Use your knowledge about parentheses and substitution to solve the following:

q = 1; r = 2; s = 3; t = 4; x = 5; y = 6

7. 2(x + 4) + 10 =

8. 3(6x) + 4 =

9. 10(xy) =

10. 5(x + y) =

11. 2(rs) + 4(x)

12. 2(q) + 2(x + t) =

13. 6(7t + 4s) =

14. 9(10x) + 10y =

15. 2x(xy) =

16. r(s)(t) =

17. (r)(s)(t)(x)(y) =

18. (7x + 2Y) =

Answer:

900

Step-by-step explanation:

\(I=Prt=(9000)(0.02)(5)=900\)

The two best examples of long-term needs that people need to save for includes:

This refer to those needs that one will be will be needing in the future or for a very long time.

The need to saving up for college is important if one want to have a bright future or a better salary.

The need to saving up for medical emergencies is also crucial because we're all human beings who, at some point, will deteriorate physically.

Therefore, the Option A and C is correct,

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The missing measurements of the triangle given include:

The value of angle B can be found thanks to the knowledge that the interior angles of a triangle add up to 180 degrees and we have two of the angle measurements :

= 180 - angles measurements

= 180 - 27 - 90

= 63 degrees

The value of AB can be found by using the Sin theta operation such that:

Sin theta = Opposite / hypotenuse

Sin ( 27 degrees ) = 12 / hypotenuse which is AB

hypotenuse = 12 / ( Sin ( 27 degrees ))

= 26 .4 units

The value of AC measurement is:

Tan ( 27 degrees ) = 12 / AC

AC = 12 / Tan ( 27 degrees )

AC = 23. 6 units

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Answer:

-4,-3

Step-by-step explanation:

Answer: I can't see the 4th answer but i and going to guess it's (-4,-3).

I think you answer is D. (-4,-3).

I hope it's right

The sequence of transformations that will map figure H onto figure H' is: Option B:  the rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6.

We are given the coordinates of the hexagon as:

Points of Hexagon H  →  (2,2), (2,6), (6,7), (8,6), (8,2), (6,1)

Points of Hexagon H' →  (2,-8), (2,-4), (4,-3), (8,-4), (8,-8), (4,-9)

The steps that can be used to transform the hexagon H into hexagon H' are:

Step 1 - Translate the hexagon in the positive x-axis direction by a factor of 10.

Step 2 - Translate the graph obtained in the above step by factor 2 in the downward direction.

Step 3 - Rotate the graph obtained in the above step 180 degrees about the origin.

Step 4 - Then take the reflection of the graph obtained in the above step about y = -6. The resulting graph shows the graph of Hexagon H'.

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Answer:

14 is 269000-2500=266500

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

In each one, they add two arrows that are to the right as much as they possibly can be

Answer:

c

Step-by-step explanation:

1. We can asume that a = 2, b = 4. Then solve and find which option matches with the answer.

2. Equation itself plugged in with a = 2, and b = 4. 2^2 + 2 x 2 x 4 + 4^2 = 36 / (2 + 4)^3

3. 36 / 216 = 1/6

Find any option that matches your answer and plug in a for 2 and b for 4.

a. a + b = 2 + 4 = 6 - No doesn’t match 1/6

b. a^2 + b^2 = 2^2 + 4^2 = 4 + 16 = 20 - No doesn’t match 1/6

c. 1 / a + b = 1 / 2 + 4 = 1/6 - Yes does match 1/6

d. 1 / (a + b)^2 = 1 / (2 + 4)^2 = 1/36 - No doesn’t match 1/6

The subshell designated by each set of quantum numbers is as follows:

a) n=3, l=1 -> 3p subshell

b) n=4, l=2 -> 4d subshell

c) n=2, l=0 -> 2s subshell

d) n=5, l=3 -> 5f subshell

In the electron configuration of an atom, each electron is described by a set of four quantum numbers, which includes the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). The second quantum number (l) determines the shape of the subshell, which in turn influences the energy level and chemical behavior of the atom. The letter designation for each subshell is based on the value of the angular momentum quantum number (l): s (l=0), p (l=1), d (l=2), f (l=3), and so on. Therefore, for a given set of quantum numbers, we can determine the subshell designation by identifying the value of l.

