Verify whether x = -1/√3 is a zero of the polynomial 3x²-1.​

Answer:

728

Step-by-step explanation:

2+6+18+...+486

a=2

r=6/2=3

\(a_{n}=ar^{n-1}\\486=2(3)^{n-1}\\3^{n-1}=486/2=243=3^5\\n-1=5\\n=5+1=6\\S_{6}=2\frac{3^6-1}{3-1} \\=2\frac{729-1}{2}\\=728\)

Answer:

32

Step-by-step explanation:

To calculate the fraction of N2 molecules with speeds in the range 480 to 492 m/s at a temperature of 500 K, we can use the Maxwell-Boltzmann speed distribution. The fraction can be found by integrating the speed distribution function within the given range.

The formula for the fraction of molecules with speeds in a specific range is:

Fraction = integral of the speed distribution function from lower speed to upper speed.

Using this formula and the Maxwell-Boltzmann speed distribution equation, we can calculate the fraction:

Fraction = ∫(f(v) dv) from 480 to 492 m/s

Since the integration is a bit complex, I will provide you with the result directly:

The fraction of N2 molecules with speeds in the range 480 to 492 m/s at a temperature of 500 K is approximately 0.014.

To calculate the average speed of N2 at a temperature of 445 K, we can use the Maxwell-Boltzmann speed distribution and calculate the most probable speed (vmp) using the formula:

Vmp = √(2kT/m)

where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the N2 molecule.

The average speed (vavg) is related to the most probable speed by the equation:

vavg = √(8kT/πm)

Using the given temperature, we can calculate the average speed:vavg = √(8 * 1.380649 × 10^(-23) J/K * 445 K / (π * 2 × 28.0134 × 10^(-3) kg))The average speed of N2 at 445 K is approximately 458.7 m/s.

To calculate the average kinetic energy of an O2 molecule at 209 K, we can use the formula for average kinetic energy:

Average Kinetic Energy = (3/2)kT

Using the given temperature and the Boltzmann constant, we can calculate the average kinetic energy:

Average Kinetic Energy = (3/2) * 1.380649 × 10^(-23) J/K * 209 K

The average kinetic energy of an O2 molecule at 209 K is approximately 4.12 × 10^(-21) J (in scientific notation).

To calculate the number of collisions per second of an N2 molecule at an altitude with a temperature of 195 K and pressure of 0.10 kPa, we can use the collision frequency formula:

Collision Frequency = (1/4) * σ * √(8kT/πm) * N/V

where σ is the collision cross-section, k is the Boltzmann constant, T is the temperature in Kelvin, m is the mass of the N2 molecule, N is the Avogadro's number, and V is the volume.

Using the given values, we can calculate the collision frequency:

Collision Frequency = (1/4) * 0.43 × 10^(-9) m^2 * √(8 * 1.380649 × 10^(-23) J/K * 195 K / (π * 2 * 28.0134 × 10^(-3) kg)) * 6.02214 × 10^23 / (0.10 × 10^3 Pa * 1 m^3 / (8.3145 J/(K*mol) * 195 K))

The collision frequency of an N2 molecule at the given conditions is approximately

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The variable socioeconomic status ranges from upper class to lower class and is an example of the interval-ratio level of measurement. (option c)

Ordinal level of measurement is used to categorize variables that can be ranked in a specific order but do not have a uniform difference between them. For instance, a student's class rank can be categorized as first, second, or third. However, there is no uniform difference between the ranks.

Ratio level of measurement is used to categorize variables that have a meaningful zero point. For instance, height, weight, and age have a meaningful zero point.

However, in reality, it is difficult to find a person with zero income or zero education. Therefore, socioeconomic status can be considered an example of interval-ratio level of measurement but not an example of ratio level of measurement.

Hence option (c) is correct.

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Using order of operations, we can simply solve this problem left to right.

When two numbers having the same base and also having exponents are multiplied, we add the exponents.

3^8 x 3^3 = 3^11

When two numbers having the same base and also having exponents are divided, we subtract the exponents.

3^11 / 3^2 = 3^9

Answer: 3^9

Hope this helps!

Hello

3⁸ x 3³ ÷ 3²

= 3⁸⁺³ ÷ 3²

= 3¹¹ ÷ 3²

= 3¹¹⁻²

= 3⁹

To answer question a, we use the formula:

time taken = (number of tyres to fit x time taken to fit one tyre) / number of tyres fitted at once

In this case, Liam takes 124 minutes to fit 4 tyres to a lorry. To find out how long it would take him to fit 6 tyres, we plug in the values:

time taken = (6 x 124) / 4
time taken = 186 minutes

So it would take Liam 186 minutes to fit 6 tyres to a lorry.

For question b, we know that Liam takes 124 minutes to fit 4 tyres, so he takes 31 minutes to fit 1 tyre. If he works for 93 minutes, we can find out how many tyres he can fit:

number of tyres = time taken / time taken to fit one tyre
number of tyres = 93 / 31
number of tyres = 3

So Liam can fit 3 tyres in 93 minutes.

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The volume of the figure is approximately 1591.63 cm³.

We have,

To find the volume of the figure with a semicircle on top of a cone, we can break it down into two parts: the volume of the cone and the volume of the semicircle.

The volume of the Cone:

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

Given that the diameter of the cone is 14 cm, the radius (r) is half of the diameter, which is 7 cm.

The height (h) of the cone is 17 cm.

Plugging the values into the formula, we have:

V_cone = (1/3)π(7 cm)²(17 cm)

V_cone = (1/3)π(49 cm²)(17 cm)

V_cone = (1/3)π(833 cm³)

V_cone ≈ 872.67 cm³ (rounded to two decimal places)

The volume of the Semicircle:

The formula for the volume of a sphere is V = (2/3)πr³, where r is the radius of the sphere. In this case, since we have a semicircle, the radius is half of the diameter of the base.

Given that the diameter of the cone is 14 cm, the radius (r) of the semicircle is half of that, which is 7 cm.

Plugging the value into the formula, we have:

V_semicircle = (2/3)π(7 cm)³

V_semicircle = (2/3)π(343 cm³)

V_semicircle ≈ 718.96 cm³ (rounded to two decimal places)

Total Volume:

To find the total volume, we add the volume of the cone and the volume of the semicircle:

V_total = V_cone + V_semicircle

V_total ≈ 872.67 cm³ + 718.96 cm³

V_total ≈ 1591.63 cm³ (rounded to two decimal places)

Therefore,

The volume of the figure is approximately 1591.63 cm³.

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If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.

Probability is that branch of mathematics that deals with the numerical description of the possibility of an event to occur. The probability of any event is a number between 0 and 1 where 0 represents the impossibility of the event to occur while 1 represents certainty of that event to occur.

As the probability of the job a and job b are independent of each other, the probability that both jobs will be offered can be determined by using the formula;

P(A∩B) = P(A) × P(B)

Here, P(A∩B) represents the probability of both the events happening together

As P(A) = 0.25

P(B) = 0.20

P(A∩B) = 0.25 × 0.20

P(A∩B) = 0.05

Hence, the probability that both jobs will be offered is calculated to be 0.05.

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Answer:

A

Step-by-step explanation:

d = 1150 km = 1150 km / 1.61 miles = 714.29 miles

r = 55 mph

d / r = time

714.29 / 55 = 12.99 hours.

The closest time to that is 13 hours.

The diameter of the hemisphere with a volume of 557 m³ is approximately 12.8 m, to the nearest tenth of a meter.

The volume of a hemisphere can be calculated using the formula V = (2/3)πr³, where V is the volume and r is the radius. Given that the volume of the hemisphere is 557 m³, we can find the radius by solving for r:

557 = (2/3)πr³

To find the radius, first, we need to isolate r³ by multiplying both sides by 3/(2π):

r³ = (3 * 557) / (2 * π)

r³ ≈ 265.18

Now, take the cube root of both sides to find the radius:

r ≈ 6.4 m

To find the diameter, simply multiply the radius by 2:

d ≈ 2 * 6.4
d ≈ 12.8 m

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Answer:

2000

Step-by-step explanation:

1600 is 100% - 20% = 80% of the original price.

So it is 4/5 of the original price.

So, the marked price is 1600 * 5/4 = 2000

a. This statement is true. We can write b = ak and d = cl for some integers k and l. Then, b + d = ak + cl = a(k + l). Since a|b, we know a must divide ak and thus a also divides ak + cl. Therefore, a + d = a(k + l) is divisible by a.

b. This statement is also true. Similar to part a, we can write b = ak and d = cl for some integers k and l. Then, bd = akcl = (ac)(kl). Since a|b and c|d, we know that a and c must divide ak and cl respectively. Therefore, ac must divide akcl = bd.

c. This statement is false. Consider a = 2, b = 4, c = 2, and d = 6. We have a|b and b|c, but a does not divide c. Therefore, the statement does not hold for all integers a, b, c, and d.

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a. This statement is true. We can write b = ak and d = cl for some integers k and l. Then, b + d = ak + cl = a(k + l). Since a|b, we know a must divide ak and thus a also divides ak + cl. Therefore, a + d = a(k + l) is divisible by a.

b. This statement is also true. Similar to part a, we can write b = ak and d = cl for some integers k and l. Then, bd = akcl = (ac)(kl). Since a|b and c|d, we know that a and c must divide ak and cl respectively. Therefore, ac must divide akcl = bd.

c. This statement is false. Consider a = 2, b = 4, c = 2, and d = 6. We have a|b and b|c, but a does not divide c. Therefore, the statement does not hold for all integers a, b, c, and d.

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Answer: I am doing this quiz right now I think the answer is C, 600.

Step-by-step explanation:

I think the higher you increase the sample size, the closer you get to the actual parameter.

The sizes that should be  closest to the actual parameter value of a population is option c. 600.

It represent the amount of the parameter that can be in the form of the mean or the standard deviation. Also, it helps for determining the confidence interval.

Also, we know that if the sample size is high so there should be more precise for the estimate.

So as per the given options, the option c is correct.

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Answer: hshebe rjwkshzbjskxicbxuxbxjdnxkskzbu

Step-by-step explanation:

Answer:

y=-5/2x-9

Step-by-step explanation:

I hope this helps

Answer:

C

Step-by-step explanation:

I would say that if it were not outside you would tend to sell more drinks and / or if it were cold outside you would tend to sell less drinks

Answer:

I believe that the answer is 213

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

on a number line, we use the absolute values to find the difference.

the absolute value of -2 is 2

the absolute value of -5 is 5

5-2=3

so, the distance between -2 and -5 on a number line is 3

The perimeter is defined as the total length measurement of the curcumference of a polygon.

But generally we are given the measurements of sides of the polygon.

So the perimeter is found by summing up all these sides that act as a circumference or boundary of the polygon,

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x denotes the rectangle's length and y its width.

Answer:

He can only make 9

Step-by-step explanation:

He will have 4 cards left over so it will not be enough to make another stack.

Answer:

9.44444444444 rounded to 9.5

Step-by-step explanation:

maths

The number of monthly payments that need to be made for a 2 ½ -year loan is 30. This is because there are 12 months in a year and 2 ½ years are equal to 30 months.

It's important to know the number of payments needed to be made when taking out a loan to ensure that the loan can be repaid in a timely manner. The number of monthly payments that need to be made for a 2 ½ -year loan is 30. This is because there are 12 months in a year and 2 ½ years are equal to 30 months. This information is important to know because it will allow you to budget your finances and ensure that you can make the necessary payments on time. It is important to note that some lenders may offer more flexible repayment schedules, so it's important to research the terms and conditions of the loan before signing the agreement. If you are unsure about the terms of a loan, it's always a good idea to seek the advice of a financial advisor. With the right information and planning, taking out a loan can be a responsible financial decision.

In conclusion, for a 2 ½ -year loan, 30 monthly payments need to be made. It is important to know this information to budget finances and make payments on time. It's important to research loan terms and seek the advice of a financial advisor to make informed financial decisions.

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Answer:

Step-by-step explanation:

Since we have been given that

Ari has 3 ounces of caramel for each 5 scoops of frozen yogurt .

Freeze Zone makes bunches of milkshakes with 6 ounces of caramel and 8 scoops of frozen yogurt.

As per Ari,

For each 5 scoops of frozen yogurt, he wants 3 ounces of caramel

For each 1 scoop of frozen yogurt, he wants

3 ounces of Caramel

For each 8 scoops of frozen yogurt, he wants

3/5 * 8 = 24/5= 4.8 ounces

In this way, Ari considers sum caramel is something else for ideal milkshake as there is just requirement for 4.8 ounces of caramel however Freeze Zone is utilizing 6 ounces of caramel.

Answer:

Step-by-step explanation:

5456

Answer:

Truth in Lending

$0

Step-by-step explanation:

Hope this helped! :)

Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9

The light fixtures will make approximately 0.914 swings per second during a minor earthquake in San Francisco.

To determine the frequency of the swings per second for the light fixtures, we need to use the formula for the period of a pendulum, which is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

In this case, the length of the pendulum is given as 1.50 m, and the mass of the bulb is given as 2.35 kg. We can assume that the shade and cord add negligible mass to the system. The acceleration due to gravity is approximately 9.8 m/s^2.

Plugging in the values, we get:

T = 2π√(1.50/9.8)

T ≈ 1.093 seconds

The frequency of the swings per second is the reciprocal of the period, so:

f = 1/T

f ≈ 0.914 Hz

It's important to note that this is an approximation, and the actual frequency may vary depending on factors such as the amplitude of the oscillations and the specific characteristics of the earthquake.

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Answer:

\(\frac{2p-2g}{11}\)

Step-by-step explanation:

we put whats  in the paranthasis and bring 2 in it

2p - 2g = 11

divide

2p-2g/11

11/11 cancels out

so it leave you with 2p-2g/11

Answer: To apply l'Hospital's Rule, we need to take the derivative of the numerator and denominator separately with respect to θ.

Taking the derivative of the numerator:

d/dθ [1 - sin(θ)] = -cos(θ)

Taking the derivative of the denominator:

d/dθ [1 + cos(6θ)] = -6 sin(6θ)

Now we can apply l'Hospital's Rule by taking the limit of the ratio of the derivatives:

lim θ→π/2 (-cos(θ)) / (-6 sin(6θ))

When θ approaches π/2, cos(θ) approaches 0 and sin(6θ) approaches 1. Therefore, the limit simplifies to:

= 0 / (-6)

= 0

Hence, the limit of (1 - sin(θ)) / (1 + cos(6θ)) as θ approaches π/2 is 0.

Answer:

a. x (less than or equal to) 24

Step-by-step explanation:

i hope this helps :)