1) find at least 3 different sequences starting with 1,2,4 where the terms are generated by a simple rule. 2) suggest a closed formula for sum . use it to compute

Answers

Answer 1

Here are three different sequences starting with 1, 2, and 4 respectively, where the terms are generated by a simple rule:

1) Sequence starting with 1: 1, 3, 5, 7, 9...
This sequence is generated by adding 2 to the previous term.

2) Sequence starting with 2: 2, 4, 8, 16, 32...
This sequence is generated by multiplying the previous term by 2.

3) Sequence starting with 4: 4, 7, 10, 13, 16...
This sequence is generated by adding 3 to the previous term.

Now, to suggest a closed formula for the sum of these sequences, we can use the formula for the sum of an arithmetic sequence:
S_n = n/2(2a + (n-1)d)

Where:
- S_n is the sum of the first n terms of the sequence
- a is the first term of the sequence
- d is the common difference between consecutive terms of the sequence
- n is the number of terms in the sequence

For the first sequence (1, 3, 5, 7, 9...), a=1 and d=2 (since we add 2 to the previous term to get the next term). If we want to find the sum of the first 10 terms of this sequence, we can plug in these values into the formula:

S_10 = 10/2(2(1) + (10-1)2)
S_10 = 10/2(2 + 18)
S_10 = 10/2(20)
S_10 = 100

Therefore, the sum of the first 10 terms of this sequence is 100.

You can use a similar method to find the sum of the other two sequences as well.

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Related Questions

please help sorry if its a lot

Answers

The values in the expression will be:

a. 4x

b. -4x

c. -16x

d. 4x + 5

e. 4x

f. 5x

g. 10 - 6x

h. 2x - 10

How to explain the expression

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

Based on the information, it should be noted that:

10x - 6x

= 4x

6x - 4x

= 2x

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A sleep study administered to US adults showed that the amount of sleep (in hours) they get in a 24- hour period is normally distributed with a mean of 6.5 hours and a standard deviation of 1.25 hours. Use normal probability calculations to answer the follwing questions. Show your calculator functions to receive full credit. Round your answers to 4 decimals. 1. (no pts) A. How many hours of sleep did you get last night (round to nearest quarter of an hour)? B. Ask an adult friend or a family member how many hours of sleep he/she got last night (round to nearest quarter of an hour). Report below. Make sure it is different than your sleep amount. 2. (2 pts) What is the probability that a randomly selected US adult slept more than you did last night? 3. (2 pts) What is the probability that a randomly selected US adult slept less than your friend or family member did last night? 4. (2 pts) Doctors recommend 8 hours of sleep per day for adults to have the health benefits of sleep. What percent of US adults sleep less than this recommended amount? 5. (2 pts) A colleague at work says that she usually sleeps less than 4 hours each day. Is her sleep amount unusual? Justify your answer by calculating its probability. 6. (2 pts) 10% of US adults sleep more than how many hours?

Answers

10% of US adults sleep more than 7.9 hours per day .

We need to calculate the z-score for your sleep amount and find the area to the right of that z-score. z = (x - μ) / σ = (x - 6.5) / 1.25. Let's assume you got 7 hours of sleep. z = (7 - 6.5) / 1.25 = 0.4. Using a standard normal table or calculator, we find that the probability of a randomly selected US adult sleeping more than you did last night is 0.3446 (or 34.46%).

We need to calculate the z-score for your friend's sleep amount and find the area to the left of that z-score. z = (x - μ) / σ = (7.25 - 6.5) / 1.25 = 0.6. Using a standard normal table or calculator, we find that the probability of a randomly selected US adult sleeping less than your friend or family member did last night is 0.2743 (or 27.43%).

We need to calculate the z-score for 8 hours of sleep and find the area to the left of that z-score. z = (8 - 6.5) / 1.25 = 1.2. Using a standard normal table or calculator, we find that the percentage of US adults sleeping less than 8 hours per day is 0.1151 (or 11.51%).

We need to calculate the z-score for 4 hours of sleep and find the area to the left of that z-score. z = (4 - 6.5) / 1.25 = -2.0. Using a standard normal table or calculator, we find that the probability of a US adult sleeping less than 4 hours per day is 0.0228 (or 2.28%). This is a very low probability, so we can say that sleeping less than 4 hours per day is unusual.

