Find the critical value χ R corresponding to a sample size of 15 and a confidence level of 90%. 023.685 06.571 O31.319 O29.141

Answer:

The sum of first five term of GP is 19607.

Step-by-step explanation:

We are given the following in the question:

A geometric progression with 7 as the first term and 7 as the common ration.

[tex]a, ar, ar^2,...\\a = 7\\r = 7[/tex]

[tex]7, 7^2, 7^3, 7^4...[/tex]

Sum of n terms in a geometric progression:

[tex]S_n = \displaystyle\frac{a(r^n - 1)}{(r-1)}[/tex]

For sum of five terms, we put n= 5, a = 7, r = 7

[tex]S_5 = \displaystyle\frac{7(7^5 - 1)}{(7-1)}\\\\S_5 = 19607[/tex]

The sum of first five term of GP is 19607.

Verification:

[tex]2801\times 7 = 19607[/tex]

Thus, the sum is equal to product of 2801 and 7.

To find the sum of a geometric progression with a common ratio of 7, we use the formula Sum = (first term) * (1 - (common ratio)^n) / (1 - common ratio). When we substitute the values given in the question, the sum comes out to be the product of 2801 and 7.

A geometric progression is a sequence in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is 7.

The sum of a geometric progression can be found using the formula:

Sum = (first term) * (1 - (common ratio)^n) / (1 - common ratio)

Plugging in the values for this problem, we have:

Sum = 7 * (1 - 7^5) / (1 - 7) = 7 * (-39304) / (-6) = 2801 * 7

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Answer:

B. stratified random sample.

Step-by-step explanation:

The Stratified sampling is a type of sampling method in which the observer divides the whole sample population in the different or the separate groups.

These separated different groups are known as strata.

And from these, probability sample also called as simple random sample is taken out from each group.

The sampling method used in this scenario is defined as stratified random sampling, where the population is divided into groups (or strata) and random samples are taken from each group.

The technique described in your question is an example of a stratified random sample. This sampling method is characterized by dividing a population into smaller groups, known as 'strata', and then selecting a simple random sample from each group. In your example, the population is first divided into men and women, these are your strata. Then, a simple random sample is chosen from each group: 500 men and 700 women. This method ensures representation from all sections of the population and can often lead to more accurate results compared to a simple random sample.

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Step-by-step explanation:

using trigonometric ratios,

sin theta= opposite ÷ hypoteneus (h)

sin 45°= 3 root 2 ÷ h

1/root 2= 3 root 2 ÷h

h= 3× root 2 × root 2

= 3×2

= 6 unit

Answer:

Step-by-step explanation:

The given triangle is a right angle triangle and also an isosceles triangle.

The hypotenuse is the longest side of the right angle triangle. To determine the hypotenuse, we will apply trigonometric ratio

Sin θ = opposite side/hypotenuse

Looking at the triangle.

θ = 45 degrees = 1/√2

opposite side = 3√2

Therefore,

Sin 45 = 3√2/hypotenuse

1/√2 = 3√2/hypotenuse

hypotenuse × 1 = √2 × 3√2

hypotenuse = 3√2 × √2

hypotenuse = 3 × 2 = 6

Alternatively,

We can apply Pythagoras theorem since both sides are equal

Since the length of one side is 3√2, then the length of the other side is also 3√2

Hypotenuse^2 = opposite side^2 + adjacent side^2

Hypotenuse^2 = (3√2)^2 + (3√2)^2

Hypotenuse^2 = 18 + 18 = 36

Hypotenuse = √36 = 6

Answer:

Each unit cost $800

Step-by-step explanation:

Annual compensation = $48,000

Annual number of units sold = 2000

Commission on each item sold = 3%

Compensation for 2000 units = $48,000

Compensation for 1 unit = $48,000/2000 = $24

Cost of one unit = compensation for one unit ÷ commission on one unit = $24 ÷ 3% = $24 ÷ 0.03 = $800

