What is [tex]x^{4} (x^{4} )[/tex]?
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The equation for the function with the given characteristics is:

f(x) = (1 * cos((x - pi)/pi)) + (5/2)

We have,

The equation for the function with the given characteristics can be written as follows:

f(x) = (1 * cos((x - pi)/pi)) + (5/2)

Amplitude: The amplitude of the cosine curve is 1, so we multiply the cosine function by 1.

Period: The period of the cosine curve is pi, which means it completes one full cycle over the interval [0, pi]. The period of the cosine function is determined by the argument inside the cosine function, (x - pi)/pi. This shifts the period to start at pi and end at 2pi.

Left phase shift: The left phase shift of pi is achieved by subtracting pi from x inside the argument of the cosine function. This shifts the curve to the left by pi units.

Vertical translation: The vertical translation up 5/2 units is achieved by adding 5/2 to the entire function.

Therefore,

The equation for the function with the given characteristics is:

f(x) = (1 * cos((x - pi)/pi)) + (5/2)

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The equation for the function is y(t) = cos(2t + pi) + 5/2.

To write an equation for the given characteristics, we can start with the general equation for a cosine curve: y(t) = A cos(wt + p).

Given that the period is pi, we know that the angular frequency w is equal to 2pi divided by the period, so w = 2pi/pi = 2. The amplitude is 1, so A = 1.

The left phase shift is pi, so p = pi. Finally, there is a vertical translation up 5/2 units, so we add 5/2 to the equation.

Putting all these values into the equation, we get: y(t) = cos(2t + pi) + 5/2.

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Answer: d) negative

Step-by-step explanation:

The term correlation is used to define the relationship between the two variables .

Here, the variables vary in the same direction.

Here, the variables vary in the opposite direction.

∴ A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a: negative correlation.

Hence, the correct answer is  d) negative

Answer:

Step-by-step explanation:

Let x represent the discount in percentage offered for the price of the shirts.

The regular price of the shirts was $20

The price for which the shirt was offered for sale is $17 which also represents the discounted price.

The discount would be

20 - 17 = $3

The percentage discount would be

The discount/ the regular price × 100%.

Therefore,

% discount = 3/20 × 100 = 0.15 × 100

= 15%

Answer:

You will have to pay $ 3.99 for the package of batteries with 20% discount

Step-by-step explanation:

Standard price of the batteries packages = $ 4.99

Discount = 20% = 0.2

Discounted price = Standard price - Discount

Discounted price = 4.99 - (0.2 * 4.99)

Discounted price = 4.99 - 1.00 (Rounding to the next tenth)

Discounted price = 3.99

You will have to pay $ 3.99 for the package of batteries with 20% discount

Final answer:

A package of batteries with a 20% discount off the original price of $4.99 would be approximately $3.99 after subtracting the discount amount, which is $0.998.

Explanation:

To calculate how much the student would have to pay for packages of batteries that normally sell for $4.99 with a 20% discount, we first need to determine the amount of the discount. To find the discount amount, multiply the original price by the discount percentage:

$4.99 × 0.20 = $0.998

Now, subtract the discount amount from the original price to get the sale price:

$4.99 - $0.998 = $3.992

The discounted price will be approximately $3.99, as the final amount is traditionally rounded to the nearest cent.

Answer:

C Less than today

Step-by-step explanation:

If i save $100 at 1% per annum after 1 year I will get $101, but with inflation rate of 2%per annum a commodity that is worth $100 now will be worth $102 after 1 year so u can't buy same commodity I can buy today after 1 year even when my money has increase.

The purchasing power of money in a savings account would decrease after 1 year due to inflation.

To calculate how much you would be able to buy after 1 year, we need to consider the effect of both the interest rate and inflation. With an interest rate of 1% per year, your savings account would increase by 1% over 1 year. However, with an inflation rate of 2% per year, the price of goods and services would also increase by 2% over the same period.

This means that the purchasing power of your money would decrease. To calculate the actual increase or decrease in purchasing power, you can subtract the inflation rate from the interest rate. In this case, 1% - 2% = -1%.

Therefore, the correct answer is c. Less than today. After 1 year, you would be able to buy less with the money in your savings account.

