a researcher found that the number of days of school missed per semester by college students was normally distributed with a mean of 4.00 and standard deviation of 1.00. what conclusion can you draw from these data?

Answer:

2.0333

Step-by-step explanation:

log 108

Express 108 in terms of 2 & 3.

108 = 2 * 2 * 3 * 3 * 3 = 2² * 3³

log 108 = log 2² * 3³ = log 2² + log 3³ [Using Product Law]

= 2log 2 + 3log 3 [Using Power Law]

Now put the values of log 2 & log 3:

2log 2 + 3log 3

= 2*0.3010 + 3*0.4771

= 0.6020 + 1.4313

= 2.0333

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Angles are Not Named but it congruent under the case of (SAS)

Answer:

-4 2/3 times (-1 1/2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Complete the following equation using , or = 3.20 ___ 3.02 A.

The following equation 3.20 > 3.02

Answer:

Bus B travels faster.

Step-by-step explanation:

The graph of the question in the attached figure

we know that

the linear equation in slope intercept form is equal to

where

m is the slope

b is the y-intercept

x ---> is the time in hours

y ---> is the distance in miles

In this problem we have

Bus A

The slope of the linear equation represent the speed of the bus

so

The speed of bus A is

Bus B

Find  the slope

take two points from the graph

(0,0) and (3,200)

The formula to calculate the slope between two points is equal to

substitute

Compare the slope Bus A with the slope Bus B

therefore

Bus B travels faster.

Answer:

Stephanie Mary and Nicole

Step-by-step explanation:

Answer:

C. 12x

Each box has 12 envelopes.

The number of total envelopes will be the number of envelopes in a box multiplied by the number of boxes. The number of boxes is unknown, so it is replaced by the variable. This gives us 12x

The function f(x) = x³ - 10x² + 31x - 30, satisfied all the three conditions of rolle's theorem on interval [2,5], that is verified it. The values of c in the interval are \(\frac{ 10 + \sqrt{7}}{3}\) and \(\frac{ 10 + \sqrt{7}}{3}\).

Rolle's theorem are important for the theorem to be true, three main conditions for it are following:

We have a function, f(x) = x³ - 10x² + 31x - 30 --(1) on interval [2,5]. We have to verify the rolle's theorem for f(x). First differentiating f(x) in equation (1),

f'(x) = 3x² - 20x + 31

Now, f'(x) is exist for every value of x in interval [2,5]. Hence, f(x) is differential function. As we know every differential function is continuous function. This implies f(x) is continuous function in

interval [2,5]. Now, value of function f(x) at x = 2 and 5

=> f( 2) = 2³ - 10×2² + 31×2 -30

= 8 - 40 + 62 - 30 = 0

f( 5) = 5³ - 10× 5² + 31× 5 - 30

= 125 - 250 + 155 - 30 = 0

So, f( 2) = f(5) = 0, thus, all three conditions of rolle's theorem are satisfied. So, rolle's theorem is verified for function f(x) = x³ - 10x² - 31x - 30. To determine the value of c , put f'(c) = 0

=> 3c² - 20c + 31 = 0, which is an quadratic equation. Solve it using quadratic formula, \(c = \frac{- (-20) ± \sqrt{20² - 4×3×31}}{2×3}\)

\(=\frac{ 20 ± \sqrt{28}}{6}\)

= \( \frac{ 10 ± \sqrt{7}}{3}\). Hence, required values of c are \( \frac{ 10 ± \sqrt{7}}{3}\).

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The total mass of the box of paperclips in scientific notation is 5.526 × 10¹ miligrams. (Correct choice: D)

In this question we must use, interpret and manipulate numbers in scientific notation to find the total mass of the paperclips in a box. The statement indicates the mass of a paperclip and the number of paperclips in the box, then the total mass of the box of paperclips is equal to the product of mass of the paperclip and the number of paperclips. Then, the total mass in the box is:

m = (9.0 × 10⁻⁴ mg) · (6.14 × 10⁴)

m = (9.0 · 6.14) · (10⁻⁴ · 10⁴)

m = 55.26 · 10⁰

m = 55.26 mg

m = 5.526 × 10¹ mg

The total mass of the box of paperclips in scientific notation is 5.526 × 10¹ miligrams. (Correct choice: D)

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Answer:

x^2-2

Step-by-step explanation:

(x^4+x^2-6)÷(x^2+3)

(x^-2) (x^2+3)

       x^2-2

The speed of the cyclist in still air is 13 mph

Let the speed of the cyclist in still air be x mph

when she rides with the wind her speed = (x + 3) mph

when she rides against the wind her speed = (x - 3) mph.

