According to a tudy conducted in one​ city, 27​% of adult in the city have credit card debt of more than​ $2000. A imple random ample of 400 adult i obtained from the city. Decribe the ampling ditribution of ​, the ample proportion of adult who have credit card debt of more than​ $2000. Round to three decimal place when neceary

Answers

Answer 1

The sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;

μ = 0.27 and σ = 0.022.

Explain the term random sample?A straightforward random sample, where each participant has an equal chance of being selected, selects a tiny, random piece of the total population for the purpose the full data set.

According to a research conducted in one town, the percentage of persons living there had credit card debt of at least $2,000:

p = 27% = 0.27.

An adult sample from the entire city was gathered: n = 400 adults.

The following two requirements should be used to determine the whether sample is adequate before obtaining a sampling distribution of the probability value p:

np ≥ 10

       400 x 0.27  = 108

       108 ≥ 10

And,

n(1 - p) ≥ 10

      400(1 - 0.27)  ≥ 10

      292  ≥ 10

We know that the as being p is nearly normally distributed the by suing  "Central limit theorem."

Mean M; μ = Pstandard deviation σ = √(p(1 - p)/n.

Mean of a sample proportion

μ = P = 0.27

The standard deviation's sample proportion P:

σ = √(p(1 - p)/n

σ = √(0.27(1 - 0.27)/400

σ = 0.022

Since the sample proportion of persons with credit card debts of further than $2,000 has a distribution that is roughly normal;

μ = 0.27 and σ = 0.022.

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Related Questions

if m angle 1= 125 what is m angle 2

Answers

Answer:

55°

Step-by-step explanation:

Assuming the angle is at 180°

180° - 125° = 55°

Morgan has 98 baseball cards in his collection, which is twelve less than the product of 5 and the number of cards Tyler has.

Answers

Answer: Tyler has 22 cards

Step-by-step explanation:

To begin, we know that Morgan has 12 less than 5x Tyler's cards, so...

12+98=110

Now that we had 110, we then read that it is the PRODUCT of 5 and the number that Tyler has, so we will show that algebraically.

110=5x

Now, divide 110 by 5 to find X.

110/5=22

Tyler has 22 cards.

How to work out if 3rackets and 3 balls cost 21.63t?

Answers

The cost of a racket and a  ball  is equal to $3.21 and  $4 as per the given data .

As given in the question,

Let us consider cost of a racket is equal to $x

Let us consider cost of a ball is equal to $y.

Equation formed using the given data we have,

3x + 3y = $21.63  ____(1)

3x + 10y = $49.63 ____(2)

Subtract equation (2) from (1) to eliminate x

3x + 10y = $49.63

3x + 3y = $21.63

0x + 7y = $28.00

⇒7y = 28.00

⇒ y = 28 / 7

⇒ y = $4

Substitute the value of y in (1) we get,

3x + 3(4) = 21.63

⇒3x = 21.63 -12

⇒3x = 9.63

⇒ x = $3.21

Therefore, from the given relation the cost of a racket and a ball is equal to $3.21 and $4.00.

The complete question is:

The cost of 3rackets and 3 balls cost $21.63.

The cost of 3rackets and 10 balls is $49.63.

Work out the cost of

a) a ball.

b) a racket

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5. question 5 a data analyst creates a scatter plot in tableau and notices an outlier. what should they do next?

Answers

Investigating an outlier that a data analyst has found is the best course of action.

What is a Data analyst?

To find the solution to a problem or provide an answer to a question, a data analyst gathers, purifies, and analyzes data sets.

They work in a variety of fields, including as government, business, finance, law enforcement, and science.

Depending on the question you're attempting to answer, data analysis might take on various shapes.

More information on different data analysis types is available here.

In a nutshell, descriptive analysis explains what happened, diagnostic analysis explains why it occurred, predictive analytics offers future projections, and prescriptive analysis generates actionable recommendations for what to do.

Hence, Investigating an outlier that a data analyst has found is the best course of action.

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Give the number of lone pairs around the central atom and the molecular geometry of scl2.

Answers

SCl2 has a Bent molecular geometry and a tetrahedral shape in nature. SCl2 consists of a single Sulfur atom surrounded by two Chlorine atoms. In its most stable state, Sulfur acts as the central atom and forms two covalent bonds with the Chlorine atoms. It also possesses two lone pairs.

What is molecular geometry?

The three-dimensional configuration of the atoms that make up a molecule is known as molecular geometry. In addition to bond lengths, bond angles, torsional angles, and any other geometrical factors that affect each atom's location, it also contains the molecule's overall structure. The arrangement of atoms in a molecule in three dimensions is known as molecular geometry, commonly referred to as the molecular structure. A compound's polarity, reactivity, phase of matter, color, magnetism, and biological activity can all be determined by knowing its molecular structure.

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Right triangle... One leg of a right triangle is 4 centimeters longer than the other leg. If the area of the triangle is 6 square centimeters, then what are the lengths of the legs?

Answers

Answer:

2 cm and 6 cm

Step-by-step explanation:

x = first leg

y = second leg


y = 4 + x

xy/2 = 6


y = 4 + x

xy = 12


x(4+x) = 12

x²+4x - 12 = 0

(x+6)(x-2) = 0

x = -6 (impossible because a length can’t be negative)

x = 2 cm


y = 2 + 4 = 6 cm

Select a function f whose zeroes are 0,-3,2 and -4

Answers

The family of all least polynomials with roots at - 4, - 3, 0, 2 is represented by the polynomial y = a · (x + 4) · (x + 3) · x · (x - 2), where a is the lead coefficient.

What is the function that contains a given set of zeros?

Herein we must determine the family of all least polynomials whose roots must be the real numbers - 4, -3, 0, 2. Polynomials are algebraic expressions, whose factor form is described below:

y = a · Π (x - rₙ), for n = {1, 2, 3, 4, ..., m - 1, m}

Where:

a - Lead coefficient (a real number).rₙ - n-th root of the polynomial.m - Grade of the polynomial.

In accordance with all these assumptions and definition, the function is defined below:

y = a · (x + 4) · (x + 3) · x · (x - 2)

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A 7-pound bag of potting soil costs $3.92. What is the unit price?

Answers

Answer:0.56

Step-by-step explanation:

First multiply $3.92 from 1 pound

Next dived the answer by 7 which will give you 0.56

it as been suggested that 4% of all cars on the freeway are going over 70 mph. if 4 cars are checked what is the probability that at lest 1 is going over 70 mph

Answers

It has been suggested that 4% of all cars on the freeway are going 70 mph. If 4 cars are examined, the probability that at least 1 is going 70 miles per hour is 0.151.

A probability is a numerical representation of the likelihood or possibility that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, it is said that 4% of all vehicles on the roadway are going more than 70 mph.

P(speed excess of 70 mph) = 0.04. Radar is used to determine the speeds of four random cars. Then, n = 4. Then, X = the number of cars going over 70 mph.

Then, the probability that at least one car is going over 70 mph

= P(x = 1, 2, 3, 4)

= 1 - P(x = 0)

= [tex]1 - 4_{C}_{0} (0.04)^{0} (1 - 0.04)^{4-0}[/tex]

= 1 - 0.849

= 0.151

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how many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s? (2019 amc 10 b)

Answers

The number of sequence of 0s and 1s of length 19 are there that begin with a 0, end with a 0 are 65 .

In the question ,

After any particular 0, the next 0 in sequence must appear exactly 2 or 3 positions down.

In this case, we start at position 1 and end at position 19,

that is , we move a total of 18 positions down the line.

So , we must add the series of 2s and 3s to get 18.

There are several number of ways to do this:

Case 1: nine 2s - there is only 1 way to arrange them.

Case 2: two 3s and six 2s - there are ⁸C₂ ways = 28 ways

Case 3: four 3s and three 2s - there are ⁷C₄ ways = 35 ways

Case 4: six 3s - there is only 1 way to arrange them.

So , the number of sequences is = 1 + 28 + 35 + 1 = 65 .

Therefore , the total number of sequence is = 65 .

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What is the density of a rock if its mass is 39.78 g and its volume is 12.45 cm³?

Answers

The density of the rock with a mass of 39.78 g and volume 12.45 cm³ is 3.2 g/cm³.

What is the density of the rock?

Density is simply the mass of a unit volume of a material substance.

It is expressed mathematically as;

p = m / v

Where m is mass and v is volume

Given the data in the question;

Mass of the rock m = 39.78 g Volume v = 12.45 cm³Density P = ?

Plug the given values into the above formula and solve for p.

p = m / v

p = 39.78g / 12.45 cm³

p = 3.2 g/cm³

Therefore, the density of the rock is approximately 3.2 g/cm³.

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find the actual distance represented by 1 cm to write the scale of a map with key 2/5 cm =8 km

Answers

Answer:

1 cm = 20 km

Step-by-step explanation:

Starting with what we know:

2/5 cm = 8 km

Need to change the left side to a 1. So multiply both sides by 5/2

5/2 × 2/5 = 8 × 5/2

1 cm = 40/2 km

1 cm = 20 km

Solve for x given y = 2
y=x+4

Answers

Answer:

x= –2

Step-by-step explanation:

y = 2

just substitute for y

2 = x + 4

2 – 4 = x

–2 = x

or x = –2

check

y=-2+4

y=2

so our answer is correct.

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Put the following equation of a line into slope-intercept form, simplifying all fractions.

12x - 20y = -100

Answers

Answer:

y = 5 + 3/5x

Step-by-step explanation:

We need to isolate y to get it in slope-intercept form. Let's subtract 12x from both sides, which gives us [tex]-20y=-100-12x[/tex]. Then, we can negate both sides, and then divide by 20, which results in [tex]y = (100+12x)/20[/tex], which we can further simplify to [tex]y=5 + 3/5x[/tex], which gives us our answer.

Graph the following equations on graphing paper or your calculator to solve the
system of equations.


Which ordered pair is the best estimate for the solution to the system?

A. (-2, 1)

B. (-2.5, 0)

C. (0, 2)

D. (0, 5)

Answers

In linear equation, the solution of equations is ( -2 , 1)

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

y = 2x + 5

y = 1/2x + 2

the solution of equations is ( -2 , 1)

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If f(x) = -4x+9
Find f(-6)

Answers

Answer:

33

Step-by-step explanation:

-4(-6) + 9

24 + 9

33

va 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 10 feet above the ground?

Answers

The foot be moving away from the wall when the top is 10 feet above the ground is 2.4077

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.

Aloud to yourself, read the issue.Make a Drawing.Ask yourself, "What am I looking for?"List the items that have been provided.Locate the key phrases, then Solve.Verify your work.

The ladder against the wall is a right triangle:

x² + y² = 15²

Top slips down => dy/dt = -2 ft/s. When y = 10 ft.  dx/dt = ?

1) Take the derivative with respect to time:

2x (dx/dt) + 2y (dy/dt) = 0

2) Substitute y = 10, x =sqrt(69) z =15

2(sqrt(69)) (dx/dt) + 2(10) (-2) = 0

dx/dt = 40/2(sqrt(69))

dx/dt = 20/(sqrt(69))

= 20/8.30

=2.4077

Hence, the foot be moving away from the wall when the top is 10 feet above the ground is 2.4077.

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what is a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up?

Answers

A good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up is count all the bytes of the data in the struct.

Rule:

In math rule refers a numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule

Given,

Here we need to find a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up.

According to the rule of thumb, the count all the bytes of the data in the struct.

and then we need to find the nearest power of 2, 4 or 8 based on the largest Data Type in your struct.

So, if the total number of bytes is larger than that power, then the struct will be the next power in size.

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in multiple regression analysis, the correlation among the independent variables is termed . select one: a. homoscedasticity b. linearity c. multicollinearity d. adjusted coefficient of determination

Answers

In multiple linear regression analysis, the correlation among independent variables is termed multicollinearity i.e. option C.

Definition:

a) Homoscedasticity: Homoscedasticity, also known as homogeneity of variances, is the presumption that variations in various groups being compared are equivalent or comparable.

b) Linearity: A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear. Proportionality and linearity are closely linked concepts.

c) Multicollinearity: Multiple independent variables in a model that are correlating from a statistical concept known as multicollinearity.

d) Adjusted Coefficient of Determination: The number of variables in a data collection is taken into account when calculating the adjusted coefficient of determination (also known as adjusted R-squared). Additionally, it penalizes you for any points that deviate from the model.

Hence, the required choice is Option C.

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Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents. DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.

(m 3n + 8)(m 3n - 5)

Answers

The simplified form of  (m + 3n + 8)(m + 3n - 8) is  m^2 + 3n^2 + 6mn - 64.

What is a factor of a polynomial?

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given,  (x+2)(x+3) = x^2+5x+6.

∴ (m + 3n + 8)(m + 3n - 8).

= m^2 + 3mn - 8m + 3mn + 3n^2 - 24n + 8m + 24n - 64.

= m^2 + 3n^2 + 6mn - 64.

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What is the x & y intercept of the equation?

1/2y + 5x = 7

Answers

Answer:

x-intercept: (7/5, 0)

y-intercept: (0, 14)

Step-by-step explanation:

The x intercept is when y is equal to 0.

1/2(0) + 5x = 7

5x = 7

x = 7/5

Put this into point form, where x is 7/5 and y is 0.

(7/5, 0)

The y intercept is when x is equal to 0.

1/2y + 5(0) = 7

1/2y = 7

y = 14

Put this into point form, where x is 0 and y is 14.

(0, 14)

X-intercept(s):
(-7/5, 0)

Y-intercepts:
(0,7/2)

How do I graph the equations x=3 and y=-8

Answers

You should look at 3 on the graph and go down to 8 and plot the point

. Review the equation 0.10(m + 1000) = 3000 + 3000 Select the appropriate column to identify the reasoning that would justify each step in solving for m.

Answers

Answer:

Step-by-step explanation: 12

Find all solutions to the equation b² = 13

Answers

Answer:  The correct answer is b = √13 or b = −√13

Step-by-step explanation:

When factoring squared variables or numbers, use the square root

b^2 = 13

Take the square root of both sides

b^2 = 13

b = 13 or b = −√13

how many ways are there to assign each of $6$ friends to either the chemistry class or the biology class if one of these six, manoj, refuses to be in a class without any of his friends?

Answers

There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.

What is the formula of combination?

Following is the fomula of combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, n is the total objects available and r is the number of object need to choose from n objects.

Let six friends are A, B, C, D, E, and manoj.

Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_6[/tex]

Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_5[/tex]

Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_4[/tex]

Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_3[/tex]

Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_2[/tex]

Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,

[tex]^6C_1[/tex]

Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,

[tex]^6C_0[/tex]

Hence, total number of ways in which classes can be assigned to 6 students is,

[tex]^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64[/tex]

Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.

Hence, subtract 2 from 64 to get the answer.

[tex]64-2=62[/tex]

Hence, there are 62 number of ways in which classes to these students can be assigned.

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This is an arithmetic sequence.
8, 7.4, 6.8, 6.2, 5.6, …
Which function describes the sequence?
A. f(x) = 0.6x + 8
B. f(x) = 0.6x + 8.6
C. f(x) = −0.6x + 8
D. f(x) = −0.6x + 8.6

Answers

The function which describes the arithmetic sequence is f(x) = −0.6x + 8.6.

The correct answer option is option D

Which function describes the sequence?

Given the sequence:

8, 7.4, 6.8, 6.2, 5.6, …

Check all the options

Where,

x = number of term

A. f(x) = 0.6x + 8

When x = 1

f(x) = 0.6x + 8

= 0.6(1) + 8

= 0.6 + 8

= 8.6

B. f(x) = 0.6x + 8.6

When x = 1

= 0.6(1) + 8.6

= 0.6 + 8.6

= 9.2

C. f(x) = −0.6x + 8

When x = 1

= -0.6(1) + 8

= 0.6 + 8

= 8.6

D. f(x) = −0.6x + 8.6

When x = 1

= -0.6(1) + 8.6

= -0.6 + 8.6

= 8

Hence, f(x) = −0.6x + 8.6 is the function which describes the sequence.

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A function f (x) is graphed on the coordinate plane. What is the function rule in slope-intercept form? Afunction f (>) is graphed on the coordinate plane What is the function rule in slope-intercept fom? Enter your answer in the box f(r) Basic x2

Answers

The required function of the line would be y = 2x + 1.

Coordinate Plane:

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

The function rule in slope-intercept form:

The slope-intercept form is one rule to represent linear function rules. f(x)=mx + b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 .

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Help meee! ;( I need to pass

Answers

Answer:

250.32 dollars

Step-by-step explanation:

The given loan amount is equal to 8,700 dollars and the number of years is 3 years and the a p r is equal to 2.31 percentage. The formula for monthly payment is a is equal to p into or divided by 12 into 1 plus or divided by 12 points the whole power and whole divided by 1 plus r divided by 12 points.The whole power n minus 1 in this formula, p is the lown amount and r is the well interest rate and n is the number of payments here. We have the number of years is 3, so the number of payments will be 36 points. Then, by this formula we have the monthly payment: a is equal to 8700 into 0.0231, divided by 12 into 0.0231 divided by 12 plus 1. The whole power 36 whole divided by 0.0231, divided by 12 plus 1, the whole power 36 minus 1, and it will be equal to 250.32 dollars. Therefore, the monthly payment is equal to 250.32 dollars.

you have nine different color paints. you want to paint five different pots such that no two pots have the same color. how many ways are there to paint the pots?

Answers

The number of ways to paint the pots can be found using permutations and is found to be 15120 ways.

What are permutations?

An arrangement of all or a portion of a collection of items, taking into account the arrangement's order, is referred to as a permutation.

Here, we know that there are 9 different paints to choose from, so we are required to find the number of ways we can paint 5 pots without repeating any color.

This can be given by [tex]9P_{5}[/tex] ways.

[tex]=\frac{9!}{(9-5)!} \\=\frac{9!}{4!} \\=15120\space\ ways[/tex].

Therefore, the number of ways to paint the pots is 15120 ways.

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Answer is below! Answer please!

Answers

Answer: 8 phones sold and 24 accessories

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The plaintiff is suing Huprey for $5,000,000. 2. Huprey can resonably estimate that a pending lawsuit will result in damages of $1,250,000. It is probable that Huprey will lose the case. 3. It is reasonably possible that Huprey will lose a pending lawsuit. Huprey and its lawyers cannot estimate what the damages will be if it loses. incorporating external partners into the ea framework can be difficult. discuss one essential aspect of being successful incorporating external partners. What is the most common type of delusion experienced by people with a schizophrenia spectrum disorder?. Evaluate the expression when a=10 .a/4+1/3 = heterotherms maintain high internal body temperatures through internal metabolic production of heat true or false which is the only completely reliable way to avoid exposure to sexually transmitted diseases? a. take antibiotics on a regular basis b. have annual medical examinations c. engage in oral sex only d. abstain from sexual activity Which type of psychotherapy has been found to help improve a variety of symptoms and protect against loss of gray matter in the brain of those with schizophrenia?. you're working with a car manufacturer that is looking to set up a campaign within campaign manager 360. they've just had their campaign manager 360 network created. what steps, in order, should you take to set up their campaign? this project is designed for you to have a complete understanding of what is entailed in buying a home. for most people, their home purchase is the largest financial purchase they will make in their lifetime, so understanding how the process works and how much it will cost you, are key elements you need to know. while there is much detail to be provided, you will need all this information when it is your turn to purchase the home of your dreams! what is the nonhuman things in the sentence the winter wrapped its icy claws around northeast pennsylvania. which measures can be taken to prevent wrong-site, wrong-client, wrong-procedure surgical errors? select all that apply. supplements of the antioxidant nutrients appear to prevent or slow the progression of cataracts. a. true b. false imagine you discover a mutation in a eukaryotic gene that leads to loss of function of the protein that it encodes. you determine the mutant genes nucleotide sequence from start site for transcription to the termination point of transcription and find no differences between the mutant gene and the normal gene. where on the dna could the mutation be? bronco the skydiver falls toward earth. the attraction of earth on bronco pulls him down. the reaction to this force is Is the skeletal system interdependent on the integumentary system? A. Yes, the skeletal system is interdependent of the integumentary system. The main objective is the bones rely on the skin for the synthesis of vitamin D3. Without vitamin D3 (a steroid that is converted to calcitriol), a normal calcium metabolism wouldnt be maintained). Calcium is one of the hearts of bone structure; with a lack of calcium, the bones would become very brittle and lead to cases such as osteoporosis and multiple fractures.B. No, because the skeletal system consists of both fused and individual bones supported and supplemented by ligaments, tendons, muscles, and cartilage. It serves as a scaffold that supports organs, anchors muscles, and protects organs such as the brain, lungs, and heart. And the integumentary system is the organ system that protects the body from damage, comprising the skin and its appendages (including hair, scales, feathers, and nails). So, therefore, we need the integumentary system to protect the skeletal system at all times, when we move our skin moves. C. Yes, the skeletal system is interdependent on the integumentary system. One function of the integumentary system is to synthesize vitamin D3. The skeletal system depends on the synthesis of vitamin D for bone growth and bone remodeling by the osteoblast and osteoclast. Vitamin D is needed to absorb calcium into the circulatory system from the digestive system.(HELP NEEDED ASAP. I REALLY APPRECIATE IT) the nurse is conducting a health assessment for a school-age child who is new to the pediatric practice. which questions would the nurse ask the child and parents related to growth? select all that apply. one, some, or all responses may be correct.