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Answer:

We are 95% confident that the true mean lies between 76.08 and 83.92.

Step-by-step explanation:

The confidence interval approach is used to calculate an interval in which the true population mean exists. The confidence level 1-α associated with confidence interval depicts that how confident we are that the population mean lies in the estimated interval. In the problem that confidence level is 95%, so we are 95% confident that the true mean lies between 76.08 and 83.92.

Answer:

The answer to your question is letter A

Step-by-step explanation:

From the graph, we conclude that it is a vertical ellipse with center (0, 0).

Also from the graph, we calculate a and b

a = 11, a is the distance from the center to the vertical vertex

b= 9,  b is the distance from the center to the horizontal vertex

Equation

                        [tex]\frac{x^{2}}{9^{2}} + \frac{y^{2}}{11^{2}} = 1[/tex]

Simplification

                      [tex]\frac{x^{2}}{81} + \frac{y^{2}}{111} = 1[/tex]

Answer:

40% students play the saxophone.

Step-by-step explanation:

Given:

Total Number of students who play woodwind instrument = 45

Number of students who play saxophone = 18

We need to find the percent of students who play saxophone.

Solution:

Now we can say that;

To find the percent of students who play saxophone we will divide Number of students who play saxophone by Total Number of students who play woodwind instrument and the multiply by 100.

framing in equation form we get;

percent of students who play saxophone = [tex]\frac{18}{45}\times100= 40\%[/tex]

Hence 40% students play the saxophone.

The percent of these students play the saxophone is 40%.

Using this formula

Percentage=Number of student that play saxophone/Number of student that play woodwind instrument×100

Where:

Number of student that play saxophone=18

Number of student that play woodwind instrument=45

Let plug in the formula

Percentage=18/45×100

Percentage=40%

Inconclusion the percent of these students play the saxophone is 40%.

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Answer:the cost of renting each chair is $2.5

the cost of renting each table is $8.75

Step-by-step explanation:

Let x represent the cost of renting each chair.

Let y represent the cost of renting each table.

The total cost to rent 5 chairs and 6 tables is $65. This means that

5x + 6y = 65 - - -- - - - - - - -1

The total cost to rent 3 chairs and 2 tables is $25. This means that

3x + 2y = 25 - - - - - - - - - - - -2

Multiplying equation 1 by 3 and equation 2 by 5, it becomes

15x + 18y = 195

15x + 10y = 125

Subtracting, it becomes

8y = 70

y = 70/8 = 8.75

Substituting y = 8.75 into equation 1, it becomes

5x + 6 × 8.75 = 65

5x + 52.5 = 65

5x = 65 - 52.5 = 12.5

x = 12.5/5 = 2.5

A.11

Step-by-step explanation:

Here apply the interpolation formula to find the value of y

From the table, you can interpolate the value of y where x is 92 by using the points (91,10) and (98,15)

The formula to apply is;

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} *(x-x_1)[/tex]

where

(x₁,y₁)=(91,10)

(x₂,y₂)=(98,15)

(x,y)=(92,?)

Substitute values in the equation;

[tex]y-10=\frac{15-10}{98-91} *(92-91)\\\\y-10=\frac{5}{7} *(1)\\\\7(y-10)=5\\7y-70=5\\7y=5+70\\\\7y=75\\\\y=75/7=10.71\\\\y=11[/tex]

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Answer:

The answer to your question is letter A.

Step-by-step explanation:

Inequality                   x + 2 ≥  5

Solve the inequality, remember that inequalities and equations are solved in similar ways.

- Subtract 2 in both sides

                                   x +2 - 2 ≥ 5 - 2

- Simplify

                                          x ≥ 3      

- Remember that this sign "≥" means that x is greater or equal to a number, and this sign "≤" means that x is lower or equal to a number.

The option that satisfies our inequality is the first option.                    

Answer:

As a fraction, the answer is exactly 86/969

In decimal form, the answer is approximately 0.08875

=====================================================

Work Shown:

The assumption is that no replacements are made for each selection.