Answer: cost of one unit = $280

Question:

A salesman has a base salary $2600 per month and makes 3% commission on each unit sold. If his total annual compensation is $48,000 and he sold 2000 units, how much does each unit cost

Step-by-step explanation:

Given;

base salary = $2600 per month

Total annual compensation = $48,000 per annum

Number of units sold = 2000

Commission = 3% per unit

Salesman's Salary per annum = $2600 × 12 = $31,200

Total commission earned = total compensation - total yearly salary

Total commission = $48,000 - $31,200 = $16,800

Commission on each unit = total commission/number of units

Unit commission = $16800/2000 = $8.4

Given that the commission per unit is 3% per unit

That is $8.4 is 3% of the cost of each unit.

Cost of each unit = $8.4/3% = $8.4/0.03 = $280

Answer:

The best option is to phone a friend which will yield a total earnings of $ 806,400

Step-by-step explanation:

From the analysis of the question, there is the probability of success and failure.

if he choose not to answer which is the probability of success, his earnings = $500,000.

if he he answers the question correctly, his earnings = $1,000,000 which in the end, is still a success for him

if he answers the question wrongly, his earnings = $32,000

the last option is to phone a friend and he will either choose option a or option b

Probability of choosing option A = 0.6

Probability of choosing option B = 0.4

expected earnings = P(choosing A) x his earnings if correct +  P(choosing B) x his earnings if wrong

= 0.6 x 1,000,000 + 0.4 x 32,000

= $612,000 will be his earning by second option

if he picks the option b = P (choosing B) x his earnings if correct + P(choosing A) x earnings if wrong = 0.4 x 1,000,000 + 0.6 x 32,000

= $419,000

from the P(success) + P( failure) =1

His earnings = Probability of success x earnings if correct + Probability of failure x earnings if incorrect = 0.8 x 1,000,000 + 0.2 x 32,000

= $806,400

from the calculation done, it is apparent that his best option is to go by phoning a friend since that will yield more earnings for him which is greater than his earnings by going for the second options hence the best option is phoning a friend as this will accrue his expected earning to be $ 806,400

The best strategy is to select an answer (a or b). The expected payout for this option is $600,000.

To find the best strategy, we can create a decision tree. The decision tree will consider the options of not answering, selecting an answer, and phoning a friend. The expected payout for each option can be calculated by multiplying the probability of that option with the payout associated with that outcome. After calculating the expected payout for each option, we can compare them to determine the best strategy.

The decision tree shows that the best strategy is to Select an answer (a or b).

The expected payout for this option is calculated by multiplying the probability of choosing (a) and winning with the payout of $1,000,000, and adding it to the probability of choosing (b) and winning with the payout of $32,000.

The expected payout for this option is $600,000.

Therefore, by selecting an answer, you can expect to win $600,000 on average.

Finding the z-value in a standard normal distribution for certain proportions involves using a standard normal (Z-score) table. For (a) the z-value is -0.36, and for (b), the z-value is 0.36.

To find the value of z that allows for a proportion of observations less or greater than it in a standard normal distribution, you need to use a standard normal (Z-score) table, or use an online calculator that allows you to find the Z-score associated with a specific proportion.

(a) For the proportion of observations that are less than z = 0.36, you would look up this proportion in the body of a standard normal table to find the associated Z-score. Alternatively, using a Z-score calculator, the z value is approximately -0.36.

(b) For the proportion of observations that are greater than Z = 0.36, it would be equivalent to looking for the proportion that is less than Z = 1 - 0.36 = 0.64 in the standard normal table. The z value here is approximately 0.36.

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Answer:

x+2a-b=5x+5a-2*3a+2*b

x+2a-b=5x+5a-6a+2b

x+2a-b=5x-a+2b

5x-x=2a-b+a-2b

4x=3a-3b

4 x=3(a-b)

x=3/4(a-b)

The answer of the vector x in the form of a and b is 3/4(a-b).

