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The mean of a standard normal probability distribution is 0.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The probability density function of a standard normal distribution is given by:

f(x) = (1/√(2π)) * e^(-x^2/2)

where x is a random variable that follows a standard normal distribution. The mean of a probability distribution is the expected value of the random variable, which is given by the integral of the product of the random variable and the probability density function over its entire range.

For a standard normal distribution, this integral is equal to:

E(x) = ∫(-∞ to ∞) x * f(x) dx = ∫(-∞ to ∞) x * (1/√(2π)) * e^(-x^2/2) dx

This integral evaluates to 0, which means that the mean of a standard normal distribution is 0.

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Answer:

k=.25068

Step-by-step explanation:

450 = 100 \(e^{6k}\)

4.5 =   \(e^{6k}\)

ln(4.5) = 6k

k= ln(4.5)/6

k=.25068

The number of bacteria after 13 hours will be 2579.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

Given that a biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favourable growth medium. Six hours later, he measures 450 bacteria.

The bacteria after 13 hours will be calculated as,

\(N=100(e)^{13\times 0.25)\)

\(N = 100\times e^{3.25}\)

N = 2579.

Therefore, the number of bacteria after 13 hours will be 2579.

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We οbtain JN  44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly  44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.

The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.

The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.

Law of sines

sin(∠A)/a = sin(∠B)/b = sin(∠C)/c

Therefore,

39/sin(53°) = JN/sin(65°)

JN = (39×sin(65°))/sin(53°)

JN = 44.3

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The translation of the C statement into an assembly program using the given registers and the MLA (Multiply Accumulate) instruction.

MOV r1, #0x000000FF   ; Load x into r1

MOV r2, #0x000000AB   ; Load y into r2

MOV r3, #0x000000CD   ; Load z into r3

MLA r0, r1, r2, r3    ; Multiply r1 (x) by r2 (y), add r3 (z), and store the result in r0

SUB r1, r0, r1        ; Subtract r1 (x) from r0 (result) and store the result in r1

In this code, we first load the values of x, y, and z into registers r1, r2, and r3, respectively. Then, we use the MLA instruction to multiply the values of x and y and add the value of z, storing the result in register r0.

Finally, we subtract the initial value of x (stored in r1) from the result (stored in r0) and store the final result back into r1.

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Answer:

47

Step-by-step explanation:

mean is found by dividing the sum of the terms by the number of terms:

(43+48+41+41+x)/5=44

173+x=220

x=220-172=47

Answer: \(y=\frac{3}{17}x-13\)

Step-by-step explanation:

Find the slope of the line between (-17, -16) and (0,-13) using \(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\), the change of y over the change of x

\(m=\frac{3}{17}\)

Use the slope and a given point to substitute for \(x_{1}\) and \(y_{1}\) in the point-slope form \(y-y_{1} =m(x-x_{1} )\).

\(y-(-16)=\frac{3}{17}(x+17)\)

Solve for y and rewrite into \(y=mx+b\)

\(y=\frac{3}{17}x-13\)

Answer:

y = -4x + 2

Step-by-step explanation:

Answer:

y = -4x + 2

Step-by-step explanation:

The domain of f is the interval [-37, ∞).

For a function to have an inverse, it must be one-to-one, which means that it must pass the horizontal line test, i.e., each horizontal line should intersect the graph of the function at most once.

The derivative of the function is:

\(f'(x) = 6 + (1/2√(x+37))\)

f'(x) is always positive because 6 is positive and the square root is positive, so f(x) is an increasing function. This means that f(x) is one-to-one and therefore has an inverse.

To determine the largest interval on which f has an inverse, we need to find the domain of f. The square root can only take non-negative values, so we must have x+37 ≥ 0, which means x ≥ -37.

Therefore, the domain of f is the interval [-37, ∞).

Since f is increasing over this interval, its inverse will also be increasing, and the largest interval on which f has an inverse is [-37, ∞).

The proper question is "Let f(x)=6x+√(x+37)Choose the form of the largest interval on which f has an inverse and enter the value(s) of the endpoint(s) in the appropriate blanks. Then find (f−1)′(0)

Endpoints(a ,b)"

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Selena needs 4 more hours to prepare 264 more pancakes.

Unitary method is a process of finding the value of a single unit, and use this value to find the value of the required number of units.

Given is Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes.

We have -

The rate at which Selena is making pancakes = 132 pancakes in 2 hours.

Number of pancakes left to be made = 264

Now, in 2 hrs she makes 132 pancakes

Then, in 1 hr she will make (132/2) or 66 pancakes.

Now, she makes 66 pancakes in 1 hour.

So, she will make 1 pancake in (1/66) hours

Therefore, she will make 264 pancakes in (264/66) or 4 hours.

Therefore, she will need 4 more hours to prepare 264 more pancakes.

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Answer:

1) La velocidad de la bala después de atravesar el muro es de aproximadamente 435,890 metros por segundo.

