Help pleaseeeee confused

(Hope that helps (= The given says the height distribution is normally distributed with the mean height equal to 68 inches. In this case, the bell-shaped curve has a vertical symmetry at 68 inches. This means, half of the mean exceeds 68 inches while the other half has height below 68 inches.

The height range out of which only 5% of the young American men (from age 18 to 24) lie is  [63.35, 72.65] (in inches)

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

\(X \sim N(\mu, \sigma)\)

(X is following normal distribution with mean \(\mu\) and standard deviation \(\sigma\) )

then it can be converted to standard normal distribution as

\(Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)\)

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

\(P(Z \leq z) = P(Z < z) )\)

Also, know that if we look for Z = z in z tables, the p value we get is

\(P(Z \leq z) = \rm p \: value\)

For this case, let we take:

Then, according to the given data, we have:
\(X \sim N(\mu = 68, \sigma = 2.5)\)

where \(\mu\) is mean value of X and \(\sigma\) is standard deviation of X (both in inches).

Also, we can write:

\(P(X < a) + P(X > b) = 5\% = 0.05\)

Since normal distribution is symmetric about its mean, we can take a and b equidistant from the mean, so as to get a symmetric range which makes much more sense than taking an asymmetric range which doesn't comply with the nature of values of X.

Thus, we have:

\(\mu - a = b - \mu\\b = 2\mu - a\)

From this result and \(P(X < a) + P(X > b) = 5\% = 0.05\), we get:
\(P(X < a) + P(X > 2\mu -a) = 0.05\)

Converting X to Z(the standard normal distribution), we get;
\(Z = \dfrac{X - \mu}{\sigma}\)

\(P(X < a) + P(X > 2\mu -a) = 0.05\\\\P(Z < z = \dfrac{x-\mu}{\sigma} = \dfrac{a-68}{2.5}) + P(Z > \dfrac{2(68) - a - 68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > \dfrac{68-a}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > -\dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z \leq \dfrac{a-68}{2.5}) = 0.05 \: \: \: \: (\because P(Z > -k) = P(Z \leq k))\\\\2P(Z < \dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) = 0.025\)

Using the z-tables, we get the value of Z for which p-value is 0.025 as

-1.96

Thus, we get:
\(\dfrac{a-68}{2.5} = -1.96\\\\a = 68 + (-1.96 \times 2.5)\\a = 63.35\)

Thus, we get: \(b = 2\mu - a = 2(68) - 63.35 = 72.65\)

Thus, the range is [a,b] = [63.35, 72.65]

Thus, the height range out of which only 5% of the young American men (from age 18 to 24) lie is  [63.35, 72.65] (in inches)

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Subtracting a multiple of an equation in a system from another equation in the same system does not affect the solution set of the system, since the equations still produce the same result.

This is because when a multiple of an equation is subtracted from another equation, the result is a new equation that is equivalent to the original equation. To prove this, let's look at an example:

Suppose we have a system:

2x + 3y = 6

-4x + y = -1

Now, let's subtract 4 times the first equation from the second equation:

2x + 3y = 6

-4x + y = -1

-8x - 12y = -24

This yields the same system as before, except that the second equation is now:

-4x - 12y = -25

We can see that the two systems have the same solutions, since both equations in the system are equivalent.

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Each flower is either red or yellow. Each flower is either a tulip or a rose. For these flowers number of tulips:number of roses 6 : 5.

1. Length of the wire = perimeter of the square = 112 cm

2. Area of the whole shape = 4[1/2(area of circle)] + area of the square = 2,014.88 cm².

Area of a circle = πr²

1. The length of the wire = perimeter of the square = 4(28)

Perimeter of the square = 112 cm

2. Area of the whole shape = 4[1/2(area of circle)] + area of the square

= 4[1/2(πr²)] + s²

Given the following:

Plug in the values into the equation:

Area of the whole shape = 4[1/2(area of circle)] + area of the square

= 4[1/2(3.14 × 14²)] + 28²

= 2,014.88 cm².