We need to find the z-score that corresponds to the top 10% of the distribution. Using a standard normal table or calculator, we find that the z-score is approximately 1.28. Then, we can solve for x: z = (x - μ) / σ -> 1.28 = (x - 6.5) / 1.25 -> x = 7.9 hours. So, 10% of US adults sleep more than 7.9 hours per day.

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Suppose follows the standard normal distribution. Use the calculator provided, or that, to determine the value of c so that the following true P(2>c) 0.2643 Round your answer to two decimal places 0 X

Answers

The z-score for 0.7129 is approximately 0.55. The value of c is 0.55, rounded to two decimal places.

1. We're given P(2 > c) = 0.2643, which means the area under the standard normal distribution curve between 2 and c is 0.2643.

2. We'll use the z-table or a calculator with a standard normal distribution function to find the corresponding z-score for c.

3. To find the area to the left of c, we need to first find the area to the left of 2. The z-score for 2 is 0.9772 (from the z-table or using a calculator).

4. Now, subtract the given area (0.2643) from the area to the left of 2: 0.9772 - 0.2643 = 0.7129.

5. Look up the z-score corresponding to the area 0.7129 in the z-table, or use a calculator with the inverse standard normal distribution function. The z-score for 0.7129 is approximately 0.55.

6. Therefore, the value of c is 0.55, rounded to two decimal places.

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When the population standard deviation is known, the confidence interval for the population mean is based on the:Chi-square statistict-statisticz-statisticF-statistic

Answers

When the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic.

When the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic.

The formula for the confidence interval for the population mean when the population standard deviation is known is given by:

CI = X ± z(α/2) * σ/√n

Where:

X is the sample mean

σ is the population standard deviation

n is the sample size

z(α/2) is the z-score corresponding to the desired level of confidence (e.g. for a 95% confidence interval, α = 0.05 and z(α/2) = 1.96)

The z-statistic is used in this formula to determine the width of the confidence interval. It is based on the standard normal distribution and represents the number of standard deviations the sample mean is from the population mean. The z-score is calculated using the formula:

z = (X - μ) / (σ/√n)

Where μ is the population mean.

The z-score is used to find the critical values for the confidence interval, which are obtained by multiplying it by the standard error of the mean (σ/√n). These critical values define the endpoints of the confidence interval.

In summary, when the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic, which is used to calculate the critical values for the confidence interval.

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In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of people it contains. Here is the assignment of probabilities for the outcome. (The probability of finding 3 people in a household is the same as the probability of finding 4 people.) What probability should replace "?" in the table? Remember: there is a larger version of the charts on my website!answer choicesa. 0.04b. 0.09c. 0.32d. 0.16

Answers

Based on the information given, we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people. Therefore, the probability that a randomly chosen American household contains 2 or 5 people is 1/6.

To determine the probability that should replace "?" in the table, we first need to recognize that the sum of probabilities for all possible outcomes must equal 1. Given that the probability of finding 3 people in a household is the same as the probability of finding 4 people, let's denote that probability as x.

Since the "?" represents the remaining probability, we can set up an equation:
x + x + ? = 1

The sum of the probabilities for all possible outcomes must equal 1. We know that there are 4 possible outcomes (households with 2, 3, 4, or 5 people).

Simplifying the equation:
3x + ? = 1

Since we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people, we can set up another equation:

Now, let's plug in the answer choices and see which one gives us a valid probability distribution:

a) 0.04:
2x + 0.04 = 1
2x = 0.96
x = 0.48 (Invalid, since x should be the probability for finding 3 or 4 people and it's greater than the maximum probability value of 1)

b) 0.09:
2x + 0.09 = 1
2x = 0.91
x = 0.455 (Invalid for the same reason as options a)

c) 0.32:
2x + 0.32 = 1
2x = 0.68
x = 0.34 (Valid, as it falls within the probability range of 0 to 1)

d) 0.16:
2x + 0.16 = 1
2x = 0.84
x = 0.42 (Invalid for the same reason as options a)

Based on the calculations, option c (0.32) should replace "?" in the table, as it creates a valid probability distribution with the given conditions.

