Please help me with this quickly, the question says show your work or explain but I just need the explanation, thank you!!

y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2

m=-2

Now let us find the y intercept

-3=-2(4)+b

-3=-8+b

-3+8=b

5=b

Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

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You need to add 3 5/9 to make 8. If you want to know what 4 4/9 goes to, to make 8, do the opposite which is subtracting. 8 turn to 7 9/9 and then subtract 4 4/9 and then you get the answer aka 3 5/9.

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

44 m2

Step-by-step explanation:

The area of the rhombus can be divided into 4 equal triangles.

The area of one triangle is A=bh/2

so:

A = 5.5*2

A = 11 squared m

Since there are four (4) triangles in the rhombus we just need to multiply 11 by 4 so:

A = 11 * 4

A = 44 squared m

The volume of the log will be 30,70,760 m³.

Mathematically, we can write Archimedes principle as -

F{buoyant} = - fluid density {ρ} x acceleration due to gravity {g} x volume {v}

Given is that a 3080 kg log of wood with a diameter of 1 m and 10 m long, it floats in the water.

Since the log floats on water, the density of both the log and water is same.

So, we can write volume as -

Volume = 3080 x 997 Volume = 30,70,760 m³

Therefore, the volume of the log will be 30,70,760 m³.

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{QUESTION IN ENGLISH -urgent A 3,080 kg log of wood with a diameter of 1 m and 10 m long, it floats in the water. What is the volume of the trunk above the surface of the water?}

The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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Answer:

IT SAYS IT 27 PEOPLE WOULD BE SEATED

Step-by-step explanation:

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

a. 1,323,002

Step-by-step explanation:

Step-by-step explanation:

Consider the left-hand side:

\(\dfrac{1+\sin{\theta}}{\cos{\theta}} + \dfrac{\cos{\theta}}{1+\sin{\theta}}\)

\(\:\:\:\:= \dfrac{(1+\sin{\theta})^2 + \cos^2{\theta}}{\cos{\theta}(1+\sin{\theta})}\)

\(\:\:\:\:=\dfrac{1+2\sin{\theta}+\sin^2{\theta} + \cos^2{\theta}}{\cos{\theta}(1+\sin{\theta})}\)

\(\:\:\:\:=\dfrac{2+2\sin{\theta}}{\cos{\theta}(1+\sin{\theta})} =\dfrac{2(1+\sin{\theta})}{\cos{\theta}(1+\sin{\theta})}\)

\(\:\:\:\:= \dfrac{2}{\cos{\theta}} = 2\sec{\theta}\)

Answer:

Step-by-step explanation:

a)  27 = 3 × 3 × 3 = 3³    Answer: 3

b)  32 = 2 × 2 × 2 × 2 × 2 = \(2^5\)     Answer: 5

c) 625 = 5 × 5 × 5 × 5 = \(5^4\)     Answer: 4

d) \(\sqrt{64} = 8 \)  ⇒  \(64^{\frac{1}{2}} \)    Answer: 1/2

e) \(\sqrt[4]{81}=3 \)  ⇒  \(81^{\frac{1}{4}} \)   Answer: 1/4

f) \(\sqrt[6]{64} =2\)  ⇒  \(64^{\frac{1}{6} }\)    Answer: 1/6

g) \((x^2)^{\frac{1}{2}}=x^1=x \)     Answer: 1/2

h)  \((x^3)^{4}=x^{12}\)    Answer: 4

i)  \((x)^8=x^8\)   Answer: 8

Answer:

Step-by-step explanation:

Prime factorize 27,32,625,

a) 27 = 3 * 3 * 3 = 3³

b) 32 = 2 * 2 * 2 * 2 *2 = 2⁵

c) 625 = 5*5*5*5 = 5⁴

\(d) \sqrt{64}= (8^{2})^{\frac{1}{2}} = 8\\\\ e) \sqrt[4]{81}=\sqrt[4]{3*3*3*3}=(3^{4})^{\frac{1}{4}} = 3\\\\ f) \sqrt[6]{64}=\sqrt[6]{2*2*2*2*2*2}=(2^{6})^{\frac{1}{6}}=2\\\\ g)\sqrt{x^{2}}=(x^{2})^{\frac{1}{2}}=x\\\\ \)

\(h) x^{12} = x^{3*4}= (x^{3})^{4}\\\\ i)x^{8}=x^{1*8}=(x^{1})^{8}\)

The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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Answer:a

Step-by-step explanation:

Answer:

As a mixed number, it is 3 5/8.

