The average class size this semester in the business school of a particular university is 39.1 students with a standard deviation of 13.6 students. The z-score for a class with 16 students is _____.

The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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By solving a system of equations and a quadratic equation, we will see that x = 2.

We know that x and y are positive integers, that x < y and:

x*y = 56

We also know that "seven times the reciprocal of the smaller integer plus 14 times the reciprocal of the larger integer equals 4"

Then we can write the equation:

7*(1/x) + 14*(1/y) = 4

So we have a system of equations:

x*y = 56

7*(1/x) + 14*(1/y) = 4

We can rewrite the first equation to get:

x = 56/y

And the second equation as:

14/y = 4 - 7/x

Then the system becomes:

56/y = x

14/y = (4 - 7/x)

Taking the quotient between these, we can remove the variable y:

(56/y)/(14/y) = x/(4 - 7/x)

56/14 = x/(4 - 7/x)

4*(4 - 7/x) = x

4*(4x - 7)/x = x

4*(4x - 7) = x^2

So now we have a quadratic equation:

x^2 - 16x + 28 = 0

Using the quadratic formula, we will get:

\(x = \frac{16 \pm \sqrt{(-16)^2 -4*1*28} }{2*1} \\\\x = \frac{16 \pm 12 }{2}\)

So the solutions are:

x = (16 - 12)/2 = 2

x = (16 + 12)/2 = 14

But notice that if x = 14, then:

14 = 56/y

y = 56/14

y = 4

And y is larger than x, then x = 14 can be discarded.

The solution is x = 2.

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The fact that z requires that you know the population standard deviation sigma is one reason why a t distribution rather than the normal curve is used to identify critical values when determining a level C confidence interval for a population mean.

C is the right response. The fact that z requires that you know the population standard deviation sigma is one reason why a t distribution rather than the normal curve is used to identify critical values when determining a level C confidence interval for a population mean.

Depending on whether we know the population standard deviation or not, we either use a z distribution or a t distribution when computing a confidence interval for a population mean. We use a z distribution when we know the group standard deviation. We employ a t distribution when it is unclear what the population standard deviation is.

The population standard deviation is not known, so we use the sample standard deviation to determine it.

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\(20p+75=35p+30\)

Step 1: Subtract \(20p\) from both \(p\) sides

\(\:\:\:\:20p+75=35p+30\\-20\:\:\:\:\:\:\:\:\:\:\:\:-20\)

20 - 20 = 0, so it is canceled out. 35 - 20 = 15, don't forget the \(p\)!

\(75=15p+30\)

Step 2: Subtract 30 from both sides

\(\:\:\:\:75=15p+30\\-30\:\:\:\:\:\:\:\:\:\:\:\:-30\)

30 - 30 = 0, so it is canceled out. 75 - 30 = 45.

\(45=15p\)

Step 3: Divide both sides by 15

\(\frac{45}{15} =\frac{15p}{15}\)

15 ÷ 15  cancels out. 45 ÷ 15 = 3.

\(20p+75=35p+30\quad :\quad \boxed {\bold {p=3}}\)

Answer:

20p+75=35p+30

Step-by-step explanation:

Answer:

The solution is h = -80.

Step-by-step explanation:

Let's eliminate fractions here by multiplying all three terms by 4:

-52 - h = 28

Subtracting 28 from both sides results in -80 = h

The solution is h = -80.

Answer:

3  52/100  or  3.52

Step-by-step explanation:

three = 3

fifty two=52

hundredths=out of /100

fifty two hundredths =52/100=0.52

3.52 or 3 52/100

Answer:

1. x=22  2. x= 28

Step-by-step explanation:

1. The total of angles in a triangle add up to 180˚.

93+65= 158

180-158=22

This means that x = 22

2. Angles on a straight line add up to 180.

180-125=55

180-83=97

55+97=152

180-152=28

This means that x = 28

Hope that this helps you.

Answer:

0

Step-by-step explanation:

(c) 336, After being struck with a hammer, a gong vibrates 48 vibrations in the first second.

In each second thereafter, it makes 6/7 as many vibrations as in the previous second. To find the total number of vibrations the gong makes before it stops vibrating, you can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.

In this case, a = 48 (vibrations in the first second) and r = 6/7 (the fraction of vibrations in each subsequent second).