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The weekly sales of Honolulu Red Oranges is given by

q = 1040 - 20р.

Calculate the price elasticity of demand when the price is $32 per orange

Answers

The price elasticity of demand when the price is $32 per orange is 2

To calculate the price elasticity of demand, we need to use the formula:

E = (%Δq / %Δp) x (p/q)

where E is the price elasticity of demand, %Δq is the percentage change in quantity demanded, %Δp is the percentage change in price, and p/q is the average price-quantity ratio.

Given that the weekly sales of Honolulu Red Oranges is given by q = 1040 - 20p, we can find the derivative of q with respect to p as follows:

dq/dp = -20

This tells us that for every $1 increase in price, the quantity demanded will decrease by 20 units.

At a price of $32 per orange, the quantity demanded is:

q = 1040 - 20(32) = 424

If the price were to increase to $33 per orange, the new quantity demanded would be:

q' = 1040 - 20(33) = 404

Using these values, we can calculate the percentage changes in price and quantity demanded as:

%Δp = [(33 - 32) / 32] x 100% = 3.125%

%Δq = [(404 - 424) / 424] x 100% = -4.72%

The average price-quantity ratio is:

(p+ p')/2q = [(32 + 33)/2]/424 = 0.015

Now we can calculate the price elasticity of demand as:

E = (%Δq / %Δp) x (p/q) = (-4.72 / 3.125) x 0.015 = -0.023

Since the price elasticity of demand is negative, we know that Honolulu Red Oranges have an inelastic demand at a price of $32 per orange. This means that a 1% increase in price will lead to a less than 1% decrease in quantity demanded.

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What type of angle pairs are form with the 75∘
angle and ∠2?

vertical angles

corresponding angles

adjacent angles


alternate interior angles

Answers

The angles 75° and ∠2 are alternate interior angles.

Option D is the correct answer.

We have,

From the figure,

55°, ∠3, and 75° forms a straight angle.

Alternate angles are pairs of angles formed when a transversal line intersects two parallel lines.

Alternate angles are equal in measure, which means they have the same angle degree value.

So,

75° and ∠2 are alternate angles.

Thus,

75° and ∠2 are alternate angles.

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Partice moves on a coordinate line with acceleration d^2s/dx^2 = 30√t- 6/√t subject to the conditions that ds/dt = 911 and s=14 when t=1. Find the velocity v=ds/dt in terms of t and the position s in terms of t.
The velocitu v = ds/dt in terms of t is v = __
The position s in terms of t is s = __

Answers

The velocity v in terms of t is: v = [tex]20t^{ \frac{3}{2} } - 12t^{\frac{1}{2} } + 923[/tex]

The position s in terms of t is: s = [tex]40t^{ \frac{5}{2} } /5 - 24t^{\frac{2}{3} } /3 + 923t - 949[/tex]

Calculating Velocity and Position:  

To find the velocity and position functions given the acceleration and initial conditions.

Use the fact that acceleration is the second derivative of position with respect to time and that velocity is the first derivative of position with respect to time, to perform the integrations.

We also used the initial conditions given for velocity and position at a specific time to solve for the constants of integration.

Here we have

Partice moves on a coordinate line with acceleration d²s/dx² = 30√t- 6/√t subject to the conditions that ds/dt = 911 and s = 14 when t = 1.  

To find the velocity, integrate the acceleration with respect to t once:

=> d²s/dx² = 30√t- 6/√t

=> ds/dt = ∫(d²s/dx²)dt

= ∫(30√t- 6/√t)dt

= [tex]20t^{ \frac{3}{2} } - 12t^{\frac{1}{2} } + C[/tex]

Using the initial condition ds/dt = 911 when t = 1, we can solve for C:

=> ds/dt = [tex]20t^{ \frac{3}{2} } - 12t^{\frac{1}{2} } + C[/tex]

=> 911 =  [tex]20(1)^{ \frac{3}{2} } - 12(1)^{\frac{1}{2} } + C[/tex]

=> C = 923

Therefore, the velocity v in terms of t is:

=> v = [tex]20t^{ \frac{3}{2} } - 12t^{\frac{1}{2} } + 923[/tex]

To find the position, we can integrate the velocity with respect to t once:

=> ds/dt = [tex]20t^{ \frac{3}{2} } - 12t^{\frac{1}{2} } + 923[/tex]

=> s = ∫(ds/dt)dt = [tex]\int\limits } \, 20t^{ \frac{3}{2} } - 12t^{\frac{1}{2} } + 923[/tex]

=> s = [tex]40t^{ \frac{5}{2} } /5 - 24t^{\frac{2}{3} } /3 + 923t + C'[/tex]  

Using the initial condition s = 14 when t = 1, we can solve for C':

=> 14 = [tex]40 (1)^{ \frac{5}{2} } /5 - 24(1)^{\frac{2}{3} } /3 + 923t + C'[/tex]

=> C' = -949

Therefore,

The velocity v in terms of t is: v = [tex]20t^{ \frac{3}{2} } - 12t^{\frac{1}{2} } + 923[/tex]

The position s in terms of t is: s = [tex]40t^{ \frac{5}{2} } /5 - 24t^{\frac{2}{3} } /3 + 923t - 949[/tex]

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What is the greatest value in the data set

Answers

Answer:

Step-by-step explanation:

Maximum :)

Assume z is a standard normal random variable. What is the value of z if the area to the right of zis 9803? 0 -2.06 4803 0.0997 3.06

Answers

The value of z, In the above statistics-based question where the area to the right of z is 0.9803, is approximately 1.81.

In statistics, the standard normal distribution is a specific distribution of normal random variables with a mean of 0 and a standard deviation of 1. The area under the curve of a standard normal distribution is equal to 1, and the distribution is symmetric around the mean of 0.

To find the value of z for a given area to the right of z, we can use a standard normal distribution table or calculator. For example, using a standard normal distribution table, we can find the value of z that corresponds to an area of 0.0197 to the left of z. This value is approximately -1.81. Since the area to the right of z is 0.9803, we can find the value of z by subtracting -1.81 from 0, which gives us approximately 1.81.

Alternatively, we can use the inverse normal distribution function in Excel or another statistical software package to find the value of z directly. For example, the Excel function NORMSINV(0.9803) returns a value of approximately 1.81, which is the same as the value we obtained using the standard normal distribution table.

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10
TIME REMA
59:4
What is the difference between marginal cost and marginal revenue?
O Marginal cost is the money earned from selling one more unit of a good. Marginal revenue is the money paid f
producing one more unit of a good.
Marginal cost is the money paid for producing one more unit of a good. Marginal revenue is the money earned
from selling one more unit of a good.
Marginal cost is the money a producer might make from one more unit. Marginal revenue is the money a produ
actually makes from one more unit.
O Marginal cost is the money a producer actually makes from one more unit. Marginal revenue is the money a
producer might make from one more unit.

Answers

The difference is: Marginal cost is the money paid for producing one more unit of a good. Marginal revenue is the money earned from selling one more unit of a good.

What is Marginal cost and Marginal revenue?

Marginal cost (MC) is the additional outlay expended by a producer when they fabricate and supply one supplementary unit of an item or service. It symbolizes the replace in total costs caused by producing one extra piece.

Marginal revenue (MR), on the other hand, is the supplementary turnover generated when an establishment deals one more piece of a good or service. It signifies the transformation in complete revenue attained from selling an supplemental product.

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0.32 + /100 = 0.54 + 32/100

Answers

Answer:

54

Step-by-step explanation:

0.32 + /100 = 0.54 + 32/100

0.32 + x/100 = 0.54 + 0.32

x / 100 = 0.54

x = 54

So, the answer is 54

Mike works a total of 59 hr per week at his two jobs. He makes $6 per hour at job A and $7 per hour at job B. If his total pay for one week is $374 before taxes, then how many hours does he work at each job?

Answers

Mike works 39 hours per week at Job A and 20 hours per week at Job B.

Calculating the work-rate of Mike

We need to formulate some expressions here.

Let:

Hours Mike works at Job A = x

Hours Mike works at Job B = y

We know that:

x + y = 59 ---------- equation 1

We also know that he makes $6 per hour at Job A, and $7 per hour at Job B, and his total pay is $374. So we can set up another equation based on his total pay:

6x + 7y = 374 --------- equation 2

Now we have two equations with two unknowns, which we can solve simultaneously.