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When x = π/2, the rate at which x is changing can be calculated by using the chain rule. The rate at which x is changing is equal to \(-5e^{(-sin(\pi /2))\), or -5.

We are given that \(y = 2e^{cos(x)\) and that y is increasing at a constant rate of 5 units per second. To find the rate at which x is changing when x = π/2, we need to differentiate y with respect to time using the chain rule.

Using the chain rule, we differentiate \(y = 2e^{cos(x)\) as follows: dy/dt = dy/dx * dx/dt. Since we know that dy/dt is 5 units per second, we can rewrite the equation as 5 = dy/dx * dx/dt.

To find dx/dt when x = π/2, we substitute x = π/2 into the equation. Now we need to find dy/dx. Taking the derivative of \(y = 2e^{cos(x)\) with respect to x, we get \(dy/dx = -2e^{cos(\pi /2)} sin(\pi /2)\)

Substituting x = π/2 into dy/dx, we have \(dy/dx = -2e^{cos(\pi /2)} sin(\pi /2)\). Since cos(π/2) = 0 and sin(π/2) = 1, we can simplify dy/dx to -2e⁰ * 1 = -2.

Finally, we can rearrange the equation 5 = dy/dx * dx/dt and substitute dy/dx = -2 to solve for dx/dt. We get -2 * dx/dt = 5, which implies dx/dt = -5/2 or -2.5.

Therefore, when x = π/2, the rate at which x is changing is -2.5.

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Answer:

3. < ACB=<DCE

Step-by-step explanation:

Both are vertical angles & they are equal

Answer:

C) -180

Step-by-step explanation:

65 + 54 + 43 + 32 + 21 + 10 - 1 - 12 - 23 - 34 - 45 - 56 - 67 - 78 - 89 = -180. Hope this helps!

Answer:License plate numbers in certain state consists of seven characters: The first character is digit (0 through 9) The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore; license plate number in this state can be any string - of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit How many license plate numbers are possible if no digit appears more than once?

Step-by-step explanation: i don't know rm

The cournot theory of oligopoly is based on the assumption that each firm believes that rivals will keep their output constant if it changes its output.

The Cournot theory of oligopoly is an economic model that analyzes the behavior of firms in an oligopolistic market structure. It is named after the French economist Antoine Augustin Cournot.

In the Cournot model, each firm in the market assumes that its rivals will keep their output constant if it changes its own output. This assumption is based on the idea that firms make strategic decisions regarding their production levels, taking into account the likely responses of their competitors.

Under the Cournot model, firms choose their output levels simultaneously, considering the current market conditions and their expectations of how their competitors will react. Each firm acts as a quantity-setter, determining its production quantity based on its own cost structure, market demand, and beliefs about how its rivals will behave.

The assumption that rivals will keep their output constant if one firm changes its output is a simplification used in the Cournot model. It implies that firms do not engage in immediate or aggressive reactions to changes in their competitors' output levels. Instead, they make decisions based on the expectation that their rivals' production decisions will remain unchanged.

By making these assumptions, the Cournot model allows economists to analyze the equilibrium outcomes and market shares that arise in oligopolistic markets. It provides insights into how firms' interdependent behavior affects prices, quantities, and overall market outcomes.

It is important to note that the Cournot model is a simplified representation of real-world oligopoly markets, and the actual behavior of firms may deviate from these assumptions. Nonetheless, the model serves as a useful tool for understanding strategic interactions among firms in oligopolistic industries.

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The provided expression "\(-20x^2√(4-x^2)\) dx" seems incomplete or incorrect. Please provide the correct equations or additional details to proceed with the evaluation of the integrals.

What is Trigonometric substitution?

Trigonometric substitution is a technique used in calculus to simplify and solve integrals involving radical expressions, especially those containing square roots. It involves making a substitution using trigonometric identities to transform the integral into a form that can be more easily evaluated.

To set up and evaluate the integrals for finding the area (A), moment about the x-axis (Mx), and moment about the y-axis (My) for the given region bounded by the graphs, we need to follow the steps:

Step 1: Determine the limits of integration based on the given region.

The region is bounded by the graphs of y = 1 and y = 0, and the x-values are between 1 and 3. Therefore, the limits of integration for x are from 1 to 3.