Sum = 48 / (1 - (6/7))
Sum = 48 / (1/7)
Sum = 48 * 7
Sum = 336

So, the gong makes 336 vibrations before it stops vibrating. The correct answer is (c) 336.

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Answer:

\(12\) books

Step-by-step explanation:

\(62 \div 5 = 12remainder2\). Get rid of the the remainder (\(2\)) because it was specified that the books were split evenly, and then answer is \(12\).

Complete data:

13.5 13.5 13.25 13.0 13.25 13.5 13.0 13.25 13.0 13.25 12.75 12.75 Part A How many dots should go above each data value in the line plot? Type a number in each box

Answer:

12.75 ___ 2 dots

13.0 ____ 3 dots

13.25 ___ 4 dots

13.5 ___ 3 dots

Step-by-step explanation:

Given the data :

13.5 13.5 13.25 13.0 13.25 13.5 13.0 13.25 13.0 13.25 12.75 12.75

To know the Number of dots for each data value, we obtain the frequency of each data value ;

Length of Rose____ Frequency

12.75 _________:__ 2

13.0 ____________ 3

13.25 ___________ 4

13.5 ____________ 3

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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Normal income: 25 $

Last week's income: 25 + 20: 45 $

% = Last week's/normal = 45/25 ×100 =180 %

Answer:

You forgot to add a picture and/or more context.

Step-by-step explanation:

Answer:

j

Step-by-step explanation:

A. the parametric equations for the line are: x = 4 - 4t, y = -5, and B. the point Q where the line intersects the yz-plane is Q(0, -5, 4).

To find the parametric equations for the line through point P(4, -5, -1) that is perpendicular to the plane -4x + 0y + 5z = 1, we need to determine the direction vector of the line.

Let's denote the parametric equations as: x = x₀ + at,

y = y₀ + bt,

z = z₀ + ct, where (x₀, y₀, z₀) is the point P(4, -5, -1) and (a, b, c) is the direction vector (-4, 0, 5).
Plugging in the values: x = 4 + (-4)t,

y = -5 + 0t,

z = -1 + 5t.
Therefore, the parametric equations for the line are: x = 4 - 4t, y = -5,

z = -1 + 5t.
To find the point Q where this line intersects the yz-plane,
we need to set x = 0 in the parametric equations.
Therefore, the point Q where the line intersects the yz-plane is Q(0, -5, 4).

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The following statements can be concluded if ∠ABC and ∠CBD are a linear pair:

B. ∠ABC and ∠CBD are supplementary.

D. ∠ABC and ∠CBD are adjacent angles.

In Mathematics, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.

According to the linear pair theorem, ∠ABC and ∠CBD are supplementary angles because BDC forms a line segment. Therefore, we have the following:

∠ABC + ∠CBD = 180° (supplementary angles)

m∠ABC ≅ m∠CBD (adjacent angles)

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Answer:

Below

Step-by-step explanation:

Rank in order of SHORTEST time to LONGEST time ....

  shorter times mean the runner was faster to the finish line.

Answer:

Step-by-step explanation:

The area of the sector is A = π cm² and amplitude is a = 0.75 cm

Given data ,

The area of a sector is given by the formula:

A = (1/2) x r² x θ

where r is the radius of the sector and θ is the central angle in radians.

On simplifying , we get

A = π cm²

r = 1.5 cm

Substituting these values into the formula, we get:

π = (1/2) x (1.5)² x θ

π = (3/4) x θ

Solving for θ, we get:

θ = (4/3) x π

The amplitude of the sector is half of the radius, so:

amplitude = (1/2) x 1.5 cm = 0.75 cm

Hence , the amplitude of the sector is 0.75 cm

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The expected number of queens that you will draw from a standard deck of cards when drawing three cards without replacement is 0.469, or approximately half a queen.

To calculate the expected number of queens that you will draw from a standard deck of cards when drawing three cards without replacement, we can use the formula for expected value:

E(X) = Σ x * P(X = x)

where X is the random variable representing the number of queens drawn, x is the number of queens drawn (in this case, x can take on values of 0, 1, 2, or 3), and P(X = x) is the probability of drawing x queens.

To calculate the probability of drawing x queens, we can use the hypergeometric distribution, which is appropriate for this scenario.

The hypergeometric distribution describes the probability of drawing x successes (queens in this case) in a sample of n items (cards drawn in this case) without replacement from a population of N items (total cards in the deck in this case).

