a brand of cereal had 1.2 1.21, point, 2 milligrams ( mg ) (mg)(, start text, m, g, end text, )of iron per serving. then they changed their recipe so they had 1.8 mg 1.8mg1, point, 8, start text, m, g, end text of iron per serving. what was the percent increase in iron?

We can simplify the expression by combining terms and simplifying further based on any specific values of u or 1.

To express the trigonometric expression cot(sin(1u)) cot(sin(1]) as an algebraic expression in u, we need to apply trigonometric identities and simplify it.

Let's start by using the identity cot(x) = 1/tan(x):

cot(sin(1u)) cot(sin(1]) = (1/tan(sin(1u))) (1/tan(sin(1]))

Next, we'll use the identity tan(x) = sin(x)/cos(x) to rewrite the tangents in terms of sine and cosine:

= (1/(sin(1u)/cos(1u))) (1/(sin(1)/cos(1]))

Simplifying further, we can multiply the reciprocals:

= (cos(1u)/sin(1u)) (cos(1)/sin(1))

Now, let's use the identity sin(2x) = 2sin(x)cos(x) to express the sines and cosines in terms of sine of half-angles:

= (cos(1u)/(2sin(1/2u)cos(1/2u))) (cos(1)/(2sin(1/2)cos(1/2)))

= (cos(1u)/2sin(1/2u)cos(1/2u)) (cos(1)/2sin(1/2)cos(1/2))

Since cos(x)cos(y) = (1/2)[cos(x+y)+cos(x-y)], we can use this identity to simplify the expression further:

= (cos(1u)/2sin(1/2u)(1/2)[cos(1/2+1/2u)+cos(1/2-1/2u)]) (cos(1)/2sin(1/2)cos(1/2))

= (cos(1u)/4sin(1/2u)[cos(1/2+1/2u)+cos(1/2-1/2u)]) (cos(1)/2sin(1/2)cos(1/2))

Now, we can simplify the expression by combining terms and simplifying further based on any specific values of u or 1.

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Value of x for which defined function f(x) = x²e⁻ˣ² gives the relative maximum value is equal to option D. -1 or  1.

Function 'f' is defined by f(x) = x²e⁻ˣ²

To get the relative maximum value of the function f(x) =  x²e⁻ˣ² find the first derivative we have,

f(x) =  x²e⁻ˣ²

Apply product rule of derivative :

d/dx ( u × v ) = v du /dx + u dv /dx

f' ( x ) =  e⁻ˣ² d/dx (x²) + x² d/dx (e⁻ˣ²)

⇒ f' (x) = 2x  e⁻ˣ² - 2x (x² ) ( e⁻ˣ² )

⇒  f' (x) = 2x  e⁻ˣ² - 2x³ e⁻ˣ²

⇒ f' (x) = 2x  e⁻ˣ²( 1 - x² )

To get the value of x for maximum function f' (x ) = 0 we get,

2x  e⁻ˣ²( 1 - x² ) = 0

⇒ 2≠0 or x =0 or  e⁻ˣ² ≠ 0 or 1 - x² = 0

⇒ x = 0 or x = ± 1

When

x = 0 ⇒ f(x) = 0

x = 1 ⇒ f(x) = e⁻¹

x = -1 ⇒ f(x) = e⁻¹

x = -1 or 1 represents the relative maximum value of f(x).

Therefore , value of x which represents the relative maximum value of the function f(x) = x²e⁻ˣ² is equal to option D. -1 or 1.

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Answer:

Of the given options, "an engine" is the most reasonable abstraction for a car.

An engine is a fundamental component of a car that powers its movement, and it is present in almost all cars. The number of miles driven and the driving car color are characteristics of a specific car rather than abstractions of a car itself. For example, a car can still be considered a car even if it has not been driven any miles yet or if it has no color at all.

Therefore, an engine is a more reasonable abstraction for a car as it captures an essential feature of a car that is present in all cars.

