A researcher focusing on birth weights of babies found that the mean birth weight is 3368 grams (7 pounds, 6.8 ounces) with a standard deviation of 582 grams. Complete parts (a) and (b)
a. Identify the variable.
Choose the correct variable below.
A. The weights of the babies at birth
B. The number of births per capita
C. The accuracy of the measurements of baby birth weights
D. The number of babies that were born
b. For samples of size 200, find the mean μ_x and standard deviation δ_x of all possible sample mean weights.
μ_x = _______(Type an Integer or a decimal. Do not round.)
δ_x =________ (Round to two decimal places as needed.)

Answers

Answer 1

a. The variable is given as follows:

A. The weights of the babies at birth

b. The mean and the standard error are given as follows:

μ_x = 3368 grams.δ_x = 41.15 grams.

How to obtain the distribution?

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The mean is the same as the population mean, of 3368 grams, while the shape is approximately normal.

The standard error is given as follows:

[tex]s = \frac{582}{\sqrt{200}} = 41.15[/tex]

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Related Questions

Write an expression in factored form to represent the area of each shaded region. Include the area formula and full steps and write your answer in simplified form. 3x a) (3 marks) 3x + y 2x +y 3x b) 3y (3 marks) B 2x 2x

Answers

a. The area of the shaded region = (3x)(5x + 2y).

b. The area of shaded region = 2x(2xπ - 3x).

Given that,

We have to write an expression in factored form to represent the area of each shaded region.

We know that,

a. In the picture we can see that the shaded region.

The area of the shaded region is area of rectangle with vertical + area of rectangle Horizontal

The area of rectangle is length × width.

The area of the shaded region = (3x)(3x + y) + (2x + y)(3x)

The area of the shaded region = (3x)(3x + y + 2x + y)

The area of the shaded region = (3x)(5x + 2y)

Therefore, The area of the shaded region = (3x)(5x + 2y)

b. In the picture we can see that circle with shaded region,

The area of shaded region is area of the circle - area of the rectangle

The area of the circle is πr² and area of rectangle is length × width.

The area of shaded region = πr² - (l×w)

The area of shaded region = π(2x)² - (2x × 3x)

The area of shaded region = 4x²π - 6x²

The area of shaded region = 2x(2xπ - 3x)

Therefore, The area of shaded region = 2x(2xπ - 3x).

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Wiseman Video plans to make four annual deposits of $2,000 each to a special building fund. The fund’s assets will be invested in mortgage instruments expected to pay interest at 12% on the fund’s balance. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Using the appropriate annuity table, determine how much will be accumulated in the fund on December 31, 2019, under each of the following situations.

1. The first deposit is made on December 31, 2016, and interest is compounded annually.

Table or calculator function: FVA of $1
Payment: $2,000
n = 4
i = 12%
Fund balance 12/31/2019: $9,559
2. The first deposit is made on December 31, 2015, and interest is compounded annually.

Table or calculator function: FVAD of $1
Payment: $2,000
n = 4
i = 12%
Fund balance 12/31/2019: $10,706
3. The first deposit is made on December 31, 2015, and interest is compounded quarterly.

Using the FV of $1 chart, calculate the fund balance:
Deposit Date i = n = Deposit Fund Balance 12/31/2019
12/31/2015 3% 16 $2,000 $3,209
12/31/2016 3% 12 2,000 2,852
12/31/2017 3% 8 2,000 2,534
12/31/2018 3% 4 2,000 2,251
$10,846
4. The first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.

Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019
$2,000 $8,000

Answers

The fund balance at the end of 2019 will be $8,000.

The given problem has four different parts, where we are supposed to calculate the accumulation of funds at the end of 2019 in different scenarios.

Scenario 1In the first scenario, the first deposit is made on December 31, 2016, and interest is compounded annually.

Using the FVA of $1 table; Payment: $2,000n = 4i = 12%

Fund balance 12/31/2019: $9,559

Hence, the fund balance at the end of 2019 will be $9,559.Scenario 2In the second scenario, the first deposit is made on December 31, 2015, and interest is compounded annually.

Using the FVAD of $1 table;Payment: $2,000n = 4i = 12%

Fund balance 12/31/2019: $10,706 Therefore, the fund balance at the end of 2019 will be $10,706.Scenario 3In the third scenario, the first deposit is made on December 31, 2015, and interest is compounded quarterly. Using the FV of the $1 chart, we get the following calculation:

Deposit Date i = n = Deposit Fund Balance 12/31/2015 3% 16 $2,000 $3,20912/31/2016 3% 12 $2,000 $2,85212/31/2017 3% 8 $2,000 $2,53412/31/2018 3% 4 $2,000 $2,251

The interest rate is 3%, and the payment is $2,000. Hence, the fund balance at the end of 2019 will be $10,846.Scenario 4In the fourth scenario, the first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.

Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019$2,000 $8,000 Hence, the fund balance at the end of 2019 will be $8,000.

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The G.M and H.M between two number are respectively 9 & 5.4. Find the numbers.

Answers

Answer:

The numbers are 3 and 27.

Step-by-step explanation:

The explanation is attached below.

What is the probability of 4 consecutive 2-sided coin tosses all coming up heads?

Answers

The probability of getting four consecutive heads in four 2-sided coin tosses is 1/16 or 0.0625 or 6.25%.

The Probability is defined as a measure of the likelihood or chance that an event will occur, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

To calculate the probability of getting four consecutive heads in a row, we multiply the probabilities of each individual toss.

The Probability of heads (H) is = 1/2,

So, The Probability of four consecutive heads (HHHH) is :

= (1/2) × (1/2) × (1/2) × (1/2) = (1/2)⁴ = 1/16,

Therefore, the required probability is 1/16 or 6.25%.

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Use Strong Induction to prove that: If p + 1/p E N, then Pn+1/Pn EN for all nEN.

Answers

We prove with the help of Strong Induction.

Let P(n) be the statement that Pn+1/Pn E N.

In order to prove this statement, we will utilize strong induction.So we are given that p + 1/p E N. We will show that P(n) is true for all n >= 1.

Let's consider the base case

P(1):P2/P1 = (p + 1/p)^2 - 2 = (p^2 + 2 + 1/p^2) - 2p/p = (p^2 + 1/p^2) - (2p - 2/p)

Since p + 1/p E N, both p and 1/p must be integers.

Hence, p^2 and 1/p^2 are also integers. This implies that (p^2 + 1/p^2) is an integer.

It only remains to show that (2p - 2/p) is an integer. This is equivalent to showing that 2p^2 - 2 E 0 mod p. But this is clearly true, since 2p^2 - 2 = 2(p^2 - 1) and p^2 - 1 is divisible by p.

Let's assume that P(k) is true for all k such that 1 <= k <= n. We need to prove that P(n+1) is true as well.

Now we need to prove that P(n+1) is true. In other words, we need to show that P(n+2)/P(n+1) E N, assuming that P(n+1)/P(n) E N and P(n)/P(n-1) E N.

Using the definition of P(n), we have:P(n+1)/P(n) E N and P(n)/P(n-1) E N imply that P(n+1) = aP(n) and P(n) = bP(n-1) for some integers a and b. Then:P(n+2)/P(n+1) = (P(n+2)/P(n+1)) * (P(n)/P(n)) = (P(n+2)P(n))/(P(n+1)P(n)) = (aP(n+1)P(n))/(bP(n)P(n+1)) = a/bIf we can show that a/b E N, then P(n+2)/P(n+1) E N, and P(n+1) satisfies the inductive hypothesis.

But this follows from the fact that a and b are integers and the product of two integers is always an integer.

Hence, P(n+1) is true for all n >= 1, by strong induction.Therefore, by strong induction, we have proved that if p + 1/p E N, then Pn+1/Pn EN for all nEN.

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There are 40 batteries in 10 packs.
Gavin wants to know how many batteries are in 1 pack.
Kylie wants to know how many batteries are in 5 packs.
Drag an expression to answer each question.

Help me Please I would appreciate your help!

Answers

:-):-):-):-):-)

Step-by-step explanation:

1) 40÷10

2) 40÷2

plz help fast!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

D) 156/100 = n/70

Step-by-step explanation:

n = 156% of 70

% indicates a fraction over 100.

"of" indicates multiplication.

n = 156/100 • 70

Let's divide both sides by 70 to have one fraction one each side.

n/70 = 156/100

This is equal to D) [tex](\frac{156}{100}) = (\frac{n}{70})[/tex]

I NEEED HELP match the equation with the term it belongs to. 3.14 *r *r. 2* 3.14 *r

Answers

Answer:

3.14 * r * r = area of circle, 2 * 3.14 * r = circumference

Step-by-step explanation:

Remember these formulas, very important.

Solve each inequality.
2s+5> 49
_

Answers

Answer: S > 22

Step-by-step explanation:

Answer:

s = 23 and above

Step-by-step explanation:

2s + 5 > 49

      -5     -5

2s > 44

44/2

= 22

However, the answer for s is not 22

Since it has this sign > not ≥ then that means s = 23 and above

Check:

2(23) + 5 > 49

46 + 5 > 49

51 > 49

Let be an equivalence relation on a set S, and let a, b e S. Show that two equivalence classes under ~ are either equal or disjoint, i.e. either [a] = [b] or [a] n [b] = 0.

Answers

Given, an equivalence relation ~ on a set S. Let a and b be two elements in the set S. Assuming that [a] and [b] are two equivalence classes under the equivalence relation ~. Now we need to prove that either [a] = [b] or [a] ∩ [b] = ∅ (disjoint).

Proof:If [a] and [b] are not equal, then there must be some element c in the intersection of the equivalence classes [a] and [b]. i.e, c belongs to [a] and c belongs to [b].Thus, [a] ∩ [b] is not empty.

Let x be an element in [a], then x~a, and a~c (since c belongs to [a]) and hence x~c. So, x belongs to [c] which implies that [a] is a subset of [c].Now, let y be an element in [b], then y~b, and b~c (since c belongs to [b]) and hence y~c. So, y belongs to [c] which implies that [b] is a subset of [c].Thus, both [a] and [b] are subsets of [c].

Therefore, if [a] and [b] are not equal, then [a] and [b] are both subsets of [c] and hence the intersection of [a] and [b] is not empty. Thus, [a] and [b] are not disjoint. Hence, the proof by contradiction.

Conversely, if [a] and [b] are disjoint, then [a] ∩ [b] = ∅. And thus, [a] is not equal to [b].Therefore, two equivalence classes under the equivalence relation ~ are either equal or disjoint.

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Find the probability using the normal distribution: P(0 P(0

Answers

The probabilities are:

P(0 < z < 1.96) = 0.4750

P(-1.23 < z < 0) = 0.3907

P(z > 0.82) = 0.2061

P(z < -1.77) = 0.0384

P(-0.20 < z < 1.56) = 0.5199

P(1.12 < z < 1.43) =0.0550

P(z > -1.43) = 0.9236

To locate the chances of the usage of the same old ordinary distribution, we will use a well-known normal desk or a calculator. Here are the calculations for the given possibilities:

P(0 < z < 1.96):

Using the standard everyday desk, the place to the left of one.Ninety-six is 0.9750, and the vicinity to the left of zero is 0.5000. Therefore, the chance between zero and 1.96 is:

P(0 < z < 1.96) = 0.9750 - 0.5000 = 0.4750

P(-1.23 < z < 0):

Using the usual ordinary table, the vicinity to the left of -1.23 is 0.1093, and the area to the left of zero is zero.5000. Therefore, the possibility between -1.23 and 0 is:

P(-1.23 < z < 0) = 0.5000 - 0.1093 = 0.3907

P(z > 0.82):

Using the standard everyday table, the region to the left of zero.82 is zero.7939. Therefore, the possibility of z being extra than 0.82 is:

P(z > 0.82) = 1 - 0.7939 = 0.2061

P(z < -1.77):

Using the same old regular desk, the vicinity to the left of -1.Seventy-seven is zero.0384. Therefore, the chance of z being much less than -1.77 is:

P(z < -1.77) = 0.0384

P(-zero.20 < z < 1.56):

Using the standard ordinary desk, the area to the left of -0.20 is 0.4207, and the area to the left of 1.56 is 0.9406. Therefore, the opportunity between -0.20 and 1. Fifty-six is:

P(-0.20 < z < 1.56) = 0.9406 - 0.4207 = 0.5199

P(1.12 < z < 1.43):

Using the standard regular desk, the place to the left of 1.12 is 0.8686, and the location to the left of one. Forty-three is zero.9236. Therefore, the opportunity between 1.12 and 1. Forty-three is:

P(1.12 < z < 1.43) = 0.9236 - 0.8686 = 0.0550

P(z > -1.43):

Using the same old normal desk, the location to the left of -1.43 is zero.0764. Therefore, the possibility of z being greater than -1. Forty-three is:

P(z > -1.43) = 1 - 0.0764 = 0.9236

Please word that the chances are rounded to 4 decimal locations for clarity.

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The correct question is:

"Find the probability using the standard normal distribution. P(0 < z <1.96), P(-1.23 < z < 0), P(z > 0.82), P(z < -1.77), P(-0.20 < z < 1.56), P(1.12 < z < 1.43), P(z > -1.43)"

You invest $32,000 in an account that earns 5.75% interest compounded yearly. What is
the total amount of money you will have in the account after 20 years if you never
deposit any additional funds?

Answers

Answer:

$97,894.33.

Step-by-step explanation

Make r the subject of x=e+r/d

Answers

Answer:

r = dx - de

Step-by-step explanation:

x = e + r/d

x - e = r/d

d (x - e) = r

dx- de = r

r = dx - de

The blood results for a particular sample unknown test from ten finalists of a medical study were recorded for further analysis. Find the following quantities below.
Blood test results: {580, 610, 530, 530, 440, 670, 480, 540, 590, 490 }
(Use only 2 decimal places. Ex. if answer is 34.568, just write 34.56. If the answer is 321 just leave as 321, do not add any decimals)
a) Mean _______
(b) Median______
(c) Mode________
(d) Range________
(e) Variance ________
(f) Standard deviation_______
(g) IQR ______
(h) Upper fence ________

Answers

Answer:

(a) Mean = 541.00

(b) Median = 535.00

(c) Mode: 530

(d) Range = 230

(e) Variance = 5340.40

(f) Standard deviation = 73.10

(g) IQR = 100

(h) Upper fence = 740.00

Step-by-step explanation:

Please help me, GodBless.

Answers

Answer:

Rate of change is 1

Step-by-step explanation:

Well rate of change in a function is basically slope

theres 1 rise and.1 run

1/1=1

So rate of change is 1

If a researcher wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he makes on a simple test. The following data is recorded.
n = 4, Σx = 20, Σy = 25, Σxy = 144 & Σx² = 120.

Find the equation of the regression line:
y = a + bx. y = (a = ____) + (b = _____)x.

b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²] = ____

a = [(Σy)(Σx²) - (Σx)(Σxy)] / [n(Σx²) - (Σx)²] = _____

Answers

The equation of the regression line is: y = 1.5 + 0.95x

How to find the equation of the regression line

To find the equation of the regression line, we can use the formulas:

b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²]

a = [(Σy)(Σx²) - (Σx)(Σxy)] / [n(Σx²) - (Σx)²]

Given the following data:

n = 4

Σx = 20

Σy = 25

Σxy = 144

Σx² = 120

Let's calculate the values step by step:

b = [4(144) - (20)(25)] / [4(120) - (20)²]

  = (576 - 500) / (480 - 400)

  = 76 / 80

  = 0.95

a = [(25)(120) - (20)(144)] / [4(120) - (20)²]

  = (3000 - 2880) / (480 - 400)

  = 120 / 80

  = 1.5

Therefore, the equation of the regression line is:

y = 1.5 + 0.95x

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Simplify.
+6 - 4 =


please help ..........

Answers

Answer:

2

Step-by-step explanation:

it's literally 6-4 = 2

Answer: 2

Step-by-step explanation: +6 is simply 6 and 6-4 is 2.

what is the volume of a right triangular prism whose height is 20 units and whose base is a right triangle with side lengths of 3,4, and 5?

Answers

Area of base= 1/2(3x4) = 6
Multiply that with the height:
6x20=120

Answer: 120

Last year, a marketing research company estimated Amazon Prime members spent $1,825 on Amazon.com. The company believes that due to the pandemic. Amazon Prime members have spent more on average at Amazon.com compared to last year. They take a sample of 150 Amazon Prime members to test their belief. These sample members spent an average of $1,950. Assume the population standard deviation is $600.

Specify the hypotheses.

Answers

Null hypothesis (H0): µ ≤ 1825, the alternative hypothesis is µ > 1825.

The hypotheses are given below:

Null hypothesis (H0): µ ≤ 1825

Alternative hypothesis (Ha): µ > 1825 where µ represents the population mean amount spent by Amazon Prime members on Amazon.com.

As given in the question, the company believes that due to the pandemic, Amazon Prime members have spent more on average at Amazon.com compared to last year.

Therefore, the alternative hypothesis is µ > 1825.

The null hypothesis is that there is no significant difference or increases in the mean amount spent on Amazon.com by Amazon Prime members last year and this year or that the mean amount spent this year is less than or equal to that of last year, which is µ ≤ 1825.

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A standard test of intelligence is scaled so that the mean IQ is 100, and the standard deviation is 15. If there are 40,00 people in a certain town , what is the percentage of people who have an IQ between 70 and 130 ?
a. 47.5%
b. 95%
c. 68 %
d. 99.7

Answers

The correct option to the sentence "The percentage of people who have an IQ between 70 and 130 ?" is:

b. 95%.

To solve for the percentage of people who have an IQ between 70 and 130, we will have to use the standard deviation and the mean IQ.

It is given that: Mean = 100, Standard deviation = 15

Now we will use these values to find the percentage of people who have an IQ between 70 and 130.

The first step to this process is to standardize the IQ scores by converting them to Z-scores.

The formula for Z-score is:

Z = (X - µ) / σ, where X represents the IQ score, µ represents the mean IQ, and σ represents the standard deviation.

IQ score of 70:

Z = (70 - 100) / 15

Z = -2

IQ score of 130:

Z = (130 - 100) / 15

Z = 2

Now that we have the Z-scores for IQ scores of 70 and 130, we can find the percentage of people who have an IQ between these two scores. We will use the Z-table to do this. The Z-table provides the area under the standard normal distribution curve for a given Z-score.

From the Z-table, we can find that the area under the curve between Z = -2 and Z = 2 is approximately 0.9545. This means that approximately 95.45% of people have an IQ between 70 and 130.

Therefore, the correct option is: b. 95%.

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What’s the website in this image called?

Answers

The website is called iRazoo
:D

A 5 meter ladder is leaning against a house when its base starts to slide away. By the time the base is 3 meter from the house, the base is moving at the rate of 2 m/sec. (a) How fast is the top of the ladder sliding down the wall then? (b) At what rate is the angle between the ladder and the ground changing then?

Answers

(a) The top of the ladder is sliding down the wall at a rate of 3/2 m/sec.

(b) The angle between the ladder and the ground is changing at a rate of 1/2 rad/sec.

To solve this problem, we can use related rates, considering the ladder as a right triangle formed by the ladder itself, the wall, and the ground.

Let's denote:

x: the distance from the base of the ladder to the house (in meters)

y: the height of the ladder on the wall (in meters)

θ: the angle between the ladder and the ground (in radians)

Given:

dx/dt = -2 m/sec (the rate at which the base of the ladder is moving away from the house)

Using the Pythagorean theorem, we have:

x^2 + y^2 = 5^2 (since the ladder has a length of 5 meters)

Taking the derivative of both sides with respect to time (t), we get:

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

(a) To find dy/dt:

We can solve the equation above for dy/dt:

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

2(3)(-2) + 2y(dy/dt) = 0 (substituting x = 3 and dx/dt = -2)

-12 + 2y(dy/dt) = 0

2y(dy/dt) = 12

dy/dt = 12/(2y)

dy/dt = 6/y

Now, we need to find y. Using the Pythagorean theorem again:

x^2 + y^2 = 5^2

3^2 + y^2 = 5^2

9 + y^2 = 25

y^2 = 25 - 9

y^2 = 16

y = 4 (taking the positive value as y represents a length)

Substituting y = 4 into dy/dt = 6/y:

dy/dt = 6/4

dy/dt = 3/2 m/sec

Therefore, the top of the ladder is sliding down the wall at a rate of 3/2 m/sec.

(b) To find dθ/dt:

We can use trigonometry to relate θ, x, and y:

tan(θ) = y/x

Differentiating both sides with respect to time (t), we get:

sec^2(θ)dθ/dt = (x(dy/dt) - y(dx/dt))/x^2

Substituting the given values:

sec^2(θ)dθ/dt = (3(3/2) - 4(-2))/3^2

sec^2(θ)dθ/dt = (9/2 + 8)/9

sec^2(θ)dθ/dt = (25/2)/9

sec^2(θ)dθ/dt = 25/18

Since sec^2(θ) is equal to 1 + tan^2(θ) and tan(θ) = y/x:

sec^2(θ) = 1 + (y/x)^2

sec^2(θ) = 1 + (4/3)^2

sec^2(θ) = 1 + 16/9

sec^2(θ) = (9 + 16)/9

sec^2(θ) = 25/9

Substituting sec^2(θ) = 25/9 into the equation:

(25/9)dθ/dt = 25/18

Simplifying and solving for dθ/dt:

dθ/dt = (25/18) * (9/25)

dθ/dt = 1/2 rad/sec

Therefore, (b) the angle between the ladder and the ground is changing at a rate of 1/2 rad/sec.

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a man sold an article at a gain of 5 percent if it had sold for rs 16.30 less he would have suffered a loss of 5 percent find the cost price?​

Answers

Answer:

Step-by-step explanation:

let CP of the article = x

at 5% gain, SP of article = x + (5/100)x = 1.05x

at 5% loss, SP of article = x - (5/100)x = 0.95x

given that 1.05x - 0.95x = 16.5

⇒ 0.1x = 16.5

⇒ x = 16.5/0.1

⇒ x = Rs. 165.

The cost price of the article is Rs. 165.

Find the measurements of DBC

Answers

Answer:

72 degrees

Step-by-step explanation:

To determine the value of DBC, we first have to determine the value of q

Angle on a straight line = 180 degrees

7q - 46 + 3q + 6 = 180

10q - 40 = 180

collect like terms

10q = 180 + 40

10q = 220

q = 22

Substitute for q in angle dbc

3(22) + 6 = 72 degrees

please answer this i will mark brainliest

Answers

Answer:

The median is 2

Step-by-step explanation:

Arrange your numbers in numerical order.

0011112233445

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

PLEASE MARK ME BRAINLIEST

HELP PWEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

rap music

Step-by-step explanation:

^

Answer:

i’m not sure if these are right or not but

Step-by-step explanation:

the first one is no

i think the second one is no

i think the third one is yes

i think the fourth one is yes

i am not sure and i’m REALLY sorry if its wrong

Compute r''(t) and r'''(t) for the following function. r(t) = (9t² +6,t + 5,6) Find r'(t). r(t) = 0.00

Answers

The derivatives of the vector function are r'(t) = (18 · t, 1, 0), r''(t) = (18, 0, 0) and r'''(t) = (0, 0, 0).

How to determine the first three derivatives in a vector function

In this question we find the definition of a vector function in terms of time, whose first, second and third derivatives must be found. This can be done by using derivative rules several times. First, define the vector function:

r(t) = (9 · t² + 6, t + 5, 6)

Second, find the first derivative:

r'(t) = (18 · t, 1, 0)

Third, find the second derivative:

r''(t) = (18, 0, 0)

Fourth, find the third derivative:

r'''(t) = (0, 0, 0)

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What’s the opposite of -5/8

Answers

The opposite of -5/8 is 5/8.
It’s 5/8, |-5/8| = 5/8

Let p(x)=x+3x²-4x-12 a) Find the x-intercepts of the graph of p(x) c) Sketch a graph of p(x) b) Find the y-intercept of the graph of p(x)

Answers

a) The x-intercepts of p(x) are x = 3 and x = -4/3.  b) The y-intercept of p(x) is y = -12.

a) To find the x-intercepts, we set p(x) = 0 and solve for x:

x + 3x² - 4x - 12 = 0

Simplifying the equation, we get:

3x² - 3x - 12 = 0

Factoring, we have:

(x - 3)(3x + 4) = 0

Setting each factor equal to zero, we find the x-intercepts:

x = 3 and x = -4/3

b) The y-intercept is the value of p(0), so we substitute x = 0 into the equation:

p(0) = 0 + 3(0)² - 4(0) - 12 = -12

Therefore, the y-intercept is -12.

c) To sketch the graph, we plot the x-intercepts (x = 3 and x = -4/3) and the y-intercept (y = -12) on a coordinate plane.

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What is the smallest solution to the equation 3x2 - 16 = 131?

Answers

Answer:

7,-7 are the solutions

Step-by-step explanation:

Not a perfect square so its

+-7

I would go with -7 since its the lowest amount

Answer:

-7

Step-by-step explanation:

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