Mathematically we can represent the problem as:

16 / (x + 3) = 10 / (x - 3)

cross multiplying and simplifying

16 (x - 3) = 10 (x + 3)

16x - 48 = 10x + 30

6x = 78

x = 13

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The area shaded below in circle S can be expressed as (18/125)π - (171/250)π².

To find the area shaded below in circle S, we need to calculate the area of the sector TSU and subtract the area of the triangle TSU.

Given information:

Length of TU = (6/5)π

m∠TSU = 72°

To find the area of the sector TSU, we need to find the central angle of the sector. Since the measure of angle TSU is 72°, the central angle will be twice that:

Central angle = 2 * 72° = 144°

The formula for the area of a sector is A = (θ/360°) * πr², where θ is the central angle and r is the radius of the circle.

Since the length of TU is given as (6/5)π, we can find the radius of the circle using the formula for the circumference of a circle:

C = 2πr

Given that the length of TU is (6/5)π, which represents half the circumference of the circle, we can set up the equation:

(6/5)π = 2πr

Simplifying, we find:

r = (6/5) * 1/2 = 3/5

Now, we can calculate the area of the sector TSU:

A_sector = (144°/360°) * π * (3/5)²

A_sector = (2/5) * π * (9/25)

A_sector = (18/125)π

To find the area of the triangle TSU, we use the formula A_triangle = (1/2) * base * height. Here, the base is TU and the height can be found using the sine of the angle TSU:

sin(72°) = height / TU

Rearranging the formula, we have:

height = sin(72°) * TU

Using a calculator, we find:

height ≈ 0.951 * (6/5)π

height ≈ (57/50)π

Now, we can calculate the area of the triangle:

A_triangle = (1/2) * TU * height

A_triangle = (1/2) * (6/5)π * (57/50)π

A_triangle = (171/250)π²

Finally, we can find the shaded area by subtracting the area of the triangle from the area of the sector:

Shaded area = A_sector - A_triangle

Shaded area = (18/125)π - (171/250)π²

Therefore, the area shaded below in circle S can be expressed as (18/125)π - (171/250)π².

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Answer:

R = 19.17 ohms

Step-by-step explanation:

Given that,

The voltage of a subwoofer, V = 115 V

The current through its coil, I = 6 A

We need to find the resistance of the subwoofer. Let it s R. Using Ohm's law to find it such that,

V = IR

So,

\(R=\dfrac{V}{I}\\\\R=\dfrac{115}{6}\\\\R=19.17\ \Omega\)

So, the resistance of the subwoofer is 19.17 ohms.

Answer:

The probability of getting a white or green gumball is 35.64%.

Step-by-step explanation:

1. calculate the total number of gumballs in the gumball machine

35 + 22 + 30 + 14 = 101 gumballs

2. calculate the number of white and green gumballs combined

22 + 14 = 36 w/g gumballs

3. divide the number of white and green gumballs combined by the total number of gumballs in the gumball machine

36 / 101 = 0.3564

Answer: the probability of getting a white or green gumball is 35.64% (0.3564).

Probability is the chance of occurring an event from the total possible outcomes.

The probability of getting a white or a green gumball is 57/101.

It is the chance of occurring an event from the total possible outcomes.

We have,

Green gumballs = 35

White gumballs = 22

Purple gumballs = 30

Blue gumballs = 14

Total gumballs = 35 + 22 + 30 + 14 = 101

The combination is given by:

= \(^nC_{r}\)

= n! / r! (n-r)!

The probability of choosing a white gumball:

= \(\frac{^{22}C_{1}}{^{101}C_{1} }\)

= 22 / 101

The probability of choosing a green gumball:

= \(\frac{^{35}C_{1}}{^{101}C_{1} }\)

= 35 / 101

The probability of getting a white or a green gumball:

= 22/101 + 35 / 101

= (22 +35) / 101

= 57 / 101

Thus the probability of getting a white or a green gumball is 57/101.

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The exponent of a linear function is 1.

exponent refers to the number of times a number is multiplied by itself.

For example: y = x + 3, Here all of them have exponent of 1.  \(y^1 = x^1 + 3^1\).

This is considered to be a linear function. Linear is a straight line.

Another example: y = x² + 8. Here x has exponent of 2 and rest 1.

But it is not a linear function as does not follow the rule of linear function:

y = mx + b

The exponent of a linear function is ____.

1) x

3) 0.5

4) 2

The stationary distribution (vector) π can be found as (C/A)ci / (co + ao).

The Ehrenfest urn problem can be generalized such that it considers m urns and n particles. The dynamics proceeds by randomly picking a particle of the first type, picking a particle of the second type, and then exchanging the two. This can only happen provided they are in different urns. Random picking is uniform over particles of that type.