As an improper fraction it is 29/8.

Hope that helps you. x

Check the picture below.

so let's recall that the area of a circle is just πr² where r = radius, so since the sizes of each pizza are 10, 14, 18 and 22, that's simply their diameter, so that means they each have a radius half of that, or namely 5, 7, 9 and 11, as you see in the picture, so, hmmm which radius gives us the most area per the fraction provided, namely per slices provided?

\(\cfrac{4}{8}\pi 5^2\implies \cfrac{25\pi }{2} ~~ \approx ~~ 39.26~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{8}\pi 7^2\implies \cfrac{147\pi }{8} ~~ \approx ~~ 57.73~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{8}\pi 9^2\implies \cfrac{81\pi }{4}~~ \approx ~~ 63.62~in^2 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}\pi 11^2\implies \cfrac{121\pi }{8}~~ \approx ~~ 47.52~in^2\)

Answer: Large

Step-by-step explanation:  Hope it helps Good luck!!!

Answer:0.0013

Step-by-step explanation:

Answer: the answer is on  the calclulator

Step-by-step explanation:

The value of the function when differentiated w.r.t "x" is -2 / 1+x^2.

To differentite the function \(f(x) = tan^{-1}(\frac{1-x}{1+x}) - tan^{-1}(\frac{x+2}{1-2x})\) w.r.t "x", we have to make use of chain rule and the derivative of the inverse tangent function. By applying both the methods, we have to find out the differentiated value of the function.

Chain rule is basically a fundamental rule in calculus that allows us to find the derivative of a function. The chain rule comes out to be very usefull when the functions are layered. On the other hand, inverse tangent function is a mathematical function that takes an input value and returns the angle whose tangent is equal to that value.

We know that;

\(tan^{-1}a - tan^{-1}b = tan^{-1}(\frac{a-b}{1+ab} )\)

So, by following the above method we get the function as:

\(f(x) = (tan^{-1}1 - tan^{-1}x) - (tan^{-1}x + tan^{-1}2)\)

\(f(x) = tan^{-1}1 - tan^{-1}2 - 2tan^{-1}x\)

Now, differentiating both the sides w.r.t "x":

f'(x) = 0 - 0 - 2/1+x^2

f'(x) = 2/1+x^2

Therefore, the value of the function when differentiated w.r.t "x" is

-2 / 1+x^2.

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Answer:

60 small and 140 large = 60 + 280 = 340 this is correct!

Step-by-step explanation:

I guess we just use the process of eleimation.

50 small and 150 Large = 50+300 = 350 so that's not right.

130 small and 70 large = 130 + 140 = 270 so, that's not right.

120 small and 80 large = 120 + 160 = 280 so, that's not right.

60 small and 140 large = 60 + 280 = 340 this is correct!

Answer:

Ellos dan las pistas de algunos problemas se pueden resolver de forma automática, los valores numéricos tienen ninguna importancia en los distintos ejemplos.

Traza 1

Uno de los lados de un rectángulo es 20 cm de largo; un segundo lado del rectángulo es de 0,85 m de largo. Calcular el perímetro y el área del rectángulo.

Traza 2

Calcular el área de un rectángulo cuyas dimensiones son 85 cm de largo y 20 cm respectivamente.

Traza 3

La base de un rectángulo es 20 cm de largo; la área es de 300 cm². Calcular la altura del rectángulo.

Traza 4

La altura de un rectángulo es 15 cm de largo; la área es de 300 cm². Calcula la base del rectángulo.

Traza 5

Un rectángulo tiene la altura que es de 3/8 de la base; la suma de las longitudes de los dos segmentos es 44 cm. Determinar el área del rectángulo y el perímetro.

Traza 6

La base de un rectángulo es de 0,40 m de largo; La altura del rectángulo es 30 cm. Calcular la diagonal.

