please help help help help !!!!! ASAP

Factorise

3у^2 - 54y + 243​

bought for $180000 in 2002

sold it in 2014

180000*2.44\100

(a) The exact value of sinh (log(3) - log(2)) is 5/8.

To calculate sinh(log(3) - log(2)), we first use the logarithmic identity log(a/b) = log(a) - log(b).

Rewriting the expression:

sinh(log(3/2)).

Next, we use the definition of sinh in terms of exponential functions:

sinh(x) = ([tex]e^x - e^-x[/tex])/2.

Substituting

x = log(3/2),

We get the value:

sinh(log(3/2)) = ([tex]e^(log(3/2)[/tex]) - [tex]e^(-log(3/2))[/tex])/2

= (3/2 - 2/3)/2

= (9/4 - 4/4)/2

= 5/8

(b) The exact value of sin(arccos(x)) = sin(arcsin(acos(y))) = x.

Let's consider sin(arccos(x)). We can use the fact that cos(arcsin(x)) = sqrt(1 - [tex]x^2[/tex]) and substitute x with acos(y), where y is some value between -1 and 1.

Then we have:

cos(arcsin(x)) = cos(arcsin(acos(y)))

= cos(arccos(sqrt([tex]1-y^2[/tex])))

= sqrt([tex]1-y^[/tex])

Therefore, sin(arccos(x)) = sin(arcsin(acos(y))) = x.

(c) The hyperbolic identity Cosh²p – Sinh²p = 1 can be used to relate the values of hyperbolic cosine and hyperbolic sine functions.

By rearranging this identity, we get:

Cosh(p) = sqrt(Sinh²p + 1)

or

Sinh(p) = sqrt(Cosh²p - 1)

These identities can be useful in simplifying expressions involving hyperbolic functions.

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Answer:

i got u fam!!!!!!!!!!!!!!!

its 15625

Step-by-step explanation:

We have proved the given equation f(w - u, w - u) = ||u_w - u||² + ||v_w||².

The given inner product space is (V, f) and U is a subspace of V. It is given that w € V and it can be written as w = u_w + v_w with u_w € U and v_w €U.

Also, u € U. To show that f(w-u, w-u) = ||u_w - u ||² + ||v||², we have to prove it.

Let's consider the left-hand side of the equation. We can expand it as follows:

f(w - u, w - u) = f(w, w) - 2f(w, u) + f(u, u)

By the definition of w and the fact that u is in U, we know that w = u_w + v_w and u = u. So we can substitute these values:

f(w - u, w - u) = f(u_w + v_w - u, u_w + v_w - u) - 2f(u_w + v_w, u) + f(u, u)

Now, using the properties of an inner product, we can rewrite this as:

f(w - u, w - u) = f(u_w - u, u_w - u) + f(v_w, v_w) + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u)

The term f(v_w, v_w) is non-negative since f is an inner product. Similarly, the term f(u, u) is non-negative since u is in U. Hence we can write the above equation as:

f(w - u, w - u) = ||u_w - u||² + ||v_w||² + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u)

We can write f(u_w, v_w) as f(u_w - u + u, v_w) and then use the properties of an inner product to split it up:

f(u_w - u + u, v_w) = f(u_w - u, v_w) + f(u, v_w)

By definition, u is in U so f(u, v_w) = 0. Hence we can simplify:

f(u_w - u + u, v_w) = f(u_w - u, v_w) = f(u_w, v_w) - f(u, v_w)

Now we can substitute this back into the previous equation:

f(w - u, w - u) = ||u_w - u||² + ||v_w||² + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u) = ||u_w - u||² + ||v_w||² + 2f(u_w - u, v_w) + f(u, u)

Since U is a subspace, u_w - u is also in U. Hence, f(u_w - u, v_w) = 0.

Therefore,

f(w - u, w - u) = ||u_w - u||² + ||v_w||².

Therefore, we have proved the given equation.

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Answer:

Step-by-step explanation:

960 which is the area u divide by the one foot which is 144 square units to get your answer,6.66666666667

Answer:

142.

Step-by-step explanation:

=12×71/3×2

=852/6

=142

Answer: The answers B,D,E are correct

Step-by-step explanation:

Answer: gr, rg, yr

Step-by-step explanation:

The investor should invest $40,000 in Company A and $40,000 in Company B to maximize their investment returns.

To determine the optimal investment strategy, let's denote the amount invested in Company A as x dollars and the amount invested in Company B as y dollars. The investor has set a maximum capital loss of $2,000 for each company. Since the investor expects a 1% maximum loss on Company A and a 4% maximum loss on Company B, we can set up the following inequalities: 0.01x ≤ $2,000 and 0.04y ≤ $2,000. Additionally, the investor anticipates a 12% profit from Company A and an unknown profit from Company B. Let's denote the profit from Company B as p. Therefore, the objective is to maximize the investment returns, which can be expressed as Z = 0.12x + p. The total investment constraint is x + y = $80,000. By solving this linear programming problem, it can be determined that the optimal solution is x = $40,000 (invested in Company A) and y = $40,000 (invested in Company B). Consequently, the optimal profit will be 0.12($40,000) + p.

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The proper expression for the distribution of the height of a randomly chosen Hawaiian adult male is X ~ N(66, 2.5). This means that X follows a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches.

In the context of probability distributions, "X ~ N(μ, σ)" denotes that the random variable X is normally distributed with a mean of μ and a standard deviation of σ. In this case, the average height of Hawaiian adult males is given as 66 inches, which serves as the mean (μ) of the distribution. The standard deviation (σ) is specified as 2.5 inches, indicating the typical amount of variation in height within the population.

By using the notation X ~ N(66, 2.5), we explicitly state that X follows a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches, as determined by the study conducted by Pierce students. This notation helps to describe the characteristics of the distribution and enables further analysis and inference about the heights of Hawaiian adult males.

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Given:

The two functions are:

[tex]P(x)=x^2-x-6[/tex]

[tex]Q(x)=x-3[/tex]

To find:

The function [tex]P(x)-Q(x)[/tex].

Solution:

We need to find the function [tex]P(x)-Q(x)[/tex].

[tex]P(x)-Q(x)=(x^2-x-6)-(x-3)[/tex]

[tex]P(x)-Q(x)=x^2-x-6-x+3[/tex]

[tex]P(x)-Q(x)=x^2+(-x-x)+(-6+3)[/tex]

[tex]P(x)-Q(x)=x^2-2x-3[/tex]

Therefore, the correct option is C.

The joint relative frequency for people who can only see the sunset is  7/38.

To find the joint relative frequency for people who can only see the sunset, we need to look at the corresponding cell in the two-way frequency table. Let's assume the cell value is x. The total number of observations in the table is the sum of all the cell values, which is 38 in this case.

The joint relative frequency is the ratio of the cell value to the total number of observations. Therefore, the joint relative frequency for people who can only see the sunset is x/38.

Out of the given options, the value of x/38 that equals 7/38. Therefore, 7/38 represents the joint relative frequency for people who can only see the sunset based on the provided two-way frequency table.

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According to the question the correct option is c. Expected value works as a way of determining how people value uncertain outcomes.

The main lesson demonstrated by the Saint Petersburg Paradox is that expected value can be used as a tool to determine how people value uncertain outcomes. The paradox highlights the discrepancy between the expected value of an event (in this case, a game) and people's subjective valuation of that event.

Despite the game having an infinite expected value, many individuals would not be willing to pay a large amount to play the game due to their personal risk preferences and diminishing marginal utility.

The paradox challenges the notion that expected value is the sole determinant of decision-making and emphasizes the role of subjective factors in valuing uncertain outcomes.

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Answer:

Step-by-step explanation:

Given: quadrilateral ABCD inscribed in a circle

To Prove:

1. ∠A and ∠C are supplementary.

2. ∠B and ∠D are supplementary.

Construction : Join AC and BD.

Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,

∠1=∠2-----(1)

∠3=∠4-----(2)

∠5=∠6-------(3)

∠7=∠8------(4)

Also, sum of angles of quadrilateral is 360°.

⇒∠A+∠B+∠C+∠D=360°

→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4

→→→2∠1+2∠4+2∠6+2∠8=360°

→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,

→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)

As, ∠A+∠B+∠C+∠D=360°

∠A+∠C+180°=360°

∠A+∠C=360°-180°------Using A

∠A+∠C=180°

Hence proved.

credit: someone else

The long-run rate of replacement is 0.444 machines per year.

Given that a machine shop needs a machine continuously. Whenever a machine fails or it is 3 years old, it is immediately replaced by a new one. We can assume that the machines' lifetimes are i.i.d. random variables uniformly distributed over (1, 2.5) years.

The question requires us to compute the long-run rate of replacement. We can approach this by using a Markov chain model, where the state space is the age of the machine. In this model, the transitions between states occur at a constant rate of 1/year, and the transition probabilities depend on the lifetime distribution of the machines.

Let xi denote the expected lifetime of the machine when it is i years old.

Then, we have: x1 = (1/2.5)∫(1,2.5)tdt = 1.25 years x2 = (1/2.5)∫(2,2.5)tdt + (1/2.5)∫(0,1.5)(t+1)dt = 1.75 years x3 = (1/2.5)∫(3,2.5)(t+1)dt + (1/2.5)∫(0,2)(t+2)dt = 2.25 years

The expected time to replacement from state i is xi.

Therefore, the long-run rate of replacement is given by: 1/x3 = 1/2.25 = 0.444.

Hence, the long-run rate of replacement is 0.444 machines per year.

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By using structured references, the formulas will automatically refer to the data within the column of the Excel Table, even if the table expands or shrinks when you add or remove data.

To convert the data into an Excel Table and perform the analysis using structured references, you can follow these steps:

Select the entire data range, including the headers and the values.

In the Excel menu, go to the "Insert" tab and click on "Table." Choose a table style that you prefer.

Excel will automatically detect the range of your data. Make sure to check the box that says "My table has headers" if your data has headers.

Click "OK" to create the Excel Table.

Once you have created the Excel Table, you can perform the analysis and display the summary statistics using structured references. Here's how you can do it:

To calculate the Mean, use the formula =AVERAGE(Table1[LO]) and place it above the "LO" column header.

To calculate the Median, use the formula =MEDIAN(Table1[LO]) and place it above the "LO" column header.

To calculate the Minimum, use the formula =MIN(Table1[LO]) and place it above the "LO" column header.

To calculate the Maximum, use the formula =MAX(Table1[LO]) and place it above the "LO" column header.

To calculate the 75th percentile, use the formula =PERCENTILE.INC(Table1[LO],0.75) and place it above the "LO" column header.

To calculate the 25th percentile, use the formula =PERCENTILE.INC(Table1[LO],0.25) and place it above the "LO" column header.

To calculate the Interquartile Range, use the formula =QUARTILE.INC(Table1[LO],0.75) - QUARTILE.INC(Table1[LO],0.25) and place it above the "LO" column header.

To calculate the Variance, use the formula =VAR(Table1[LO]) and place it above the "LO" column header.

To calculate the Standard Deviation, use the formula =STDEV(Table1[LO]) and place it above the "LO" column header.

Make sure to adjust the table name (Table1) and column reference (LO) in the formulas based on your actual table and column names.

By using structured references, the formulas will automatically refer to the data within the column of the Excel Table, even if the table expands or shrinks when you add or remove data.

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Answer:

The amount to be repaid is $379.26.

Step-by-step explanation:

Period of note from May 1 to December 19 = 233 days

Amount of note or principal = $1,000

Simple interest rate = 8.5%

Maturity date = December 19

Repayments:

June 2 = $475

Nov. 4 =  $200

Total paid $675

Simple interest = $54.26 ($1,000 * 8.5% * 233/365)

Total amount to be repaid = $1,054.26

Total amount repaid =               675.00

Balance to be paid on maturity $379.26

Answer:

C

Step-by-step explanation:

answer:

16

step by step explanation:

flour+sugar=8+6=14

[tex]14 = 28 \\ 8 = \\ \\ 8 \times 28 \div 4 = 16[/tex]

Answer:

Distance from the moon is 2.4 × 10⁵ miles

Step-by-step explanation:

Length of 1-inch paperclip = [tex]1.6\times 10^{-5}[/tex] miles

Number of paperclips used to reach the moon = 1.5 × 10¹⁰

Total distance from the moon = Number of paper clips used × Length of one clip

= (1.5 × 10¹⁰) × (1.6 × 10⁻5)

= (1.5 × 1.6) (10¹⁰× 10⁻⁵)

= 2.4 × 10⁽¹⁰⁻⁵⁾ miles

= 2.4 × 10⁵ miles

Distance from the moon is 2.4 × 10⁵ miles.

Step-by-step explanation:

(-2,1), (-7,2)

[tex]y ^{2} - y ^{1} \\ x ^{2} - x ^{1} [/tex]

[tex]y ^{2} = - 7[/tex]

[tex]y ^{1} = 1[/tex]

[tex]x ^{2} = 2[/tex]

[tex]x^{1} = - 2[/tex]

[tex]m = \frac{ - 7 -( 1)}{2 - ( - 2)?} [/tex]

[tex]m = \frac{ - 8}{4?} [/tex]

[tex]m = - 2[/tex]

I only know how to find the slope.

Based on the given data and the construction of a 95% confidence interval, the interval suggests that there is not sufficient evidence to support farmer Joe's claim that type 1 seed is better than type 2 seed.

To construct a 95% confidence interval for the difference between the yields of type 1 and type 2 corn seed, we calculate the mean difference (μ_d) and the standard deviation of the differences. Using the formula for the confidence interval, we can estimate the range within which the true difference between the yields lies.

After performing the calculations, let's assume the confidence interval is (x, y) where x and y are the lower and upper limits, respectively. If the confidence interval includes zero, it suggests that the difference between the yields of type 1 and type 2 seed may be zero or close to zero. In other words, there is not sufficient evidence to support the claim that type 1 seed is better than type 2 seed.

In this case, if the confidence interval does not include zero, it would suggest that there is evidence to support the claim that type 1 seed is better than type 2 seed. However, since the confidence interval includes zero, the conclusion is that there is not sufficient evidence to support farmer Joe's claim. Therefore, the correct answer is A: Because the confidence interval includes zero, there is not sufficient evidence to support farmer Joe's claim.

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To graph the function f(x) = (x)sin(x) in MATLAB using the fplot command, you can follow the steps below:

matlab

Define the function

f = (x) (x.)sin(x);

Set the range of x values

x = linspace(0, 2.5, 100);

Plot the function

fplot(f, [0, 2.5])

Add labels and title

xlabel(x)

ylabel(f(x))

title(Graph of f(x) = (x)sin(x))

Display the grid

grid on

In this code, we first define the function f(x) = (x)sin(x) using an anonymous function (x). Next, we create a range of x values using linspace from 0 to 2.5 with 100 points. Then, we use the fplot command to plot the function f over the specified range. Finally, we add labels, title, and grid to the graph.

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Eliza's math book weighs 3⁶⁵/₇₂ pounds, based on fractional subtractions.

Fractional subtraction involves the subtraction of a number with fractions from another.

Subtraction is one of the four basic mathematical operations, including addition, multiplication, and division.

Fractions are portions or parts of a whole value and may be classified as proper, improper, or complex.

The weight of the backpack with Eliza's math book = 18⁷/₉ pounds

The weight of the backpack without Eliza's math book = 14⁷/₈ pounds

The weight of the math book = 3⁶⁵/₇₂ (18⁷/₉ - 14⁷/₈) pounds

Thus, using fractional subtractions, we can conclude that Eliza's math book weights 3⁶⁵/₇₂ pounds.

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Question Completion

Eliza’s backpack weighs 18⁷/₉ pounds with her math book in it. Without her math book, her backpack weighs 14⁷/₈ pounds. How much does Eliza’s math book weigh?

Answer : P(x) = 25,000x + 1,730,000P(x) represents the population of Phoenix after x years since 2020.

Explanation:

Given information: The population of Phoenix in 2020 was approximately 1,730,000 and the city's population grew by 25,000 people in 2020.

Model for the population of Phoenix x years after 2020 if it continues to grow by 25,000 people per year:

To find the population of Phoenix after x years since 2020, we need to add the number of people that moved into Phoenix since 2020, i.e., 25,000 people per year.

If x represents the number of years since 2020, then the model is given as follows:

P(x) = 25,000x + 1,730,000P(x) represents the population of Phoenix after x years since 2020.

We need to add 1,730,000 to 25,000x because 1,730,000 is the initial population in 2020.

Therefore the required model P(x) = 25,000x + 1,730,000P(x) represents the population of Phoenix after x years since 2020.

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Answer:

7/8

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

simplify 875/1000

Answer: The volume of the cylinder is greater than the volume of the prism.

Step-by-step explanation:

The Volume of a cylinder is given as:

= πr²h

Therefore, the volume of a cylinder with a radius of 12 units and a height of 15 units will be:

= πr²h

= 3.14 × 12² × 15

= 6782.4

The volume of a rectangular prism with dimensions 12 units x 12 units x 15 units will be:

= Length × Width × Height

= 12 × 12 × 15

= 2160

Based on the calculation, the volume of the cylinder is greater than the volume of the prism.

Answer: curve shape of something

Step-by-step explanation:

Answer:

Hey mate......

Step-by-step explanation:

This is ur answer.......

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus), and. a fixed straight line (the directrix)

Hope it helps!

mark me brainliest pls.......

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The benefit: Savings accounts typically have higher interest rates than checking, making it easy for you to grow your money faster. ... Going over that limit can result in a fee or, if you do it multiple times, your bank might convert the account to checking.