"A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head."

Here,

[tex]x + 2a - b = 5(x + a) - 2(3a - b) x[/tex]

[tex]x+2a-b=5x+5a-6a+2b\\\\x+2a-b=5x-a+2b\\\\5x-x=2a-b+a-2b\\\\4x=3a-3b\\\\4 x=3(a-b)\\\\x=3/4(a-b)\\[/tex]

Hence the vector x = 3/4(a-b)

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Answer:7

Step-by-step explanation:

Answer:

a) The population is all the Hispanic residents of Denver.

The sample is 300 adults which very visited by the officer.

b) The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.

Step-by-step explanation:

This is a common statistic method.

If you want to estimate something about a big population, you select a random sample of the population, and estimate for the entire population.

For example, if you want to estimate the proportion of residents of Buffalo, New York, that are Buffalo Bills fans, you are going to ask, for example, 1000 Buffalo residents. The population is all the residents of Buffalo, New York. and the sample are the 1000 Buffalo residents.

However, if you send a Bills player to ask this question, people will try to make him happy, which could lead to a biased answer.

So, for this question

a. What are the population and the sample?

The population is all the Hispanic residents of Denver.

The sample is 300 adults which very visited by the officer.

b. Why are the results likely to be biased even though the sample is an SRS?

The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.

Answer:

1413 square yards of lawn receives water.

Step-by-step explanation:

We are given the following in the question:

Radius of garden, r = 36 yards

Rotating angle, [tex]\theta[/tex]  = [tex]125^\circ[/tex]

First converts the given angle measure in radians.

[tex]\text{Radians} = \dfrac{\pi}{180}\times \theta[/tex]

Thus, the rotating angle in radians is:

[tex]\dfrac{\pi}{180}\times 125 = 2.18\text{ Radians}[/tex]

Area of lawn =

[tex]\displaystyle\frac{1}{2}r^2 \times \text{Radian measure of angle}\\\\=\frac{1}{2}(36)^2\times 2.18 = 1412.64 \approx 1413\text{ square yards}[/tex]

Thus, 1413 square yards of lawn receives water.

Final answer:

1413 square yards of lawn receives water.

Explanation:

1413 square yards of lawn receives water.

Step-by-step explanation:

We are given the following in the question:

Radius of garden, r = 36 yards

[tex]Rotating angle, \theta = 125^\circ[/tex]

First converts the given angle measure in radians.

[tex]\text{Radians} = (\pi)/(180)* \theta[/tex]

Thus, the rotating angle in radians is:

[tex](\pi)/(180)* 125 = 2.18\text{ Radians}[/tex]

Area of lawn =

[tex]\displaystyle(1)/(2)r^2 * \text{Radian measure of angle}\n\n=(1)/(2)(36)^2* 2.18 = 1412.64 \approx 1413\text{ square yards}[/tex]

Thus, 1413 square yards of lawn receives water.

Answer:

Step-by-step explanation:

Hello!

Missing Questions:

1) The probabylity of P(121 < X ≤ 129) is:

You can rewrite it as:

P(X ≤ 129) - P(X < 121)

Now the expression " P(X < 121)" does not include 121 so to calculate this interval you have to substract the cummulative probability to the previoous value of the variable " P(X ≤ 120)"

Then the interval is

P(X ≤ 129) - P(X ≤ 120)= 0.978 - 0.533= 0.445

2) The approximation to normal (without correction of continuity) of P(121 < X ≤ 129) is:

To use the normal approximation you have to calculate the mean and variance of the variable.