Traza 7

Un tamaño de un rectángulo es un medio del lado de un cuadrado que tiene el perímetro de 20 cm. Sabiendo que los dos polígonos tienen el mismo perímetro, calcula la medida del tamaño del rectángulo.

Traza 8

La diagonal de un rectángulo es de 50 cm; la base es de 3/4 de la altura. Calcular el perímetro y el área del rectángulo.

Traza 9

La diagonal de un rectángulo mide 50 cm; ella es 5/3 de altura. Calcular el perímetro y el área del rectángulo.

Traza 10

Una mesa rectangular tiene lados de 180 cm y 90 cm respectivamente. Cuál es el perímetro y el área de un mantel que cuelga de 20 cm alrededor de la mesa?

Traza 11

Calcular el área de un rectángulo que tiene la altura 10 cm de largo, sabiendo que la medida de la base es el doble de la altura.

Traza 12

La diferencia entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

Traza 13

La suma entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

Traza 14

La suma de la base y la altura de un rectángulo es 50 cm; la base es superior a la altura de 4 cm. Calcular el área del rectángulo.

Traza 15

El semi-perímetro de un rectángulo es 32 cm y una dimensión es de 3/5 de la otra. Calcular el área del rectángulo.

Traza 16

El semi-perímetro de un rectángulo es 30 cm y una dimensión es igual a los sus 2/5. Calcular el área del rectángulo.

Traza 17

Un rectángulo tiene una base de 20 cm y una altura igual a 2/5 de la base. Calcular el perímetro y el área del rectángulo.

Traza 18

Un rectángulo tiene el área de 600 cm² y la base es 20 cm de largo. Cuál es su perímetro ?

Traza 19

Un rectángulo tiene un perímetro de 100 cm y la base es 30 cm de largo. Calcula su área.

Traza 20

Un rectángulo tiene un perímetro de 120 cm. Sabiendo que un tamaño es tres veces la otra, calcula el área del rectángulo.

Traza 21

La diferencia entre el tamaño de un rectángulo es 10 dm. Sabiendo que el perímetro es 100 dm, calcula el área del rectángulo.

Traza 22

Un rectángulo tiene un perímetro de 100 cm. Calcula su área sabiendo que la medida de la base es superior a la de la altura de 10 cm.

Traza 23

En el perímetro de un rectángulo es de 100 cm y la altura es de 20 cm de largo. Calcular el perímetro de un rectángulo equivalente a el mismo y que tiene su base de 40 cm de largo.

Traza 24

Un rectángulo es formado por dos cuadrados congruentes que tienen cada uno el perímetro de 24 cm. Calcular el perímetro y el área del rectángulo.

Traza 25

Un rectángulo es formado por tres cuadrados congruentes con cada lado 20 cm de largo. Calcular el perímetro y el área del rectángulo.

Traza 26

Un rectángulo es formado por dos cuadrados congruentes. Sabiendo que el perímetro del rectángulo es de 180 cm, calcular su área.

Traza 27

Un rectángulo y un cuadrado tienen el mismo perímetro. El lado de un cuadrado de 45 cm y las dimensiones del rectángulo son una 1/2 de la otra. Calcular el área del rectángulo.

Traza 28

Dos rectángulos son equivalentes. Sabiendo que las dimensiones de el primero miden respectivamente 30 cm y 20 cm, y que la base del segundo rectángulo es 40 cm de largo, calcula la diferencia entre los dos perímetros.

Traza 29

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

Traza 30

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

Traza 31

Un constructor ha comprado un terreno que tiene la planta mostrada en el dibujo y las dimensiones en metros se indican en la figura. Calcula el área y el perímetro de la tierra.

Traza 32

Una parcela de tierra tiene una forma rectangular con unas dimensiones de 50 m y de 30 m de largo. En el interior se ha construido una casa que ocupa una superficie rectangular de longitud 20 m y de 8 m de ancho. Calcular el área de la tierra permanecida libre.

Traza 33

Step-by-step explanation:

Answer:

A= 84cm

Step-by-step explanation:

length x width= area

plug in the given information.

