A factory that makes granola bars uses 1⁄6 of a barrel of raisins in each batch. Yesterday, the factory used 5⁄6 of a barrel of raisins. How many batches did the factory make yesterday?

The breadth is 8 inches, the height is 13 inches, and the supplied statement indicates that x = 8.

If the circumference and one of the sides of the rectangle are known, the area may be computed. The missing side may be located using the perimeter, and or the area of a triangle can then be calculated using the same formula: Area of triangle = Length * Width.

They inform us that the rectangle in this instance, which has a surface area of 104 square inches, has a length that is 5 inches longer than its breadth. Also, we get the equation (x+5)x = 104, where "x" stands for the thickness of the rectangular.

The area of a rectangle is determined by the following formula:

A = l*x

Where:

l: It's the lenght

x: It is the width

A = 104 square inches

We factor the equations to discover the answers for the width. To do this, we seek for two integers that, when multiplied, yield the result -104 and, when added together, yield the result +5. Hence, these are really +13 & -8.

13 * (-8) = -104

13 - 8 = +5

So, we have:

(x+13) (x-8) = 0

The roots are:

x₁ = -13

x₂ = 8

The answer that provides context for the rectangle's width is: x_ 2 = 8.

Hence, the rectangle's width of x = 8 inches.

If the breadth is 5 inches wider than with the thickness, then

l = 5+8

l = 13 inches

Verifying the area, we have:

A = 13*8 = 104 square units

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The sketch to illustrate the question is given below

Since each of the bags are filled equally with 2 kilograms 450 grams of sand

Then we can sum two bags and compare the mass with 5 kilogram

We can see that the sum of two bags weighs 4 kilograms and 900 grams (4.90 kilograms) which is 100 grams less than 5 kilograms.

Thus we can conclude that the mass of 2 bags is LESS THAN 5 kilograms

The equation Y=4.25x-9 is a non-proportional equation.

A proportional equation is one that can be written in the form Y=kx, where k is a constant. This means that the equation shows a constant rate of change, and the graph of the equation will be a straight line that passes through the origin (0,0).

In the equation Y=4.25x-9, there is a constant term (-9) that is not multiplied by the variable x. This means that the equation does not show a constant rate of change, and the graph of the equation will not pass through the origin. Therefore, the equation is non-proportional.

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Answer:

2.471 if you need to round it should be 2.5

Step-by-step explanation:

Let L be a context-free language. Then there exists an n≥1 such that for any string w∈L with ∣w∣≥n, there exist strings x,y,z,u,v satisfying the conditions: i. ∣yzu∣≤n, ii. ∣y∣+∣u∣>0, and iii. xyizuiv∈L for all i≥0. Using this, we can show that the language L={ai3∣i≥2} is not context-free.

The Pumping Lemma is a useful tool to prove that certain languages are not context-free. It states that for any context-free language L, there exists a pumping length n such that any string in L with length at least n can be divided into five parts: x, y, z, u, and v. These parts satisfy the conditions mentioned above.

Now, let's apply the Pumping Lemma to the language L={ai3∣i≥2}. We assume that L is context-free. Therefore, there exists a pumping length n such that any string w∈L with ∣w∣≥n can be divided into x, y, z, u, and v satisfying the conditions.

Considering the properties of L, we know that every string in L has the form a^n3, where n is greater than or equal to 2. Now, if we choose a string w=a^n3 from L, we can divide it into x, y, z, u, and v as per the Pumping Lemma.

Next, we choose i=0, which allows us to pump down the number of 'a's in the string. However, this contradicts the condition that xyizuiv∈L for all i≥0, as pumping down the 'a's would result in a string that does not belong to L.

Hence, we have reached a contradiction, which proves that the language L={ai3∣i≥2} is not context-free.

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Based on the information in the image, we can infer that the surface area is 863.5cm³.

To find the surface of the figure we must divide the figure in two, into the cone and the cylinder and find the surface of each one separately and then add it.