2) La potencia del automóvil es 96438,272 watts o 131,208 caballos de vapor.

3) La velocidad del objeto al llegar al suelo es aproximadamente 14,005 metros por segundo.

Step-by-step explanation:

1) La velocidad final de la bala puede determinarse mediante el Teorema del Trabajo y la Energía, a partir del cual se tiene la siguiente fórmula:

\(\frac{1}{2}\cdot m\cdot v_{o}^{2} -F\cdot \Delta s = \frac{1}{2}\cdot m \cdot v_{f}^{2}\) (1)

Where:

\(m\) - Masa de la bala, en kilogramos.

\(v_{o}, v_{f}\) - Velocidades inicial y final de la bala, en metros por segundo.

\(F\) - Resistencia del muro al avance de la bala, en newtons.

\(\Delta s\) - Espesor del muro, en metros.

Si sabemos que \(m = 0,01\,kg\), \(v_{o} = 500\,\frac{m}{s}\), \(F = 3000\,N\) and \(\Delta s = 0,1\,m\), entonces la velocidad final de la bala es:

\(v_{f}^{2}=v_{o}^{2} -\frac{2\cdot F\cdot \Delta s}{m}\)

\(v_{f} = \sqrt{v_{o}^{2}-\frac{2\cdot F\cdot \Delta s}{m} }\)

\(v_{f} \approx 435,890\,\frac{m}{s}\)

La velocidad de la bala después de atravesar el muro es de aproximadamente 435,890 metros por segundo.

2) Asumamos que el automóvil acelera a tasa constante, significando que la fuerza neta será constante. Para un sistema cuya fuerza neta sea constante, la potencia experimentada queda descrita por la siguiente ecuación:

\(P = m\cdot a(t)\cdot v(t)\) (2)

\(a(t) = a\) (3)

\(v(t) = v_{o} + a\cdot t\) (4)

Donde:

\(P\) - Potencia, en watts.

\(m\) - Masa del automóvil, en kilogramos.

\(a(t)\) - Aceleración, en metros por segundo al cuadrado.

\(v(t)\) - Velocidad, en metros por segundo.

\(v_{o}\) - Velocidad inicial del automóvil, en metros por segundo.

Si sabemos que \(m = 1000\,kg\), \(a = 3,472\,\frac{m}{s}\), \(v_{o} = 0\,\frac{m}{s}\) y \(t = 8\,s\) entonces la potencia experimentada por el automóvil es:

\(P = 96438,272\,W\) (\(131,208\,C.V.\))

La potencia del automóvil es 96438,272 watts o 131,208 caballos de vapor.

3) El cuerpo experimenta un Movimiento de Caída Libre, el cual es un Movimiento Uniformemente Acelerado debido a la gravedad terrestre. La velocidad del cuerpo al llegar al suelo se determina mediante la siguiente fórmula cinemática:

\(v_{f} = \sqrt{v_{o}^{2}+2\cdot g\cdot h}\) (5)

Donde:

\(v_{o}\) - Velocidad inicial del cuerpo, en metros por segundo.

\(v_{f}\) - Velocidad final del cuerpo, en metros por segundo.

\(g\) - Aceleración gravitacional, en metros por segundo al cuadrado.

\(h\) - Altura recorrida por el cuerpo, en metros.

Si sabemos que \(v_{o} = 0\,\frac{m}{s}\), \(g = 9,807\,\frac{m}{s^{2}}\) y \(h = 10\,m\), entonces la velocidad al llegar al suelo es:

\(v_{f} \approx 14,005\,\frac{m}{s}\)

La velocidad del objeto al llegar al suelo es aproximadamente 14,005 metros por segundo.

The ride that has the greatest elevation based on the information is B. Lightning bolt : 327 feet.

The term elevation is typically used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.

Elevations show how your house will appear from various perspectives. Regarding these particular angles, there are many elevation kinds. Some varieties include split elevations, rear elevations, side elevations, and front elevations.

From the information, it was stated that the lightning bolt starts at an elevation of 15ft from the platform and speeds the passengers to an elevation of 327 ft.

It should be noted that the information is to simply find the elevation that is the greatest.

Based on the figures given, the appropriate elevation will be 327 feet.

Therefore, the correct option is B.

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Answer:

$110

Step-by-step explanation:

The computation is shown below:

Provided that

Number of desk purchased    Fund Left $

           0                                   700

           1                                    590

           2                                   480

           3                                   370

           4                                   260

           5                                   150

           6                                    40

Now the Fund decreased while purchasing is

= 5 desks - 2 desks

= 3 desks

i.e

= $480 - $150

= $330

Now the amount of money left for decreased the desk fund is

\(= \frac{Fund\ decreased }{number\ of\ desk\ decreased}\)

\(= \frac{\$330}{3\ desk}\)

= $110

Answer:

A)$110

Step-by-step explanation:

Answer:

37,440

Step-by-step explanation:

To find volume the formula is : Length x Width x Height... So 30 x 24 x 52 = 37, 440

:D

The function is called an if/else statement function lets you test if something is true or false and then do different things depending on which result you get.