There are two types of assets, dollars and stocks, in this model of a simple financial market, where there are m traders who have total assets.

Suppose that the total number of dollars in the market is C and the total number of stocks is A.

For simplicity, assume that ao + co ≤ min{A, C}.

The processes c = {ck}k ∈ N and a = {ak}k ∈ N evolve randomly, and the trader may not buy or sell at all on some time steps.

In spite of that, c is a Markov chain and the stationary distribution (vector) π can be found. The reason c is a Markov chain is that it satisfies the Markov property, which states that the future state of a process depends only on the present state and not on its history.

A Markov chain is therefore defined by its state space, which in this case is {0, 1, ..., A + C}, and its transition probabilities.

The transition probabilities for this model are given as follows:

P(i, i + 1) = min{ci, A − ai} / ACP(i, i − 1) = min{ai, C − ci} / C ( where i is the present state of the system)

For the stationary distribution (vector) π, we can use the balance equations as follows:

π(i) P(i, i + 1) = π(i + 1) P(i + 1, i)     [for i = 0, 1, ..., A + C − 1 ]

This can be used to obtain the balance equations that are needed to find π(0), π(1), ..., π(A + C).

The solution is given by:

π(i) = (C/A)ci / (co + ao) for i = 0, 1, ..., min{A, C}.

Therefore, the stationary distribution (vector) π can be found as (C/A)ci / (co + ao).

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Answer:

$8.50 = 0.17 kg. So, 0.01 kg = $0.50.

$1 = 0.02 kg of fresh herbs.

0.25 kg = $ 12.50.

Step-by-step explanation:

Hope this helps!!

Answer:

D

Step-by-step explanation:

The rest you can elimate because of obvious inferring and reasoning so process of elimination

The construction that uses the compass for only one step in addition to drawing the circle itself is an equilateral triangle inscribed in a circle.

This is referred to a drawing instrument which is usually used in the construction of an arc or circle.

The compass is used in only one step which is drawing the circle in an equilateral triangle hence why it was chosen.

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Answer:

19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

12<=x-7.  add 7 to both sides.

x>=19

Based on the information given, it can be seen that the length or the book will be 20cm.

From the information given, Leena read a book that had a perimeter of 72 cm and one side of the book is 16 cm. Therefore, the length will be calculated thus:

Perimeter = 2(Length + Width)

72 = 2(Length + 16)

72 = 2L + 32

2L = 72 - 32

2L = 40

L = 40/2

L = 20

Therefore, the length is 20cm.

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Answer:

Com o aumento da população no início da Baixa Idade Média, muitas pessoas saíram do campo para viver nas cidades. Quais trabalhos eles passaram desempenhar?

Step-by-step explanation:

Answer:

$33,600

Step-by-step explanation:

2,800 x 12

The temperature at which the given reaction will proceed 4.50 times faster than it did at 357 K is 451.23 K.

We have to determine the temperature (in Kelvin) at which the given reaction will proceed 4.50 times faster than it did at 357 K given that the reaction has an activation energy of 26.09 kJ/mol.The rate constant, k is given by the Arrhenius equation as:k = Ae^(-Ea/RT)where:

k = rate constant

A = pre-exponential factor or frequency factor

e = base of natural logarithm

Ea = activation energy

R = gas constant

T = temperature in Kelvin Rearrange the equation to get the ratio of rate constants:

k1/k2 = (Ae^(-Ea/RT1)) / (Ae^(-Ea/RT2))Cancel out the pre-exponential factor,

A:k1/k2 = e^(-Ea/R) x (1/T1 - 1/T2)

Let k1 and k2 be the rate constants at temperatures T1 and T2 respectively. We have to solve for T2 given that k2 = 4.50k1 and T1 = 357 Substituting the values:

k1/(4.50k1) = e^(-26.09/(8.314 x 357) x (1/357 - 1/T2))1/4.50

= e^(-7.02 x 10^-4 x (1/357 - 1/T2))

Taking the natural logarithm of both sides, we get:

-ln(4.50) = -7.02 x 10^-4 x (1/357 - 1/T2)T2

= 357 / (1 + (4.50 x e^(-ln(4.50)/7.02 x 10^-4)))

= 451.23 K

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Answer:

? = 5

Step-by-step explanation:

You use cross-multiplying. Let's say ? is x.

First step:  \(\frac{30}{x}=\frac{48}{8}\)

Second step: You cross them so 30(8)= 280. 48(x)= 48x.

Third step: \(\frac{280}{48x}\)= 5

To double check this:

30/5= 6

48/8= 6

42/7= 6

I hope this helps.

I did this while struggling with my homework too lol.

Answer:

47.292

Step-by-step explanation:

Answer:

The slope is 20x

The y-intercept is 175