Using substitution method:

solve for x in terms of y:

x = 59 - y

We can substitute this expression for x into equation 2:

6(59 - y) + 7y = 374

Simplifying and solving for y:

354 - 6y + 7y = 374

y = 20

So Mike works 20 hours per week at Job B. We can substitute this value for y into equation 1 to find x:

x + 20 = 59

x = 39

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Which of the following equations has infinitely many solutions?

A
2x + 3 = 5 + 2x

B
2x + 3 = 5 + 3x

C
3x - 5 = -5 + 3x

D
2x - 5 = -5 + 3x

Answers

A. 2x + 3 = 5 + 2x has infinitely many solutions because the variable terms cancel out, leaving the statement 3 = 3, which is always true, regardless of the value of x.

Which expressions will help you find the surface area of this net? Select all that apply.

Answers

The expression that will help in finding the surface area of the net are

9 x 51/2 x 4 x 6

What is surface area?

The external surface area of three-dimensional objects is referred to as the surface area, and is generally calculated in square units.

Calculating the surface area of certain 3D shapes requires one to use different formulas. depending on the shapes

The shapes encountered here are

rectangle = 9 x 5triangle = 1/2 x 4 x 6

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At the burger palace, 2 hamburgers and 1 small order of fires cost 6. 9

Answers

The cost of one small order of fries at the Burger Palace is $1.09. The correct answer is not given in any option.

The price is another name for the cost of a thing from the perspective of a consumer. This is the price the seller sets for a product, which takes into account both the cost of manufacture and the markup the seller adds to increase profits.

Let's say a hamburger costs x dollars and a small order of French fries costs y dollars.

x--------> the cost of one hamburger

y--------> the cost one small order fries

we know that

2x+y=6.50

5x+5y=17.75

using a graph tool

see the attached figure

the solution is

x=2.5

y=1.09

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The complete question is

At The Burger Palace, 2 hamburgers and 1 small order of fries costs $6.50. The Clarke family ordered 5 hamburgers and 5 small orders of fries and paid $17.75.

Select the TWO equations that fit the scenario described above.

A) 2x+y=6.50

B) 6.50x+17.75y=5

C) 2x+5y=24.25

D) 5x+5y=6.50

E) 5x+5y=17.75

The probability that X is a 2, 11, or 12 is:
a.) 1/36
b.) 2/36
c.) 3/36
d.) 4/36

Answers

Answer:

The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.

Step-by-step explanation:


Help WILL GIVE BRAINLIEST HEELLPPO

Answers

Answer:

B: 4.5

Step-by-step explanation:

QUESTION 1 of 10: A manufacturer buys a new machine that costs $50,000. The estimated useful life for the machine is ten years. The

machine can produce 1,000 units per month. If the machine ran at its capacity for ten years, what would be the fixed cost per unit based on

the cost of the machine per part manufactured? (Round to the nearest penny)

a) $. 42 / unit

ООО

b) $1. 00/unit

c) S4,167 / unit

d) $5. 000/unit

Answers

The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit. Option ( A )

What is multiplication ?

Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.

To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.

The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:

10 years x 12 months/year x 1,000 units/month = 120,000 units

The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:

$50,000 ÷ 120,000 units = $0.4167 per unit

Rounding this to the nearest penny gives us the final answer of:

$0.42 per unit (option a)

Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.

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Why is the Confusion Matrix so named?-Data mining is very confusing and the Confusion Matrix reflects thatconfusion.-It is very confusing to understand.-Because it captures metrics that show how the trained model may beconfused in distinguishing between positive and negative classes ofthe output variable.

Answers

The Confusion Matrix is so named :

because it captures metrics that show how the trained model may be confused in distinguishing between positive and negative classes of the output variable.

In the context of data mining, the Confusion Matrix helps to measure the performance of a classification algorithm. It displays the true positive, true negative, false positive, and false negative values, which provide insight into how well the model is performing and where it might be making errors.

The matrix presents a tabular representation of predicted and actual classification results, which can be used to evaluate the performance of a classification model. The confusion arises from the fact that the model may misclassify samples, leading to confusion about the true performance of the model. The Confusion Matrix provides a way to quantify and visualize this confusion, and is a useful tool for evaluating the accuracy of machine learning models.