Therefore, the area of the whole shape = 4[1/2(area of circle)] + area of the square = 2,014.88 cm².

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The new standard deviation of the distribution of X + 4 is also 14, for the given mean of 47 and standard deviation of 14.

Given:

Mean = 47

Standard deviation = 14

Adding 4 to each score, we get the new set of scores.

Let X be a random variable which represents the scores.

So the new set of scores will be X + 4.

Now,

Mean of X + 4 = Mean of X + Mean of 4

Therefore,

Mean of X + 4

= 47 + 4

= 51

So, the new mean of the distribution of X + 4 is 51.

Now, we will find the new standard deviation.

Standard deviation of X + 4 = Standard deviation of X

Since we have only added a constant 4 to each score, the shape of the distribution remains the same.

Hence the standard deviation will remain the same.

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A car engine has an efficiency of about 30% is a true statement.

the  factual  effectiveness of a auto machine can vary grounded on  colorful factors  similar as machine size, type, and design, as well as driving conditions and  conservation.   The  effectiveness of an machine is a measure of how  important of the energy produced by the energy is converted into useful work,  similar as turning the  bus of a auto.

In an ideal situation, an machine would convert all the energy from the energy into useful work. still, due to  colorful factors  similar as  disunion and heat loss, this isn't possible.   The  effectiveness of a auto machine is  generally calculated by dividing the  quantum of energy produced by the energy by the  quantum of energy used by the machine. This is known as the boscage  thermal  effectiveness( BTE) of the machine.

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Answer:

5

Step-by-step explanation:

multiplying each number with 5 will get you the next number

Answer:

Step-by-step explanation:

The answer is 5 multiplying each answer by 5 will give you the correct answer

Answer:

ooo me

Step-by-step explanation:

pls

Answer:

24=4 ten

27=7 ten

Step-by-step explanation:

Answer:

(6,-3)

Step-by-step explanation:

;-;

Answer:

The player is running about 4 yards a second

Step-by-step explanation:

Answer:

2.5m a second

Step-by-step explanation:

Answer:

r = - 4

Step-by-step explanation:

The common ratio r of the geometric sequence is

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{8}{-2}\) = - 4

Answer:

5

Step-by-step explanation:

Answer: Which questions?

Answer:

The two questions are not available for the question.

Step-by-step explanation:

Answer:

The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30. Otherwise, the mean and the standard deviations holds, but the distribution will not be approximately normal.

Standard deviation 4 minutes.

This means that \(\sigma = 4\)

A sample of 25 wait times is randomly selected.

This means that \(n = 25\)

What is the standard deviation of the sampling distribution of the sample wait times?

\(s = \frac{4}{\sqrt{25}} = 0.8\)

The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.

The volume of the smaller cone is approximately equal to 9.78 cm³ (rounded to the nearest tenth).

Given data: A bigger cone with a volume of 66 cm³ and a radius of 3A smaller cone with a radius of 2 To find: What is the volume of the smaller cone? Formula used: The volume of the cone is given by V = 1/3πr²hWhere, r is the radius of the cone h is the height of the cone Calculation: Let's consider the bigger cone first.

Now, the radius of the bigger cone is given as 3 cm.

Thus, the volume of the bigger cone is given by, V = 1/3πr²h ⇒ 66 = 1/3π(3)²h ⇒ h = 22/π cm.

Therefore, the height of the bigger cone is 22/π cm.

The radius of the smaller cone is given as 2 cm. The height of the smaller cone can be calculated using the ratio of the radii of the bigger and smaller cones, which is given by, Ratio of radii = radius of bigger cone / radius of smaller cone ⇒ 3/2 The height of the smaller cone will be h/3 because the smaller cone is similar to the bigger cone.