Step 2: Set up the integral for the area (A).

The area (A) can be calculated by integrating the difference in the y-values (1 - 0) over the given interval:

A = ∫[1 to 3] (1 - 0) dx

Step 3: Set up the integrals for the moments Mx and My.

The moments Mx and My can be calculated by integrating the product of the y-value and x-value squared over the given interval:

\(Mx = ∫[1 to 3] y * x^2 dx\)

My = ∫[1 to 3] y * x dx

Step 4: Evaluate the integrals.

To evaluate the integrals, we need additional information or equations defining the relationship between x and y. The provided expression \("-20x^2√(4-x^2) dx"\)seems incomplete or incorrect. Please provide the correct equations or additional details to proceed with the evaluation of the integrals.

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Answer:

Step-by-step explanation:

If you want to know what you have to multiply by 5 to get a product of 70, you would divide 70 by 5 to get that other number. Because 70 divided by 5 is 14, you know that the other number is 14. It's the same when you have one factor of a polynomial and want to know the other. You divide your polynomial by the one factor to get to the other factor, because when you multiply them together, you get back the polynomial you started with. Like when we found that 70 / 5 = 14, we know that when we multiply 14 by 5 we'll get the 70 we started with.

Long division of polynomials will be difficult to illustrate within this forum, but I'll do my best. What we want to do is divide \(6x^2+x-15\) by 2x - 3:

          __________

2x - 3 | \(6x^2+x-15\)

First divide the 6 x-squared by the 2x (forget about the rest of what's inside the box for now, and also forget about the -3 for now. We'll deal with them later).  2x goes into 6 x-squared 3x times, because 2x * 3x = 6x-squared, right? So the 3x goes above the 6x-squared:

           3x_______

2x - 3 | \(6x^2+x-15\)

Now we multiply the 3x by the 2x and put that product under the 6x-squared. The product is 6x-squared (which will always be the case in division that they will subtract each other away. That's why we do this!)Then multiply the 3x by the -3 which is -9 and put that under the "+x" term:

           3x________

2x - 3 | \(6x^2+x-15\)

           6x^2-9x        

At this point we change the signs and have

            3x                

2x - 3   | 6x^2 + x - 15

          -  6x^2 +9x

And then we add and bring down the -15:

           3x                  

2x - 3 | 6x^2  + x - 15

         - 6x^2 + 9x

                       10x - 15

Now do the division process again, this time dividing 10x by 2x (again the -3 will wait). 10x divided by 2x is 5 (because 2x * 5 = 10x, right?). The 5 goes above the +x on top:

           3x    +   5      

2x - 3 | 6x^2 +  x - 15

        -  6x^2 + 9x

                       10x - 15

Now we wwill multiply the 5 by both the 2x and the -3 and subtract:

           3x     +  5    

2x - 3 | 6x^2 +  x - 15

         - 6x^2 + 9x

                       10x - 15

                     - 10x + 15

Notice that when we subtracted, the 10x changed from + to -, and the -15 changed to a positive. The remainder is 0.

That tells us that the other factor of the polynomial is 3x + 5. You could also have done synthetic division, but it would be more difficult than this to illustrate because you would be dividing by 3/2.  :/  

Yesterday, 5 more rooms were occupied than today.

The number of occupied rooms is obtained applying the proportions in the context of the problem.

Yesterday, the number of rooms occupied was given as follows:

4/5 x 100 = 0.8 x 100 = 80 rooms.

Today, the number of rooms occupied is given as follows:

3/4 x 100 = 0.75 x 100 = 75 rooms.

80 > 75, and the difference is given as follows:

80 - 75 = 5.

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Answer:

They are proportional

Step-by-step explanation:

Solve by cross multiplication :)

Since we have 2/5 & 20/50, we multiply 2 by 50 and 5 by 20.

2 ✕ 50 = 100

5 ✕ 20 = 100

I hope this helped!