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Need help quick please!!!

Answers

Answer:

b = 12 Km

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

b² + 16² = 20²

b² + 256 = 400 ( subtract 256 from both sides )

b² = 144 ( take square root of both sides )

b = [tex]\sqrt{144}[/tex] = 12

consider the results of a poll where 48% of 331 americans who decide to not go to college do so because they cannot afford it. calculate a 90% confidence interval for the proportion of americans who decide to not go to college because they cannot afford it.

Answers

The 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it can be calculated using a statistical formula. The formula for a confidence interval is: CI = p ± zsqrt((p(1-p))/n)

Where CI is the confidence interval, p is the proportion of interest (in this case, 0.48 or 48%), and z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.645 for 90% confidence), sqrt is the square root function, and n is the sample size (in this case, 331).

Plugging in the values, we get:

CI = 0.48 ± 1.645sqrt((0.48(1-0.48))/331)

CI = 0.48 ± 0.062

Thus, the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is (0.418, 0.542). This means that we can be 90% confident that the true proportion of Americans who decide not to go to college because they cannot afford it falls between 41.8% and 54.2%.

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Un televisor costaba $1250 y al comprarlo nos han hecho un 20% de descuento ¿cuánto nos han descontado?

Answers

They discount you $250 from the television cost.

How to calculate how much did they discount?

Discount is defined as a deduction from the usual cost of something.

Since the television cost $1250 and when you bought it they gave you a 20% discount. We can say:

discount = 20% of $1250

discount = 20/100 * $1250

discount = $250

Therefore, they discount you $250

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Question in English

A television cost $1250 and when we bought it they gave us a 20% discount. How much did they discount us?

The circle below has center C, and its radius is 7 yd. Given that mZDCE = 100°, find the length of the major arc DFE. Give an exact answer in terms of , and be sure to include the correct unit in your answer. F 100 Length of major arc DFE: D/O 8 JT yd yd² X yd³​

Answers

The length of the major arc DFE is 10.11 π ft.

Given that, a circle C, with central angle 100°, and radius 7 yards,

We need to find the length of the major arc DFE,

The length of an arc = central angle / 360° × circumference

The central angle for the arc DFE = 360° - 100° = 260°

So, the length = 260° / 360° × π × 14

= 10.11 π ft

Hence, the length of the major arc DFE is 10.11 π ft.

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The null and alternative hypotheses for a population proportion, as well as the sample results, are given. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey tip: Use "Test for a Single Proportion" and then "Edit Data" to enter the sample information.
Hypotheses: H0:p=0.5 vs Ha:p<⁢0.5;
Sample data: p^=38100=0.38 with n=100
Round the p-value to three decimal places.
p-value = Enter your answer in accordance to the question statement

Answers

We do not have enough evidence to reject the null hypothesis at the 5% significance level.

To generate a randomization distribution and calculate the p-value for this problem, we can use StatKey and select "Test for a Single Proportion" under the "Randomization Test" section. We then enter the sample information by clicking "Edit Data" and inputting p^=0.38 and n=100. The null hypothesis is that the population proportion is equal to 0.5, while the alternative hypothesis is that the population proportion is less than 0.5. Our sample result is p^=0.38. Using StatKey, we can generate a randomization distribution by clicking "Simulate" and then "Randomize".

We can then calculate the p-value by finding the proportion of randomization samples that have a proportion less than or equal to our sample proportion of 0.38. After running the simulation, we obtain a p-value of 0.168. Rounding to three decimal places, the p-value is 0.168.

Therefore, we do not have enough evidence to reject the null hypothesis at the 5% significance level.

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Solve the inequality 3y<6​

Answers

Answer:

Solving the inequality for y in 37<7 would be

y<2

pls help <333 (don’t mind the white part, it was wrong)

Answers

The length of MS is 10 cm and diameter of the circle is RS

Given that the midpoint of PQ is M

RM is 10 cm and PQ is 24 cm

We have to find the length of MS

As M is midpoint then RM=MS

MS = 10 cm

Now the diameter of the circle is RS because it passes through middle of the circle which is center O

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Find the smallest number n of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6. k=1 n=

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The smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.