E(X)= np= 150*0.8= 120

V(X)= np(1-p)= 150*0.8*0.2= 24

Now you can standardize the given interval:

P(X ≤ 129) - P(X < 121)= P(Z ≤ (129-120)/√24) - P(Z < (121-120)/√24)

P(Z ≤ 1.84) - P(Z < 0.20) = 0.967 - 0.579= 0.388

3) The approximation to normal (with correction of continuity) of P(121 < X ≤ 129) is:

P(121 < X ≤ 129)

Applying the correction of continuity:

For X ≤ n + 0.5

For X > n + 0.5

P(121.5 < X ≤ 129.5) = P(X ≤ 129.5) - P(X < 121.5)

P(Z ≤ (129.5-120)/√24) - P(Z < (121.5-120)/√24)

P(Z ≤ 1.94) - P(Z < 0.31) = 0.974 - 0.622= 0.352

4) The approximation of poisson of P(121 < X ≤ 129) is:

First define the rate of successes of the distribution λ= np= 150*0.8= 120

Then you look at the individual cummulative probabilities using the tables of the distribution:

P(X ≤ 129;  λ= 120)= 0.808

P(X < 121;  λ= 120)= P(X ≤ 120;  λ= 120)= 0.524

P(121 < X ≤ 129) =  P(120 ≤ X ≤ 129)= P(X ≤ 129) - ≤ 129)= 0.808 - 0.524= 0.284

I hope it helps!

Answer:

28

Step-by-step explanation:

People he interviewed on that day (x)

1.50x + 10 = 52

1.50x = 42

x = 42/1.50

x = 28

The number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.

Let's suppose the people he interviewed on that day x

The linear equation can be framed as per the question:

1.50x + 10 = 52

After solving:

x = 42/1.50

x = 28

Thus, the number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.

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Answer:

Randomized experiment

Step-by-step explanation:

Such a statement is said to be Randomized experiment as the kids in the school have been selected at random and their performances are observed and recorded. Later it is inquired if they are breast fed or not. This information is later assessed and a conclusion is reached. This type of research or experiment is Randomized experiment.

Considering that the experiment is Randomized, the statement should be "Link found between breast-feeding and school performances". This statement does not restrict the performances of the student specifically on breast-feeding but shows a probable affect of it.

Vectors u, v, and w are represented graphically in ℝ². Scalars λ₁ and λ₂ for w = λ₁u + λ₂v are found as λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.

a) Vector Representation:

To draw vectors u, v, and w in ℝ², we can use their respective components. Vector u = (1, 2) starts at the origin and extends to the point (1, 2). Vector v = (-3, 4) starts at the origin and extends to the point (-3, 4). Vector w = (5, 0) starts at the origin and extends to the point (5, 0).

b) Scalar Representation:

We want to find scalars λ₁ and λ₂ such that w = λ₁u + λ₂v. This can be expressed as a system of equations:

w₁ = λ₁u₁ + λ₂v₁

w₂ = λ₁u₂ + λ₂v₂

Substitute the values:

5 = λ₁(1) + λ₂(-3)

0 = λ₁(2) + λ₂(4)

Solve the system of equations to find λ₁ and λ₂. Multiplying the first equation by 2 and adding it to the second equation:

10 = 2λ₁ - 3λ₂ + 0

10 = 2λ₁ - 3λ₂

Solving for λ₁:

2λ₁ = 3λ₂ + 10

λ₁ = 3/2λ₂ + 5

Now, let λ₂ = t, then λ₁ = 3/2t + 5.

So, the scalars λ₁ and λ₂ are λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.

Answer:

there a bad football team probably the raiders  

Step-by-step explanation:

but take 72.5 and take away 13.5

                     72.5

                  -  13.5

                   -----------

                      59

Answer: [tex]5\frac{4}{5}[/tex]

Step-by-step explanation:

The first step is to make 7&2/5 a improper fraction, using the rule [tex]a\frac{b}{c}= \frac{ac+b}{c}[/tex].