5 red, 6 blue, 8 green

5+6+8 = 19 total

A = P(3 red) = (5/19)*(4/18)*(3/17) = 10/969

B = P(3 blue) = (6/19)*(5/18)*(4/17) = 20/969

C = P(3 green) = (8/19)*(7/18)*(6/17) = 56/969

D = P(3 all same color)

D = A+B+C

D = 10/969 + 20/969 + 56/969

D = (10+20+56)/969

D = 86/969

D = 0.08875

Answer:

E=I(R+r)

R+r=30

I=E/(R+r)

I=120/30

I=4A

Step-by-step explanation:

Final answer:

Using Ohm's Law (I = E/R), the current in a circuit with a resistance of 30 ohms and electromotive force of 120 VAC is calculated as 4 amperes.

Explanation:

To calculate the current (I) in a circuit when given the resistance (R) and electromotive force (E), we can use Ohm's Law, which states that current is equal to voltage divided by resistance (I = E/R). Using the values from the question, the resistance is 30 ohms and the electromotive force is 120 VAC. Therefore, the current in the circuit can be calculated as follows:

I = E/R = 120 V / 30 Ω = 4 A

So, the current in the circuit is 4 amperes.

Answer:

Principal Fund Y = $18,750

Principal Fund X = $31,250

Step-by-step explanation:

Given;

Total amount to invest = $50,000

Maximum amount of interest =$4,500

For fund Y;

Let y represent the amount invested(principal) in fund Y

Interest = 14% = 0.14

Time = 1 year

Interest = principal × rate × time

Interest on fund y = y × 0.14 × 1= 0.14y

For fund X;

The amount invested in fund X can be given as

x =50,000-y

Rate = 6% = 0.06

Time = 1 year

Interest on fund X = x × 0.06 ×1 = 0.06x = 0.06(50,000-y)

Total interest = interest on fund Y + fund X

$4,500 = 0.14y + 0.06(50,000 - y)

4500 = 0.14y - 0.06y + 3000

0.8y = 4500-3000

0.8y = 1500

y = 1500/0.08

y = $18,750

x = $50,000 - $18,750

x = $31,250

The expression for the given sequence of operations is 2(x-4)+8.

The given statement is "subtract 4 from x, double, and add 8".

We need to write an expression for the sequence of operations.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Now, subtract 4 from x=x-4

Double the difference that is 2(x-4)

Add 8=2(x-4)+8

Therefore, the expression for the given sequence of operations is 2(x-4)+8.

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Answer:

its a combination

Step-by-step explanation:

because three horses is a combination of horses

Answer:

The ratio of mangers to sales people of the stores are not equivalent as the ratios in their simplest form are not equal.

Step-by-step explanation:

Given:

One store has:

3 Managers and 12 sales persons

Another store has:

4 Managers and 15 sales persons.

To find if the ratio of mangers to sales people are equivalent.

Solution:

Store A:

Managers = 3

Sales people = 12

Ratio of mangers to sales people for store A = [tex]\frac{3}{12}[/tex] =[tex]\frac{3\div3}{12\div 3}=\frac{1}{4}[/tex]  (Simplest ratio)

Store B:

Managers = 4

Sales people = 15

Ratio of mangers to sales people for store B = [tex]\frac{4}{15}[/tex]

The ratio is in the simplest form and cannot be reduced further.

We can see that : [tex]\frac{1}{4}\neq \frac{4}{15}[/tex]

Hence, the ratio of mangers to sales people of the stores are not equivalent.

Answer:

Correct answer: s₁ = - 2

Step-by-step explanation:

The relationship between the slope of two lines that are perpendicular is:

s₁ = - 1/s = - 1/(1/2) = - 2

God is with you!!!

Answer:

The population in 2001 was = 23.95 millions

Step-by-step explanation:

Given

Population in 2006 = 30.3 million

Rate of growth since 2001 = 4.7%

To find the population in 2001.

Solution:

The population growth formula is give as:

[tex]P=P_0\times e^{rt}[/tex]

[tex]P\rightarrow[/tex] New population

[tex]P_o\rightarrow[/tex] Initial population

[tex]r\rightarrow[/tex] rate of growth

[tex]t\rightarrow[/tex] time

Data given to us:

New population [tex]P[/tex] (2006) = 30.3 million

Rate = 4.7% = 0.047

Time = [tex]2006-2001[/tex]= 5 years

Plugging in the data in the formula.

