A circle has a radius of 6 in.
What is the exact length of an arc formed by a central angle measuring 45°?

Express your answer using π

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

There is a geometric sequence:

where a₁ = 2

r = √2

We need to find a₉:

As we know the formula for "nth term ":

[tex]a_n=ar^{n-1}\\\\a_9=ar^{9-1}\\\\a_9=ar^8\\\\a_9=2\times (\sqrt{2})^8\\\\a_9=32[/tex]

Hence, First option is correct.

factor X + 1 is the answer

The value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees) can be found by using the identity sin(90° - x) = cos(x), leading to x = 22.67° (or in radians by converting degrees to radians).

To find the value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees), we can utilize the trigonometric identity sin(90° - x) = cos(x). By setting the angle inside the cosine to equal 90° - (x + 22°), we can equate this to (2x - 7°) as both represent the same cosine value.

So we have the equation 90° - (x + 22°) = 2x - 7°. Solving for x, we combine like terms: 68° = 3x, which then gives us x = 68°/3. Therefore, x = 22.67°, which is the angle in degrees.

If we needed to find x in radians, we would have to convert degrees to radians by using the conversion factor: π radians = 180°. This would yield x as x = (22.67°/180°) * π.

The probability of getting at least 1 correct answer when guessing on a multiple-choice test can be found by subtracting the probability of getting all answers wrong from 1. Whether it is reasonable to expect to pass by guessing depends on the passing percentage and the probability of getting at least 1 answer correct.

To find the probability of getting at least 1 correct answer when making random guesses for 10 multiple-choice test questions, we can look at the probability of getting 0 correct and subtract it from 1. Since each question has 5 possible answers, the probability of getting a question wrong is 4/5. So the probability of getting all 10 questions wrong is (4/5)^10. Therefore, the probability of getting at least 1 correct answer is 1 - (4/5)^10.

To determine if you can reasonably expect to pass the test by guessing, we need to compare the probability of getting at least 1 correct answer to the passing percentage. If the probability of passing is higher than the passing percentage, then it is reasonable to expect to pass by guessing.

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Answer:

1/7,776

Step-by-step explanation:

the odds of getting an end zone seat once is 1/6 so you multiply that by itself 5 times to get your answer.

1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 = (1/6)^5 = 1/7,776.

The probability that a certain student would get end zone seats at all 5 home games is [tex]\frac{1}{7776}[/tex]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given,

A university football stadium has 1/6 of its students' seats in the end zones

Probability = Number of Favorable outcome / Number of total outcome

Probability that a certain student would get end zone = [tex]\frac{1}{6}[/tex]

Probability that a certain student would get end zone in 5 game = [tex](\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )=\frac{1}{7776}[/tex]

Hence, the probability that a certain student would get end zone seats at all 5 home games [tex]\frac{1}{7776}[/tex]

Learn more about Probability here

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Solution:

Let volume of cylinder be K times more than volume of Cone.

⇒K × Volume of Cone = Volume of Cylinder

[tex]K \times \frac{\pi\times r^2 \times h }{3}=\pi \times R^2 \times H\\\\K \times 5^2 \times 10= 3 \times 10^2 \times 20\\\\250 K=3 \times 100 \times 20\\\\K=\frac{6000}{250}\\\\K=24[/tex]

⇒Number of times one needs to use the completely fill cone to completely fill the cylinder with water is=24

Answer:

[tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream

Step-by-step explanation:

Using unitary method,  

Unitary method is a method use to find the value of a unit quantity.

[tex]6\frac{3} {10}[/tex] gallon of milk needed to make [tex]4\frac{1}{2}[/tex] gallon of milk

[tex]\frac{63}{10}[/tex] gallon of milk needed to make [tex]\frac{9}{2}[/tex] gallon of ice cream

One gallon of ice cream needed = [tex]\frac{63}{10} \times \frac{2}{9}[/tex] gallon of milk

                                                        = [tex]\frac{7}{5}[/tex] gallon of milk

                                                         = [tex]1\frac{2}{5}[/tex] gallon of milk

Thus, [tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream.

Answer:

[tex]x=9.5[/tex]  

[tex]y=8.8[/tex]  

Step-by-step explanation:

We have been given a diagram of triangles. We are asked to find the value of x and y.

We can see that triangle JKL and JMN share same vertex that is angle J. Since line KL is parallel to line MN, therefore, there corresponding angles will be equal.

