Order set of numbers from least to greatest
3/4, 0.72%, 69%, .63

Answer:

x₁  =  400    x₂  =   1000

z(max)  =  380 $

Step-by-step explanation:

Production:

                                      Flour      yeast     Almond paste      Profit $

Bear claws B  (x₁)            6 ou       1 ou            2 TS                   0.2

Almond-filled ( x₂)          3 ou       1  ou           4 TS                   0.3

Availability                    6600      1400           4800

The Model:

z  =   0.2*x₁   +  0.3*x₂       to maximize

Subject to

1.-Quantity of flour   6600 ou

6*x₁  +  3*x₂   ≤  6600

2.-Quantity of yeast  1400 ou

1*x₁   +   1*x₂   ≤  1400

3.-Quantity of Almond paste   4800 TS

2*x₁   +  4*x₂   ≤  4800

General constraints:

x₁ ≤  0    x₂  ≤ 0   both integers

After 6 iterations using an on-line solver. Optimal solution is:

x₁  =  400    x₂  =   1000

z(max)  =  380 $

The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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Answer:

x= -4

Step-by-step explanation:

3 + 2x + 5 = 0

8 + 2x = 0

2x = -8

2x/2 = -8/2

x= -4

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be \(h(t) = -16\cdot t^{2} + 128\cdot t + 320\), the first and second derivatives are, respectively:

First Derivative

\(h'(t) = -32\cdot t +128\)

Second Derivative

\(h''(t) = -32\)

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

\(-32\cdot t +128 = 0\)

\(t = \frac{128}{32}\,s\)

\(t = 4\,s\) (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

\(h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320\)

\(h(4\,s) = 576\,ft\)

The highest altitude that the object reaches is 576 feet.

The ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

If two solids that are similar to each other, have volumes A and B respectively, and have a scale factor of a:b, thus, the ratio of their volumes would be expressed as:

Volume of solid A/Volume of solid B = a³/b³

or

Volume of solid A : Volume of solid B = a³ : b³

Thus, the given similar solids have a scale factor of 5:3, therefore, the ratio of their volumes would be expressed as shown below:

5³ : 3³

125 : 27

Thus, the ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

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Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.

A cross section is the intersection of a figure in three-dimensional space with a plane. It is the face you obtain by making a "slice" through a solid object. A cross section is two-dimensional. The figure (face) obtained from a cross section depends upon the orientation (angle) of the plane doing the cutting.

Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.

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Answewhen x=-2 h(x)=32 when x=-8 h(x)=224

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

5% of 2000 is 100

Answer: 100

Step-by-step explanation:

Sub in 5 for b in the expression

\(4b^2\\4(5)^2\)

You must do the exponent first as it comes before multiplication in the order of operations

\(4(5)^2\\4(25)\)

Now multiply

\(4(25)\\100\)

Answer:

B) a local beach.

At a local beach, you might find quiet a few different perspective from people who like or don't like swimming, whether going to a swimsuit store, you most likely will find people buying the swimsuit because they enjoy it, and plan on swimming in it.

Step-by-step explanation:

Hope it helps! =D

The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / Total Number of voters) x 100.

Proportion of favor stem cell research = (Number of voters who favor stem cell research / Total Number of voters) x 100

In order to estimate the proportion of voters who favor stem cell research, a survey has to be taken. Suppose the survey results indicate that out of a total of 500 voters, 300 of them favor stem cell research. Then, the proportion of favor stem cell research would be calculated as follows: Proportion of favor stem cell research = (300/500) x 100 = 60%. This means that 60% of the total voters favor stem cell research.

The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / +++Total Number of voters) x 100.

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The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.

Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.

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Answer:

1080 seconds

Step-by-step explanation:

We need to multiply the 0.3 hours by 3600 to convert it to seconds.

0.3*3600=1080

Answer:

1200 sec

Step-by-step explanation:

.30 hours is equal to 20 minutes

60 sec in 1 min

60x20

6x2=12

1200

Answer:

C 304.8

Step-by-step explanation:

Answer:

C 304.8 mm

Step-by-step explanation:

12*25.4 = 304.8

By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.

Physically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:

x · 24 + (1 - x) · 40 = 28

40 - 16 · x = 28

16 · x = 40 - 28

16 · x = 12

x = 3/4

By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.

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Answer:

Aimee's garbage disposal has 11/40 more power than Vincent's garbage disposal.

Step-by-step explanation:

Aimee's garbage disposal horse power = 7/8

Vincent's garbage disposal horse power = 3/5

All we need is to subtract Vincent's power from Aimee's power.

i.e.

