + x^(1/2))].

Let u(x) = √4. Then we can write the given function as d/dx[tan^-1(u(x))].

Recall that the chain rule for differentiation states that d/dx[f(g(x))] = f'(g(x)) * g'(x). Applying this to our function, we have:

d/dx[tan^-1(u(x))] = [d/dx(tan^-1(u))] * [d/dx(u(x))]

To find d/dx(tan^-1(u)), we use the formula for the derivative of the inverse tangent function: d/dx[tan^-1(u)] = u'(x) / [1 + u(x)^2].

To find u'(x), we differentiate u(x) = sqrt4 with respect to x using the chain rule as follows:

d/dx[√4] = (1/2)x^(-3/4) * (d/dx)(x) = (1/2)x^(-3/4)

Therefore, u'(x) = (1/2)x^(-3/4).

Substituting u(x) and u'(x) into the formula for the derivative of the inverse tangent function, we get:

d/dx[tan^-1(u(x))] = [1 / (2x^(3/4) * (1 + x))]

Finally, substituting this expression for d/dx(tan^-1(u)) and d/dx(u(x)) back into our original chain rule expression from step 2, we get:

d/dx[tan^-1(√4)] = [1 / (2x^(3/4) * (1 + x))] * (1/4)x^(-3/4)

Simplifying the expression in step 6 by multiplying the two terms in the denominator and bringing x to the common denominator, we get:

d/dx[tan^-1(√4)] = 1 / [4x^(3/4) (1 + x^(1/2))]

Therefore, the derivative of the function d/dx[tan^-1(√4)] is 1 / [4x^(3/4) (1 + x^(1/2))].

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Answer:92 centimetres

Step-by-step explanation:

Y follows a binomial distribution, where P(Y=1) is the likelihood that one interval includes.

the likelihood that between 950 and 970 of these intervals will contain the corresponding value

The likelihood that a parameter will fall between two values close to the mean is shown by a confidence interval1. Although there is a known likelihood of success2, there is no assurance that a particular confidence range does indeed capture the parameter. The population parameter is fixed, whereas the confidence interval is a random variable.

Let Y represent one of the 1000 intervals that contain the value. With parameters n=1000 and p=P(Y=1),

Y follows a binomial distribution, where P(Y=1) is the likelihood that one interval includes.

Using the normal approximation to the binomial distribution with continuity correction,

one can determine the likelihood that between 950 and 970 of these intervals will contain the corresponding value.

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In the question, we can draw the conclusion that, according to the formula, it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of [tex]415 miles[/tex]per day.

A formula is a set of mathematical signs and figures that demonstrate how to solve a problem.

Formulas for calculating the volume of [tex]3D[/tex] objects and formulas for measuring the perimeter and area of [tex]2D[/tex] shapes are two examples.

A formula is a fact or a rule in mathematical symbols. In most cases, an equal sign connects two or more values. If you know the value of one, you can use a formula to calculate the value of another quantity.

We need to know the average pace at which they went to figure how long it would take to get from City A to City B at the same rate.

total distance / time taken = average speed

[tex]415 miles[/tex] per day [tex]2075/ 5[/tex], it would take them [tex]10[/tex] days to get from City A to City B because

Time taken = [tex]2075/415[/tex] per days [tex]= 5 days[/tex]

Therefore it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of [tex]415 miles[/tex]per day.

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The answer of the given question based on distance is at the moment 4 seconds later, the distance between them is 12.776 m and  the distance between them changing at that moment is 3.056 m/s.

Speed is measure of how fast object is moving. It is defined as distance traveled by an object divided by time it takes to travel that distance. The standard unit of speed is meters per second (m/s) in International System of Units (SI). Speed can also be measured in other units such as kilometers per hour (km/h), miles per hour (mph), or feet per second (ft/s), depending on the context of the problem.

Since Brooke and Jamail are walking towards each other on parallel paths, the distance between them is decreasing at a rate of (6 + 5) km/h = 11 km/h.

To solve for how far apart they are after 4 seconds, we first need to convert their speeds to m/s and their distance to meters:

Brooke's speed = 6 km/h = (6/3.6) m/s = 1.667 m/s

Jamail's speed = 5 km/h = (5/3.6) m/s = 1.389 m/s

Distance between the paths = 25 m

The initial distance between Brooke and Jamail is 25 m, and it is decreasing at a rate of 11 km/h = (11/3.6) m/s = 3.056 m/s.