Using the hypergeometric distribution with N=52, n=3, and the number of successes (queens) as x, we get:

P(X = 0) = (48 choose 3) / (52 choose 3) = 0.5728

P(X = 1) = (4 choose 1) * (48 choose 2) / (52 choose 3) = 0.3855

P(X = 2) = (4 choose 2) * (48 choose 1) / (52 choose 3) = 0.0417

P(X = 3) = (4 choose 3) / (52 choose 3) = 0.0001

Plugging these probabilities into the formula for expected value, we get:

E(X) = 0 * 0.5728 + 1 * 0.3855 + 2 * 0.0417 + 3 * 0.0001

E(X) = 0.469

This means that on average, you would not expect to draw any queens in this scenario, but there is a small chance of drawing one or two queens.

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The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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The expression -3.1^4x * -3.1^2x + 7 has an equivalent of 887.503681x^2 + 7

From the question, the expression is given as

-3.1^4x * -3.1^2x + 7

Evaluate the exponents in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 92.3521x * 9.61x + 7

Evaluate the products in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 887.503681x^2 + 7

Hence, the equivalent expression of -3.1^4x * -3.1^2x + 7 is 887.503681x^2 + 7

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Infinitely many position vectors with length 2 in xyz-space are orthogonal to the nonzero position vector v. (D)

A position vector in xyz-space is a vector that starts at the origin and ends at a point in xyz-space. The length of a position vector is the distance from the origin to the point it ends at.

If we want to find position vectors with length 2 that are orthogonal (perpendicular) to a given nonzero position vector v, we can use the dot product.

Let w be a position vector with length 2 that is orthogonal to v. Then, the dot product of v and w must be zero, since they are orthogonal. That is, v · w = 0. Since the length of w is 2, we can write w as 2u for some unit vector u. Thus, v · w = v · (2u) = 2(v · u) = 0.

This means that v and u are orthogonal as well, since the dot product of two vectors is zero if and only if they are orthogonal.

There are infinitely many unit vectors u that are orthogonal to v, and therefore, there are infinitely many position vectors with length 2 that are orthogonal to v. Therefore, the answer is (d) infinitely many.

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To simplify the expression secθ cosθ - cos²θ, we can use trigonometric identities to rewrite the terms in a more simplified form.

Recall the definitions of trigonometric functions:

secθ = 1/cosθ

Substitute this definition into the expression:

secθ cosθ - cos²θ = (1/cosθ) * cosθ - cos²θ

Simplify the expression:

= 1 - cos²θ

Now, we can apply the Pythagorean identity for cosine, which states that sin²θ + cos²θ = 1. By rearranging this identity, we have cos²θ = 1 - sin²θ.

Substitute cos²θ = 1 - sin²θ into the expression:

1 - cos²θ = 1 - (1 - sin²θ)

= 1 - 1 + sin²θ

= sin²θ

Therefore, the simplified expression for secθ cosθ - cos²θ is sin²θ.

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The probability that the second card is a jack given that the first card was a 2 is 52/51.

To calculate the probability that the second card is a jack given that the first card was a 2, we need to consider the remaining cards in the deck after the first card is drawn.

When the first card is drawn and it is a 2, there are 51 cards remaining in the deck, out of which there are 4 jacks.

The probability of drawing a jack as the second card, given that the first card was a 2, can be calculated using conditional probability:

P(Second card is a jack | First card is a 2) = P(Second card is a jack and First card is a 2) / P(First card is a 2)

Since the first card is already known to be a 2, the probability of the second card being a jack and the first card being a 2 is simply the probability of drawing a jack from the remaining 51 cards, which is 4/51.

The probability of the first card being a 2 is simply the probability of drawing a 2 from the initial deck, which is 4/52.

P(Second card is a jack | First card is a 2) = (4/51) / (4/52)

Simplifying the expression:

P(Second card is a jack | First card is a 2) = (4/51) * (52/4)

P(Second card is a jack | First card is a 2) = 52/51

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Answer:

2 half

Step-by-step explanation:

sjbidbasbndjonajndbljak

Answer:

Cant find the measure but do know the equation

Step-by-step explanation:

acute angle= angle<90 degrees

obtuse angle= angle>90

(x>90[/3])-8

Use this and fill in the numbers.

Answer:

should be 89 since it's directly across

Answer:

Your answer is 82

Step-by-step explanation: