Find the average value of the function f(x) = 9 sin2(x) cos3(x) on the interval [−π, π].

Quotients are used to represent the division of  numbers

The number is -0.52

Let the number be represented with x.

So, the quotient of a number (x) and 0.2 is -2.6 is represented as:

[tex]\frac x{0.2} = -2.6[/tex]

Multiply both sides of the equation by 0.2

[tex]0.2 * \frac x{0.2} = -2.6 * 0.2[/tex]

Evaluate the quotient, on the left hand side

x = -2.6 * 0.2

Evaluate the product on the right hand side

x = -0.52

Hence, the number is -0.52

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Answer:

Option A.

Step-by-step explanation:

The table made by the painter shows the amount of paint required to cover a certain amount of area of the wall.

Amount of paint is directly proportional to the area covered

In other words Amount of paint (y) ∝ Area covered (x)

y ∝ x

As we know when proportionality sign is removed, a constant known as proportionality constant is multiplied with the variable.

So y = k(x) where k is the proportionality constant

Now from the table to cover the area of 64 square feet, 4 pints of paint is required.

Now from the formula

4 = 64x

x = [tex]\frac{4}{64}=\frac{1}{16}[/tex]

Now we have to calculate the amount of paint required to cover the area of 256 square feet.

y = [tex]\frac{1}{16}\times 256[/tex]

y = 16 pints

Therefore, 16 pints of the paint will be required to cover 256 square feet.

Option A is correct.

Answer:

Just Pick 16 Pints

Step-by-step explanation:

Final answer:

When multiplying 0.07 by 1.22, the product is 0.0854. This result is calculated by first multiplying the numbers as whole numbers and then placing the decimal point so that the total number of decimal places in the product matches the sum of the decimal places in the factors.

Explanation:

Therefore, 0.07 multiplied by 1.22 equals 0.0854.

Final answer:

When multiplying 0.07 by 1.22, we first ignore the decimals and multiply 7 by 122 to get 854, and then we place the decimal point so the result has the same number of decimal places as the sum of the factors, resulting in 0.0854.

Explanation:

To find the product of two decimal numbers, you multiply them just as you would with whole numbers, taking care to place the decimal point in the correct position in the final answer. For the multiplication of 0.07 by 1.22, you perform the multiplication ignoring the decimals first, and then place the decimal in the final answer so that the total number of decimal places equals the sum of the decimal places in the factors.

Multiplying 7 by 122 equals 854. Since 0.07 has two decimal places and 1.22 has two decimal places, the product must have four decimal places. Therefore, the correct placement of the decimal point in 854 would be after four digits from the right, which gives us a final answer of 0.0854.

The standard form is x⁵ + 2x³ + 6x + [tex]\frac{1}{5}[/tex].

To write the given equation x⁵ + 2x³ + 6x + [tex]\frac{1}{5} \\[/tex] in standard form, follow these steps:

Answer:

Sorry that I’m late, answer is C. y=7x

Step-by-step explanation:

14/2 = 7

28/ = 7

Answer:

g(x)=(x+4)^2+5(x+4)-6

The graph of the line change is, It will shift down 6 units.

The given function is,

y = 15x + 2

Now, We want to find how the graph of this function will change if the function is transformed to

y = 15x  -4

We rewrite this function in terms of the first one to get:

y = 15x + 2 + (-6)

Hence, the function with shift down 6 units.

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The monthly interest rate on this annuity is approximately 0.4318%.

To find the monthly interest rate on the annuity, we need to use the present value formula for an annuity:

PV = A * (1 -[tex](1+r)^{(-n)[/tex]) / r

Where PV is the present value, A is the monthly payment, r is the monthly interest rate, and n is the total number of payments. In this case, PV = $90,000, A = $850, and n = 15 (since the professor's remaining life expectancy is 15 years).

By plugging in these values and solving for r, we can find the monthly interest rate on the annuity.

$90,000 = $850 * (1 - [tex](1+r)^{-15)[/tex] / r

After solving this equation, we find that the monthly interest rate on this annuity is approximately 0.4318%.

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The monthly interest rate is approximately 0.58%.

To determine the monthly interest rate on the annuity, we need to solve for the rate that equates the present value of the annuity payments to the initial payment of $90,000. The payments of $850 are made for the expected life of 15 years, which translates to 180 monthly payments.

The present value (PV) of an annuity can be calculated using the formula:

[tex]PV = Pmt * [(1 - (1 + r)^{-n}) / r][/tex]

Where:
Pmt = $850 (monthly payment)
r = monthly interest rate
n = 180 (total number of payments)

Given PV = $90,000, we need to solve for r:

$90,000 = $850 × [(1 - (1 + r)^-180) / r]

This requires solving the equation iteratively or using a financial calculator, as it's a non-linear equation. By trial and error or using a financial calculator or spreadsheet:

We find that r ≈ 0.0058 or 0.58%

Thus, the monthly interest rate on this annuity is approximately 0.58%.