After 4 seconds, the distance between them will be:

d = 25 m - (3.056 m/s x 4 s) = 12.776 m

To find the rate at which the distance between them is changing, we can take the derivative of the distance equation with respect to time:

d' = -11 km/h = -(11/3.6) m/s = -3.056 m/s

Therefore, at the moment 4 seconds later, the distance between them is 12.776 m and is decreasing at a rate of 3.056 m/s.

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a finite group with an even number of elements contains an even number of elements such that. x inverse = x.

a similar statement for a finite group with an odd number of elements

For a finite group with an even number of elements, we can prove that it contains an even number of elements such that their order is 2.

Let G be a finite group of even order.

We can define t(G) as the set { g ∈ G | g ≠ g − 1 }.

if g ∈ t(G), then g − 1 ∈ t(G), and by definition g − 1 ≠ g.

Now let A = { { g, g − 1 } | g ∈ t (G) }.

Thus we have | t (G) | = ∑ α ∈ A | α | = 2 k for some positive integer k;

in particular, t (G) contains an even number of elements 1.

Hence [tex]x^{-1}=x[/tex]

For a finite group with an odd number of elements, we can prove that it contains an odd number of elements such that their order is 2. For any element in G-{e}, there must be an inverse of that element in G-{e}. Take any element in G-{e}, say b, If bb=e, then the proof is done. If the inverse of b is not itself, then there must be one element in G-{e}, say c, such that bc=e. Because there are an odd number of elements, I keep doing this until I have left with one

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The solutions to the equation:

8. The value of the integral is 0.

9. The value of the integral is approximately -0.336.

10. The value of the integral is π(b - a)/4

11. The value of the integral is π/4 - (1/2)(1 - e^4).

12. The value of the integral is -8π.

13. The value of the integral is π/64 + π/(32√2).

8. To evaluate the integral ∫∫R(2x-y) dA over the region R in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x, we can use polar coordinates.

First, we convert the equations of the circle and line into polar coordinates:

x² + y² = 4 becomes r² = 4

y = x becomes θ = π/4

The region R can be described in polar coordinates as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/4. The differential element dA can be expressed in polar coordinates as dA = r dr dθ.

Now we can evaluate the integral:

∫∫R(2x-y) dA = ∫₀^(π/4) ∫₀² (2r²cosθ - rsinθ) r dr dθ

= ∫₀^(π/4) ∫₀² (2r³cosθ - r²sinθ) dr dθ

= ∫₀^(π/4) [r⁴cosθ/2 - r³sinθ/3]₀² dθ

= ∫₀^(π/4) 8cosθ/3 - 8sinθ/3 dθ

= [8/3(sinθ - cosθ)]₀^(π/4)

= 8/3(1/√2 - 1/√2 - (0 - 0))

= 0

Therefore, the value of the integral is 0.

9. To evaluate the integral ∫∫Rsin(x² + y²) dA over the region R in the first quadrant between the circles with center the origin and radii 1 and 3, we can again use polar coordinates.

In polar coordinates, the region R can be described as 1 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.

Now we can evaluate the integral:

∫∫Rsin(x² + y²) dA = ∫₀^(π/2) ∫₁³ r sin(r²) dr dθ

= ∫₀^(π/2) [-cos(r²)]₁³ dθ

= ∫₀^(π/2) cos(1) - cos(9) dθ

= sin(1) - sin(9)

≈ -0.336

Therefore, the value of the integral is approximately -0.336.

10. To evaluate the integral ∫∫R y²/x² + y²dA over the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b, we can use polar coordinates.

In polar coordinates, the region R can be described as a ≤ r ≤ b and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.

Now we can evaluate the integral:

∫∫R y²/x² + y²dA = ∫₀^(2π) ∫ₐᵇ (r⁴cos²θsin²θ)/(r⁴cos²θ) r dr dθ

= ∫₀^(2π) ∫ₐᵇ sin²θ cos²θ dr dθ

= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) d

= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) dθ

= [(b-a)/8] ∫₀^(2π) (1 - sin(2θ)) dθ

= [(b-a)/8] (2π - 0)

= π(b - a)/4

Therefore, the value of the integral is π(b - a)/4.

11. To evaluate the integral ∫∫D e^(-x²-y²) dA, where D is the region bounded by the semicircle x = √(4 - y²) and the y-axis, we can use polar coordinates.

In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.

