Help me on this please I need it

Always that we have an integer, let's say 2, we can rewrite it like:

This will help us when multiplying fractions. To multiply two fractions, we simply multiply the numerator with the numerator and denominator with denominator. In this case:

And then solve:

Now we can further simplify this fraction, because 14 and 4 are divisible by 2, then:

14 = 2 x 7

4 = 2 x 2

Then the final answer is:

Range = max- min= 3

acc to our question-

max = 4

min = 1

range max - min

4-1 = 3

Hence,  range: 3

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The Bode, amplitude, and phase diagrams for the transfer function H(s) = 100(1 + 100s) / [(1 + s*10^-1)(1 + 10s)] can be sketched.

The sketching of Bode, amplitude, and phase diagrams for a transfer function involves a systematic procedure. For the given transfer function H(s) = 100(1 + 100s) / [(1 + s*10^-1)(1 + 10s)], the following steps can be followed to construct the diagrams.

Determine the Break Frequencies: Find the poles and zeros of the transfer function. The break frequencies are the frequencies at which the poles and zeros have their maximum effect on the transfer function. In this case, there are two poles at 1 and 10, and no zeros. So, the break frequencies are ωb1 = 1 rad/s and ωb2 = 10 rad/s.

Calculate the Magnitude: Evaluate the magnitude of the transfer function at low and high frequencies, as well as at the break frequencies. At low frequencies (ω << ωb1), the transfer function approaches 100. At high frequencies (ω >> ωb2), the transfer function approaches 0. At the break frequencies, the magnitude can be calculated using the equation |H(jωb)| = |H(1)| / √2 = 100 / √2.

Plot the Amplitude Diagram: Sketch the amplitude diagram on a logarithmic scale. Start from the lowest frequency, and plot the magnitude at each frequency point using the calculated values. Connect the points smoothly. The diagram will show a flat response at low frequencies, a roll-off near the break frequencies, and a decreasing response at high frequencies.

Determine the Phase Shift: Evaluate the phase shift introduced by the transfer function at low and high frequencies, as well as at the break frequencies. At low frequencies, the phase shift is close to 0°. At high frequencies, the phase shift is close to -180°. At the break frequencies, the phase shift can be calculated using the equation arg(H(jωb)) = -45°.

Plot the Phase Diagram: Sketch the phase diagram on a logarithmic scale. Start from the lowest frequency, and plot the phase shift at each frequency point using the calculated values. Connect the points smoothly. The diagram will show a minimal phase shift at low frequencies, a sharp change near the break frequencies, and a phase shift of -180° at high frequencies.

By following these steps, the Bode, amplitude, and phase diagrams for the given transfer function can be accurately sketched, providing a visual representation of its frequency response characteristics.

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The maximum area that the 60 m can enclose is 225m², the dimensions of the maximal region are 15m x 15m, and the height as an fcn of the base is 30 - b.

Let the base of the rectangular region be "b",

and the height be "h" and,

it is given that the perimeter of the rectangular region = 60m

(a) write height as an fcn of base

by using the formula of the perimeter of a rectangle,

2(h+b) = 60m

we can write, h = 30 - b

⇒Area of the rectangular region

area(A) = height × base

substituting the value of h.

= (30 - b) × b

thus, A(b)= 30b - b²

to find the maximum area that the 60 m can enclose

\(\frac{dA(b)}{db}\) should be equal to 0.

substituting the value of A(b).

30 - 2b = 0

thus, b = 15

maximum area = 30b - b²

substituting the value of b.

= (30 × 15) - 15²

thus, maximum area = 225m².

dimensions of the maximum region,

for maximum area height = base = 15m

thus, the dimensions of the maximum rectangular region are 15m x 15m.

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The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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Answer: \(\dfrac{1}{\sqrt{2}}\)

Step-by-step explanation:

The value of \(\cos 45^{\circ}\) is the fixed value i.e. \(\frac{1}{\sqrt{2}}\)

The values of cosine changes from a maximum at \(0^{\circ}\) to a minimum at \(180^{\circ}\)

for example, \(\cos 0^{\circ}=1, \quad \cos 90^{\circ}=0,\quad \cos 180^{\circ}=-1\)

The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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Answer:

The answer is explained below

Step-by-step explanation:

Let x be the price of fertilizer A, y be the price of fertilizer B, and z be the price of fertilizer C

The first combination  costs $384 and consists of 6 liters of fertilizer A, 5 liters of fertilizer B, and 3 liters of fertilizer C. The first combination is given by the equation:

6X + 5Y + 3Z = 384

The second combination consists of 10 liters of A, 2 liters of B, and 6 liters of C, and it costs $516. The second combination is given by the equation:

10X + 2Y + 6Z = 516

The last combination consists of 4 liters of A, 8 liters of B, and 2 liters of C,  with a cost of $368. The last combination is given by the equation:

4X + 8Y + 2Z = 368

In Matrix form it can be represented as:

\(\left[\begin{array}{ccc}6&5&3\\10&2&6\\4&8&2\end{array}\right]\left[\begin{array}{c}X\\Y\\Z\end{array}\right]=\left[\begin{array}{c}384\\516\\368\end{array}\right]\)

\(\left[\begin{array}{c}X\\Y\\Z\end{array}\right]=\left[\begin{array}{ccc}6&5&3\\10&2&6\\4&8&2\end{array}\right]^{-1}\left[\begin{array}{c}384\\516\\368\end{array}\right]\\\\\left[\begin{array}{c}X\\Y\\Z\end{array}\right]=\left[\begin{array}{ccc}1.5714&-0.5&-0.857\\-0.142&0&0.2142\\-2.571&1&1.3571\end{array}\right]\left[\begin{array}{c}384\\516\\368\end{array}\right]\\\\\left[\begin{array}{c}X\\Y\\Z\end{array}\right]=\left[\begin{array}{c}30\\24\\28\end{array}\right]\)

Therefore:

X = $30, Y = $24, Z = $28

The price of fertilizer A = $30 per liter, The price of fertilizer B = $24 per liter and The price of fertilizer c = $28 per liter

Answer:

X = $30, Y = $24, Z = $28

Step-by-step explanation:

PLATO <3

The shape of the distribution of the number of siblings can vary depending on the specific data set.

However, if we are considering the general case, the most common shape of the distribution is likely to be unimodal and skewed to the right.

This means that the majority of individuals are likely to have fewer siblings,

and as the number of siblings increases,

the frequency of individuals with that number decreases.

The distribution may also have a long tail on the right side,

indicating a few individuals with a significantly larger number of siblings.

However, it is important to note that this is just a general observation, and in specific cases,

the distribution may be different.

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The difference between 1/9 and 1/3 in simplest form is -2/9.

To find the difference between two fractions, you need to follow these steps:

1. Find the least common denominator (LCD) of the fractions, which is the smallest multiple of their denominators. In this case, the denominators are 9 and 3.

The LCD is 9 since it is the smallest number that both 3 and 9 can divide into.

2. Convert the fractions to equivalent fractions with the LCD as the new denominator.

For 1/9, you don't need to do anything as it already has the denominator 9. For 1/3, multiply the numerator and denominator by 3 to get 3/9.

3. Now you have the fractions 1/9 and 3/9. Subtract the numerators while keeping the denominator the same: (1 - 3)/9.

4. Simplify the resulting fraction. In this case, you get -2/9.

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The order of the numbers from least to greatest will be;

⇒ - 2/3, -0.2 , 0.8 , √2 , √11

What is Number system?

A system of writing to express the number is called number system.

Given that;

All the numbers are,

a. √2

b. - 2/3

c. √11

d. 0.8

e. - 0.2

Now,

Solve all the number as;

a. √2 = 1.414

b. - 2/3 = - 0.67

c. √11 = 3.32

d. 0.8 = 0.8

e. - 0.2 = - 0.2

So, Order of the numbers from least to greatest will be;

⇒ - 0.67 , -0.2 , 0.8, 1.414, 3.32

This is same as;

⇒ - 2/3, -0.2 , 0.8 , √2 , √11

Therefore, The order of the numbers from least to greatest will be;

⇒ - 2/3, -0.2 , 0.8 , √2 , √11

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Answer:

The products of -3(1) and -3(-1) are the same because both expressions result in the multiplication of -3 and a number, where one of the numbers is positive and the other is negative. The product of these two numbers is always negative.

Step-by-step explanation:

-3(1) means multiplying -3 by 1, which gives -3 as the product.

