What is the period of the function f(x) =sin 1/6x

The area of the circle is 12.56 square yards.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The circumference of a circle is given by the formula:

Circumference = π x diameter

If the diameter of the circle is 4 yards, then the radius is half of the diameter, or:

radius = diameter / 2 = 4 / 2 = 2 yards

Using the formula for circumference, we can find:

Circumference = π x diameter = 3.14 x 4 = 12.56 yards

Therefore, the circumference of the circle is 12.56 yards.

To find the area of the circle, we can use the formula:

Area = π x radius²

Plugging in the value for radius, we get:

Area = 3.14 x 2² = 3.14 x 4 = 12.56 square yards

Therefore, the area of the circle is 12.56 square yards.

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Answer:

See explanation

Step-by-step explanation:

The given options are not properly formatted; so, I will give a general explanation instead

An equation is said to be radical if its variable is in a radicand sign.

For instance, the following equation is a radical;

\(\sqrt x + 2 = 4\)

In the above equation, x is the variable, and it is in \(\sqrt\) sign

However, the following equation is not a radical equation

\(x + \sqrt 4 = 2\)

Because the variable is not in a radicand

The expression (f+g)(-5) simplifies to 29.

To find the expression (f+g)(-5), we need to first evaluate f(-5) and g(-5), and then add the results together.

Given that f(x) = x + 4 and g(x) = x^2 - x, we can evaluate f(-5) and g(-5) as follows:

f(-5) = (-5) + 4 = -1

g(-5) = (-5)^2 - (-5) = 25 + 5 = 30

Now, we can add f(-5) and g(-5) together:

(f+g)(-5) = (-1) + (30) = 29

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The triangle is drawn and attached

The length of BC is 3.9 cm

The length of BC is solved using Pythagoras Theorem as follows hypotenuse² = opposite² + adjacent²

where

hypotenuse = AB = 2 + 2 = 4

the hypotenuse is the diameter of the circle while given side is the radius and radius + radius = diameter

opposite = AC = 1

adjacent = BC = ?

AB² = AC² + BC²

substituting in to the values

4² = 1² + BC²

rearranging the equation

BC² = 4² - 1²

BC² = 16 - 1

BC = √15

BC = 3.873

BC = 3.9 to one decimal place

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Answer:

14

Step-by-step explanation:

5(2)² - 2 - 4 = 14

The required value of the given expression 5z²-z-4 is 14 when z = 2,

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.

The expression is given in the question below as:

5z²-z-4​

To determine the value of the expression 5z²-z-4 when z=2, we need to substitute 2 for every occurrence of z in the expression and then simplify the expression.

5z²-z-4 when z = 2 is :

= 5(2²)-2-4

= 5(4)-2-4

= 20-2-4

= 14

Therefore, the required value is 14.

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If a random sample of 29 time intervals between eruptions has a mean greater than 106, it may be concluded that the average time between eruptions is longer than 106 units of time. However, it is important to note that the sample size of 29 may not be representative of the entire population of time intervals between eruptions, and therefore the conclusion drawn may not be entirely accurate.
Additionally, it is important to consider the variability of the data. If the standard deviation of the sample is high, it may indicate that there is a wide range of time intervals between eruptions, making it difficult to draw a definitive conclusion. On the other hand, if the standard deviation is low, it may indicate that the time intervals are more consistent, and the conclusion drawn may be more reliable.

Overall, it is important to consider both the mean and variability of the sample when drawing conclusions about the population of time intervals between eruptions. Further research and analysis may be necessary to validate the findings and provide a more accurate answer.

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Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.

As given in the question,

Perimeter of the rectangular area encloses for fencing = 3200 yards

Let 'x' and 'y' be the length and width of the rectangle.

2( x + y ) = 3200

⇒ x + y = 3200/2

⇒y = 1600 - x

Area of rectangular field 'A' = xy

⇒ A = x ( 1600 - x )

⇒ A = 1600x - x²

Differentiate both the side of the equation we get,

dA/dx = 1600 - 2x

For Maximum Area dA/dx = 0

1600 -2x =0

⇒ 2x = 1600

⇒ x= 800 yards

Now, y = 1600 - 800

          = 800 yards

Maximum area = (800) (800)

                        = 640,000 square yards

Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.

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Answer:

-------------------

Given three interior angle measures of a triangle:

Use the triangle sum theorem to find the missing angle:

So the missing angle is 67°.

The distribution of the cost for a randomly selected private nonprofit four-year college follows a normal distribution with a mean of $27,277 and a standard deviation of $6,744. The probability that a randomly selected college will cost less than $22,340 per year is approximately 0.2357, or 23.57%.

a. The distribution of X, the cost for a randomly selected college, follows a normal distribution. We can denote this as X ~ N(μ, σ), where μ represents the mean (average) cost and σ represents the standard deviation.

In this case, the mean cost (μ) is given as $27,277, and the standard deviation (σ) is $6,744.

Therefore, the distribution of X can be represented as X ~ N(27,277, 6,744).

b. To compute the probability that a randomly selected private nonprofit four-year college will cost less than $22,340 per year, we need to calculate the cumulative probability up to that value.