14cm x 6cm = A

A=84

with a length of 14cm and a width of 6cm multiply them for an area of 84cm.

Group B has lower range.

Group A shows variability.

Mean is the best to make concussion about age of Salsa students.

Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.

This inference is supported by the observation that the majority of data points in Group B are concentrated around younger ages.

In contrast, Group A exhibits a more dispersed distribution of data points across a wider range of ages, including higher.

So, Group B has lower range.

and, Group A shows variability.

Lastly, Mean is the best to make concussion about age of Salsa students.

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Answer:

$1.00

Step-by-step explanation:

20.00 dollars x 5% =1.00

Answer:

$1.00

Step-by-step explanation:

Sales price ($20) x tax rate (.05) = $1.00

Answer:

who's john?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Because A GAY couple can adopt or its hypothetical that they can have a baby obviously

We have the following:

replacing:

the geometric mean of 54 and 18 is 31.18

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).

The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.

In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.

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Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Answer:

=0.7f−5.84

Step-by-step explanation:

Let's simplify step-by-step.

f(0.7)−6.32−0.8+1.28

=0.7f+−6.32+−0.8+1.28

Combine Like Terms:

=0.7f+−6.32+−0.8+1.28

=(0.7f)+(−6.32+−0.8+1.28)

=0.7f+−5.84

Answer:

=0.7f−5.84

Pls Brainliest

The probability of their first child having green eyes is 0.125, and the probability of their second child not having them is 0.875.

Probability is an estimate of how likely an occurrence is to occur. It's a figure between 0 and 1, where 0 means the event is unlikely and 1 means the event is certain. A likelihood of 0.5 (or 50%) indicates that the occurrence has an equal chance of occurring or not occurring.

In the given question,

a) The probability of their first child having green eyes is 0.125. The probability of their second child not having green eyes is 1 - 0.125 = 0.875. Therefore, the probability that their first child will have green eyes and the second will not is 0.125 x 0.875 = 0.1094.

b) The probability of exactly one of their two children having green eyes can be calculated in two ways: either the first child has green eyes and the second doesn't, or the first child doesn't have green eyes and the second does. The probability of the first scenario was calculated in part (a) to be 0.1094, and the probability of the second scenario is the same, so the total probability is 2 x 0.1094 = 0.2188.

c) The probability of exactly two out of six children having green eyes can be calculated using the binomial distribution with n = 6, p = 0.125, and k = 2. The formula for this probability is:

P(k=2) = (6 choose 2) x \(0.125^2 x (1 - 0.125)^4\) = 0.1936

where (6 choose 2) = 6!/(2!4!) = 15 is the number of ways to choose 2 children out of 6.

d) The probability of at least one of their six children having green eyes is the complement of the probability that none of them do. The probability that any one child doesn't have green eyes is 1 - 0.125 = 0.875, so the probability that none of the six children have green eyes is \(0.875^6\) = 0.1779. Therefore, the probability that at least one of their six children has green eyes is 1 - 0.1779 = 0.8221.

e) The probability that the first green-eyed child will be the fourth child is the probability that the first three children do not have green eyes, multiplied by the probability that the fourth child has green eyes, multiplied by the probability that the fifth and sixth children do not have green eyes. The first three children have a probability of \((1-0.125)^3\) = 0.578 to not have green eyes. The fourth child has a probability of 0.125 to have green eyes. The probability that the fifth and sixth children do not have green eyes is \((1-0.125)^2\) = 0.765625. Therefore, the probability that the first green-eyed child will be the fourth child is 0.578 x 0.125 x 0.765625 = 0.0557.

f) It would depend on the context and the specific definition of "unusual." If the expected number of brown-eyed children is 0.75 x 6 = 4.5, then having only 2 out of 6 children with brown eyes is below average. However, the probability of this exact outcome can be calculated using the binomial distribution with n = 6 and p = 0.75:

P(k=2) = (6 choose 2) x \(0.75^2 x (1 - 0.75)^4\) = 0.0986

where (6 choose 2) = 6!/(2!4!) = 15 is the number of ways to choose 2 children out of 6. This probability is not very low (less than 10%), so it might not be considered unusual in a statistical sense.

To know more about probability, visit

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