Answer:

a) Permutations

b) combination

Step-by-step explanation:

a)

Since the order of 15 most important artwork pieces matter, with most popular at first and then at N0.2, 3,4, and so on. Whenever we are dealing with "order of placement" the question at hand is of permutations.

b)

Out of 320 pieces, 125 pieces are to be "selected" and displayed, the process of selection incurs Combinations in which the order in which we select does not matter.  

Scenario a) represents a permutation and the 15 popular pieces can be arranged in 15! ways.

Scenario b) represents a combination and the 125 pieces can be selected in 320 choose 125 ways.

a) This scenario is an example of a permutation. In a permutation, the order of the items matters. In this case, the 15 popular pieces can be arranged in 15! (15 factorial) ways.
b) This scenario is an example of a combination. In a combination, the order of the items does not matter. In this case, the 125 pieces can be selected from the total of 320 pieces in a total of 320 choose 125 ways.

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Answer:

36

Step-by-step explanation:

We have been given that you have 8 friends, of whom 5 will be invited to your big party in IV on Friday night. We are asked to find the number of choices if 2 of the friends are feuding and will not attend together.

We can choose 5 friends from 8 friends in [tex]^8C_5[/tex] ways.

[tex]^8C_5=\frac{8!}{5!(8-5)!}=\frac{8!}{5!(3)!}=\frac{8*7*6*5!}{5!*3*2*1}=8*7=56[/tex]

Therefore, we can choose 5 friends from 8 friends in 56 ways.

Since two friends are feuding, so we need to choose 3 friends from 6 friends and subtract them from total ways.

We can choose 3 friends from 6 friends in [tex]^6C_3[/tex] ways.

[tex]^6C_3=\frac{6!}{3!(6-3)!}=\frac{6!}{3!(3)!}=\frac{6*5*4*3!}{3!*3*2*1}=5*4=20[/tex]

[tex]56-20=36[/tex]

Therefore, we have 36 choices, if 2 of the friends are feuding and will not attend together.

Final answer:

The number of different choices for inviting friends to the party without the feuding friends attending together is 41 different choices.

Explanation:

The student's question deals with a combinatorial problem where they have 8 friends but can only invite 5 to a party. However, there is a constraint: 2 of the friends are feuding and cannot attend together. To solve this, we calculate the number of ways to choose 5 friends out of 8 without the feuding friends both attending.

Calculating Combinations with Restrictions

First, we find the total number of ways to invite 5 friends out of 8 without any restrictions, which is calculated using the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of friends and k is the number of friends to be invited.

C(8, 5) = 8! / (5!(8 - 5)!) = (8 × 7 × 6) / (3 × 2 × 1) = 56 ways.

Next, we calculate the number of combinations where the feuding friends would attend together. We treat them as a single entity and find combinations of the remaining 6 friends to invite 4 plus the 'unit' of feuding friends.

C(6, 4) = 6! / (4!(6 - 4)!) = (6 × 5) / (2 × 1) = 15 ways.

To get the total number of combinations without the feuding friends attending together, we subtract the 15 'restricted' combinations from the total 56 combinations.

56 - 15 = 41.

Therefore, there are 41 different choices for inviting friends to the party without the feuding friends attending together.

Answer:

Step-by-step explanation:

from the word Bi "meaning two"

Bivariate data are two different variables obtained from the same population element. Bivariate data are used if the sampled data cannot be graphically displayed using a single variable.

To form a bivariate data, there are three combinations of variable

1. Both variables are qualitative i.e attribute in nature

2. Both variables are quantitative i.e numerical

3. One of them is qualitative whilee the other is quantitative

Qualitative data are data that are measure of type which could represent a name, colour,symbol. traits or characteristics

Quantitative data are data that can be counted, measured and expressed using numbers/

Answer:

$2743.66

Step-by-step explanation:

Data provided in the question:

Interest rate = 5%

Future value = $55,000

Time, t = 4.5 years

Now,

Since the interest is compounded quarterly

therefore,

Number of periods in a year = 4

Interest rate per period = 5% ÷ 4 = 1.25% = 0.0125

Total number of periods in 4.5 years = 4.5 × 4 = 18

also,

PMT = Future value × [ r × (( 1 + r )ⁿ - 1)⁻¹ ]

therefore,

PMT = $55,000 × [ 0.125 × ( ( 1 + 0.0125 )¹⁸ - 1 )⁻¹ ]

or

PMT = $55,000 × 0.0498

or

PMT = $2743.66

Answer:

  (a) 4.00×10^7 m

  (b) 5.10×10^14 m^2

  (c) 1.083×10^21 m^3

Step-by-step explanation:

Put the given value of radius into the various formulas and do the arithmetic. Your scientific calculator can show you the results in scientific notation.

  C = 2πr = 2π·6.37×10^6 m ≈ 4.00×10^7 m* . . . circumference

  A = 4πr^2 = 4π(6.37×10^6 m)^2 ≈ 5.10×10^14 m^2 . . . area

  V = (4/3)πr^3 = (4/3)π(6.37×10^6 m)^3 ≈ 1.083×10^21 m^3 . . . volume

_____

* An early definition of the meter was 10^-7 times the distance from the North Pole to the Equator as measured through Paris, France.

Answer:

160/100+60+0/one hundred sixty

OR JUST 160 LIKE YOU ASKED

The product of thirty-two and five will be equal to 160.

A product is the result of multiplication or an expression that indicates factors that are to be multiplied, in mathematics.

The multiplication will be given as:-

32  x  5  =  160

Or we can also do it like the addition of 32 five times:-

32  +  32  + 32  +  32  +  32 = 160

Therefore products of thirty-two and five will be equal to 160.

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Answer:the total discounted price for two dogs to be groomed is 22.75

Step-by-step explanation:

A dog groomer is offering 20% off a full groom for one dog, and 15% off for each additional dog. Normally, a full groom costs $65 for each dog.

If you decide to take your two furry friends to be groomed,

the discount on the first one would be

20/100 × 65 = 0.2 × 65 = 13

the discount on the second one would be

10/100 × 65 = 0.15 × 65 = 9.75

the total discounted price for two dogs to be groomed would be

13 + 9.75 = 22.75

Answer:

First, calculate the discounted price for the first dog,

Discount=(20/100) $65=$13.

The discounted price is $65−$13=$52. Now, we can calculate the discounted price for the second dog,

Discount=(15/100) $65=$9.75.

The discounted price for the second dog is $65−$9.75=$55.25. The total discounted price for both dogs is,

$52+$55.25=$107.25

Step-by-step explanation:

Answer:

a) [tex] 61-35.8=25.3[/tex]

b) [tex] \frac{25.2}{11.3}=2.23[/tex] deviations

c) [tex] z = \frac{61- 35.8}{11.3}= 2.23[/tex]

d) For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.

Step-by-step explanation:

Assuming this complete question : "Helen Mirren was 61 when she earned her Oscar-winning Best Actress award. The Oscar-winning Best Actresses have a mean age of 35.8 years and a standard deviation of 11.3 years"

a) What is the difference between Helen Mirren’s age and the mean age?

For this case we can do this:

[tex] 61-35.8=25.2[/tex]

b) How many standard deviations is that?

We just need to take the difference and divide by the deviation and we got:

[tex] \frac{25.2}{11.3}=2.23[/tex] deviations

c) Convert Helen Mirren’s age to a z score.

The z score is defined as:

[tex] z = \frac{x- \mu}{\sigma}[/tex]

And if we replace the values given we got:

[tex] z = \frac{61- 35.8}{11.3}= 2.23[/tex]

d) If we consider “usual” ages to be those that convert to z scores between –2 and 2, is Helen Mirren’s age usual or unusual?

For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.

Final answer:

The wind chill table can be used to determine how cold it feels at different combinations of temperature and wind speed.

Explanation:

Wind chill is a measure of how cold it feels when the temperature is combined with wind speed. To determine how cold it feels when the temperature is 0°F and the wind speed is 10 mph, we can look at the table provided. At 0°F and 10 mph wind speed, the temperature adjusted for wind chill is -10°F.

If the temperature is 35°F and we want to know the wind speed that makes it feel like 25°F, we can look at the table and find that at 35°F, a wind speed of 15 mph makes it feel like 25°F.

If the wind speed is 10 mph and we want to know the approximate temperature that feels like 0°F, we can look at the table and find that at 10 mph wind speed, a temperature of 5°F feels like 0°F.

(a) At 0°F with a wind speed of 10 mph, it feels like -11°F.

(b) To make 35°F feel like 25°F, a wind speed of 15 mph is needed.

(c) With a wind speed of 10 mph, a temperature of 5°F feels like 0°F.

To find the adjusted temperature for wind-chill, we can use the given table which provides adjustments based on both temperature and wind speed.

(a) If the temperature is 0°F and the wind speed is 10 mph, we can find the adjusted temperature from the table:

Temperature: 0°F

Wind speed: 10 mph

From the table:

Adjusted temperature: -11°F

So, it feels like -11°F when the temperature is 0°F with a wind speed of 10 mph.

(b) If the temperature is 35°F, and we want it to feel like 25°F, we need to find the wind speed that corresponds to this adjusted temperature from the table:

Temperature: 35°F

Adjusted temperature desired: 25°F

From the table, look for the entry where the adjusted temperature is 25°F:

Adjusted temperature: 25°F

Wind speed corresponding to this adjusted temperature: 15 mph

So, a wind speed of 15 mph would make a temperature of 35°F feel like 25°F.

(c) If the wind speed is 10 mph and we want to find the temperature that feels like 0°F, we can find this from the table:

Wind speed: 10 mph

Adjusted temperature desired: 0°F

From the table, look for the entry where the adjusted temperature is 0°F:

Adjusted temperature: 0°F

Corresponding temperature: 5°F

So, approximately, a temperature of 5°F would feel like 0°F with a wind speed of 10 mph.

Answer:

Test scores of 10.2 or lower are significantly low.

Test scores of 31.4 or higher are significantly high.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 20.8, \sigma = 5.3[/tex]

Identify the test scores that are significantly low or significantly high.

Significantly low

Z = -2 and lower.

So the significantly low scores are thoses values that are lower or equal than X when Z = -2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2 = \frac{X - 20.8}{5.3}[/tex]

[tex]X - 20.8 = -2*5.3[/tex]

[tex]X = 10.2[/tex]

Test scores of 10.2 or lower are significantly low.

Significantly high

Z = 2 and higher.

So the significantly high scores are thoses values that are higherr or equal than X when Z = 2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2 = \frac{X - 20.8}{5.3}[/tex]

[tex]X - 20.8 = 2*5.3[/tex]

[tex]X = 31.4[/tex]

Test scores of 31.4 or higher are significantly high.

Final answer:

Using the z-score formula, test scores below 10.2 are significantly low, and scores above 31.4 are significantly high for the college readiness test with a mean of 20.8 and a standard deviation of 5.3.

Explanation:

To identify test scores that are considered significantly high or low based on their z-scores, we use the provided mean score (μ = 20.8) and standard deviation (σ = 5.3) of the college readiness test. According to the criteria, a z-score less than or equal to -2 is significantly low, while a z-score greater than or equal to 2 is significantly high. To find the actual test scores corresponding to these z-scores, we apply the formula:

Z = (x - μ) / σ

For a significantly low score (Z = -2):

-2 = (x - 20.8) / 5.3

x = -2 × 5.3 + 20.8 = -10.6 + 20.8 = 10.2

For a significantly high score (Z = 2):

2 = (x - 20.8) / 5.3

x = 2 × 5.3 + 20.8 = 10.6 + 20.8 = 31.4

Thus, test scores below 10.2 are considered significantly low, and scores above 31.4 are considered significantly high.

Answer:

  none of the above (only i and ii are correct)

Step-by-step explanation:

The given numbers appear on the number line left-to-right in this order:

  -4.3  -3.7  -2.6  -1.8  -0.9

The "<" relationship is true if the number on the left is to the left on the number line. That is the case for -4.3 < -3.7, and for -3.7 < -2.6.

The ">" relationship is true if the number on the left is to the right on the number line. That is NOT THE CASE for -4.3 > -2.6 or -1.8 > -0.9.

Hence, only options i and ii are true. None of the answer choices A, B, C, or D lists only these two options.

When comparing these negative rational numbers remember that on the number line numbers get smaller as you move to the left. This means -4.3 is less than -3.7, -3.7 is less than -2.6, and -4.3 is certainly not greater than -2.6. Similarly, -1.8 is not 'greater' than -0.9. So the correct answer is D. i and iii.

In Mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Here, we are comparing some negative rational numbers. To interpret these, remember that on the number line, numbers become smaller as you move to the left. So, -4.3 is less than -3.7, -3.7 is less than -2.6, -4.3 is not greater than -2.6 because it is more to the left on the number line, and -1.8 is not greater than -0.9 for the same reason. So option A. i,ii,iii,iv is not correct, option B. iii and iv is not correct, option C. ii,iii is not correct but option D. i and iii is correct according to the comparison results of the rational numbers.

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Final answer:

To solve the given separable differential equation, we separate the variables, integrate both sides, and then apply the initial condition to find the particular solution that fits x(0) = 6.

Explanation:

The question asks to solve the separable differential equation dx/dt = x^2 + (1/9) and find the particular solution that satisfies the initial condition x(0) = 6. To solve this, first, we separate the variables and integrate both sides. The separated form of the equation is dx / (x^2 + (1/9)) = dt. Integrating both sides, we utilize the integral form that applies to the left side, leading us to an arctan function after simplification. This results in the solution to the differential equation. Subsequently, to find the particular solution satisfying the initial condition, we substitute x(0) = 6 into the obtained general solution and solve for the integration constant.

With x(0) = 6, we determine the value of the constant that makes the solution particular to the initial condition provided. By inserting this constant back into the general solution, we acquire the exact expression for x(t) that meets the initial condition specified.

Answer:

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=21-1=20[/tex]  

Since is a one side left tailed test the p value would be:  

[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Step-by-step explanation:

Data given and notation  

[tex]\bar X[/tex] represent the mean

[tex]s[/tex] represent the sample standard deviation

[tex]n=21[/tex] sample size  

[tex]\mu_o =140[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t=-0.024 would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 140[/tex]  

Alternative hypothesis:[tex]\mu < 140[/tex]  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

The statistic is given by: [tex] t = -0.024[/tex]

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=21-1=20[/tex]  

Since is a one side left tailed test the p value would be:  

[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected [tex]\alpah=0.01,0.05,0.1[/tex]

Answer:

aₙ = 6n - 6

Step-by-step explanation:

a1 = 6 x 1 - 6 = 0

a₂ = 6 x 2 - 6 = 6

Answer:

The equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]

Step-by-step explanation:

Considering the logarithmic function

[tex]f(x)=log(x)[/tex]

As we know that when a constant c gets added to the parent function, the result would be a vertical shift c units in the direction of the sign of c.

So,

[tex]g(x)=log(x)+4[/tex] is basically the shift up by 4 units, and the graph also showing the same situation.

Therefore, the equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]

Also, the graphs of both [tex]f(x)=log(x)[/tex] and  [tex]g(x)=log(x)+4[/tex] is attached where black mark graph represents  [tex]f(x)=log(x)[/tex] and red mark graph represents [tex]g(x)=log(x)+4[/tex].

Keywords: transformation, vertical shift, graph

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