Using the z-score formula: z = (x - μ) / σ

Where:

x = $22,340 (the value we want to find the probability for)

μ = $27,277 (mean)

σ = $6,744 (standard deviation)

z = (22,340 - 27,277) / 6,744

z = -0.7207

Next, we need to find the cumulative probability associated with the z-score of -0.7207. This can be done using a standard normal distribution table or a calculator.

The probability can be calculated as P(X < 22,340) = P(Z < -0.7207).

Looking up the z-score -0.7207 in a standard normal distribution table or using a calculator, we find that the cumulative probability is approximately 0.2357.

Therefore, the probability that a randomly selected private nonprofit four-year college will cost less than $22,340 per year is approximately 0.2357, or 23.57% (rounded to two decimal places).

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Second option is correct 0.04772.

The probability of a weight between 420 kilos and the mean of 400

kilos = 0.4772

Mean of a normal probability distribution is μ = 400 kilos

And standard deviation σ = 10 kilos

Let x be the variable in kilos.

X is between 400 kilos and 420 kilos

P( 400 < X < 420 ) = P ( 400 -  μ < X -  μ < 420 -  μ)

= P ( (400-μ)/σ < (X-μ)/σ < (420-μ)/σ )

= P ( (400 - 400) /10 < Z < (420 - 400)/10 )

= P ( 0 < Z < 2 )

= 0.4777 from the table appendix B1.

The link for the appendix table B1 :

www.webassign.net%2Faswsbe13%2Fappendix-b.pdf&usg=AOvVaw3QlkaDTdGZ1Z01YZPYCL6h

The probability of a weight between 420 kilos and the mean of 400

kilos = 0.4772

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2D maximum shearing stress is 495 ksi and 3D maximum shearing stress is 1976.9 ksi.

Given,Pressure = 45 ksi

Outer radius = 22 in

Wall thickness = 1 in

The formula for Lateral (01) normal stress is

σ01 = Pr / t

Where,

σ01 = Lateral (01) normal stress

P = Internal Pressure = 45 ksi (Given)

r = Outer radius = 22 in.

t = Wall thickness = 1 in

Substitute the given values,

σ01 = Pr / t

= 45 × 22 / 1

= 990 ksi

The formula for Longitudinal (a2) normal stress is

σa2 = Pr / 2t

Where,σa2 = Longitudinal (a2) normal stress

P = Internal Pressure = 45 ksi (Given)

r = Outer radius = 22 in.

t = Wall thickness = 1 in

Substitute the given values,

σa2 = Pr / 2t

= 45 × 22 / (2 × 1)

= 495 ksi

Therefore, Lateral (01) normal stress is 990 ksi and Longitudinal (a2) normal stress is 495 ksi.

2D maximum shearing stress can be given as

τ2D = σ01 / 2

Where,

τ2D = In-plane maximum shearing stress

σ01 = Lateral (01) normal stress = 990 ksi (Calculated in step 1)

Substitute the given values,

τ2D = σ01 / 2

= 990 / 2

= 495 ksi

3D maximum shearing stress can be given as

τ3D = (σa2^2 + 3σ01^2)1/2 / 2

Where,

τ3D = Out of plane maximum shearing stress

σa2 = Longitudinal (a2) normal stress = 495 ksi (Calculated in step 1)

σ01 = Lateral (01) normal stress = 990 ksi (Calculated in step 1)

Substitute the given values,

τ3D = (σa2^2 + 3σ01^2)1/2 / 2

= (495^2 + 3 × 990^2)1/2 / 2

= 1976.9 ksi

Therefore, 2D maximum shearing stress is 495 ksi and 3D maximum shearing stress is 1976.9 ksi.

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The value of the integral \(\int\limits^1_0 {\frac{r^3}{\sqrt{16+r^2} } } \, dr\) after the evaluation of the integral is 0.0612.

Given an integral:

\(\int\limits^1_0 {\frac{r^3}{\sqrt{16+r^2} } } \, dr\)

It is required to find the value of the integral.

There is a formula to find the integration by parts of definite integrals as:

\(\int(udv)=uv-\int(vdu)\)

Here, let u = r².

Then, du = 2r dr

Then, using the formula:

\(dv=\frac{r}{\sqrt{16+r^2} }\)

Then, \(v=\sqrt{16+r^2}\).

Applying the formula,

\(\int\limits^1_0 {\frac{r^3}{\sqrt{16+r^2} } } \, dr=[r^2\sqrt{16+r^2} ]_0^1-\int\limits^1_02r\sqrt{16+r^2} dr\)

For the second integral, let x = 16 + r².

Then, dx = 2r dr

So, the integral becomes \(\int\sqrt{x} dx\) which is \(\int\sqrt{16+r^2} dr\).

