How many Pieces of ribbon .6m long can be cut from 13.2m ribbon?

By chain rule, the first derivative of the composite function f(x) = [tex]4^{5\cdot x - 9}[/tex] is equal to  [tex]4^{u}[/tex] · 5 · ㏑ 4.

Herein we have the case of a composite function, that is, a function of the form f[u(x)]. Chain rule is a derivative rule used to find the derivative of composite functions, which is now defined:

df / dx = (df / du) · (du / dx)

If we know that u(x) = 5 · x - 9 and f(u) = [tex]4^{u}[/tex], then the derivative of the compond function is:

df / du = [tex]4^{u}[/tex] · ㏑ 4

du / dx = 5

Then, by chain rule:

df / dx = [tex]4^{u}[/tex] · 5 · ㏑ 4

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n(x) is a vertical dilation of scale factor 4 followed by a translation of 2 units upwards of the parent linear function.

The parent linear function is:

f(x)= x

And the function n(x) is:

n(x) = 4x + 2

If first we apply a vertical dilation of scale factor 4 to the parent linear function, we will get:

n(x) = 4*f(x)

And if now we apply a translation of 2 units upwards, then we get:

n(x) =4*f(x) + 2

Replacing f(x) by x we get:

n(x) = 4*x + 2

And we returned to n(x), so these are the transformations that define our function in terms to the parent function.

And the slope 4 means that each month 4 books are added, the y-intercept 2 means that she starts with 2 books.

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Answer:

236 for children and 288 for adults

Step-by-step explanation:

→ Set up 2 simultaneous equations

a + c = 524

2.25a + 1.25c = 891

→ Multiply 1st equation by 1.25

1.25a + 1.25c = 655

2.25a + 1.25c = 891

→ Minus from each other

-a = -236 ⇔ a = 236

→ Substitute into first equation

236 + c = 524 ⇔ c = 288

The solution for this system of equations. 12x+ 15y = 34 -6x+ 5y = 3

is (x,y) =(2/3, 8/5)

Given a system of equations,

12x + 15y = 34  ------(1)

-6x + 5y = 3 ------(2),

To solve this we use the elimination method

In the elimination method, you either add or subtract the equations to get an equation in one variable.

Equation (1) + 2 × Equation (2),

We get,

(12x+15y=34)+(-12x+10y=6)

⇒ 15y+10y=34+6

⇒ 25y=40

⇒ y=40/25

⇒ y=8/5

From equation (2),

⇒  -6x+5(y)=6

⇒  -6x+5(8/5)=6

⇒  -6x+8=6

⇒  -6x=-2

⇒ x=2/3

Hence the solution for this system of equations. 12x 15y = 34 -6x 5y = 3

is (x,y =(2/3, 8/5)

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The probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

In the given question we have to find the probability of first tile is less than 15 and the second tile is even or greater than 25.

Tiles numbered 1 through 20 are placed in a box.

Tiles numbered 11 through 30 are placed in a second box.

One tile is randomly drawn from each box.

Now finding the probability of first tile is less than 15.

Since in first box tile is numbered as 1 to 20.

So the outcomes of less than 15 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

So favourable outcome = 14

Total number of tile = 20

So the probability = 14/20 = 70%

Now finding the probability of second tile is even or greater than 25.

Since in second box tile is numbered as 11 to 30.

So the outcomes of even or greater than 25 = 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30

So favourable outcome = 12

Total number of tile = 20

So the probability = 12/20 = 60%

Hence, the probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.

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The right question

"Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30 are placed in a second box. One tile is randomly drawn from each box. Find each probability. The first tile is less than 15 and the second tile is even or greater than 25."

The graph is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.as stated

The term "range" refers to every potential value in a graph's output.

The result of range is seen in the y coordinate, and the range of potential values is given here.

0 ≤ y ≤ 5

The term "domain" refers to every conceivable value in a graph's input.

The x coordinate is the input, and the extent of potential values is

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The dimensions and area of the parts of the composite figure are as follows;

A composite figure is a figure that consists of two or more simpler figures.

The width of the whole figure of length 14 consists of the the missing dimension and the expression (x - 3)

Therefore;

14 = Missing dimension + (x - 3)

Missing dimension = 14 - (x - 3) = 17 - x

The expression for the missing dimension is = 17 - x

The area of the large rectangle = 14 × 12 = 168

Area of the smaller unshaded rectangle = (x - 3) × 12 = 12·x - 36

Area of the shaded figure = Area of the whole figure less the area of the unshaded figure

Therefore;

Area of the shaded figure = 168 - (12·x - 36) = 204 - 12·x

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Step-by-step explanation:

since it is a mid-segment, DGH and DEF are similar triangles with the constant scaling factor of 2 for the lengths of all sides and other lines in the triangle.

e.g.