-3(-1) means multiplying -3 by -1, which gives 3 as the product.

Even though the two expressions are different, we can see that both involve multiplying -3 with a number, where one of the numbers is positive and the other is negative.

When we multiply a negative number and a positive number, the product is always negative. Similarly, when we multiply a negative number and a negative number, the product is always positive.

So, in both -3(1) and -3(-1), we are multiplying a negative number (-3) with a positive number (1 in the first expression and -1 in the second expression). Therefore, the products of both expressions are negative (-3 in the first expression and 3 with a negative sign in the second expression).

Hence, we can conclude that the products of -3(1) and -3(-1) are the same and equal to -3.

The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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Answer:

58-51

why to have the speed of a cucumber you need a potato on a skateboard at 1000kmh, ok?

Answer: 4 I think

on each side it has 4

As there is a greater linear relationship between the variables in the data set with an  R² value of 0.95, it is more linear. The solution given in option a, "The one with  R² = 0.95 is more linear," is correct.

In a linear regression model, the coefficient of determination, or  R², quantifies the percentage of the dependent variable's variation that is explained by the independent variable(s).

Strong linear relationships between the variables are indicated by an R² value that is close to 1, whereas weak linear relationships are indicated by a value that is close to 0.

Therefore, Because there is a stronger linear relationship between the variables in the data set with an R² value of 0.95 than in the data set with an R² value of 0.81, it is more linear.

The more closely the data points are grouped around a single line, the stronger the linear relationship, and the closer the R² number is to 1.

Therefore, We can deduce that the proper response is an option a, "The one with R²= 0.95 is more linear." Write your response in two lines.

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The expression that represent the area of the figure is  (3 x 2) + (3 x 4).

The area of the rectangle can be found as follows:

area of a rectangle  = lw

where

Therefore, the expression that represent the area of the figure is as follows:

area of the figure = lw

l = 6 ft

w = 3 ft

area of the figure = 6 × 3 = 18 ft²

or

area of the figure = (3 x 2) + (3 x 4) ft²

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Answer:

The equation of the tangent line at (3, f(3)) is y = 4x - 4.

Given that f(3) = 16 and f'(3) = 4, we know the point (3, f(3)) lies on the graph of the function, and the slope of the tangent line at that point is equal to the derivative at that point.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can plug in the values to find the equation of the tangent line.

The given point is (3, f(3)), so x1 = 3 and

y1 = f(3)

= 16.

The slope m is equal to f'(3) = 4.

Plugging these values into the point-slope form, we get:

y - 16 = 4(x - 3)

Expanding and rearranging the equation:

y - 16 = 4x - 12

y = 4x - 12 + 16

y = 4x - 4

Therefore, the equation of the tangent line at (3, f(3)) is y = 4x - 4.

The equation of the tangent line at (3, f(3)) when f(3) = 16 and f'(3) = 4 is y = 4x - 4. This equation represents a line that passes through the point (3, 16) and has a slope of 4, which is equal to the derivative of the function at x = 3.

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The minimum value of the expression x^2 + y^2 - 6x + 4y + 18 for real x and y is 13.

The minimum value of the expression x^2 + y^2 - 6x + 4y + 18 for real x and y can be found by completing the square.

Step 1: Rearrange the expression by grouping the x-terms and y-terms together:
x^2 - 6x + y^2 + 4y + 18

Step 2: Complete the square for the x-terms. Take half of the coefficient of x (-6) and square it:
(x^2 - 6x + 9) + y^2 + 4y + 18 - 9

Step 3: Complete the square for the y-terms. Take half of the coefficient of y (4) and square it:
(x^2 - 6x + 9) + (y^2 + 4y + 4) + 18 - 9 - 4

Step 4: Simplify the expression:
(x - 3)^2 + (y + 2)^2 + 13

Step 5: The minimum value of a perfect square is 0. Since (x - 3)^2 and (y + 2)^2 are both perfect squares, the minimum value of the expression is 13.

Therefore, the minimum value of the expression x^2 + y^2 - 6x + 4y + 18 for real x and y is 13.

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I tried but I kinda forgot to make your hair shorter. I got a little carried away.

Answer:

she baked 3 times as many cranberry than blueberry muffins

Step-by-step explanation:

i think that because 9×3=27

the amount of the cranberry muffins are 9

The distributive property to find the product the value of the polynomial is (a.4.)