Cylinder surface area:

To calculate the surface area of a cylinder we must apply the following formula:

\(A = 2\pi r h ++ 2 \pi r^{2} \\A = 2 * \pi * 5 * 15 + 2 * \pi * 5^{2} \\A = 471 + 157\\A = 628cm^{3}\)

Cone surface area:

\(A = \pi rh + \pi r^{2} \\A = \pi * 5 * 10 + \pi * 5^{2} \\A = 157 + 78.5 \\A = 235.5 cm^{3}\)

Surface area of the entire figure:

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Answer:

.5

Step-by-step explanation:

3/6 = 1/2 = 0.5

hope this helps :)

Answer:

c

Step-by-step explanation:

3/6, 3 is half of 6. so 0.5

The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Solution:

Given a triangle;

Where

To find the measure of angle S, i.e.

Where

Then,

Recall that;

Hence, the measure of angle S is 55°

Answer:

Step-by-step explanation:

ISSA PARADE INSIDE MY CITY YEAHHHHH

Answer:25

Step-by-step explanation:

Rolle's theorem:

If a function \(f\) is continuous on the closed interval \( [a, b] \) and differentiable on the open interval \((a,b)\) such that \(f(a) = f(b)\), then [tex)f′(x) = 0\) for some \(x\) with \( a \leq x \leq b\).

Tangent:

A tangent is parallel to the x-axis if the slope of the tangent is 0. So, using Rolle's theorem, if we consider \(x=-\pi/2\) and \(x=\pi/2\), then \(f(-\pi/2)=f(\pi/2)=-1\).

Since \(f(x)\) is continuous on \([-\pi/2, \pi/2]\) and differentiable on \((-\pi/2, \pi/2)\), \(f'(x)=0\) for some \(-\pi/2 \leq x \leq \pi/2\), and thus there is a point in this interval which is parallel to the x-axis.

The volume of one piece of pizza is π cubic inches.

To find the volume of one piece of pizza, we need to first find the total

volume of the pizza and then divide by the number of pieces.

Find the volume of the entire pizza.

The pizza is a cylinder with a height (thickness) of 1/3 inches and a

diameter of 12 inches.

We can find the radius by dividing the diameter by 2, so the radius is 6

inches. The formula for the volume of a cylinder is

V = πr²h,

where V is the volume, r is the radius, and h is the height.

V = π(6²)(1/3) V = π(36)(1/3) V = 12π cubic inches

Divide the total volume by the number of pieces.

There are 12 congruent pieces, so we need to divide the total volume by 12.

Volume of one piece = (12π cubic inches) / 12 The 12's cancel out, leaving

us with: Volume of one piece = π cubic inches

So, the volume of one piece of pizza is π cubic inches.

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The cost of producing 25 chairs monthly is $1272.875.

Based on the given information, the cost function for producing x chairs is:

C(x) = 0.005x^3 + 0.07x^2 + 18x + 700

We are told that currently 25 chairs are produced monthly, so we can substitute x = 25 into the cost function to find the cost of producing 25 chairs:

C(25) = 0.005(25)^3 + 0.07(25)^2 + 18(25) + 700

Simplifying the expression:

C(25) = 0.005(15625) + 0.07(625) + 450 + 700

C(25) = 78.125 + 43.75 + 450 + 700

C(25) = 1272.875

It is worth noting that the cost function is a cubic polynomial, indicating that the cost of production increases as the number of chairs produced (x) increases. This is expected as producing more chairs typically incurs higher expenses.

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Answer:

5

Step-by-step explanation:

Answer:

2.5 meters a second

Step-by-step explanation:

Because I said so

1)The pdf of U is f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

2)U follows a gamma-distribution with parameter a = 3/2 or a = 1/2.

3)x = (y²/2) and dx = y dy using exponential distribution

We can rewrite the integral as:

I(1/2) = ∫₀^∞ y exp(-y²) dy

       = 1/2 ∫₀^∞ exp(-u/2) du

This is the same as the integral for f(u) when u = 1/2.

Therefore, we have:

I(1/2) = V1

(1) For U = Z², we can use the method of transformations.

Let g(z) be the transformation function such that

U = g(Z)

   = Z².