The solution is, D. Driving, a reasonable abstraction for a car includes. Driving is an action or behavior associated with a car, as it involves operating or using the car to travel from one place to another. It is an essential aspect of the car's purpose and function.

Here, we have,

we know that,

An engine is a machine designed to convert fuel into mechanical energy that can be used to power other machines or devices. In the context of automobiles, an engine is the primary source of power that drives the vehicle. It typically operates by burning fuel in a combustion chamber to generate high-pressure gases that drive a piston, which in turn rotates a crankshaft that ultimately powers the car's wheels.

Car color and number of miles driven are characteristics or properties of a car, while an engine is a component that helps to power the car. Driving, on the other hand, is an action or behavior associated with a car, as it refers to the act of operating or using the car to travel from one place to another.

Therefore, driving is a reasonable abstraction for a car, as it captures an essential aspect of the car's purpose and function.

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Answer:

X²-2X-15

Step-by-step explanation:

The given linear time-invariant (LTI) system is described by a third-order linear constant coefficient differential equation. To determine the frequency response of the system, we can take the Laplace transform of the differential equation and solve in the Laplace domain

(a) To find the frequency response, we start by taking the Laplace transform of the given differential equation. Let \(Y(s)\) and \(X(s)\) represent the Laplace transforms of \(y(t)\) and \(x(t)\) respectively. By applying the Laplace transform, we obtain:

\[2s^3Y(s) + 4s^2Y(s) + 10sY(s) = 5X(s) + 2sX(s)\]

Simplifying the equation, we get:

\[Y(s) = \frac{5X(s) + 2sX(s)}{2s^3 + 4s^2 + 10s}\]

This equation represents the transfer function of the system in the Laplace domain. To obtain the frequency response, we substitute \(s = j\omega\) into the transfer function, where \(\omega\) represents the angular frequency.

(b) To approximate the Bode plot, we analyze the frequency response at low and high frequencies. At low frequencies (\(\omega \to 0\)), the terms involving \(s\) dominate, and the transfer function can be approximated as:

\[Y(j\omega) \approx \frac{2j\omega X(j\omega)}{2j\omega}\]

Simplifying, we find that the low-frequency gain is 1, indicating that the system passes low-frequency signals without significant attenuation.

At high frequencies (\(\omega \to \infty\)), the terms involving \(s\) become negligible compared to the constant term. Thus, the transfer function can be approximated as:

\[Y(j\omega) \approx \frac{5X(j\omega)}{10j\omega}\]

In this approximation, the gain decreases by -20 dB/decade, indicating that the system attenuates high-frequency signals.

The cutoff frequencies of the system can be determined from the Bode plot where the gain decreases by -3 dB. These frequencies represent the boundary between the passband and stopband of the system.

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Answer:

B  bro, the salad.

Step-by-step explanation:

Answer:

Length of the string let out by Jim is 156.9 m.

Step-by-step explanation:

From the figure attached,

Jim observes the angle of elevation of the kite = 85°

And Patty observes the angle of elevation of the kite = 40°

Angle formed between the lines joining kite to Jim and Patty = 180° - (85 + 40)° = 55°

Distance between Jim and Patty = 200 m

Let the length of the string between Jim and the kite = x meters

By applying Sine rule in the triangle formed between Jim, Patty and the kite,

\(\frac{\text{Sin}55}{200}=\frac{\text{Sin}40}{x}\)

x = \(\frac{200\times \text{Sin}40}{\text{Sin}55}\)

x = 156.94 m

  ≈ 156.9 m

Therefore, length of the kite string from Jim and the kite is 156.9 m.

To graph an absolute value function, choose several values of x and find some ordered pairs. Plot the points on a coordinate plane and connect them.

Absolute value equations are the equations in which the absolute value operator is used.

To graph such an equation, we must first get rid of the absolute value equation by dividing the equation into different parts. Then graph the equations of these parts separately.