Therefore, the height of the smaller cone will be, h' = h/3 = (22/π)/3 = (22/3π) cm. Now, we can use the volume of the smaller cone formula to find its volume. V' = 1/3πr'²h'Where, r' is the radius of the smaller cone. Putting the values, we get, V' = 1/3π(2)²(22/3π) cm³V' = 88/9π cm³V' = 9.78 cm³ (rounded to the nearest tenth)

Therefore, the volume of the smaller cone is approximately equal to 9.78 cm³ (rounded to the nearest tenth).

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Answer:

2 ( x − 32 )

Step-by-step explanation:

use an algebra calculator

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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Answer: 96 calories

Step-by-step explanation:

There are 72 calories in a 3/4 cup, you can think of 3/4 as three 1/4 cups, and divide 72 by 3, and you get 24. 1/4 cup has 24 calories. Then you do 24 times 4, 96 calories per cup.

Answer:

$12

Step-by-step explanation:

36÷3=12

Each ticket costs $12

Answer:

$12 per ticket

Step-by-step explanation:

$36 / 3 = 12

$12 per ticket

Therefore, each ticket costs 12 dollars.

Can I please have brainliest, thanks:)

Answer:

No

Step-by-step explanation:

It is not being multiplyed evenly on both sides with each other

Answer:

$2.34

Step-by-step explanation:

30x0.078=2.34

The marginal utility functions for the given utility function are \(U_{1} = 1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\) and \(U_{2} = Abq_{1} ^{a} q_{2}^{(b-1)}+ 1\). The MRS is equal to the ratio of the marginal utilities, or MRS = U₁/U₂ = \(1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\)/ \((Abq_{1}^aq_{2}^{(b-1)} + 1)\).

a) The marginal utility functions can be obtained by taking the partial derivatives of the utility function with respect to each good. For the given utility function U(q₁, q₂) = \(q_{1} + Aq_{1}^{(a)}q_{2}^{(b)} + q_{2}\) the marginal utility of good 1 (U₁) is equal to\(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)}\), and the marginal utility of good 2 (U₂) is equal to \(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1\).

b) The marginal rate of substitution (MRS) represents the rate at which a consumer is willing to exchange one good for another while maintaining the same level of utility. It is defined as the ratio of the marginal utilities of the two goods. In this case, the MRS can be calculated as MRS = U₁/U₂, which gives \(\frac{(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)})}{(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1)}\).

The explanation above summarizes the process of obtaining the marginal utility functions and the MRS for the given utility function. The utility function is differentiated with respect to each good to find the marginal utilities. The MRS is then calculated as the ratio of the marginal utilities. The specific expressions for the marginal utilities and the MRS are provided based on the given utility function.

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Answer:

y-intercept is (0,5)

Step-by-step explanation:

When a graph passes through (0,a), that's y-intercept. y-intercept is a point on y-plane that a graph passes through.

For Ex. If a graph passes through (0,4) then the y-intercept would be (0,4).

But remember that it must be (0,a) for it to be y-intercept (Because it has to intersect the y-plane)

Answer:

AB ≈ 7.21

Step-by-step explanation:

Calculate AB using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = A (2, 5 ) and (x₂, y₂ ) = B (- 2, - 1 )

AB = \(\sqrt{(-2-2)^2+(-1-5)^2}\)

     = \(\sqrt{(-4)^2+(-6)^2}\)

     = \(\sqrt{16+36}\)

     = \(\sqrt{52}\)

     ≈ 7.21 ( to the nearest hundredth )

Answer:

Step-by-step explanation:

a)The percentage of the students who have done their homework and attended lectures and will obtain a grade of A on this multiple-choice examination is 99.99%.

b)The percentage of students who have done their homework and attended lectures and will obtain a grade of C on this multiple-choice examination is 0.54%.

c) The probability that this student will answer 28 or more questions correctly and pass the examination is 0.0000006 or 6 × 10⁻⁷ (rounded to 2 decimal places).

(a) The number of questions to be answered correctly to obtain grade A is 44. Each question has four possible answers. Therefore, if a student who has done the homework and attended lectures has a 65% chance of answering any question correctly, the probability of getting the question wrong is 1 - 0.65 = 0.35.

The number of successes, x = 44. Hence, the number of failures, n - x = 6.

The mean, µ, is given by:

µ = np = 50 × 0.65 = 32.5

The standard deviation, σ, is given by:

σ = √(npq) = √(50 × 0.65 × 0.35) = 3.02

Using the standard normal distribution table, the z-score for obtaining a grade of A is given by:

z = (44 - 32.5)/3.02 = 3.80P(Z ≤ 3.80) = 0.9999

The percentage of the students who have done their homework and attended lectures and will obtain a grade of A on this multiple-choice examination is 99.99%.

Therefore, the answer is 99.99%.

(b) The number of questions to be answered correctly to obtain grade C is between 34 and 39. We can calculate the probability of obtaining each grade and then take the difference to get the probability of obtaining grade C.

The probability of obtaining 39 questions correctly or less is:

P(X ≤ 39) = ΣP(X = x) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 39) = 0.0054

The probability of obtaining 34 questions correctly or less is:

P(X ≤ 34) = ΣP(X = x) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 34) = 0.1055

Therefore, the probability of obtaining a grade between 34 and 39 questions is:

P(34 ≤ X ≤ 39) = P(X ≤ 39) - P(X ≤ 33) = 0.0054 - 0.00002 = 0.0054

The percentage of students who have done their homework and attended lectures and will obtain a grade of C on this multiple-choice examination is 0.54%.

Therefore, the answer is 0.54%.

(c) The number of questions to be answered correctly to pass the examination is 28.

Using the same formulae as in parts (a) and (b), we can obtain the mean, µ, and standard deviation, σ, as follows:

µ = np = 50 × 0.65 = 32.5σ = √(npq) = √(50 × 0.65 × 0.35) = 3.02

Using the standard normal distribution table, the z-score for passing the examination is given by:

z = (28 - 32.5)/3.02 = -1.49P(Z ≤ -1.49) = 0.067

The percentage of students who have done their homework and attended lectures and will pass the examination is 6.7%.

Therefore, the answer is 6.7%.

(d) If a student who has not attended class and has not done the homework for the course, guesses at the answer to each question, the probability of getting the question correct is 0.25. The number of questions to be answered correctly to pass the examination is 28. Hence, the number of successes, x = 28.

The probability of obtaining 27 questions or less is:

P(X ≤ 27) = ΣP(X = x) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 27) = 0.0034

The probability of obtaining 28 questions or more is:

P(X ≥ 28) = 1 - P(X ≤ 27) = 1 - 0.0034 = 0.9966

Using the standard normal distribution table, the z-score for obtaining 28 questions or more is given by:

z = (28 - 12.5)/2.69

= 5.75P(Z ≥ 5.75)

= 1 - P(Z ≤ 5.75)

= 1 - 0.9999994

= 0.0000006

Therefore, the probability that this student will answer 28 or more questions correctly and pass the examination is 0.0000006 or 6 × 10⁻⁷ (rounded to 2 decimal places).

Hence, the answer is 6 × 10⁻⁷.

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Answer: 0

Step-by-step explanation:

Answer:

a) Because the confidence interval  does not include  0​ it appears that there

is  a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

b)There is​ 95% confidence that the interval from  −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2

c)   1.62 < μ1−μ2< 1.76

Step-by-step explanation:

a) What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men?

Given:

95% confidence interval for the difference between the two population​ means:

−1.76g/dL< μ1−μ2 < −1.62g/dL

population 1 =  measures from women

population 2 =  measures from men

Solution:

a)

The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in​ men is not equal and that the  women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in​ men.

b)  

There is​ 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.

c)

If we interchange men and women then

                                          1.62 g/dL<μ1−μ2<1.76 g/dL.

There is a significant difference between the mean level of hemoglobin in women and in men.

The confidence interval of the mean is given as:

\(-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL\)

The above confidence interval shows that the confidence interval is exclusive of 0.

This means that 0 is not part of the confidence interval

Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.

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