DE = 2 × DG

DF = 2 × DH

and therefore,

28 = 2 × GH = 2× (x - 3)

14 = x - 3

x = 17

HF = x - 7 = 17 - 7 = 10

DH = HF = 10

so,

y + 8 = 10

y = 2

and DF = 10 + 10 = 20

[tex](- \frac{3}{2} , -\frac{1}{4} )[/tex] will be located in Quadrant III

What are Quadrants?

A two-dimensional Cartesian plane system's x- and y-axes divide the plane into four infinite regions known as quadrants. The x-axis, sometimes known as the horizontal line, and the y-axis, often known as the vertical line, meet at a right angle. The reference point is often where two lines connect. This point serves as the reference (or initial point) for all measurements made using the coordinate system.

Simply said, a quadrant is the area of a cartesian plane where the x- and y-axes cross each other.

Coordinate plane with four quadrants

According to those values, the graph is then divided into four quadrants or portions.

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[tex]\boldsymbol{\sf{Your\:exersice \to \dfrac{1}{x+9}+\dfrac{1}{5}=\dfrac{1}{4} }}[/tex]

Variable x cannot be equal to −9 as division by zero is undefined. Multiply both sides of the equation by 20(x+9), the lowest common denominator of x+9,5,4.

[tex]\boldsymbol{\sf{20+20(x+9)\times\left(\dfrac{1}{5}\right)=5(x+9) }}[/tex]

Multiply 5 and 1/5 to get 4.

[tex]\boldsymbol{\sf{20+4(x+9)=5(x+9)}}[/tex]

Use the distributive property to multiply 4 by x+9.

[tex]\boldsymbol{\sf{20+4x+36=5(x+9)}}[/tex]

Add 20 and 36 to get 56.

[tex]\boldsymbol{\sf{56+4x=5(x+9)}}[/tex]

Use the distributive property to multiply 5 by x+9.

[tex]\boldsymbol{\sf{56+4x=5x+45}}[/tex]

Subtract 5x on both sides.

[tex]\boldsymbol{\sf{56+4x-5x=45}}[/tex]

Combine 4x and −5x to get −x.

[tex]\boldsymbol{\sf{56-x=45}}[/tex]

Subtract 56 from both sides.

[tex]\boldsymbol{\sf{-x=45-56}}[/tex]

Subtract 56 from 45 to get −11.

[tex]\boldsymbol{\sf{-x=-11}}[/tex]

Multiply both sides by −1.

[tex]\boldsymbol{\sf{x=11}}[/tex]

the second and last one

The answer is  

AEB and IAE

DEA and CED

The other diagonal is $70 long.

Given:

Rhombus $abcd$ has perimeter $148$, and one of its diagonals has length $24$.

P = 148 and d = 24

Area [tex]= 1/4 d \sqrt{P^2-4d^2}[/tex]

= 1/4(24)[tex]\sqrt{148^2 - 4*24^2}[/tex]

= 6 [tex]\sqrt{21904-4*576}[/tex]

= 6*[tex]\sqrt{21904-2304}[/tex]

= 6*[tex]\sqrt{19600}[/tex]

= 6*140

= 840

Area = d*d1 / 2

840 = 24 * d1 / 2

840 * 2 = 24 * d1

1680/24 = d1

d1 = $70

Therefore The other diagonal is $70 long.

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Answer:

70

Step-by-step explanation:

The four sides of a rhombus all have equal length, so if the perimeter is 148, then each side has length 148/4 = 37. Also, the diagonals of a rhombus bisect each other at right angles, so the diagonal of length 24 is cut into two pieces of length 12. We can show this information in a diagram (shown below.)

Applying the Pythagorean Theorem to any of the four right triangles in our diagram, we have

12² + x² = 37².

Solving this equation for positive x, we get x = √37² - 12² = √1369 - 144 = √1225 = 35. The length of the long diagonal is x + x = 70.

Answer: C: 62

Step-by-step explanation: -7 + -12 = -19

-19 + 81 = 62

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6629\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A=6629\left(1+\frac{0.1}{1}\right)^{1\cdot 4} \implies A \approx 9705.52~\hfill \underset{earned~interest}{\stackrel{9705.52~~ - ~~6629}{\approx\text{\LARGE 3076.52 }}}[/tex]

Answer:

Area = 1/2 * base * height

Area = 1/2 * 155 * 175

Area = 13,563.75

The polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

The polynomial having the highest power of 3 is called the cubic polynomial.

Given that the roots 2, -3, and 4 that has to pass through the point (1, 10).

The polynomial will be written as,

Y = (x-2)(x+3)(x-4)

Y = x³+x²-6x-4x²-4x=24

Y = x³-3x²-10x+24

Therefore, the polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.

