ALGEBRA 2 HELP


(Please show work!)


A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)


a. Describe and correct the error in the notation.


b. Evaluate the corrected summation of the arithmetic series above.

[tex]S_8=[/tex]


c. Write the explicit and recursive formulas for the arithmetic series above,

Explicit:
[tex]a_n=[/tex]

Recursive:
If [tex]a_1=[/tex]

Then for n > 1

[tex]a_n=[/tex]

Geometric relationships refer to the ways in which different geometric figures or objects are related to each other. These relationships can include measures of angles,lengths of sides or edges, areas, volumes, and other properties.

Some common geometric relationships include:

These are just a few examples of the many geometric relationships that can be studied in mathematics. Understanding these relationships can help us solve problems, make predictions, and create new designs or structures.

The supply of average eggs is decreasing at a rate of approximately -550 cartons per week as the price decreases 7 cents per carton per week.

The equation given states that the weekly supply x (in thousands of cartons) of a certain brand of medium-sized eggs is related to the wholesale price p (in dollars/carton) by the following equation: 625p2 − x2 =100. In order to determine the rate at which the supply is changing, we must first calculate the value of p when x = 37,000, which is the number of cartons available at the beginning of the week. To do this, we can solve the equation for p when x = 37,000[tex]p = (100 + x2)1/2/625[/tex]. When x=37,000, p=3.65. Therefore, if the price is falling at the rate of 7¢/carton/week, then the new price p = 3.65 - 0.07 = 3.58. When we plug this new value of p into the supply equation, we get[tex]x^2[/tex] = 4,225. Taking the square root of both sides gives us x = 65. Therefore, the supply is decreasing at a rate of approximately -550 cartons per week as the price decreases 7 cents per carton per week.

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The square root of the difference between the square of thirteen and the square of twelve by first calculating the squares of 13 and 12 is 5.

First, we need to find the square root of thirteen and the square of twelve. The square of a number is the number multiplied by itself. So, [tex]$13^2$[/tex] means [tex]$13$[/tex] multiplied by itself and [tex]$12^2$[/tex] means [tex]$12$[/tex] multiplied by itself.

[tex]$13^2[/tex] = 13 \times 13 = 169

[tex]$12^2[/tex] = 12 \times 12 = 144

Next, we need to find the difference between the square of thirteen and the square of twelve by subtracting the smaller number from the larger one.

169 - 144 = 25

Finally, we take the square root of the difference to find the solution. The square root of a number is the value that, when multiplied by itself, gives the original number.

[tex]\sqrt{25} = 5[/tex]

Therefore, the square root of the difference between the square of thirteen and the square of twelve is 5.

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 900\\ P=\textit{initial amount}\dotfill &700\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\\\ \end{cases} \\\\\\ 900 = 700(1 + 0.06)^{t} \implies 900=700(1.06)^t[/tex]

Answer: X-intercept: (38/7, 0)

Y intercept: (0, -38)

Step-by-step explanation:

To find X-intercept(s), substitute in 0 for y and solve for x

(0)−4=7(x−6) Solve the equation

rewrite the equation as: 7 (x-6) = (0) -4

subtract 4 from 0: 7 (x-6) = -4

Divide each term in 7 (x-6) = -4 by 7 and simplify

x-6= -4/7

Move all terms not containing x to the right side of the equation.

x= 38/7

X-intercept(s) in point form.

X-intercept(s): (38/7,0)

Sry cant upload a photo to save my life (for y-intercept(s):)

Answer:

the a give the x value twords the b and adds up the equation

Answer:

Step-by-step explanation:

I think to get the height is length x width

for distance you need to so SOH CAH TOA

By using a counting method, the driver can keep track of how many passengers have boarded the van, and by measuring the distance driven, they can update the odometer.

The formula for calculating the total number of passengers that can board a shuttle van is:

Total Passengers = Number of Seats in the Van - 1 (Driver)

For example, if the van has 10 seats, the total number of passengers that can board the van is 9 (10 - 1).