To find the value of 'a' in the polynomial obtained by applying the distributive property to the expression (y - 4x)(y² + 4y + 16),  to match the terms with 'ay' in them.

When  the expression using the distributive property,

(y - 4x)(y² + 4y + 16) = y³ + 4y² + 16y - 4xy² - 16xy - 64x

Comparing this with the given polynomial,  that the term '-4xy' in the expanded expression corresponds to the term '-axy' in the given polynomial.

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Answer:

C. 4 2/3

Step-by-step explanation:

1) Use this rule: a/b * c = ac/b.

7 * 6/9

2)  Simplify 7 * 6 to 42.

42/9

3) Simplify.

14/3

4) Convert to mixed fractin form.

4 2/3

Answer:

The product of 7/9 and 6:

\(\\7/9 x 6 \\\\7x6=42\\\\42/9\\4 6/9\\\\4 is the whole number\\6/9 is the fraction that if we remove the 3 from both of us, it gives us the result 2/3\\ The answer is the B \\\)

Step-by-step explanation:

the answer is the B

Because You only had to multiply 6 by 7 and the result, which would be 42 over 9, should be converted to a mixed number, which would be dividing 42 by 9, which is 4, and us over 6, which is four, which is the whole number, and 6 is the numerator and you don't change the nine since it is still the denominator.

Because the 4 is the whole number

And 6/9 is the fraction that if were move the 3 from both of us , it gives us the result is 2/3

So we have 4 2/3

the answer is the B

Answer:

x + 37 ≥ 65

Step-by-step explanation:

Given:

Money Micah wants = $65

Money Micah had = $37

Find:

Money Micah need

Computation:

Money Micah need(x)

x + 37 ≥ 65

So,

Money Micah need = 65 - 37

Money Micah need = $28

To calculate Stephanie Ambrose's annual base premium, we need to sum up the costs of her bodily injury, property damage, comprehensive, and collision insurance.

Given that the bodily injury limits are $100/300 and the property damage limits are $100,000, we can calculate the cost of bodily injury and property damage insurance. The cost for bodily injury insurance is $100 for every $100,000 of coverage, and the cost for property damage insurance is $100 for every $100,000 of coverage.

For bodily injury insurance, the cost is calculated as:

(100/300) * 100 = $33.33

For property damage insurance, the cost is:

(100,000/100,000) * 100 = $100

Adding up the costs of bodily injury, property damage, comprehensive, and collision insurance:

Base premium: $292.50

Comprehensive insurance: $75.90

Collision insurance: $225.79

Bodily injury insurance: $33.33

Property damage insurance: $100

Total annual base premium = Base premium + Comprehensive insurance + Collision insurance + Bodily injury insurance + Property damage insurance

Total annual base premium = $292.50 + $75.90 + $225.79 + $33.33 + $100 = $727.52

Therefore, Stephanie Ambrose's annual base premium is $727.52.

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Answer:

m1 = 118 degrees, because it is a reflection of the other side of this line. m2 will be 180-118 = 62. This is because a straight line is always 180 degrees.

Therefore,

m1 = 118 degrees

m2 = 62 degrees

Answer:

∠ 1 = 118° , ∠ 2 = 62°

Step-by-step explanation:

∠ 1 and 118° are alternate angles and are congruent , then

∠ 1 = 118°

∠ 2 and 118° are same- side interior angles and sum to 180° , then

∠ 2 = 180° - 118° = 62°

run me my points .

Step-by-step explanation:

Answer:

the answer

Step-by-step explanation:

Answer:

K?

Step-by-step explanation:

The answer of the answer is the answer.

Hope this helped :D

Answer:

60%

Step-by-step explanation:

In the camp 15 out of 25 boys chose to go swimming. 15 is 60% of 25, so 60% of boys chose to go swimming.

Important information:

We need to find the percentage of the boys who chose to swim.

The percentage of the boys who chose to swim is:

\(\text{\% of boys who chose to swim}=\dfrac{\text{Boys chose to go swimming}}{\text{Total boys}}\times 100\)

                                              \(=\dfrac{15}{25}\times 100\)

                                              \(=15\times 4\)

                                              = 60

Therefore, 60% of boys chose to go swimming.

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