Answer:

176 of 12% vinegar

44 of 7% vinegar

Step-by-step explanation:

Percentage vinegar required = 11%

Volume = 220 mL

First brand % = 7%

Second brand % = 12%

Let p = volume of 12% vinegar material

Mixture :

0.12p + 0.07(220 - p) = 220 * 0.11

0.12p + 15.4 - 0.07p = 24.2

0.05p = 8.8

p = 8.8 / 0.05

p = 176

176 of 12% vinegar and

220 - 176 = 44

44 of 7% vinegar

Answer:

i would need to see all four to be able to answer ?

Step-by-step explanation:

Answer:

x= 17

HJ= 27

JK= 153

HK= 180

Step-by-step explanation:

If HJ=x+10

JK=9x

KH=14x−58

a) Draw a sketch of the segments described above

Find attached to this answer the diagram of the sketch of the segments described above

b) Write an equation using the segment addition postulate that will help you solve the problem

HJ + JK = KH

x + 10 + 9x = 14x - 58

c) combine like terms ( x terms on one side of the equal sign and numbers in the other side of the equal sign) x + 10 x + 10 + 9x = 14x - 58

10 + 58 = 14x - x -9x

68 = 14x - 10x

68 = 4x

x = 68/4

x  = 17

d)

x= 17

HJ= x + 10

= 17 + 10

= 27

JK= 9x

= 9 × 17

= 153

HK=14x −58

HK = 14 × 17 - 58

= 238 - 58

= 180

The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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A rule which best describes this transformation is: A. (x,y) → (x, -y).

Generally, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection over the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative. Therefore, a reflection over the x-axis is given by this rule (x, y) → (x, -y).

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Complete Question:

Pentagon VWXYZ is shown on the coordinate grid. A student reflected pentagon VWXYZ across the x-axis to create pentagon V’W’X’Y’Z’.

Which rule describes this transformation?

A. (x,y) → (x, -y)

B. (x,y) → (x, y+8)

C. (x,y) → (-y, x)

D. (x,y) → (-x, y)

Answer:

2nd option

Step-by-step explanation:

Using the sine ratio in the right triangle

sin32° = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AC }\) = \(\frac{BC}{6}\) ( multiply both sides by 6 )

6sin32° = BC

The statement is True. Since $n^2(1+\sqrt{n})$ is neither $o(n^2 \log n)$ nor $\omega(n^2 \log n)$, we can conclude that $n^2(1+\sqrt{n}) \neq O(n^2 \log n)$.

Problem 5: The statement $\sqrt{n} = O(\log n)$ is False.

To determine whether $\sqrt{n}$ is big-O of $\log n$, we need to consider the growth rates of both functions.

As $n$ approaches infinity, the growth rate of $\sqrt{n}$ is slower than the growth rate of $\log n$. This is because $\sqrt{n}$ increases as the square root of $n$, while $\log n$ increases at a much slower rate.

In big-O notation, we are looking for a constant $c$ and a value $n_0$ such that for all $n \geq n_0$, $\sqrt{n} \leq c \cdot \log n$. However, no matter what constant $c$ we choose, there will always be a value $n$ where $\sqrt{n}$ surpasses $c \cdot \log n$ in terms of growth rate. Therefore, $\sqrt{n}$ is not big-O of $\log n$, and the statement is False.

Problem 6: The statement $n^2(1+\sqrt{n}) \neq O(n^2 \log n)$ is True.

To prove this, we can make use of the fact that if $f(n) = o(g(n))$, then $f(n) \neq \Omega(g(n))$, and if $f(n) = \omega(g(n))$, then $f(n) \neq O(g(n))$.

First, let's simplify $n^2(1+\sqrt{n})$:

$$

n^2(1+\sqrt{n}) = n^2 + n^{5/2}

$$

Now, let's compare it with $n^2 \log n$. We can see that the term $n^{5/2}$ grows faster than $n^2 \log n$ as $n$ approaches infinity. This implies that $n^2(1+\sqrt{n})$ is not big-O of $n^2 \log n$.

Since $n^2(1+\sqrt{n})$ is neither $o(n^2 \log n)$ nor $\omega(n^2 \log n)$, we can conclude that $n^2(1+\sqrt{n}) \neq O(n^2 \log n)$.

Therefore, the statement is True.

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Attached is the pedigree. I found this exercise on the Internet.

The probability that both john and sue are carriers is:

The missing characters are: II-5, II-6, II-8, III-10, III-11, III-12, III-13.