Now we can evaluate the integral:

∫∫D e^(-x²-y²) dA = ∫₀^(π/2) ∫₀² e^(-r²) r dr dθ

= ∫₀^(π/2) [-1/2 e^(-r²)]₀² dθ

= ∫₀^(π/2) (1/2 - 1/2e^4) dθ

= π/4 - (1/2)(1 - e^4)

Therefore, the value of the integral is π/4 - (1/2)(1 - e^4).

12. To evaluate the integral ∫∫D cos(√(x²+y²)) dA, where D is the disk with center at the origin and radius 2, we can again use polar coordinates.

In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.

Now we can evaluate the integral:

∫∫D cos(√(x²+y²)) dA = ∫₀^(2π) ∫₀² r cos(r) dr dθ

= ∫₀^(2π) [2 sin(r) - 2r cos(r)]₀² dθ

= ∫₀^(2π) (-4) dθ

= -8π

Therefore, the value of the integral is -8π.

13. To evaluate the integral ∫∫R arctan(y/x) dA, where R = {(x,y) | 1 ≤ x² + y² ≤ 4, 0 ≤ y ≤ x}, we can use polar coordinates.

In polar coordinates, the region R can be described as π/4 ≤ θ ≤ π/2 and 1/√2 ≤ r ≤ 2. The differential element dA can be expressed as dA = r dr dθ.

Now we can evaluate the integral:

∫∫R arctan(y/x) dA = ∫π/4^(π/2) ∫1/√2² r arctan(tan(θ)) dr dθ

= ∫π/4^(π/2) [(r²θ/2 - r²tan(θ)/4)]1/√2² dθ

= ∫π/4^(π/2) [(2θ - π/2)/8] dθ

= [θ²/16 - (θ - π/4)/8]π/4^(π/2

= [π/16 - (π/4 - π/4√2)/8] - [(π/16 - (π/8 - π/8√2)/8)]

= π/64 + π/(32√2)

Therefore, the value of the integral is π/64 + π/(32√2).

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The question in text format:

8. ∫∫R(2x-y) dA, where R is the region in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x

9. ∫∫Rsin(x² + y²) dA, where R is the region in the first quadrant between the circles with center the origin and radii 1 and 3

Answer

10. ∫∫R y²/x² + y²dA, where R is the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b

11. ∫∫D e⁻ˣ²⁻ʸ²dA, where D is the region bounded by the semi-circle x = √4 - y² and the y-axis

12. ∫∫D cos √x² + y² da, where D is the disk with center the origin and radius 2

13. ∫∫R arctan (y/x) dA, where R= {(x,y) | 1 ≤ x² + y² ≤ 4,0 ≤ y ≤ x}

Answer: 18+p

Step-by-step explanation:

The way we find the perimeter is we add up all the sides

9+p+9 = 18+p

Erica can buy a maximum of 4 sweatshirts by rounding the cost to the nearest ten.

A number is approximated to a certain degree of accuracy by rounding it off. The purpose of doing this is usually to make the number easier to deal with or to portray it in a clearer, more accessible manner.

You must take the following actions in order to round off a number:

The digit in the number that you want to round off is known as the rounding digit. The rounding digit is the third digit following the decimal point, or 1, in the example above, if you wish to round off 3.1416 to two decimal places.

Look at the digit that is directly above it: You should round up if this digit is 5 or higher. You should round it down if it is less than 5.

Replace the digits to the right of the rounding digit with zeros: If you are rounding to a certain number of decimal places, you will need to add zeros to the right of the rounding digit to maintain the correct level of precision. For example, if you are rounding 3.1416 to two decimal places, you will need to replace the digits to the right of the rounding digit with zeros, giving you 3.14.Adjust the rounding digit if necessary: If you round up, you will need to

To estimate the maximum number of sweatshirts Erica can buy, we need to divide her total amount of money by the cost of each sweatshirt rounded to the nearest ten.

Rounding $28.99 to the nearest ten gives us $30.

Dividing $120 by $30 gives us:

$120 ÷ $30 = 4

Therefore, Erica can buy a maximum of 4 sweatshirts by rounding the cost to the nearest ten.

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It will take Mr. White at least 3 years to earn $165 in interest at an annual simple interest rate of 5% on his $550 deposit.

To solve the given problem, we can use the formula for simple interest:

I = P × r × t

P = $550 is the initial deposit

r = 0.05 is the annual interest rate

I = $165 is the amount of interest earned

We can rearrange the formula to solve for t:

t = I ÷ (P × r)

Substituting in the values we know,

t = $165 × ($550 × 0.05)

t = 3 years

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