[tex]30.3=P_0\times e^{0.047\times 5}[/tex]

[tex]30.3=P_0\times e^{0.235}[/tex]

[tex]30.3=P_0\times 1.265[/tex]

Dividing both sides by 1.265

[tex]\frac{30.3}{1.265}=\frac{P_0\times 1.265}{1.265}[/tex]

[tex]23.95=P_o[/tex]

∴ [tex]P_o=23.95[/tex]

Thus, population in 2001 was = 23.95 millions

To answer this question, first, we need to understand the concept of an inverse operation, especially in the context of binary operations. A binary operation is a calculation that combines two elements to produce another element. Common binary operations are addition, subtraction, multiplication, and division in mathematics.

The inverse of a binary operation, denoted here as x y, is an operation, which when performed after the initial operation, returns the original value. This means, if we take x and y to produce z through the operation x y (denoted as x y -> z), the inverse operation will bring us back to the original x or y value. In mathematical terms, if we perform z (inverse) x operation, it should give us y, and z (inverse) y should return x.

From the given options, we can clearly observe that only one option obeys the rules of the inverse operation, that is 'yx' (option 3). Because only 'yx' will satisfy, z(inverse) x = y and z (inverse) y = x.

So, option 3, 'yx' is the inverse operation of x y in the sense of the inverse element.

Answer:yx

Answer:

70

Step-by-step explanation:

220-150=70

Answer:

A) [tex]2x[/tex]

Step-by-step explanation:

Given:

Number of calculator made by Adnan in this week = [tex]'x'[/tex]

We need to write an algebraic expression for the number of calculators that Maya made this week.

Solution:

Now given:

Maya made twice as many calculators.

So we can say that;

Number of calculators made by Maya this week is equal to 2 times Number of calculator made by Adnan this week.

framing in equation form we get;

Number of calculators made by Maya this week = [tex]2\times x = 2x[/tex]

Hence an algebraic expression for the number of calculators that Maya made this week is [tex]2x[/tex].

Answer:

Step-by-step explanation:

Let d represent the cost of a drink, and p represent the cost of a pizza slice. Then the two purchases can be represented by ...

To solve these equations by elimination, choose a variable to eliminate and look at the coefficients of that in the two equations. If we choose to eliminate p, we see the coefficients of p are 6 and 4. The least common multiple of these numbers is 12. We can multiply the first equation by -2 and the second equation by +3 and the resulting coefficients of p will be -12 and +12. Adding the results of these multiplications will make the p terms add to zero.

  -2(4d +6p) +3(3d +4p) = -2(6.70) +3(4.65)

  -8d -12p +9d +12p = -13.40 +13.95 . . . . . . . . . eliminate parentheses

  d = 0.55 . . . . . . . . . collect terms

Now, we can substitute this value into either equation to find the value of p. Using the first equation, we get ...

  4(0.55) +6p = 6.70

  6p = 4.50 . . . . . . . . . subtract 2.20

  p = 0.75 . . . . . . . . . . divide by 6

The cost of a drink is $0.55; the cost of a slice of pizza is $0.75.

Answer:each drink costs $0.55

Each slice of pizza costs $0.75

Step-by-step explanation:

Let x represent the cost of each drink.

Let y represent the cost of each slice of pizza.

You buy 4 drink and 6 slices of pizza for $6.70. This means that

4x + 6y = 6.70 - - - - - - - - - - - - 1

Your friend buys 3 drinks and 4 slices of pizza for $4.65. This means that

3x + 4y = 4.65 - - - - - - -- - - 2

Multiplying equation 1 by 3 and equation 2 by 4, it becomes

12x + 18y = 20.1

12x + 16y = 18.6

Subtracting, it becomes

2y = 1.5

y = 1.5/2 = 0.75

Substituting y = 0.75 into equation 1, it becomes

4x + 6 × 0.75 = 6.70

4x + 4.5 = 6.70

4x = 6.7 - 4.5 = 2.2

x = 2.2/4 = 0.55

The distance traveled by the particle is determined as [tex]\int\limits^0_t {v(t)} \, dt=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex].