Individual II-5 will have half black/half white squares. It's a square because it shows in the book that John's grandmother (I-2) fell ill.

Half black/half white transmits an allele that requires the disease allele because his mother has the disease, and his father does not carry or show the disease, so from him, John's father (II-5) only got one. normal allele.

The person will ask II-6 questions in a circle. A circle because John's mother once father is Example II-5. Since she has a daughter (John's Sister) with the disease, it means that John's sister inherited both alleles for the disease.

The Personal II-8 will have a half-black/half-white circle.

Circle because Sue's mother and father Probability Example II-7 (square). Half black/half white transmits an allele that requires the disease allele because her father has the disease, and her mother does not carry or show the disease, meaning she is from her, Sue's mother (II-8). take an old allele.

The person will ask the III-10 questions in a circle. The circle is because she is John's sister mentioned in the text. The question mark is that we can't be sure if this is an allele.

We know from the records that he has no symptoms of the disease, but if his mother is infected with only one allele, he may have inherited an allele from his father or mother, or he will inherit the disease allele. The disease allele comes from the mother, not from the father if the mother has the disease.

John, There will be questions in the People III-11 box. Square because John is a man. The question mark is that we can't be sure if this is an allele. We know from the literature that he has no symptoms of the disease, but if his mother is a carrier of only one of the disease alleles, he may have inherited the disease allele from his father. disease allele. If her mother has a disease, it is not from her father, but from her mother.

SU will have questions in the Humans III-12 circle. Circle it because she's Sue, the woman. The question mark is that we can't be sure if this is an allele. From the instructions, we learn that he has no symptoms of the disease, but that he may have inherited the disease allele from his mother, and that after his mother has the disease allele, he too can be a carrier or transmit the disease to others. The disease allele has inherited the normal allele from its mother. He inherited only one normal allele from his father.

III-13 individuals will have questions in the square. A square because according to the guide, he is Su's brother. The question mark is that we can't be sure if this is a disease allele. We know from the records that she did not show any signs of the disease, but she probably inherited the disease allele from her mother, and when her mother has the disease allele, she will also be a carrier or inherited. original allele from its mother. He inherited only one normal allele from his father.

Complete Question:

John and sue are expecting a child, but are concerned about a rare autosomal recessive disease that is present in both of their families. in the pedigree below, john is represented as individual iii-11 and sue is represented as individual iii-12. john\'s sister, iii-10, and sue\'s brother, iii-13, both do not show evidence of the disease, but john\'s paternal grandmother and sue\'s maternal grandfather both had the disease. assign the appropriate symbol to each individual in the pedigree. what is the probability that john is a carrier? probability: 66.7 % what is the probability that both john and sue are carriers?

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The equation of the known line is

y = 3/4x

The slope intercept equation of a line is expressed as

y = mx + c

where

m represents slope

c respresents y intercept

By comparing with the given equation, slope, m = 3/4

If two lines are parallel, it means thta they have the same slope. Therefore, the slope of the para;llel line is 3/4

Given that the line parallel to this line passes through (3, 3), we would determine the y intercept, c of this line by substituting x = 3, y = 3 and m = 3/4 into the slope intercept equation. it becomes

3 = 3 * 3/4 + c

3 = 9/4 + c

c = 3 - 9/4 = - 3/4

Therefore, the equation of the line is

y = 3x/4 - 3/4

Answer:

44 days

Step-by-step explanation:

165 divided by 3 3/5 (3.75)

stream Why Not? by Loona :D

The remainder when 2x² - 5x - 1 divided by x - 3 is (2x + 1)

Let p(x) represents a polynomial  2x² − 5x − 1 and m(x) represents a polynomial x - 3

i.e., p(x) =  2x² − 5x − 1

and m(x) = x - 3

we need to find the remainder when 2x² − 5x − 1 divided by x − 3

If we divide a polynomial  p(x) =  2x² − 5x − 1  by m(x) = x - 3 using polynomial long division method, the result is:

p(x) / m(x)

= ( 2x² - 5x - 1 ) ÷ (x - 3)

= [ ( 2x² - 5x - 1 ) × ( 2x + 1)] + 2

This means, the quotient is  ( 2x + 1) and the remainder is 2

(see in attachment)

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