To keep track of how many passengers have boarded the van, we can use a simple counting method. Each time a passenger boards the van, the counter should be increased by 1. When the counter reaches the maximum number of passengers the van can hold, the driver should not allow any more passengers to board.

To update the odometer, the driver can measure the distance the van has driven since the last update. This can be done by using a GPS device or by measuring the distance between two points on a map. The total number of miles driven since the last update can then be added to the previous odometer reading to find the new odometer reading.

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The New York station and the Boston station are 280 miles apart. The trains will pass each other 2 hours after 3:00 pm, which is at 5:00 pm.

Distance is the separation between two points or things. It has magnitude but no direction because it is a scalar quantity. Typically, it is measured in terms of distances like metres, kilometres, feet, and miles.

Let's assume that the trains meet at time t hours after 3:00 pm. In this time, the freight train will travel a distance of 80t miles, and the passenger train will travel a distance of 60t miles. The total distance covered by both trains will be the sum of these distances, which is 80t + 60t = 140t miles.

We know that the total distance between the two stations is 280 miles. Therefore, we can write an equation based on the distance covered by both trains:

80t + 60t = 280

Simplifying this equation, we get:

140t = 280

Dividing both sides by 140, we get:

t = 2

This means that the trains will pass each other 2 hours after 3:00 pm, which is at 5:00 pm.

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It is likely that it will take Jacob more time to plant the perennials than the annuals.

Time is an abstract concept that is not tangible and cannot be seen, touched, or heard. It is a measure of the passage of events and is used to set and track schedules, create goals, and even measure the lifespan of an individual. Time is a precious commodity that cannot be replaced or taken back. Once it has passed, it is gone forever. Time is also a powerful force that can bring us joy and sorrow, success and failure. It is a constant reminder of how quickly our lives can change and how important it is to make the most of every moment.

Perennials require more attention when planting because they have a longer lifespan and are meant to come back year after year. Annuals, on the other hand, only last for one season. Therefore, they require less attention when planting. Jacob will need to make sure that he carefully places the perennials in the soil, as well as taking care to not damage the roots. He may also need to take extra time to trim any overgrowth from the plants. This extra care and attention will likely take more time than it would to plant the annuals.

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If the fire department brought a 35-foot ladder, Can they save the family: = √(325) feet. And They can't save family because √400  > √325

Given that :- height - 30 feet , ladder - 35 feet

[tex]AC^2 = AB^2+ BC^2[/tex]

BC =  √([tex]AC^2-AB^2[/tex])

     = √([tex]35^2 -30^2[/tex])

     = √( 1225 - 900)

     = √(325) feet

but the fire department must be so face from the bream of the building

  20 = √[tex](20)^2[/tex]

= √400 > √325

They can't save family because √400  > √325

Pythagorean theorem, the notable mathematical theorem that the amount of squares on the legs of a right triangle is equivalent to the square on the hypotenuse (the side inverse the right point) — or, in recognizable logarithmic documentation, a2 + b2 = c2.

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Answer:

a = 21, b = 70, c = 89

Step-by-step explanation:

opposite angles of intersecting lines are the same, 21 = 21

adjacent angles of intersecting lines add up to 180, 180 - 110 = 70

angles of a triangle add up to 180, 180 - 70 - 21 = 89

Answer:

a = 21, b = 70, c = 89

Step-by-step explanation:

Answer:

Step-by-step explanation:

The initial value, a, is 350, and the growth rate, b, is 1.75 so this is an exponential growth function.

a. the factors of equation is [tex]f(x)=(x-1)(x-10)(2x-3)[/tex]

b. the factors of equation is [tex]f(x)=(x-1)(x^2+x+4)[/tex]

A polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, with non-negative integer exponents.

a. Given function,

[tex]f(x)=2x^3 -25x^2 + 53x - 30[/tex]