\(\frac{7}{8}-\frac{3}{5}\)

Thus,

\(\frac{7}{8}-\frac{3}{5}\:=\frac{35}{40}-\frac{24}{40}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}\)

         \(=\frac{35-24}{40}\)

         \(=\frac{11}{40}\)

Thus,  Aimee's garbage disposal has 11/40 more power than Vincent's garbage disposal.

Answer: 12

Step-by-step explanation:

Answer:

Slope = ⅓ Y-intercept = -2

Step-by-step explanation:

by transforming the equation to y= ⅓x -2

then it becomes Y= ⅓x +(-2)

then you should get m= ⅓ and b = -2

Step-by-step explanation:

(a)

y = mx + b

y = (1/3)x + (-2)

y = 1/3x - 2

(b)

x - 3y = 6

x - 3(0) = 6

x - 0 = 6

x = 6

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

x=18-2/5y

y=-5/2x+45

Step-by-step explanation:

5x+2y=90

Nosotros queremos resolver para x o y

5x=90-2y

x=18-2/5y

o

2y=90-5x

y=-5/2x+45

Answer:

x=18-2y/5

Step-by-step explanation:

Answer:

please mark my answer brainliest

Step-by-step explanation:

these types of input variables are called integer...

Answer:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

Step-by-step explanation:

Given vector equation:

\(\textbf{r} = \textbf{i} - 5\textbf{j} + 4\textbf{k} + \lambda(3\textbf{i} + \textbf{j} - 2\textbf{k}) + \mu(-\textbf{i} + 2\textbf{j} + \textbf{k})\)

The vector 3i + j - 2k is perpendicular to n.

The vector -i + 2j + k is perpendicular to n.

\(\textsf{So}\;\;\textbf{n}=\left|\begin{array}{ccc}\textbf{i}&\textbf{j}&\textbf{k}\\3&1&-2\\-1&2&1\end{array}\right|\)

        \(=\textbf{i}\left|\begin{array}{rr}1&-2\\2&1\end{array}\right|-\textbf{j}\left|\begin{array}{rr}3&-2\\-1&1\end{array}\right|+\textbf{k}\left|\begin{array}{rr}3&1\\-1&2\end{array}\right|\)

        \(=\textbf{i}(1 \cdot 1 - (-2) \cdot 2)-\textbf{j}(3 \cdot 1-(-2) \cdot (-1))+\textbf{k}(3 \cdot 2-1 \cdot (-1))\)

        \(=\textbf{i}(1 +4)-\textbf{j}(3-2)+\textbf{k}(6+1)\)

        \(=5\textbf{i}-\textbf{j}+7\textbf{k}\)

So the equation of the plane written in Cartesian form is:

\(5x-y+7z+d=0\)

Substituting (1, -5, 4) gives:

\(5(1)-(-5)+7(4)+d=0\)

\(5+5+28+d=0\)

\(38+d=0\)

\(d=-38\)

Therefore, the given vector equation in Cartesian form is:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

Answer:

-3/2   y+12

or 12- 3y/2

Step-by-step explanation:

the lines are the line for a fraction not dividing

Answer:

the x- intercept shows they can take 12 cars and 0 vans.

the y intercept shows they can take 0 cars and 8 vans.

Step-by-step explanation:

Answer: The solution is the point (-14, -54)

Step-by-step explanation:

When we have a system of linear equations like:

y = a*x + b

y = c*x + d

The solution of this system is the point (x, y) that is a solution for both equations, if we graph the lines, this point would be the point where the lines intersect.

To start with this, we need to find the equations of the lines, we will use the following:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now, for the first table, we can use the points: (-3, -10) and (0, 2)

The slope of this line is:

a = (2 - (-10))/(0 - (-3)) = 12/3 = 4

then we have:

y = 4*x + b

To find the value of b, we can just replace one of the points in the equation, for example, we can use the point (0, 2), this means that we need to replace x by 0, and y by 2.

2 = 4*0 + b

2 = b

Then the equation for the first table is y = 4*x + 2

For the second table, we can use the points (0, -12) and (3, - 3)

Then the slope is:

a = (-3 - (-12))/(3 - 0) = 9/3 = 3

Then we have:

y = 3*x + c

And to find the value of c, we can do the same as before, now we use the point (0, -12) then:

-12 = 3*0 + c

-12 = c

Then the equation for this line is:

y = 3*x - 12

The system of linear equations is then:

y = 4*x + 2

y = 3*x - 12

To find the solution of the system, we must have that y = y, then we can write:

4*x + 2 = y = 3*x - 12

4*x + 2 = 3*x - 12

Now we can solve this for x.

4*x - 3*x = -12 - 2

x = -14

x = -14

Now we can replace this in one of the equations to find the value of y.

y = 3*(-14) - 12 = -54

Then the solution is the point (-14, -54)