The domain of the function is [tex][0,3.5][/tex] and the range of the function is [tex][0,1750][/tex].

Speed [tex]= 500[/tex] mph

Distance [tex]= 1750[/tex] miles

Distance [tex]=[/tex] Speed [tex]\times[/tex] Time

The distance Jackson has traveled in miles is a function of time in hours he has been flying.

[tex]f(t)=500t.[/tex]

For maximum distance, [tex]f(t)=1750[/tex] miles.

[tex]1750=500t.[/tex]

[tex]t=\frac{1750}{500}[/tex]

[tex]t=3.5[/tex] hours

So, domain [tex]= [0,3.5][/tex]

Range [tex]= [0,1750][/tex]

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The diameter of the field is 83 yards.

To find the diameter of a circular field, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Given that the circumference of the field is 260.62 yards, we can solve for the radius by dividing the circumference by 2π.

Using the value of π as 3.14, we can calculate:

260.62 / (2 * 3.14) = 41.50 yards

Since the diameter of a circle is twice the radius, the diameter of the field is 2 * 41.50 = 83 yards.

Answer:

D. x + 15 ≤ 60

Step-by-step explanation:

Let x be the amount you have left to spend after you purchase the shirt.

We must add to x the cost of the shirt, $15.  This gives us x+15.

We only have $60 to spend; this means we can spend anything up to and including $60.  This means we want "less than or equal to."  This gives us the inequality

x+15 ≤ 60

The inequality of the form x + 15 ≤ 60 is the correct choice.

An inequality is a comparison between two non equal expression or terms or numbers.

According to the given question You have a gift card for your favorite clothing store for the amount of $60.

You have found a shirt you want to buy that costs $15 but you don't want to spend more than the amount of the gift card.

Assuming the amount you will have is x dollars.

∴ x + 15 ≤ 60

As x ≤ 60 - 15

x ≤ 45.

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Answer:

Option C. 12 years

Step-by-step explanation:

Let principal amount taken = x

We know the formula of compound interest

Final amount = Principal amount×[tex](1+\frac{r}{n})^{nt}[/tex]

Where r = rate of interest (per year)

n = number of times compounded (annually)

t = time in years (years)

Here we have to find the time in which principal amount is doubled.

From the question r = 6% = .06

n = 1

Principal amount = P

Final amount = 2P

Now we put these values in the formula

[tex]2P=P(1+.06)^{t}[/tex]

[tex]2=(1.06)^{t}[/tex]

Now we take log on both the sides

[tex]log(2)=log(1.06)^{t}[/tex]

0.301 = tlog(1.06)

0.301 = t×(.025)

[tex]\frac{0.301}{0.25}=t[/tex]

t = 12 years.

Option C. 12 years is the answer.

Final answer:

Using a quadratic equation, we found that there are 24 orange trees in each row of the orchard.

Explanation:

To determine how many orange trees are there in each row, we will set up an equation based on the information provided. Let's let x represent the number of trees per row. According to the problem, the number of rows is x + 5. Since the total number of trees in the orchard is 864, we can create the following equation:

x * (x + 5) = 864

To solve this quadratic equation, we need to find the value of x that satisfies the equation:

First, expand the left side of the equation: [tex]x^{2}[/tex] + 5x.

Write the equation in standard form: [tex]x^{2}[/tex] + 5x - 864 = 0.

Factor the quadratic equation: (x + 36)(x - 24) = 0.

Solve for x: x = -36 or x = 24.

Since we cannot have a negative number of trees per row, we disregard x = -36.

Therefore, there are 24 trees in each row.

Answer:

24 miles per hour.

Step-by-step explanation:

So in order to calculate this you just need to use the formula for the speed:

Speed=Distance/time

Speed= 2 miles/ 5 minutes

Speed= 2 miles/,083 hours

Speed= 24

So the speed at the final 5 minutes will be 24 miles per hour.

The use of the normal distribution as an approximation for the sampling distribution of[tex]\( \bar{p} \)[/tex] requires both [tex]\( np \)[/tex] and [tex]\( n(1 - p) \)[/tex] to be at least 5. So, the answer is (b) 5.

The normal approximation for the sampling distribution of [tex]\( \bar{p} \),[/tex] the sample proportion, relies on the conditions that both[tex]\( np \)[/tex] and [tex]\( n(1 - p) \)[/tex] are greater than or equal to 5. Here, [tex]\( n \)[/tex]  represents the sample size, and [tex]\( p \)[/tex] is the probability of success in a binary outcome. These conditions ensure that the distribution of[tex]\( \bar{p} \)[/tex] is approximately normal, allowing for the application of statistical techniques based on the normal distribution. When[tex]\( np \)[/tex]and [tex]\( n(1 - p) \)[/tex]are both at least 5, the central limit theorem asserts that the distribution of [tex]\( \bar{p} \)[/tex] is sufficiently close to normal, facilitating the use of standard normal tables and z-scores for making probability calculations and inferences about the population proportion. This approximation is pivotal in hypothesis testing and confidence interval construction for proportions in statistical analyses.