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The equation of the polynomial equation P(x) = (x + 3)²(x - 5)²

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zero 5 is 2

The equation of the polynomial is then calculated as

P(x) = (x - zero)^multiplicity

So, we have

P(x) = (x - (-3))² * (x - 5)²

This gives

P(x) = (x + 3)²(x - 5)²

Hence, the equation is P(x) = (x + 3)²(x - 5)²

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Possible question

Form a polynomial with real coefficients having the given degree and zeros.

Degree​ 4; ​

Zeros: -3 and 5 with multiplicity 2

1/16 is the ratio of a blue and unbarred parrot as offspring

Dihybrid cross is a cross between two individuals with two observed traits that are controlled by two distinct genes. The idea of a dihybrid cross came from Gregor Mendel when he observed pea plants that were either yellow or green and either round or wrinkled. Crossing of two heterozygous individuals will result in predictable ratios for both genotype and phenotype in the offspring. The expected phenotypic ratio of crossing heterozygous parents would be  Deviations from these expected ratios may indicate that the two traits are linked or that one or both traits has a non-Mendelian mode of inheritance.

When two heterozygous parents for color (Gg) and barring (Bb) are crossed, each parent's genotype is GgBb. Each parent produces four gametes, such as GB, Gb, gB, and gb. As a result, the total number of offspring will be 16, as each parent produces four gametes. Nine will be G B_, three will be G bb, three will be ggB_, and one will be ggbb.

Therefore, 1/16 is the ratio of a blue and unbarred parrot as offspring

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Explanation:

Each component has 1/3 as the probability of failure.

1 - 1/3 = 2/3 is the probability a particular component works.

Each component is independent of one another, allowing us to multiply the probabilities: (2/3)*(2/3)*(2/3) = 8/27

8/27 is the probability that all three components work simultaneously, and it's the probability that the machine works.

1 - 8/27 = 19/27 represents the probability that at least one component fails, and hence causes the entire machine to fail also.

19/27 = 0.7037 = 70.37% approximately. It appears this machine fails pretty often.

Step-by-step explanation:

[tex] \frac{1}{u} + \frac{1}{v} = \frac{1}{f} [/tex]

[tex] \frac{1}{v} = \frac{1}{f} - \frac{1}{u} [/tex]

[tex] \frac{1}{v} = \frac{u - f}{uf} [/tex]

[tex]v = \frac{uf}{u - f} [/tex]

Answer:

I think 28.6

Step-by-step explanation:

the water level in the stream rises by 10.125 inches.

What is water level?

The elevation of a sea, stream, lake, or reservoir's free surface in relation to a given vertical datum is referred to as the water level, also known as gauge height or stage.

Main body:

According to question water level in stream rises by 2.25 inches every hour.

Total rise can be calculated by using simple multiplication.

Total time for ride = 4.5 hours

Total rise in stream level = total time * total rise in 1 hour

                                         = 2.25*4.5

                                         = 10.125 inches

Therefore total rise in stream is 10.125 inches.

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The length of the side a = 9.43 cm and b = 12.04 cm

Consider the first triangle

The hypotenuse of the triangle = a

The base of the triangle = 5 cm

The length of the vertical side = 8 cm

Apply the Pythagorean theorem here

[tex]a= \sqrt{8^2+5^2}[/tex]

Find the square of the terms

a = [tex]\sqrt{64+25}[/tex]

a = [tex]\sqrt{89}[/tex]

a = 9.43 cm

Consider the second triangle

The hypotenuse of the triangle = 17 cm

The base of the triangle = 12 cm

The length of vertical side = y cm

Apply the Pythagorean theorem

b = [tex]\sqrt{17^2-12^2}[/tex]

b = [tex]\sqrt{289-144}[/tex]

b = [tex]\sqrt{145}[/tex]

b = 12.04 cm

Hence, the length of the side a = 9.43 cm and b = 12.04 cm

The complete question is

Work out the lengths of sides a and b give your answer to the 1st decimal

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Answer:

D or C

Step-by-step explanation:

Answer:

y = -3/4 -1

Step-by-step explanation:

The slope will be a negative recipricol of the original line

Edit : Grammar

Answer:

Step-by-step explanation:

so by putting  (0,0) into the first equation  it's false,  y of 0 does not become greater than 4

for the second equation, putting in (0,0) it is true.  6 is greater than 0

i'm attaching a graph also  :) of both equations graphed together

[tex]\sf y > -2x+4\\\\Broken\ line\\\\Substitute\ (0,0)\\\\0 > -2(0)+4\\0 > 4\\\\False[/tex]

[tex]\sf 3x+2y \leq 6\\\\Solid\ line\\\\Substitute\ (0,0)\\\\3(0)+2(0) \leq 6\\0\leq 6\\\\True[/tex]