To find the smallest number of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6, we need to use the formula for the partial sum of a series. The partial sum of the given series up to n terms is:

S(n) = IM8 + 12e + 0.49(2^2) + 0.49(3^2) + ... + 0.49(n^2)

We want to find the smallest value of n such that the error between S(n) and the true value of the series is less than 10^-6. The error between S(n) and the true value of the series can be approximated by the absolute value of the next term in the series:

|an+1| = 0.49((n+1)^2)

So we need to find the smallest value of n such that:

|an+1| < 10^-6

0.49((n+1)^2) < 10^-6

(n+1)^2 < (10^-6)/0.49

n+1 < sqrt((10^-6)/0.49)

n < sqrt((10^-6)/0.49) - 1

n < 11.75

Since n must be a whole number, the smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.

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The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.9 mm. in USE SALT (a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.) at most 20mm _____
less than 20mm _____
(b) What is the 75th percentile of the defect length distribution-that is, the value that separates the smallest 75% of all lengths from the largest 25%? (Round your answer to four decimal places.)
______ mm (c) What is the 15th percentile of the defect length distribution? (Round your answer to four decimal places.) _____mm (d) What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%? (Round your answers to four decimal places.) smallest 10%_____ mm largest 10%______ mm

Answers

A) The same z-score and find the area to the left of it, which is 0.1562.

b) The 75th percentile of the defect length distribution is 33.32 mm.

C) The 15th percentile of the defect length distribution is 19.21 mm.

d)The values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10% are 17.95 mm and 38.05 mm, respectively.

(a) To find the probability that the defect length is at most 20 mm, we need to calculate the z-score first:

z = (20 - 28) / 7.9 = -1.0127

Using a standard normal table or a calculator, we can find that the probability of a z-score less than or equal to -1.0127 is 0.1562. Therefore, the probability that the defect length is at most 20 mm is 0.1562.

To find the probability that the defect length is less than 20 mm, we can use the same z-score and find the area to the left of it, which is 0.1562.

(b) To find the 75th percentile of the defect length distribution, we need to find the z-score that corresponds to the area of 0.75 in the standard normal distribution. Using a standard normal table or a calculator, we can find that this z-score is approximately 0.6745.

Then, we can solve for the defect length:

z = (x - 28) / 7.9

0.6745 = (x - 28) / 7.9

x - 28 = 0.6745 * 7.9

x = 33.32

Therefore, the 75th percentile of the defect length distribution is 33.32 mm.

(c) To find the 15th percentile of the defect length distribution, we need to find the z-score that corresponds to the area of 0.15 in the standard normal distribution. Using a standard normal table or a calculator, we can find that this z-score is approximately -1.0364.

Then, we can solve for the defect length:

z = (x - 28) / 7.9

-1.0364 = (x - 28) / 7.9

x - 28 = -1.0364 * 7.9

x = 19.21

Therefore, the 15th percentile of the defect length distribution is 19.21 mm.

(d) To find the values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%, we need to find the z-scores that correspond to the areas of 0.1 and 0.9 in the standard normal distribution. Using a standard normal table or a calculator, we can find that these z-scores are approximately -1.2816 and 1.2816, respectively.

Then, we can solve for the defect lengths:

z = (x - 28) / 7.9

-1.2816 = (x - 28) / 7.9

x - 28 = -1.2816 * 7.9

x = 17.95

z = (x - 28) / 7.9

1.2816 = (x - 28) / 7.9

x - 28 = 1.2816 * 7.9

x = 38.05

Therefore, the values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10% are 17.95 mm and 38.05 mm, respectively.

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Why is the straightedge of a ruler not the same as a line?

Answers

Since a straightedge lacks measurement gradients, it can only be used to create or draw straight lines—not to measure length.

An instrument for drawing straight lines or ensuring their straightness is a straightedge or straight edge. It is typically referred to as a ruler if its length is marked with uniformly spaced markings. If no markings are present, it is just a straight edge.

Straight lines can be measured and marked with a ruler. A straight edge won't help you measure, but since they are typically more robustly constructed than rulers, they are a better tool for drawing straight lines. Most of the time, rulers can be used as a straight edge.

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