Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?

Final answer:

To find the nth term equation of an arithmetic sequence, we first determined the common difference to be 92 by given terms, and then found the first term by using the formula for arithmetic sequences. The nth term equation for the sequence is: an = -1489 + (n-1)(92).

Explanation:

To find the nth term equation of the arithmetic sequence, we need to determine the common difference and the first term of the sequence. Since we know the 18th term, a18 = 97, and the 20th term, a20 = 281, we can find the common difference, d, by subtracting the two given terms and dividing by the number of terms between them:

d = (281 - 97) / (20 - 18) = 184 / 2 = 92.

Once we have the common difference, we can use the following formula to find the first term (a1):

an = a1 + (n-1)d.

Let's substitute n = 18 and d = 92 into the formula:

97 = a1 + (18-1)(92)

a1 = 97 - (17)(92) = -1489.

Now we can write the equation for the nth term of the arithmetic sequence:

an = -1489 + (n-1)(92).

The expression which represents a difference of m and 7 increased by 15 will be (m - 7) + 15.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

The difference between m and 7 is

m - 7

Increased also referred for addition so

Increased by 15 is ( m - 7) + 15

Hence "The expression which represents a difference of m and 7 increased by 15 will be (m - 7) + 15".

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Final answer:

To construct a fence around a 90 ft by 175 ft lot at $1.25 per linear foot and $.825 per square foot for materials, it would cost a total of $13,656.25.

Explanation:

To calculate the cost of constructing a fence for a lot that measures 90 ft by 175 ft with a fence height of 6'6" (6.5 ft), we need to determine both the perimeter of the lot for the linear feet cost and the total area for the material cost per square foot.

The perimeter of the lot is 2*(90 + 175) = 2*265 = 530 feet. So, the cost of erecting the fence at $1.25 per linear ft is 530 ft * $1.25/ft = $662.50.

The total area that needs to be fenced is 90 ft * 175 ft = 15,750 square feet. Thus, the cost of materials at $.825 per square ft is 15,750 sq ft * $0.825/sq ft = $12,993.75.

The total cost of constructing the fence is the sum of the cost of erecting the fence and the cost of materials, which adds up to $662.50 + $12,993.75 = $13,656.25.

Answer: The length of PQ = 64

Step-by-step explanation:

We are given that ΔPQR and ΔABC are similar right triangles .

Since, we know that the corresponding sides of similar triangles are proportional.

Therefore, we get

[tex]\dfrac{PQ}{AB}=\dfrac{QR}{BC}\\\\\Rightarrow\dfrac{PQ}{16}=\dfrac{80}{20}\\\\\Rightarrow\ PQ=4\times16\\\\\Rightarrow\ PQ=64[/tex]

Hence, the length of side PQ = 64 units

Answer: 95%

Step-by-step explanation:

A P E X

Option A. is the correct answer. Using the empirical rule and the provided narrow interval, the confidence level for the confidence interval of 46.6% to 47.4% is most likely 68%.

The question is asking to find the confidence level for a given confidence interval. In the scenario, a building manager finds that 47% of the time, people turn off the lights when they leave the room, with a sample standard deviation of 4%. To calculate the confidence level for the interval of 46.6% to 47.4%, we'd typically use a Z-score or t-score formula along with the sample size to determine which confidence level corresponds to the given interval. However, the provided question does not give us enough information to perform a calculation; thus, it is likely that the question expects us to understand the empirical rule (also known as the 68-95-99.7 rule).

Based on the empirical rule, the intervals corresponding to one, two, and three standard deviations from the mean (for a normal distribution) contain approximately 68%, 95%, and 99.7% of the data, respectively. Since the given confidence interval, 46.6% to 47.4%, is quite narrow and is likely to correspond to a plus or minus one standard deviation from the sample mean, the correct confidence level would be approximately 68% (Answer A). This assumption is due to the small range of the interval (0.4%) compared to the sample standard deviation (4%).

Answer:

Apply the Distance Formula to show that opposite sides pq and rs are congruent

Answer:

3(x+12)

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10

(three times x plus twelve OVER ten)

Step-by-step explanation:

You are given the mass of CaH₂ which is 14 grams and H₂O which is 28 grams. You are required to find the maximum volume of H₂ gas at STP. The balanced chemical reaction is CaH₂ + 2H₂O → Ca(OH)₂ + H₂. Note that for every one mole of CaH₂, 2 moles of H₂O is needed to completely react and produce Ca(OH)₂ + H₂. So the CaH₂ and H₂O are at equal proportions. At STP, temperature is at 0°C(273K) and pressure at 1 atm. The molar mass of CaH₂ is 42 grams per mole.

14g CaH₂(1mol CaH₂/42 grams CaH₂)(1mol H₂/1mol CaH₂) = 0.333 moles H2

The ideal gas equation is PV = nRT, with R(gas constant) = 0.08206 L-atm/mol-K. get the equation for volume, we have

V = nRT/P

V = (0.333mol H₂)(0.08206 L-atm/mol-K)(273K)/1atm

V = 7.47L

The answer is a positive integer.

The set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

All outcomes in flipping 3 coins then the number of samples will be:-

Sample space of all outcomes

Sample space = {HHH,THH, HTH, HHT, TTT, HTT, THT, TTH} = 8 =All possible outcomes.

Sample space of all favorable outcomes (more tails than heads)

Favourable outcomes= {TTT, HTT, THT, TTH} = 4 = All favorable outcome.

Therefore, the set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.

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Final answer:

To determine the distance from the ends of the couch to the nearest wall, convert all measurements to inches, find the difference between the room and couch lengths, and divide by two. The ends of the couch will be 0.75 feet or 9 inches from the nearest wall.

Explanation:

The question involves determining the distance from the ends of a couch to the nearest wall when the couch is centered in a 12 feet by 12 feet room. The couch is 10 feet and 6 inches long.

To solve this, first convert the couch length to inches. 10 feet is 120 inches, and adding 6 inches gives us a total of 126 inches for the couch length. Since 1 foot equals 12 inches, the room's length in inches is 12 feet times 12 inches per foot, which equals 144 inches.

Now, to find the distance from each end of the couch to the nearest wall, we subtract the couch length from the room's length:

Divide the difference by 2 to get the distance from each end of the couch to the wall:

Finally, convert this distance back to feet:

Therefore, each end of the couch will be 0.75 feet, or 9 inches, from the nearest wall when the couch is centered in the room.

Hello:
the equation is : y = ax+b
the slope is a : a×(2/3) = -1......( perpendicular to a line : 2x-3y =7 with a slope of 2/3 because : y = (2/3)x-7/3)
a = -3/2         y=(-3/2)x+b
the line that passes through (-2, 1) : 1 = (-3/2)(-2)+b
b = -2
 the equation is :  y  = (-3/2)x-2

Using trigonometric functions, specifically the tangent function, we create two equations corresponding to two right triangles formed by the lines of sight from the ground floor and from 60 feet high in the elevator. Solving those equations simultaneously, we can calculate that the height of the building across the street is approximately 149 feet.

This is a trigonometry problem where we're going to establish two right triangles with the elevator as one side, the building across the street as another (the one we're trying to find), and the line of sight as the hypotenuse. From the ground, we form a triangle with the angle of elevation of 51 degrees. Then from 60 feet above the ground, we form another triangle with an angle of elevation of 34 degrees.

Here, we apply tangent of an angle which equals the opposite over adjacent sides in a right triangle. So, we get tan(51) = h/x and tan(34) = (h-60)/x. We have two unknowns here: 'h' which is the height of the building and 'x' the distance from the elevator to the building. Solving these equations simultaneously, we can find 'h'.

If we solve these equations, we'll get 'h' equals approximately 149 feet (rounding to the nearest foot). So, the building across the street is around 149 feet tall.

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Final answer:

The frequency of the function y = cos5x is 5/2π.

Explanation:

The given function is y = cos5x. To find the frequency of this function, we need to determine the coefficient of x in the argument of the cosine function. In this case, the coefficient is 5, which means the argument of the cosine function will complete 5 full cycles in an interval of 2π.

The frequency of a function is the reciprocal of the period. The period is found by dividing 2π by the coefficient of x. So, the period of the given function is 2π/5, and the frequency is the reciprocal of the period, which is 5/2π.

Therefore, the frequency of the function y = cos5x is 5/2π.