Therefore, Angle-angle-angle similarity [tex]\Delta JKL\sim \Delta JMN[/tex].

Since corresponding sides of similar triangles are always proportional, so we can set a proportion for the sides of our given triangles as:

[tex]\frac{x-2}{5}=\frac{12}{8}[/tex]

Upon cross multiplying our equation we will get,

[tex]8(x-2)=12*5[/tex]

[tex]8x-16=60[/tex]

Let us add 16 to both sides of our equation.

[tex]8x-16+16=60+16[/tex]

[tex]8x=76[/tex]

Let us divide both sides of our equation by 8.

[tex]\frac{8x}{8}=\frac{76}{8}[/tex]  

[tex]x=9.5[/tex]  

Therefore, x equals 9.5.

We can also set a proportion to solve for y as:

[tex]\frac{y}{22}=\frac{8}{12+8}[/tex]

[tex]\frac{y}{22}=\frac{8}{20}[/tex]

Upon cross multiplying our equation we will get,

[tex]20y=22*8[/tex]

[tex]20y=176[/tex]

Let us divide both sides of our equation by 20.

[tex]\frac{20y}{20}=\frac{176}{20}[/tex]

[tex]y=8.8[/tex]

Therefore, y equals 8.8.

She invests some amount in a saving account of fixed interest compounded half-yearly. It says to find its Future Value after six years.

The principal amount is P = $4,848.

Annual interest rate is 5% i.e. r = 0.05

Compounding period is two times per year i.e. n = 2.

Time of investment is t = 6 years.

We know the formula of Future Value is given by :-

[tex] FV=P*(1+\frac{r}{n})^{nt} [/tex]

We can plug the given values in the formula to calculate the answer.

[tex] FV = 4848*(1+\frac{0.05}{2})^{(2*6)} \\\\
FV = 4848*(1+0.025)^{(12)} \\\\
FV = 4848*(1.025)^{(12)} \\\\
FV = 4848*(1.344888) \\\\
FV = 6520.02102 [/tex]

Hence, future value of investment after six years is 6,520.02 dollars.

The question involves calculation of compound interest. The formula to use is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.

This question involves the concept of compound interest. Compound interest is calculated each period on the original deposit, or principal, along with any interest previously earned. Unlike simple interest which only takes into account the principal amount, compound interest accounts for the interest that accumulates on the initial amount as well as the interest that has previously been added.

In Brenda's case, as she's benefiting from compounded interest, the formula to use here is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.

So, plug in the given values: P=$4848, r=0.05 (as 5% = 5/100), t=6, and n=2 (since it's compounded semi-annually). This will allow us to find the final account balance after 6 years.

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answer= 28.26

Step-by-step explanation:

your welcome

Answer:

Step-by-step explanation:

11.4

central angle theta (in radians) = arc length / radius

So theta = 5.6/8 = 0.7 radians

The central angle measure for a circle with an 8 cm radius and a 5.6 cm intercepted arc length is 0.7 radians.

The question asks to find the measure in radians for the central angle of a circle with a radius of 8 cm and an intercepted arc length of 5.6 cm. To calculate the central angle in radians, we use the formula θ = [tex]\frac{l}{r}[/tex], where θ is the central angle in radians, l is the arc length, and r is the radius of the circle. Substituting the given values, we get θ =  [tex]\frac{5.6}{8}[/tex]

Through calculation, θ = 0.7 radians. So, the measure of the central angle that intercepts an arc length of 5.6 cm in a circle with a radius of 8 cm is 0.7 radians.

To simplify expressions, one needs to apply rules correctly, such as combining like terms and using exponentiation rules. The process includes correctly applying the rule that simplifies multiplications of the same base by adding their exponents. Cubing exponentials involves multiplying the original exponent by 3.

To simplify mathematical expressions, it's crucial to follow the correct rules and operations. In this case, the example provided shows the exponentiation and multiplication rules. Specifically, when dealing with expressions like 3².3⁵, this is equivalent to multiplying 3 x 3 and then taking that result and multiplying it by 3 five more times. According to the rule xPx9 = x(p+q), where x is the base and p and q are the exponents, it simplifies to adding the exponents when the base number is the same and multiplied together.

The process of simplifying expressions involves several steps:

Additionally, when cubing exponentials, one should cube the digit normally and multiply the existing exponent by 3, a rule demonstrated in squaring operations as well.