Then, the inverse function of g is given by h(u) = ±√u.

Thus, we can apply the transformation theorem as follows:

f(u) = |h'(u)| g(h(u)) f(u)

     = |1/(2√u)| exp(-u/2) for u > 0 f(u) = 0 otherwise

Therefore, the pdf of U is given by:

f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

(2) We are given that f(1/2) = VT, where V is a constant.

We can substitute u = 1/2 in the pdf of U and equate it to VT.

Then, we get:VT = (1/(2√(1/2))) exp(-1/4)VT

                            = √2 exp(-1/4)

This gives us the value of V.

Now, we can use the pdf of the gamma distribution to find the parameter a such that the gamma distribution matches the pdf of U.

The pdf of the gamma distribution is given by:

f(u) = (u^(a-1) exp(-u)/Γ(a)) for u > 0 where Γ(a) is the gamma function.

We can use the following relation between the gamma and the factorial function to simplify the expression for the gamma function:

Γ(a) = (a-1)!

Thus, we can rewrite the pdf of the gamma distribution as:

f(u) = (u^(a-1) exp(-u)/(a-1)!) for u > 0

We can now equate the pdf of U to the pdf of the gamma distribution and solve for a.

Then, we get:

(1/(2√u)) exp(-u/2) = (u^(a-1) exp(-u)/(a-1)!) for u > 0 a = 3/2

Therefore, U follows a gamma distribution with parameter

a = 3/2 or equivalently,

a = 1/2.

(3) We need to show that I(1/2) = V1.

Here, I(1) = ∫₀^∞ exp(-x) dx is the integral of the exponential distribution with rate parameter 1 and V is a constant.

We can use the change of variables y = √(2x) to simplify the expression for I(1/2) as follows:

I(1/2) = ∫₀^∞ exp(-√(2x)) dx

Now, we can substitute y²/2 = x to obtain:

x = (y²/2) and

dx = y dy

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Answer:

AB, BC, AC

Step-by-step explanation:

Hi there,

In order to solve this problem, we should know that the longest side of the triangle is always opposite of the largest angle in a triangle. The first step is to find the angle measures. We are given the measures of ∠A and ∠C.

To find m∠B, just subtract the sum of the other angles and subtract the value from 180.

m∠A + m∠C + m∠B = 180°

65° + 40° + m∠B = 180°

105° + m∠B = 180°

m∠B = 75°

Now that we know all of the angle measures, we can identify the the lengths of the sides from least to greatest by looking at the angle value. The greater the angle measure, the longer the opposite side would be.

m∠A = 65° ⇒ opposite of side BC = medium side

m∠B = 75° ⇒ opposite of side AC = longest side

m∠C = 40° ⇒ opposite of side AB = shortest side

Hope this explanation helps. Cheers.

The values of the variables are y =50 and x = 130

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

The isosceles trapezoid

An isosceles trapezoid is a quadrilateral with two parallel sides of equal length and two non-parallel sides of unequal length.

This means that the base angles are congruent

Using the above as a guide, we have the following for the variable y

y = 50

Solving further, we have the following equation for variable x

x + 50 = 180

Evaluate the equation

x = 130

Hence, the value of x is 130

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Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer: x1= -3, x2=3

Step-by-step explanation:

3xlxl=8+1

3xlxl=9

lxl=3

x=3

=-3

solution

x1= -3, x2=3

Answer:

10x+4b+3

Step-by-step explanation:

x+x+x+x+x+x+x+x+x+x+b+b+b+b+3

There are 10 x

4 b

and one number

10x+4b+3

Answer:

10x+4b+3

Step-by-step explanation:

x+x+x+x+x+x+x+x+x+x+b+b+b+b+3

So when we add them we get 10x and 4b, which makes the equation

=> 10x+4b+3

2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The initial equation is:

So if we use the distribution propertie, we have to multiply the 4 for all term in the parenthesis so:

and then we simplify:

So is option D)

Answer:

75x24 is...

Step-by-step explanation:

Answer:

The letter E

In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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