So, the integral is:

\(\int\limits^1_0 {\frac{r^3}{\sqrt{16+r^2} } } \, dr=\sqrt{17} -[\frac{2}{3} (16+r^2)^\frac{3}{2}]_0^1\)

                  \(=\sqrt{17} -\frac{2}{3} ((17)^\frac{3}{2} -(16)^\frac{3}{2} )\)

                  \(=0.0612\)

Hence, the integral value is 0.0612.

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Answer:

3(−7)(+2)

5(+5)²

Step-by-step explanation:

f() = 3² - 15 - 42 = 3(−7)(+2)

f() = 5² + 50 + 125 =  5(+5)²

That is how you factor them. Hope this helps :)

Aiden's balance after 15 years will be approximately $1,130.86.

The formula accrued amount in a compounded interest is expressed as;

\(A = P( 1 + \frac{r}{n})^{nt}\)

Where A is accrued amount, P is the principal, r is the interest rate and t is time.

Given that:

Principal P = $675

Compounded annually n = 1

Time t = 15 years

Interest rate r = 3.5%

Accrued amount A =?

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035

Plug the given values into the above formula and solve for accrued amount A:

\(A = P( 1 + \frac{r}{n})^{nt}\\\\A = 675( 1 + \frac{0.035}{1})^{1*15}\\\\ A = 675( 1 + 0.035})^{15}\\\\A = 675( 1.035})^{15}\\\\A = \$ 1,130.86\)

Therefore, the accrued amount is $1,130.86.

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Answer:

- into + equals to -

so -1+ -1= -1 -1

Answer is -2

Step-by-step explanation:

Answer:

the answer is 10/22 when i calculated it

Answer:

Step-by-step explanation:

Answer:

150 people were surveyed.

45/150 = 30% of the people surveyed prefer turkey sandwiches.

B is the correct answer.

Answer:

The rise divided by the run is the slope of a line. The rise and run are used to estimate the slope of a line from its graph.

To determine the intercepts from a graph,  We put y equal to zero and solve for x to find the x-intercept. Similarly, we put x equal to zero and solve for y to find the y-intercept.

Answer:

5/24 or 20.8%

Step-by-step explanation:

Probability that the 7th grader is a boy = number of boys/(total kids) = 4/(4+4) = 1/2

Probability that the 8th grader is a boy = 5/(5+7) = 5/12

Probability that both are boys = 1/2*(5/12) = 5/24 or 20.8%

Answer:

40 gallons

Step-by-step explanation:

Answer:

40 gallons

Step-by-step explanation:

Answer:

Police officers, whether plain-clothed or uniformed, carry a variety of equipment with them on service calls. Police in uniform carry much more equipment than those in plain clothes, and members of special operations teams, such as SWAT and crowd-control units, carry even more, sometimes including full body armour complete with helmet, leg pads, and shield.

Step-by-step explanation:

hope it helped!

p.s it would be cool it you would give me brainliest

The "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values a predetermined percentage of the time.

Thus, the "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

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The length of side AB of the isosceles triangle is 8x + 5.

The formula for finding the length of a isosceles triangle side is given by:

Length of side = √x² +  y²

Where x and y are the lengths of the other two sides.

To find the length of the side AB, we need to first calculate x and y. We know that BC = 4x + 4 and CA = 3x + 9.

Therefore, \(x = BC - CA = 4x + 4 - 3x - 9 = x + -5\)

And \(y = CA - BC = 3x + 9 - 4x - 4 = -x + 5\)

Substituting these values in the formula, we get:

Length of side AB = √((x + -5)² + (-x + 5)²)

= √((x² + 25) + (x² + 25))

= √(2x² + 50)

= √(2(8x + 5)²)

= √(16x2 + 80x + 25)

= 8x + 5

Therefore, the length of side AB is 8x + 5.

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Answer: $ 618

Step-by-step explanation:

Money borrowed =  $1,854

Total months taken to repay = 18  (Number of installments)

Money paid per month = \(\dfrac{\text{Money borrowed}}{\text{Number of installments}}\)

\(=\dfrac{1854}{18}=\$103\)

Now , money paid in 1 year = 12 x $ 103 =$ 1236     [1 year = 12 months ]

After a year , Haley still owe =  $1,854 -  $ 1236= $ 618

Hence, Haley still owe her parents $618 after a year .

The length of the metal tray can be determined by adding the given dimensions of the tray, which are 20 inches and 14 inches, along with the unknown dimensions represented by "X."

To find the length of the metal tray, we need to consider the given dimensions and the unknown dimensions represented by "X." Let's assume that the length of the metal tray is L. From the given diagram, we can observe that the 20-inch dimension corresponds to one end of the tray, and the 14-inch dimension corresponds to the other end of the tray. In between, there are three sections denoted by "X."

Therefore, the expression for the length of the metal tray can be written as L = 20 + X + X + X + 14, which simplifies to L = 54 + 3X. Thus, the length of the metal tray can be calculated by adding the fixed dimensions and three times the value of "X."

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Answer:

The answer should be 11-2x because you cannot break this down any further. And since we are not solving for x, we don't do division. Even if so, it would turn out to be a decimal.

Answer:

Time since the person starts walking is the input

t represents the input

Step-by-step explanation: