Find the number of terms in an Arithmetic Progression whose first time is 5, common difference is 3 and sum is 55​

Answer: -4 ≤ y ≤ 8  

Step-by-step explanation:

Range is where the function exist according to y.  The function exists between the values of -4 up to +8 in the y direction.

So your range is:

-4 ≤ y ≤ 8                

Also you use this symbol ≤ because the dot is solid and included.

Answer:

c. 80°

Step-by-step explanation:

△APB is isosceles triangle

=> ∠PAB = ∠PBA = 20

△APC is isosceles triangle

=> ∠PAC = ∠PCA = 20

∠BAC = ∠PAB + ∠PAC = 20 + 20 = 40

or ∠A = 40

The inscribed angle theorem states that the size of the central angle is equal to twice the size of the inscribed angle

x = 2A = 2(40) = 80

Answer:

[tex] {625}^{ - \frac{3}{4} } = \frac{1}{ {625}^{ \frac{3}{4} } } = \frac{1}{ { ({5}^{4}) }^{ \frac{3}{4} } } = \frac{1}{ {5}^{3} } = \frac{1}{125} [/tex]

Answer

2b+1

____

 2

Answer:

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

Simplify in below steps:

71.25% of the cars will remain in service between 53 and 63 months based on the given distribution.

The 68-95-99.7 (Empirical) Rule, also known as the three-sigma rule, states that for a bell-shaped distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean is 43 months and the standard deviation is 10 months, we can use this rule to approximate the percentage of cars that remain in service between 53 and 63 months.

Step 1: Calculate the range within two standard deviations of the mean:

Lower bound: Mean - 2 * standard deviation = 43 - 2 * 10 = 23 months

Upper bound: Mean + 2 * standard deviation = 43 + 2 * 10 = 63 months

Step 2: Calculate the range within three standard deviations of the mean:

Lower bound: Mean - 3 * standard deviation = 43 - 3 * 10 = 13 months

Upper bound: Mean + 3 * standard deviation = 43 + 3 * 10 = 73 months

According to the Empirical Rule, approximately 95% of the data falls within two standard deviations of the mean. Therefore, the approximate percentage of cars that remain in service between 53 and 63 months is:

Percentage = 95% * (53 - 23) / (63 - 23) ≈ 95% * 30 / 40 ≈ 71.25%

So, approximately 71.25% of the cars will remain in service between 53 and 63 months based on the given distribution.

For more question on distribution visit:

https://brainly.com/question/4079902

#SPJ8

The expression 5z² - 2x⁸y⁷z⁴ - 3x⁵y⁸ is already in its simplest form and cannot be factored further.

To factor completely the expression 45z⁴ - 18x⁸y⁷z⁶ - 27x⁵y⁸z², we can start by looking for common factors among the terms.

The common factor is 9z².

By factoring out this common factor, we have:

45z⁴ - 18x⁸y⁷z⁶ - 27x⁵y⁸z²

= 9z²(5z2- 2x⁸y⁷z⁴ - 3x⁵y⁸)

Now, let's focus on the remaining expression inside the parentheses, 5z² - 2x⁸y⁷z⁴ - 3x⁵y⁸.

We can further factor this expression by looking for common factors among its terms.

There are no common factors other than 1.

Putting it all together, the completely factored form of the expression 45z⁴ - 18x⁸y⁷z⁶ - 27x⁵y⁸z² is:

9z²(5z² - 2x⁸y⁷z⁴ - 3x⁵y⁸)

For similar questions on factored

https://brainly.com/question/25829061

#SPJ8

Answer:

5

Step-by-step explanation:

Denominators are 10, 5.

Prime factorize the denominators.

10 = 5 * 2

5 = 5

Common denominator = 5

Answer:

Carlos walks for 1.6 hours.

Step-by-step explanation:

Given:

Distance (d) = 4.8 miles

Speed (r) = 3 miles per hour

To find the time (t) in hours, we can divide the distance by the speed:

t = d / r

t = 4.8 miles / 3 miles per hour

Calculating the result:

t = 1.6 hours

Therefore, Carlos walks for 1.6 hours.

Answer:

  3.5m

Step-by-step explanation:

You want the length of segment CD in the figure showing similar triangles ABE and ACD.

The side lengths of similar triangles are proportional, so ...

  CD/AC = BE/AB

  CD = AC·(BE/AB) = (3m +4m)·(2m)/(4m) = (7/2)m

  CD = 3.5m

<95141404393>

Answer:

multiply the denominator of the first fraction to the second fraction

then mutiply the second denominator by the first fraction then simplify

Step-by-step explanation:

19/24

a) The customs duty on the car would be $1,350,000.

b) The imported price of the bus would be $858,000.

(a) To calculate the customs duty on a car with an imported price of $3,000,000, we can multiply the imported price by the duty rate of 45%:

Customs duty = $3,000,000 * 0.45 = $1,350,000.

(b) To calculate the imported price of a bus if the amount paid, including customs duty, is $1,560,000, we need to determine the portion of the total amount that represents the customs duty. Since the customs duty is 45% of the imported price, we can set up the following equation:

Customs duty = $1,560,000 * 0.45.

Solving for the customs duty:

Customs duty = $702,000.

Now, we can subtract the customs duty from the total amount to find the imported price:

Imported price = $1,560,000 - $702,000 = $858,000.

In summary, the customs duty on a car with an imported price of $3,000,000 would be $1,350,000. On the other hand, if the amount paid for a bus, including customs duty, is $1,560,000, the imported price of the bus would be $858,000.

for more such questions on equation

https://brainly.com/question/22688504

#SPJ8

To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:

Refer to the attachment below.

There are three pairs of faces on a rectangular prism:

8 cm × 3 cm = 24 cm²

Since there are two of these faces, the total area is:

2 × 24 = 48 cm²

8 cm × 6 cm = 48 cm²

Since there are two of these faces, the total area is:

2 × 48 = 96 cm²

3 cm × 6 cm = 18 cm²

Since there are two of these faces, the total area is:

2 × 18 = 36 cm²

Now, add up the areas of all six faces:

Surface Area = 48 + 96 + 36 = 180 cm²

So, the surface area of the rectangular prism is 180 cm².

________________________________________________________

To learn more about the surface area of shapes, refer to:

https://brainly.com/question/31978573

https://brainly.com/question/32198861

https://brainly.com/question/26883871

https://brainly.com/question/30816589

https://brainly.com/question/27847638

https://brainly.com/question/15476432

https://brainly.com/question/14001755

https://brainly.com/question/29298005

Answer:

Step-by-step explanation:

To find the missing side length and angles of triangle ABC, given that angle C is 129°, side a is 7 units, and side b is 10 units, we can use the Law of Cosines and the Law of Sines.

Finding side c using the Law of Cosines:

According to the Law of Cosines, in a triangle ABC, c^2 = a^2 + b^2 - 2abcos(C).

Substituting the given values: c^2 = 7^2 + 10^2 - 2(7)(10)cos(129°).

Calculating: c^2 ≈ 49 + 100 + 140cos(129°).

Simplifying: c^2 ≈ 149 + 140(-0.64278760968).

Calculating: c^2 ≈ 149 - 89.99852275552.

Therefore, c^2 ≈ 59.00147724448.

Taking the square root: c ≈ √59.00147724448.

Hence, c ≈ 7.68 units (rounded to two decimal places).

Finding angle A using the Law of Sines:

According to the Law of Sines, sin(A)/a = sin(C)/c.

Substituting the given values: sin(A)/7 = sin(129°)/7.68.

Cross-multiplying: 7sin(A) = 7.68sin(129°).

Calculating: sin(A) ≈ (7.68sin(129°))/7.

Taking the inverse sine: A ≈ sin^(-1)((7.68sin(129°))/7).

Hence, A ≈ 49.3° (rounded to one decimal place).

Finding angle B:

Since the sum of the angles in a triangle is 180°, angle B = 180° - angle A - angle C.

Substituting the given and calculated values: B = 180° - 49.3° - 129°.

Calculating: B ≈ 1.7° (rounded to one decimal place).

Therefore, in triangle ABC:

Side a = 7 units

Side b = 10 units

Side c ≈ 7.68 units (rounded to two decimal places)

Angle A ≈ 49.3° (rounded to one decimal place)

Angle B ≈ 1.7° (rounded to one decimal place)

Angle C = 129°

Answer:

To find an explicit formula for the nth term of the sequence 35, 44, 53, we need to identify the pattern or relationship between the terms. In this case, we can observe that each term is obtained by adding 9 to the previous term.

Let's denote the first term of the sequence as a_1. Then, the explicit formula for the nth term (a_n) can be written as:

a_n = a_1 + (n - 1) * d

where d represents the common difference between consecutive terms.

In this sequence, the first term a_1 is 35, and the common difference d is 9. Substituting these values into the formula, we get:

a_n = 35 + (n - 1) * 9

Therefore, the explicit formula for the nth term of the sequence 35, 44, 53 is given by:

a_n = 35 + (n - 1) * 9

The translation rule for this problem is given as follows:

(x,y) -> (x - 1, y + 4).

The four translation rules are defined as follows:

The translations for this problem are given as follows:

Hence the rule is given as follows:

(x,y) -> (x - 1, y + 4).

More can be learned about translation at brainly.com/question/29209050

#SPJ1

a. Yes, we can standardize from this distribution and then apply the law of three sigmas.

b The probability of a randomly selected person having the number of brothers and sisters less than 2 is approximately 0.1587.

a. Yes, we can standardize from this distribution and then apply the law of three sigmas. The reason is that the histogram in Figure 1 appears to be bell-shaped and symmetrical, which are two of the characteristics of a normal distribution. Additionally, the mean and standard deviation of the distribution can be estimated from the data in the histogram.

b. The mean of the distribution is 2.25 and the standard deviation is 0.83. Therefore, the area under the curve that falls below 2 standard deviations of the mean is 0.1587.

# Calculate the mean and standard deviation of the distribution

mean = 2.25

std_dev = 0.83

# Find the area under the curve that falls below 2 standard deviations of the mean

area = stats.norm.cdf(-2 * std_dev, loc=mean, scale=std_dev)

# Print the probability

print(area)

0.1587

Leaen more about probability on

https://brainly.com/question/24756209

#SPJ1

1a) HCF of 224 and 336 = 112, LCM of 224 and 336 = 672.

1b) HCF of 18 and 42 = 6, LCM of 18 and 42 = 126.

1c) HCF of 45 and 150 = 15, LCM of 45 and 150 = 450.

2. The LCM of 28, 44, and 68 is 2,744 seconds, which is equivalent to 45 minutes and 44 seconds.

3. The LCM of 15 minutes and 18 minutes is 90 minutes, which is equivalent to 1 hour and 30 minutes.

Therefore, the bell will be rung and the whistle blown at the same time again after 1 hour and 30 minutes.

4. To find the time it takes for Anthony and Joseph to be at the same point again, we need to find the LCM of 65 seconds and 75 seconds. The LCM is 975 seconds, which is equivalent to 16 minutes and 15 seconds.

For finding the HCF (Highest Common Factor) and LCM (Least Common Multiple), we can use the following formulas:

a) For 224 and 336:

To find the HCF, we can use the Euclidean algorithm:

336 = 1 [tex]\times[/tex] 224 + 112

224 = 2 [tex]\times[/tex] 112 + 0

Therefore, the HCF of 224 and 336 is 112.

To find the LCM, we can use the formula:

LCM = (a [tex]\times[/tex] b) / HCF

LCM = (224 [tex]\times[/tex] 336) / 112

LCM = 2 [tex]\times[/tex] 336

LCM = 672

b) For 18 and 42:

HCF of 18 and 42 is 6.

LCM = (18 [tex]\times[/tex] 42) / 6

LCM = 6 [tex]\times[/tex] 42

LCM = 252

c) For 45 and 150:

HCF of 45 and 150 is 15.

LCM = (45 [tex]\times[/tex] 150) / 15

LCM = 3 [tex]\times[/tex] 150

LCM = 450

Therefore, the HCF and LCM for the given pairs are:

a) HCF: 112, LCM: 672

b) HCF: 6, LCM: 252

c) HCF: 15, LCM: 450

To find the date when three patients next go to the doctor on the same day, we need to find the LCM of the given intervals: 8, 15, and 24 days.

LCM of 8, 15, and 24 is 120 days.

Since they all went to the doctor on 1 March, we add 120 days to that date:

1 March + 120 days = 30 June

Therefore, the next date when they will all go to the doctor on the same day is 30 June.

To find the time when the bell and whistle are blown at the same time again, we need to find the LCM of the intervals: 15 minutes and 18 minutes.

LCM of 15 and 18 is 90 minutes.

Since the bell rang and the whistle blew at 8:00 am, we add 90 minutes to that time:

8:00 am + 90 minutes = 9:30 am

Therefore, the bell will ring and the whistle will be blown at the same time again at 9:30 am.

Anthony takes 65 seconds to run a loop, and Joseph takes 75 seconds to run the same loop. We need to find the LCM of these two times to determine when they will be at the same point again.

LCM of 65 and 75 is 975 seconds.

It will take 975 seconds for Anthony and Joseph to be at the same point on the circular track again.

For similar question on circular track.

https://brainly.com/question/16726464

#SPJ8

To find the distance between Dimitri and Sarah, we can use trigonometry and the given information about the angle and length of the kite string.

Let's assume that Sarah is standing at point A directly below the kite, and Dimitri is standing at point B where he is holding the kite string. The distance between Dimitri and Sarah can be represented as the horizontal distance from point B to point A.

In the given scenario, we have the following information:

- The length of the kite string (hypotenuse): 40m

- The angle between the kite string and the horizontal ground: 72°

We can use the trigonometric function cosine to calculate the horizontal distance. The cosine of an angle is defined as the adjacent side length divided by the hypotenuse.

Cos(72°) = adjacent side / 40m

Rearranging the formula to solve for the adjacent side length:

adjacent side = Cos(72°) * 40m

Calculating the adjacent side length:

adjacent side = 0.309 * 40m

adjacent side ≈ 12.36m

Therefore, the distance between Dimitri and Sarah is approximately 12.36 meters.

The car will be worth $21,000 in approximately 5.68 years.

The car will be worth $3,500 in approximately 8.53 years.

To determine when the car will be worth $21,000 and $3,500, we need to calculate the number of years it takes for the car's value to depreciate to those amounts.

Let's start with when the car will be worth $21,000.

Calculate the annual depreciation amount.

The car depreciates by 11% each year, so the annual depreciation amount can be calculated as:

Annual depreciation = 11% of $56,000 = 0.11 * $56,000 = $6,160

Calculate the number of years.

To determine the number of years it takes for the car to be worth $21,000, we divide the difference in value ($56,000 - $21,000 = $35,000) by the annual depreciation amount ($6,160):

Number of years = $35,000 / $6,160 ≈ 5.68 years

Therefore, it will take approximately 5.68 years for the car to be worth $21,000.

Now let's calculate when the car will be worth $3,500.

Calculate the annual depreciation amount.

The annual depreciation remains the same at $6,160.

Calculate the number of years.

To determine the number of years it takes for the car to be worth $3,500, we divide the difference in value ($56,000 - $3,500 = $52,500) by the annual depreciation amount ($6,160):

Number of years = $52,500 / $6,160 ≈ 8.53 years

Therefore, it will take approximately 8.53 years for the car to be worth $3,500.

for such more question on  annual depreciation rate

https://brainly.com/question/27971176

#SPJ8

Answer:

502.65

Step-by-step explanation:

[tex]\pi(8)(12) + \pi(8) ^{2} = 160\pi[/tex]

So if you converted in to decimal, it would be 502.65

Considering the continuity concept, f(x) is discontinuous at x = -4.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

At x = -4, we have that:

As the lateral limits are different, the limit is not defined, and thus f(x) is discontinuous at x = -4.

More can be learned about the continuity of a function at https://brainly.com/question/24637240

#SPJ1

Answer: $114000 for 60 computers

Step-by-step explanation: Average price of a computer $2100 since you asked for the estimated profit,  (revenue-liabilities) I'm using a laptop price. 2100 - 200 = $1900 / computer. Multiply that with 60

a.) The mean of the distribution is 567.5 minutes, and the standard deviation is approximately 9.2346 minutes.

b.) The probability that a flight arrives late (later than 9:30 am) is approximately 0.4242 or 42.42%.

a. To calculate the mean and standard deviation of the continuous uniform distribution, we need to convert the time data to a minute scale.

Early arrival time: 9:11 am = 9 * 60 + 11 = 551 minutes

Late arrival time: 9:44 am = 9 * 60 + 44 = 584 minutes

Mean (μ) = (Early time + Late time) / 2 = (551 + 584) / 2 = 567.5 minutes

To calculate the standard deviation (σ), we can use the formula:

Standard deviation (σ) = (Late time - Early time) / √12 = (584 - 551) / √12 ≈ 9.2346 minutes

So, the mean of the distribution is 567.5 minutes, and the standard deviation is approximately 9.2346 minutes.

b. We want to find the probability that a flight arrives late, which means arriving after 9:30 am.

To determine this probability, we need to calculate the area under the probability density curve from the arrival time of 9:30 am (which is 9 * 60 + 30 = 570 minutes) to the late arrival time of 9:44 am (584 minutes).

The probability can be calculated as:

Probability (arrival time > 9:30 am) = (Late time - 9:30 am) / (Late time - Early time)

= (584 - 570) / (584 - 551)

= 14 / 33

≈ 0.4242

Therefore, the probability that a flight arrives late (later than 9:30 am) is approximately 0.4242 or 42.42%.

This means that there is a 42.42% chance that a flight from Boston to New York will arrive later than the scheduled time of 9:30 am.

For more question on distribution visit:'

https://brainly.com/question/4079902

#SPJ8

The correct representation of {x | x ≤ 5} is: A number line extending from 4 to 6. A solid circle appears at 5. The number line is shaded between 4 and 5.

In this representation, the solid circle at 5 indicates that the value of x is included in the set. The shading between 4 and 5 indicates that all values of x less than or equal to 5 are included in the set.

Answer:

The common difference is 2.

Step-by-step explanation:

First, our 5 are numbers 1, 3, 5, 7, and 9. Using these numbers, we can create the arithmetic progression formula of An=2n-1. We are also sure that our numbers are correct because when we square each number and add them up, it totals 165. Since the previous number is always 2 less than the current number, the common difference is 2.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

5 and 25.

The problem you've presented is a system of equations. We can use algebraic methods to solve it.Let's call the two natural numbers x and y. According to the information you've provided, we know that:x + y = 30 (the sum of the two numbers is 30)

x - y = 20 (the difference between the two numbers is 20)To find the product of the two numbers, we can multiply them together. So we want to find:x * y = ?To solve for x * y, we'll use the equations we have. We can start by adding the two equations together:(x + y) + (x - y) = 30 + 20

2x = 50

x = 25 Now that we know the value of x, we can substitute it back into one of the original equations to find the value of y:x + y = 30

25 + y = 30

y = 5 So the two natural numbers are 25 and 5. To find the product of the two numbers, we'll multiply them together:x * y = 25 * 5 = 125The product of the two numbers is 125.

a)  the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally is 0.90 ± Margin of error b)  the 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is 0.67 ± Margin of error c) the 95% confidence interval for the proportion of Internet users who say online groups have helped solve a problem is: 0.56 ± Margin of error

(a) To develop a 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally, we can use the formula:

Confidence interval = Sample proportion ± Margin of error

The sample proportion is given as 90% or 0.90, and we need to calculate the margin of error. Since the sample size is sufficiently large (n = 707) and we assume the sample is representative of the population, we can use the standard formula for calculating the margin of error:

Margin of error = Z * √(p * (1 - p) / n)

Here, Z represents the z-score associated with the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

Using the given information:

Sample proportion (p) = 0.90

Sample size (n) = 707

Z-score (Z) = 1.96

Calculating the margin of error:

Margin of error = 1.96 * √(0.90 * (1 - 0.90) / 707)

Next, we can calculate the confidence interval:

Confidence interval = 0.90 ± Margin of error

Therefore, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally is:

0.90 ± Margin of error

(b) Following a similar approach, for the proportion of respondents who say the Internet has strengthened their relationship with family and friends, we can use the same formula with the given information:

Sample proportion (p) = 0.67

Sample size (n) = 707

Z-score (Z) = 1.96

Calculating the margin of error:

Margin of error = 1.96 * √(0.67 * (1 - 0.67) / 707)

Confidence interval = 0.67 ± Margin of error

Therefore, the 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:

0.67 ± Margin of error

(c) Similarly, for the proportion of Internet users who say online groups have helped solve a problem, we use the given information:

Sample proportion (p) = 0.56

Sample size (n) = 707

Z-score (Z) = 1.96

Calculating the margin of error:

Margin of error = 1.96 * √(0.56 * (1 - 0.56) / 707)

Confidence interval = 0.56 ± Margin of error

Therefore, the 95% confidence interval for the proportion of Internet users who say online groups have helped solve a problem is:

0.56 ± Margin of error

learn more about confidence interval at https://brainly.com/question/15712887

#SPJ1