By using trial and error method, put values of x =1, x= 10, and x= 3/2 are satisfied values for above function,

[tex]f(x)=(x-1)(x-10)(2x-3)[/tex]

therefore, the factors of equation is (x-1) (x-10) (2x-3)

b. Given function,

[tex]f(x)=x^3 +3x - 4[/tex]

Similarly using trial and error method,

[tex]f(x)=(x-1)(x^2+x+4)[/tex]

therefore, the factors of equation is (x-1) (x² + x + 4)

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Factor of given polynomials are a. (x-1)(x-10)(2x-3), b. (x-1)(x² + x + 4) .

In mathematics, a polynomial is an expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, but not division by a variable. The variables in a polynomial can only have non-negative integer exponents.

Polynomials can have different degrees, which is the highest power of the variable in the expression. For example, the polynomial 3x² - 5x + 2 is a quadratic polynomial, since its highest power of x is 2. If the degree of a polynomial is n, then it has at most n roots, which are the values of x that make the polynomial equal to zero.

Polynomials are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are used to model and analyze many different types of phenomena, such as motion, population growth, and electrical circuits.

Polynomials can also be added, subtracted, and multiplied together to form new polynomials. Additionally, polynomials can be factored, which involves breaking them down into simpler polynomials that multiply together to give the original polynomial.

a) f(x)= 2x³ - 25x² + 53x - 30
⇒(x-1)(x-10)(2x-3)

b) f(x)= x³ + 3x - 4
⇒(x-1)(x² + x + 4)

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The complete question is:

Answer: 12=7

Step-by-step explanation: add one side ten add the other

Yes, this is a solution because the point(s) at which all the lines intersect are the solutions to the system.

x = 7/3.

To solve this equation, you need to first simplify the left side of the equation. The left side of the equation can be simplified to -3/(2x). Then, you can set the two expressions equal to each other and solve for x.

-(3)/(2x) = (1)/(6x)

-(6x)/(2x) = (1)/(6x)

-3 = 1

-2 = 1

Therefore, x = 7/3.

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If the perimeter is 27 yards, then the length of the other side of the rectangle is 3.5 yards.

Let's start by defining our variables. Let x be the length of one side of the rectangle (in yards), and let y be the length of the other side. We know from the problem statement that one side is three yards longer than twice the length of the other side, so we can express this algebraically as:

x = 2y + 3

The perimeter of a rectangle is given by the formula P = 2(x + y), so we can substitute our expression for x into this formula:

P = 2(2y + 3 + y) = 2(3y + 3) = 6y + 6

We are given that the perimeter of the rectangle is 27 yards, so we can set up an equation:

6y + 6 = 27

Solving for y, we can subtract 6 from both sides and then divide by 6:

6y = 21

y = 3.5

To check our answer, we can plug it back into our equation for x:

x = 2y + 3 = 2(3.5) + 3 = 7 + 3 = 10

So the other side of the rectangle is 10 yards long. We can verify that the perimeter is indeed 27 yards:

P = 2(x + y) = 2(10 + 3.5) = 2(13.5) = 27

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Complete question is:

One side of a rectangle is three yards longer than twice the length of the other side. If the perimeter is 27 yards, what is the length of the other side?

Answer:

its 240

Step-by-step explanation: 10 x 8 x 3 = 240 :)

Answer:

a) Volume= length x width x height  v=l x w x h

b) 240 cm^3 (cm cubed)

Step-by-step explanation:

Substitute into this formula

v=l x w x h

 10 x 8 x 3 = 240

So 240 cm^3 (cm cubed)

Important note: Remember to include units, as they may not be given to you in the exam

Answer:Factorise. 15(k+g)² - 20 (k+g)​

Step-by-step explanation:=[15(k+g)-20] (k+g)

                                            =15 k²+15kg-20k+15kg+15g²-20g                                                  

                                            =15k²+15g²+30kg-20k-20g

The probability the chosen volunteer does not possess yq 77 is 0.655 (nearest to three decimal places).

Given information: One of the volunteers whose sam 77 test result was positive will be chosen at random.

To find: The probability the chosen volunteer does not possess yq 77.

Let P(Y) be the probability that a volunteer possesses yq77 and P(Y') be the probability that a volunteer does not possess yq77. It is given that out of 150 volunteers, 77 tested positive for SAM.

Therefore, the probability of testing positive for SAM is:

P(SAM) = number of volunteers who tested positive for SAM / total number of volunteers= 77/150

Now, using the probability law of total probability, we can find the probability of a volunteer not possessing yq77, as follows:

P(Y') = P(Y'|SAM) P(SAM) + P(Y'|SAM') P(SAM')

It is given that yq77 is found in 60% of volunteers who tested positive for SAM, and in 30% of those who did not test positive for SAM.

Therefore:

P(Y'|SAM) = 0.6, P(Y'|SAM') = 0.3

Now, substituting the given values in the equation,

P(Y') = (0.6 × 77/150) + (0.3 × 73/150)≈ 0.655

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The correct decision rule for a test hypothesis with a significance level of 0.02, with two tails, is given as follows:

C. Reject H0 if Zstat< -2.33 or Zstat > +2.33.

The decision regarding the null hypothesis depends on if the p-value is less or more than the significance level:

For a two-tailed test with a significance level of 0.02, the critical value is given as follows:

z = 2.33.

Hence the decision rule is given as follows:

Hence option C is the correct option for this problem.

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Option D. 12x + 6y = 10, -4x - 6y = -16. To eliminate y from the system of equations, we need to multiply one or both equations by a constant so that the coefficients of y have opposite signs.

Then we can add or subtract the equations to eliminate y.

We can do this by multiplying one or both equations by a constant that will make the coefficients of y add to zero. The goal is to create additive inverses of the coefficients of y in the two equations.

Looking at the two equations:

12x + 6y = 10

2x + 3y = 8

We can see that the coefficients of y are 6 and 3. To eliminate y, we need to find a common multiple of 6 and 3 that will make the coefficients of y additive inverses of each other. The least common multiple of 6 and 3 is 6, so we can multiply the second equation by -2 to get:

-4x - 6y = -16

Now we can add this equation to the first equation to eliminate y:

12x + 6y = 10

(-4x - 6y = -16)

8x = -6

Therefore, the correct pair of equations after multiplying to eliminate y is:

12x + 6y = 10

-4x - 6y = -16

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Answer:

Answer and Explanation below

Step-by-step explanation:

You can get 50 ounces of yogurt with a $15 gift card

Divide 15 by 2.40 ounces should equal 6.25 then multiply by 8 because those are the starting ounces answer is 50

The length of the rectangular prism is 1 inch.

The volume of a rectangular prism can be calculated using the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, the volume of the prism is given as 1 cubic inch and the width and height are given as 1 inch and 1 inch, respectively. To solve for the length of the prism, we can rearrange the equation to l = V/wh. Plugging in our given values, we can calculate the length of the prism as l = 1/1 x 1 = 1 inch. Thus, the length of the rectangular prism is 1 inch.Therefore, the length of the rectangular prism is 1 inch.

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The equation that shows the relation ship between t and p is 0 ≤ t < 270.

A linear equation is an algebraic equation where the highest power of the variable is 1, and the equation represents a straight line when graphed.

Break down the information given in the problem to form an equation that relates the time t and the number of yards of painted fence p:

Tom painted 8 yards before running away, so Sid had to paint the remaining length of the fence, which is L - 8 yards, where L is the total length of the fence.

From noon to 12:30 p.m., Sid painted 14 - 8 = 6 yards.

From 12:30 p.m. to 2:00 p.m., Sid painted 32 - 14 = 18 yards.

