a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?

Answers

Answer 1

If the expected value of d is not equal to d, then the property that d hat exhibit is option (E) d hat is biased

Here a certain statistic d cap is being used to estimate a population parameter d

The central limit theorem states that "the distribution of sample means approximates a normal distribution as the sample size gets larger."

According to the central limit theorem,

The expected value is μ = p

Then the standard error will be

s = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

Here it is given that the expected value of d cap is not equal to d. So it is different from the expected value  μ = p.

Therefore, the d hat is biased

I have answered the question in general, as the given question is incomplete

The complete question is :

A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. What property does d hat exhibit?

A. The sampling distribution of d hat is normal.

B. The sampling distribution of d hat is binomial.

C. The sampling distribution of d hat is uniform.

D. d hat is unbiased.

E. d hat is biased.

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Related Questions

2

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Inequalities on the Number Line: Mastery Test

2.

Select the correct rational numbers.

Identify the numbers that are located to the right of - 4 on a horizontal number line.

2

52

WIN

co

WIN

WIN

-5

1

12 / 를

-4

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Answers

The numbers that are located to the right of - 4 on a horizontal number line is

A.) - 1/2

B.) 5 1/2

D.) - 3 2/3

E.) - 1 2/3

G.) 2 /3

H.) - 4

What is number line?

A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

Given the numbers :

A. -1/2 ; B. 5 1/2 ; C. -4 2/3 ; D. -3 2/3 ; E. -1 2/3 ; F. -5 1/2 ; G. 2/3 ; H. -4

Select which are located to the right of - 4 1/3 on an horizontal number line;

Kindly note that ; numbers located to the right of - 4 1/3 will be greater.

Hence, all numbers in the option greater Than - 4 1/3 are correct.

All positive numbers are located to the right ;

All negative greater than - 4 1/3

A.) - 1/2

B.) 5 1/2

D.) - 3 2/3

E.) - 1 2/3

G.) 2 /3

H.) - 4

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List 5 rational number between -1 and 0

Answers

Answer: [tex]-\frac{1}{2}, -\frac{1}{4} , -\frac{1}{6}, -\frac{1}{7} , -\frac{2}{3}[/tex]

Step-by-step explanation:

A simple way to find a rational number is to make sure the fraction is between the given numbers. Below are five examples, but there are many more.

[tex]-\frac{1}{2}, -\frac{1}{4} , -\frac{1}{6}, -\frac{1}{7} , -\frac{2}{3}[/tex]

please help me: find the measure of each angle indicated​

Answers

Answer:

137

Step-by-step explanation:

triangles always equal 180 degrees for internal angles

20+23-180

Desiree ran at a speed of 16 km/hr for 30 minutes. She then walked at 8 km/hr for 45 minutes.
What was the total distance that she travelled?

Answers

The total distance Desiree travelled was 14km.

Always remember,

Average speed= Total distance travelled/ Total time taken

So, in this case, we have to find the distance,

Distance= Speed × Time

When she  ran 16km per hour for 30 minutes,

⇒ Distance= 16×30/60

⇒ Distance= 8km --------------------(1)

When she ran 8km per hour for 45 minutes,

⇒ Distance= 8×45/60

⇒ Distance= 6km --------------------(2)

Adding equations (1) and (2) we get,

⇒ Distance = 8+6=14km

Hence, the Total Distance travelled was 14km.

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Amy buys 12 envelopes for 26p each and pays with a £5 note.

How much change does she get?

Give your answer in pounds, £

Answers

Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

What is ratio and proportion?

Mathematics deals with the relationship between two numbers or quantities using the notions of ratio and proportion. Two numbers are compared in a ratio, which is often represented as a fraction. For example, the ratio of pounds to oranges in a basket could be 3:2, implying that there are three apples for every two oranges. Contrarily, proportion is the connection between two ratios. It is an equation, in other words, when two ratios are equal. The ratio of apples to oranges in a basket may be 3:2, whereas the ratio of apples to all the other fruits in the basket might be 9:11. In this case, the two ratios are proportionate since 3/2 = 9/11.

How to solve?

Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

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Simplify the expression.

w+w+5w =

Answers

The answer is 7w

Combine like terms
the answer would be 7w :)

Place then to the correct matching terms also explaing why

Answers

If UV≅PM then UV≅PM → Definition of congruence, EF≅EF → Reflexive property of congruence, If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence.

What are postulates?

A statement that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry.

A) If and only if two segments have equal amounts of each, they are congruent.

If UV≅PM then UV≅PM → Definition of congruence

B) An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.

EF≅EF → Reflexive property of congruence

C) According to the transitive characteristic of congruence, "all sides are congruent to each other if two sides are congruent to the third side."

If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence

D) Actually fairly straightforward, equality has the symmetric condition. According to this criterion, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the equation still makes sense.

If AB=XY then XY =AB  → Symmetric property of equality

E) The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.

If 2x-3=13 then 2x=16 → Addition property of equality

Add 3 on both the sides of equation we get

2x-3+3=13+3

⇒ 2x=16

Therefore, the statement If 2x-3=13 then 2x=16 follows addition property of equality.

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If
x-x²y-2y² = 0 then find the equations of all tangent lines to the curve when
y = -1.

Answers

The equation of the tangent line to the curve when y = -1 is y = -4x - 1.

To find the equations of all tangent lines to the curve when y = -1, we can use the definition of a tangent line, which is a line that touches a curve at a single point and has the same slope as the curve at that point.

To find the slope of the curve at a given point, we can use the slope formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, we can set y₁ = -1 and y₂ = -1 + h, where h is a small positive number, and find the corresponding value of x₂ by substituting these values into the equation x - x²y - 2y² = 0. This will give us the slope of the curve at the point (x, -1).

Substituting these values into the equation, we get:

x - x²(-1) - 2(-1 + h)² = 0

Expanding the second term and rearranging, we get:

x - x² + 2(1 - 2h + h²) = 0

This simplifies to:

x - x² + 2 - 4h + 2h² = 0

This can be rewritten as:

x - x² + 2h² - 4h + 2 = 0

To find the slope of the curve at the point (x, -1), we can take the derivative of this equation with respect to x and evaluate it at x = x and h = 0:

slope = (2h² - 4h)'|h=0

= 0 - 4

= -4

Now that we have the slope of the curve at the point (x, -1), we can use the point-slope form of a linear equation to find the equation of the tangent line:

y - (-1) = -4(x - x)

y + 1 = -4x

y = -4x - 1

Therefore, when y = -1, the equation of the tangent line to the curve is y = -4x - 1.

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A business invests $45,000 in an account that earns 1.8% interest that is compounded monthly.
What type of function best represents the growth of the investment?
Choose...

Answers

The exponential function best represents the growth of the investment.

What is exponential function?

An exponential function can be used to depict the investment's growth. The formula for an exponential function is y = a * b^x, where an is the starting point (in this case, 45,000), b is the growth factor (in this case,

1 + 0.018 = 1.018), and x is the number of time periods (in this case, the number of months).

For example, if we let x represent the number of months, the function would be:

y = 45,000 * 1.018^x

This function represents the growth of the investment as a function of the number of months. As the number of months increases, the value of the investment will grow exponentially according to the formula.

Hence, the exponential function best represents the growth of the investment.

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An airliner carries 350 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d).

A. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending:

B. If half the passengers are men, find the probability that the mean height of the 175 men is less than 72 in

C. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?

D. When considering the comfort and safety of passengers, why are women ignored in this case?

Answers

Answer: A. To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the probability that his height is less than or equal to 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, we can use the standard normal distribution to find this probability.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the height of a male passenger from the given distribution to the standard normal distribution by using the formula:

$z = \frac{x - \mu}{\sigma}$

where $x$ is the height of the male passenger, $\mu$ is the mean height of 69 inches, and $\sigma$ is the standard deviation of 2.8 inches. Substituting these values into the formula gives us:

$z = \frac{72 - 69}{2.8} = \frac{3}{2.8} = 1.0714$

Since the standard normal distribution is symmetric, the probability that a male passenger's height is less than or equal to 72 inches is the same as the probability that his height is greater than or equal to 72 inches. We can find this probability by looking up the value of $z = 1.0714$ in a standard normal table, which gives us a probability of 0.8413. Therefore, the probability that a male passenger can fit through the doorway without bending is 0.8413.

B. To find the probability that the mean height of the 175 men is less than 72 inches, we need to find the probability that the sample mean is less than 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, the sample mean will also be normally distributed with a mean of 69 inches and a standard deviation of $\frac{2.8}{\sqrt{175}} = 0.32$. We can use the standard normal distribution to find the probability that the sample mean is less than 72 inches.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the sample mean from the given distribution to the standard normal distribution by using the formula:

$z = \frac{x - \mu}{\sigma}$

where $x$ is the sample mean, $\mu$ is the mean of 69 inches, and $\sigma$ is the standard deviation of 0.32. Substituting these values into the formula gives us:

$z = \frac{72 - 69}{0.32} = \frac{3}{0.32} = 9.375$

Since the standard normal distribution is symmetric, the probability that the sample mean is less than 72 inches is the same as the probability that the sample mean is greater than 72 inches. We can find this probability by looking up the value of $z = 9.375$ in a standard normal table, which gives us a probability of 0.0000. Therefore, the probability that the mean height of the 175 men is less than 72 inches is 0.0000.

C. When considering the comfort and safety of passengers, the result from part (a) is more relevant than the result from part (b). This is because part (a) tells us the probability that a randomly selected male passenger can fit through the doorway without bending, which is directly relevant to the comfort and safety of the passengers. In contrast, part (b) tells us the probability that the mean height of the 175 men is less than 72 inches, which is not directly relevant to the comfort

D. Women are ignored in this case because the problem only asks about the heights of men. The problem states that the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, and does not provide any information about the heights of women. Therefore, we cannot use the given information to find the probability that a female passenger can fit through the doorway without bending.

How would I solve this question? I know that x and y will be equal but I'm not sure of their values.
Please look at the file attached

Answers

Answer: y = 160° y' = 0

Step-by-step explanation:

y = 160°

take the derivative of both sides

y'= d÷dx(160°)

the derivative of a constant is always 0

y' = 0

Reflection of point across x-axis
Reflection of point across y-axis
---------------------------------------------------------------------

Reflection of point across x-axis and
then Reflection across y-axis
HELP ?!

Answers

Reflection of point across x-axis

preimage (-3, 2)         Image (-3, -2)

Reflection of point across y-axis

preimage (-3, 2)         Image (3, 2)

How to find the coordinates of the reflected image

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection to be done is (-3, 2)

Transformation for reflection over x-axis → (-3, -2)

Transformation for reflection over line y-axis  → (3, 2)

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For an A.P. find S12 if a 4 and d=3.

Answers

Answer:

The answer is 246

Step-by-step explanation:

Given;n = 12a = 4d = 3Formula;Sₙ = n/2 [2a + (n - 1)d]

So,

S₁₂ = 12/2 [2(4) + (12 - 1)3]

S₁₂ = 6 [8 + (11)3]

S₁₂ = 6 × (8 + 33)

S₁₂ = 6 × 41

S₁₂ = 246

Thus, The S₁₂ of given A.P is 246

I roll a pair of fair dice and let X= the sum of the spots on the two sides facing up. The probability that X is 2, 11, or 12 is...

Answers

Answer:

12? lol

Step-by-step explanation:

<3

7. In a triangle there are two sides that have the same length and the third
side is 1.5 times longer than the length of the other two. Define a variable
to represent the unknown quantity. Then write an algebraic expression to
represent the perimeter of the triangle.

Answers

x=length of one of the equal sides
3.5x

Cuál e el capital que e coloca al 25% durante 3 año, para obtener un interé de $. 1620

Answers

On solving the provided question, the capital that is placed at 25% for 3 years, to obtain an interest of $ 1620 will be $3,164.06

Explain what compound interest is.

interest you receive is equal to as - compound interest. Using simple math, you can see how this works: if you have $100 and it earns 5% interest annually, you will have = $105 at the end of the 1st year. You'll have = $110.25 at the conclusion of the 2ndyear.

To calculate, we will use the following

[tex]First, convert R as a percent to r as a decimal[/tex]

r = R/100

r = 25/100

r = 0.25 rate per year,

Then solve the equation for A

[tex]A = P(1 + r/n)^{(nt)}[/tex]

[tex]A = 1,620.00(1 + 0.25/1)^{(1)(3)}[/tex]

A = 1,620.00(1 + 0.25)(3)

A = $3,164.06

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What is the equation for the line in slope-intercept form?



Enter your answer in the box.

Answers

Answer: y=-4x+6

Step-by-step explanation:

What type of exponential function is f(x)=0. 75(2. 1)^x what is the function's percent rate of change? select from the drop box menus to correctly complete each statement? the functoin is an exponential (drop box) function growth decay percent rate of change of the function is (drop box) % 210 110 75 25

Answers

The function is an exponential growth function growth decay percent rate of change of the function is 110 %.

Given :

What type of exponential function is f(x)=0. 75(2. 1)^x what is the function's percent rate of change.

we know that,

exponential growth function in the form of y = a ( 1 + r )^x

on comparing both functions we get ,

1 + r = 2.1

r = 2.1 - 1

r = 21 / 10 - 1

= 21 - 10 / 10

= 11 / 10

= 1.1

converting into percentage:

= 1.1 * 100 %

= 110 %

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12, 23, 34, 45, ... what is the arithmetic sequence?

Answers

Answer:

The arithmetic sequence in the given series of numbers is 11. The common difference in an arithmetic sequence is the number that is added to each term to get the next term in the sequence. In this case, the common difference is 11, because when we add 11 to the first term, 12, we get 23, which is the second term in the sequence. Similarly, when we add 11 to the second term, 23, we get 34, which is the third term in the sequence, and so on. Therefore, the arithmetic sequence in the given series of numbers is 11

In January the depth of a lake wa 943 feet in Augut the depth of the lake wa 754. 4 what i the percentage decreae of the depth of the lake from January to Augut

Answers

19.89% is the percentage decrease of the depth of the lake from January to August.

What is percentage?

A quantity or ratio can be expressed as a percentage of 100 by using the word "percentage." Comparing two or more numbers and illustrating how significantly one number differs from the other in proportion to the whole is a popular usage for this technique. If a baseball originally costs $12 and is discounted by 20%, for instance, its new price would be $12 x 20/100 = $2.40 less than the original price. In other words, after the reduction, the ball will cost $12 - $2.40 = $9.60. A percentage may often be determined by dividing a quantity by its entirety and multiplying the result by 100. For instance, if a baseball bat costs $100 and is reduced by 30%, its new cost would be $100 x 30/100, which equates to $30 less.

How to solve?

The depth of the lake decreased by 943 - 754.4 = 188.6 feet from January to August.

The percentage decrease is (188.6 / 943) x 100 = 19.89%

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Find the quotient. ÷n¹²n4
n=

Answers

Step-by-step explanation:

you did not write this question well

The perimeter of a triangle is 40 centimeters. If two sides are equally long and the third side is 7 centimeters longer
than the others, find the lengths of the three sides.

Answers

Answer:

L1 = L2 = 16.5 cm and L3 = 7cm

Step-by-step explanation:

Triangle perimeter = L1 + L2 + L3 = 40 cm

L1 = L2 = L

L3 = 7

Then:

40 = 2L +7

33 = 2L

L = 33/2

L = 16.5 cm

which of the following is the graph of
[tex]y = - 4 \sqrt{x} [/tex]


Answers

I am assuming the one with the check mark that says it’s correct
It’s the one with a check mark on it

Graph the line with y-intercept 3 and slope -2/3

Answers

Answer: I think its 3.5

Step-by-step explanation:

Josh is 3 years older than 4 times Kim's age. The sum of their ages is less than 43. Select the correct inequality for the situation, then determine the oldest age Kim could be. Question 6 options: (3 + 4k) + k > 43 3 + 4k > 43 3 + 4k < 43 (3 + 4k) + k < 43 A. The oldest Kim could be is 4 years old. B. The oldest Kim could be is 5 years old. C. The oldest Kim could be is 6 years old. D. The oldest Kim could be is 7 years old.

Answers

The required solution of the given numerals is,
1. 3 + 4k + k < 43, Option D is correct.
2. The oldest Kim could be 7 years old. Option D is correct.

Given that,
Josh is 3 years older than 4 times Kim's age. The sum of their ages is less than 43. Select the correct inequality for the situation, then determine the oldest age Kim could be.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
J = 4k + 3
And
J + K < 43
4K + 3 + K < 43
5k < 40k
k < 8
K could be K = 7

Thus, the required solution of the given numerals is,
1. 3 + 4k + k < 43, Option D is correct.
2. The oldest Kim could be 7 years old. Option D is correct.

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Mandy is setting up for a reception. For the number of seats needed, she knows she can use either 8 seats at each table with none left over or 10 seats at each table with none left over. Which is the least number of seats she is setting up? A. 80 B. 20 C. 120 D. 40

Answers

The least number of seats she is setting up 40 seats are needed.

What is least number?

The least number is zero (0). Zero (0) is the smallest natural number and is the additive identity of the set of whole numbers. It is the only number that is neither positive nor negative and is, therefore, regarded as neither odd nor even. Zero (0) is essential in mathematics and is used to represent the absence of a quantity. It is also used to represent the additive identity of real numbers and complex numbers.

Given: Mandy can place 8 seats at each table or 10 seats at each table with no left over.

We have to find the least number of seats needed.

Find the prime factors of 8:

⇒ 8 = 2 x 2 x 2 = 8 = 2³

Find the prime factors of 10:

⇒ 10 = 2 x 5

Find the LCM of 8 and 10:

⇒ 8 = 2³

10 = 2 x 5

LCM = 2³ x 5

LCM = 40

Hence, a minimum of 40 seats are needed.

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Reduce 28/56 to the standard form

Answers

Dividing by 2 we get
14/28
7/14
1/2
Hence 1/2 is the standard form.

On a team, 7 girls and 5 boys scored a total of 86 points. The difference between the number of points scored by the 7 girls and the number of points scored by the 5 boys is 26. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.

Answers

Answer:

Each Girl scored 3.71 points

Each boy scored 12 points

please give me a hand cause i don t get it ​

Answers

Answer:

The range is found by the y axis. Find the length by comparing it to the graph.

Step-by-step explanation:

(1.) Convert 25 in base 10 into base 2
(2.)Convert 101011 in base 2 into base 5

Answers

answer here!

sry it is a bit messy

Answer:

1) 11001 base 2

2)133 base 5

1) To convert base 10 into base 2

25/2= 12remainder 1

from this point on, the remainders will be replaced by r

12/2= 6r0

6/2=3r0

3/2=1r1

1/2=0r1

The remainders are then written down from the bottom up

= 11001

2) To convert 101011 base 2 into base 5

101011= 1×2⁵ + 0×2⁴+ 1×2³+ 0×2² + 1×2¹ + 1×2⁰

=1×32 + 0×16 + 1×8+ 0×4+1×2+1×1

=32+0+8+0+2+1

=43 base 10

Then convert 43 base 10 to base 5

43/5=8r3

8/5=1r3

1/5=0r1

=133 base 5

Other Questions
1ofestionAll of the following terms are spelled correctly except.Select one:O A. tympanic.OB. labryinthitis.OC. otosclerosis.OD. acoustic. A store sells two competitive products, A and B. A model for the revenue from selling qA units of product A and qB units of product B is R = 40qA + 50qB 6qA2 9qB2 4qAqB. What values of qA and qB maximize the revenue? (Fractional amounts of the products are permitted) Joe i reponible for reerving hotel room for a company trip. Hi company change plan and increae how many people are going on the trip, o they need at leat 505050 total room. Joe had already reerved and paid for 161616 room, o he need to reerve additional room. He can only reerve room in block, and each block contain 888 room and cot \$900$900dollar ign, 900. Let BBB repreent the number of additional block that Joe reerve. 1) Which inequality decribe thi cenario?Chooe 1 anwer: panish moss is not a moss, but a flowering plant (Tillandsia usneoides) often seen draped from the branches of live oaks, cypress, and other large trees in the southeastern United States. The trees on which it grows provide support but no nutrients or moisturethe plant provides those things for itself, without apparently harming its support tree. What type of interspecific interaction is this an example of? Which is a role of cellular respiration in cycling materials between the atmosphere and the biosphere?. one human chromosome set consists of about 3.2 mb (mega base pairs). how many mb would you find in a human skin cell during the g2 phase regarding the experiment where the children watched a boxing match with an adult, what was a correct finding? In angle JKL, if angle L is thirteen more than angle k and angle j is seven more than six times angle k, find the measure of each angle fiddlehead greens are the curled, young fronds of a fern. harvested very early and trimmed close to the ground, they provide a tasty addition to salads. these multicellular, photosynthetic, vascularized organisms that do not produce seeds belong to the kingdomplantae what are natural rights? how do people get natural rights? A body of mass 1 kg has weight 10N at a certain place. What is the weight of 100g, Which u. S. Congressman wrote the legislation to revamp the g. I. Bill in the 1980s, strengthening the educational benefits for the post-vietnam war era?. john deere relies on hundreds of vendors to produce component parts for its farm equipment. this illustrates which secret of small business success? A nurse is caring for a client who overdosed on acetylsalicylic acid (aspirin) 24 hours ago. The nurse should expect to note which findings associated with an anticipated acid-base disturbance?1.Disorientation and dyspnea 2.Drowsiness, headache, and tachypnea 3.Tachypnea, dizziness, and paresthesias 4.Decreased respiratory rate and depth, cardiac irregularities A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,340 ft Determine the flag's width and length if the length is 410 ft greater than the width. you are planning a server virtualization implementation using hyper-v. your virtualization solution must meet the following requirements: both 32-bit and 64-bit operating systems will be installed as virtual machines. you need to install six virtual machines. all virtual machines must be able to communicate with each other. virtual machines should not be able to communicate with any other network devices. virtual machines should not be able to communicate with the management operating system. what should you do? answer create a private network create an external network create an internal network create a wireless network solve for n n/12=300 n=__ what does Janie do that shes never done before, and what prompts her to act this way? a measurement of how much a person or household owns once all debts have been paid. how should the $2.3 million be allocated to each of the loan/investment alternatives to maximize total annual return?