If the value of the expression or the number inside the operator is negative, then the result is the negative of the expression or the number.

Suppose we have an expression: |x+1|

If (x+1) is positive or equal to 0, then  |x+1| =x+1

However, if (x+1) is negative, then |x+1| =-(x+1)=-x-1.

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Answer:

78 Students

Step-by-step explanation:

Answer:

I hope your joking but it is 78 like it says in the table.

Step-by-step explanation:

Answer:

214.50

Step-by-step explanation:

A = lw

13 x 11 = 143 (13 is a guess)

143 x 1.50 = 214.50

im not 100 % but give it a try

hope this helps

pls mark brainliest

The slope of the points (-1,4) and (5,-5) is -1.5 and the graph is attached below.

Slope of the line:

The slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line.

Formula,

m = (y2-y1)/x2-x1)

Given,

Points are (-1,4) and (5,-5)

Now we need to find the slope of the line and we have to plot it.

Apply the given values on the formula, then we get,

m = (-5-4)/5-(-1)

m = -9/6

m = -3/2

m= -1.5

Now we have to plot the graph for it

To graph the line going through the two points, we plot the two points and then draw a line through the points,

Then we get the graph like the following:

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1) 12/1

2) 517/100

3) 2/25

4) 67/800

5) 5/2

Kilograms (kg) is a unit of mass that is commonly used in the metric system. However, in some countries, such as the United Kingdom and the United States, the customary unit of measurement for weight is stone and pounds.

67 kg in stones is equivalent to approximately 147.71 pounds.

It's important to note that while the conversion from kilograms to stone and pounds is straightforward, the conversion is not exact due to rounding. However, this difference is generally small and can be ignored for most practical purposes.

Overall, understanding the conversion from kilograms to stone and pounds can be useful for students who are studying or traveling between countries that use different units of measurement for weight. Additionally, the process of converting from one unit of measurement to another can help reinforce important mathematical skills, such as division and rounding.

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Answer:

8 x 12 = 96!

Step-by-step explanation:

It is the same as 8 x 12, which would have the answer of 96.

Answer:

5^n-1

Step-by-step explanation:

5^n-1*30

Answer:

243

Step-by-step explanation:

\(5( \sqrt{ {x}^{2} + 2x - 14} + x) = 20 \\ \\ \sqrt{ {x}^{2} + 2x - 14} + x= \frac{20}{5} \\ \\ \sqrt{ {x}^{2} + 2x - 14} + x= 4 \\ \\ \sqrt{ {x}^{2} + 2x - 14} = 4 - x\\ \\ {(\sqrt{ {x}^{2} + 2x - 14} )}^{2} = {(4 - x)}^{2} \\ \\ \cancel{ {x}^{2}} + 2x - 14 = 16 - 8x + \cancel{ {x}^{2} } \\ \\ 2x - 14 = 16 - 8x \\ \\ 2x + 8x = 16 + 14 \\ \\ 10x = 30 \\ \\ x = \frac{30}{10} \\ \\ x = 3 \\ \\ 3 {x}^{4} = 3 {(3)}^{4} = 3 \times 81 \\ \\ \huge \red {3 {x}^{4}= 243}\)

Answer:

ANSWER, A

Step-by-step explanation:

\(\frac{x^{2} }{20} +\frac{y^{2} }{36} =1\)

The first 3 terms of the sequence using the expression are -5, -4 and -1

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

n(n – 2) – 4

This means that

T(n) =  n(n – 2) – 4

Set n = 1, 2 and 3

So, we have

T(1) =  1 * (1 – 2) – 4 = -5

T(2) =  2 * (2 – 2) – 4 = -4

T(3) =  3 * (3 – 2) – 4 = -1

Hence, the first 3 terms of the sequence using the expression are -5, -4 and -1

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Answer: 4

Step-by-step explanation:

If you have 12 feet of ribbon and it takes 3 feet per gift 3feet will go into 12 4 times.