From 2:00 p.m. to 2:30 p.m., Sid painted 38 - 32 = 6 yards.

We want to find an equation that relates the time t (in minutes) to the number of yards of painted fence p.

Based on the information above, we can create a piecewise equation that relates t and p:

p = { 8 + 0.2t, 0 ≤ t < 30

14 + 0.6(t - 30), 30 ≤ t < 90

32 + 0.4(t - 90), 90 ≤ t < 150

38 + 0.2(t - 150), 150 ≤ t < 210 }

Explanation of the equation:

The first segment of the piecewise equation, 8 + 0.2t, represents the yards of fence painted by Tom (8) plus the yards painted by Sid in the first 30 minutes (0.2t), where 0 ≤ t < 30.

The second segment, 14 + 0.6 (t - 30), represents the additional yards painted by Sid between 12:30 p.m. and 2:00 p.m., where 30 ≤ t < 90. The expression (t - 30) represents the time elapsed since 12:30 p.m., and the coefficient 0.6 represents the rate at which Sid is painting the fence in yards per minute during this period.

The third segment, 32 + 0.4 (t - 90), represents the additional yards painted by Sid between 2:00 p.m. and 2:30 p.m., where 90 ≤ t < 150. The expression (t - 90) represents the time elapsed since 2:00 p.m., and the coefficient 0.4 represents the rate at which Sid is painting the fence in yards per minute during this period.

The fourth segment, 38 + 0.2 (t - 150), represents the additional yards painted by Sid between 2:30 p.m. and 4:30 p.m., where 150 ≤ t < 210. The expression (t - 150) represents the time elapsed since 2:30 p.m., and the coefficient 0.2 represents the rate at which Sid is painting the fence in yards per minute during this period.

Note that we have limited the time t to be between noon and 4:30 p.m., which corresponds to 0 ≤ t < 270.

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Step-by-step explanation:

We can use the formula for pressure:

pressure = force/area

We know the pressure and the area, so we can rearrange the formula to solve for the force:

force = pressure x area

Plugging in the values, we get:

force = 180 N/m² x 0.03 m² = 5.4 N

Therefore, the force that the brick exerts on the table is 5.4 N

on using  disjunctive syllogism to derive Q from the second premise and the derived value of A. if P is true, then Q must also be true..

In logic, a compound statement is made up of two or more simple statements, known as premises or assumptions, that are combined using logical operators such as "and," "or," and "not." To prove a compound statement, we use rules of inference to derive a conclusion based on the given premises.

In the first proof question, we are given three premises: P, P or R, and not S or A. We need to prove the statement Q using these premises. To do so, we use the disjunctive syllogism rule, which states that if one of two disjunctive statements is false, then the other must be true. By assuming ~P, we derive ~S from the third premise using the rule of disjunction. Then, using modus ponens, we derive A from the assumption of ~P and the third premise. Finally, we use disjunctive syllogism to derive Q from the second premise and the derived value of A.

In the second proof question, we are given three premises: not P or S, not S, and R or Q. We need to prove the statement P implies Q using a conditional world proof. We assume P is true and derive S using the first premise. Using the second premise and modus tollens, we derive not R. Finally, using disjunctive syllogism, we derive Q from the third premise and the derived value of not R. Therefore, we show that if P is true, then Q must also be true..

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The count of TV to be sold to give the maximum profit are 24 and 48, respectively

The objective function is given as

P(n, m) = 175b + 205m

The constraints, and their evaluated values are given as

P(0, 0) =175(0) + 205(0) = 0

P(0, 64) =175(0) + 205(64) =13,120

P(24, 48) =175(24) + 205(48) =14,040

P(72, 0) =175(72) + 205(0) = 12,600

From the above computations, we have the maximum value to be

Maximum = 14040

These values are at

b = 24 and m = 48

Hence, the number of TV to be sold are 24 and 48, respectively

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