Given data:

To determine the distance traveled by the particle during the first t seconds, integrate the velocity function with respect to time over the interval [0, t].

Given the velocity function:

[tex]v(t) = t^2 * e^{(-t)}[/tex]

To find the distance traveled, integrate the absolute value of the velocity function over the interval [0, t]:

[tex]\text{distance} = \int\limits^0_t {v(t)} \, dt[/tex]

Since the velocity can be negative (indicating a change in direction), taking the absolute value ensures that we consider the magnitude of the velocity.

Now, calculate the integral:

[tex]D = \int\limits^0_t {t^2 * e^{(-t)}} \, dt[/tex]

To simplify this integral, split it into two parts, considering the cases when the velocity is positive and negative:

[tex]D=[-e^{-t}t^2-\int\limits^0_t {-2e^{-t}} \, dt]_0^t[/tex]

The first integral represents the distance traveled when the velocity is positive, and the second integral represents the distance traveled when the velocity is negative.

Integrating each term separately:

[tex]\int\limits^0_t {v(t)} \, dt=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex]

Hence, the distance is [tex]D=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex].

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The complete question is attached below:

A particle that moves along a straight line has velocity [tex]v(t) = t^2e^{-t}[/tex] meters per second after t seconds. How far will it travel during the first t seconds?

The function v(t) = t2 e−t defines the velocity of a particle. The displacement or distance covered by the particle in the first t seconds is given by the integral from 0 to t of the velocity function.

The given velocity function for the particle is v(t) = t2 e−t. The distance (or displacement) traveled by an object is the integral of the velocity over a given interval. So, to find the distance covered by the particle in the first t seconds, you would set up the following integral:

∫0t t2 e−t dt

We won't compute this integral here, as it requires knowledge of methods beyond basic calculus, specifically the use of integration by parts and possibly a tabular method for successive integrations by parts. However, this setup gives you the right starting point to find the distance covered in the first t seconds.

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Answer:

x = $3,521

Step-by-step explanation:

let the amount of money that she put towards a house be represented by the variable x

Hence,

total savings = amount put towards house + amount left

$40,000 = x + $36,479   (rearrange)

x + $36,479  = $40,000   (subtract $36,479 from both sides)

x   = $40,000 -  $36,479

x = $3,521

Final answer:

To find the cost of a youth ticket, you can set up a system of equations using the given information. Solve the system of equations to find the cost of a youth ticket.

Explanation:

To find the cost of a youth ticket, we can set up a system of equations using the given information. Let x be the cost of an adult ticket and y be the cost of a youth ticket. From the problem, we know that 7x + 12y = 525 and x - y = 18. We can solve this system of equations using substitution or elimination.

First, let's solve for x in terms of y using the second equation. Adding y to both sides gives x = y + 18.

Next, substitute this expression for x in the first equation: 7(y + 18) + 12y = 525. Simplifying this equation gives 7y + 126 + 12y = 525. Combining like terms, we get 19y + 126 = 525. Subtract 126 from both sides: 19y = 399. Finally, divide both sides by 19 to solve for y: y = 21.

Therefore, the cost of a youth ticket is $21.

Answer: 5.5 seconds

Step-by-step explanation:

30=5/4 ×(-20) + 10t

30 =-25 +10t

10t=55

t=5.5seconds

The cord will first touch the corner of the building after 5.5secs

Answer:

a). 18

b). 26%

c). 39

Step-by-step explanation:

Given question is incomplete; here is the complete question attached.

a). In this part we have to calculate the number of the people surveyed who make less than 5 calls.

From the given table,

Number of people surveyed who make less than 5 calls Or 1 - 4 calls = 18

b). Total number of people surveyed = 18 + 11 + 5 + 3 + 2 = 39

Number of people surveyed, make at least 9 calls = 5 + 3 + 2 = 10

Percentage of these people = [tex]\frac{\text{People who make calls more than 9 calls per day}}{\text{Total number of people surveyed}}\times 100[/tex]

= [tex]\frac{10}{39}\times 100[/tex]

= 25.64%

≈ 26%

c). Total number of people surveyed = 18 + 11 + 5 + 3 + 2 = 39