Answer: she can wrap 4 presents

Step-by-step explanation:

12 divided by 3 equals 4, and if each present needs 3 feet of ribbon, there will be enough for 4 presents with no ribbon left over

The possible coordinates of point G on the number line is -15 and 7.

On the number line, point E has the coordinates of - 4, and EG = 11 .

The possible coordinates of point G are as follows:

A number line is a horizontal straight line with numbers placed at equal distances from each other along that line.

Negative numbers are on the left side while the positive numbers are on the right side.

Therefore, the possible coordinates of G is when we go left or right side of E on the number line.

Hence,

Let's go left E to G on the number line

Let's go right E to G on the number line

Therefore, the possible coordinates of point G on the number line is -15 and 7.

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Answer:

2 2/15 hours from noon the stock prices will be the same.

Step-by-step explanation:

Sorry if it's incorrect.

Answer:

57.87

Step-by-step explanation:

First, we need to find the area of the rectangle.

12x6=72

Next, we need to find the area of the full circle.

r=3

The area of the full circle is 28.26.

So half of the circle's area is 14.13.

Now, we subtract the area of half the circle from the total rectangle.

72-14.13=57.87

The answer is 57.87

Answer:

0.001

Step-by-step explanation:

The volume of a cube when the area of a face is 0.01 square units is 0.001 cubic units

Cube is a three dimensional solid with a special characteristics such as having all the sides equal and intersecting at an angle of 90 degrees. A cube has six faces and each face has same properties as a square.

Given data

Area of face of a cube = 0.01 square units

solving for a side for the cube we have:

let a side of the cube be x

\(x = \sqrt{0.01}\)

x = 0.1

The volume of a cube is calculated by multiplying the three sides. We have earlier made a side to be x, so we have:

volume of a cube = x * x * x

volume of a cube = x^3

substituting the value of x gives

volume of a cube = 0.1^3

volume of a cube = 0.001 cubic units

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

-7.2

Step-by-step explanation:

(-3.3 -0.9 + 1.2)=-3

-3•2.4=-7.2

The solution is -7.2

How to simplify Equations?

Given data ,

Let the equation be x

The equation is x = 2.4 ( -3.3 - 0.9 + 1.2 )

x = 2.4 ( -4.2 + 1.2 )

x = 2.4 ( -3 )

x = -7.2

Hence , the solution to the equation is -7.2

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We have defined the criteria for SAS congruency of triangles.

What is SAS?

The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."

According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.

Hence, we have defined the criteria for SAS congruency of triangles.

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Answer:

Step-by-step explanation:

Student's t test for correlated groups reduces to Student's t test for single samples using difference scores. Therefore, the correct answer is (b).

In a t test for correlated groups (also known as paired-samples or dependent-samples t test), the same group of participants is measured twice, under two different conditions or at two different times. The difference between the two measurements for each participant is calculated and used as the sample data. The t test for correlated groups compares the mean difference score to zero to determine if there is a significant difference between the two conditions or times.

This can be seen as equivalent to a t test for single samples using difference scores, where the mean difference score is compared to a known or hypothesized value of the population mean difference. In fact, the formula for calculating the t statistic is the same in both cases.

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True. In 2016, the percentage of the ageing population (55 years or older) in state prisons surpassed the percentage of people aged 18-24 for the first time.

This trend reflects the overall growth of the ageing population within the United States and is a result of various factors such as longer life expectancy, harsher sentencing laws, and an increase in older individuals being convicted of crimes.
As the ageing population in state prisons continues to grow, it poses several challenges for the correctional system. These challenges include providing appropriate healthcare and accommodations for older inmates and addressing the specific needs of this population, such as mobility assistance and specialized medical care.
In conclusion, the shift in the age demographics of state prisons has significant implications for the management and administration of correctional facilities. It is crucial to address the unique needs of the ageing population within these institutions and adapt policies and practices accordingly to ensure the well-being and fair treatment of all inmates, regardless of their age.

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