An if/else statement is a type of control flow statement that allows a program to execute different instructions depending on the result of a logical expression. The statement begins with an if condition, followed by a set of instructions to be performed if the condition is true. If the condition is false, the program executes the instructions after the optional else statement. The syntax for an if/else statement looks like this: if (condition) { // Instructions to execute if condition is true } else { // Instructions to execute if condition is false } By using an if/else statement, a program can make decisions and perform different actions based on the results of a logical expression.

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Answer:

3/2

Step-by-step explanation:

Answer:

The two triangles are similar.

What is the value of x?

Enter your answer in the box.

x=

The value of x is 7 units.

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

Given :

AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and              

∠DEB ≅ ∠ACB

Now, AB = AD + BD

              = 8 + 6 = 14 units

Now, In ΔABC and ΔDBE,

∠DBE = ∠ABC ( Each of 90° )

∠DEB = ∠ACB ( given )

So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE

Now, proportion of the corresponding sides will be equal.

AD/ DB= BC/ BE

14/8 = 3x/ 2x-2

4x= 28

x= 7

Hence, the value of x is 7 units.

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Answer:

a=14

Step-by-step explanation:

-a+28=14

So -a=-14

so a=14

Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

Answer:

Billy can buy 19 or less than 19 stickers.

Step-by-step explanation:

  Let the unknown variable - number of stickers be 'x'.

   Cost of one sticker = $1.34

   Cost of 'x' stickers = 1.34 * x = 1.34x

   Maximum amount that can be spent for buying stickers = 80 - 54.50

                                                                                                 = $25.50

   Inequality:

          1.34x ≤ 25.50

 Solving:

         Divide both sides by 1.34,

            \(\sf x \leq \dfrac{25.50}{1.34}\)

            x ≤ 19.03

            x ≤ 19

Billy can buy 19 or less than 19 stickers.

Answer:

Step-by-step explanation:

8+2*3-5*2+(82+4+4):(12+6+12)+3=
Firstly, we should use the BODMAS rule.
B: Brackets
O: Off
D: Division
M:Multiplication
A:Additioin
S:Subtraction
by this format we should start our problem.
Now, we solve the brackets
=8+2*3-5*2+(90):(28)+3
Now, we solve the multiplication
=8+6-7+(90):(28)+3

Now, we solve the addition part
=108-7:31
Now, the subtraction
=101:31 is the answer

Answer:

C=1

Step-by-step explanation:

5/6=5/6c which is 1.

Answer: (7,10)

Step-by-step explanation:

The solutions to the quadratic equation f(x) = x² + 10x - 1 are x = -5 + √26 and x = -5 - √26

To solve the quadratic equation f(x) = x² + 10x - 1

we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, a = 1, b = 10, and c = -1.

Substituting these values into the quadratic formula:

x = (-(10) ± √((10)² - 4(1)(-1))) / (2(1))

= (-10 ± √(100 + 4)) / 2

= (-10 ± √104) / 2

Simplifying further:

x = (-10 ± 2√26) / 2

= -5 ± √26

Therefore, the solutions to the quadratic equation f(x) = x² + 10x - 1 are:

x = -5 + √26 and x = -5 - √26

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Answer:

The function expressed in the graph has a steeper slope than the function in the table.

The y-intercept is the same for both functions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

the triangles have two equal sides

and one angle

To calculate the expected number of die rolls it takes to reach either condition (A) or condition (B), we need to first calculate the probability of each scenario occurring and then use those probabilities to find the expected value of X.

To find the expected value of X, we need to first calculate the probability of each scenario occurring. Let's start with condition (A), rolling a "1" on any given roll. Since the die is fair and uniformly distributed, the probability of rolling a "1" on any given roll is 1/6. We can express this probability as P(A) = 1/6 + ((5/6) * 1/6) + ((5/6)^2 * 1/6) + ... + ((5/6)^(n-1) * 1/6), where n is the number of rolls it takes to roll a "1". Using some probability theory, we can simplify this expression as P(A) = 6/11.

Finally, we can use these probabilities to find the overall probability of reaching either condition (A) or condition (B) on any given roll. Since these events are mutually exclusive (i.e. you can't roll a "1" and two "2"s in a row at the same time), we can simply add their probabilities together: P(A or B) = P(A) + P(B) - P(A and B) = 6/11 + 1/36 - (1/6)*(1/36) = 201/396.

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Answer:

C

Step-by-step explanation:

beccause it has four sides

(quad) ,

a. The dominant term is n^3, so the big-O notation is O(n^3).

b. The dominant term is n^4log(n), so the big-O notation is O(n^4log(n)).

c. The dominant term is 12nlog(n), so the big-O notation is O(nlog(n)).

d. The dominant term is n^2, so the big-O notation is O(n^2).

a) T(n) = (n^2 + 8)(n + 2)

Expanding the expression:

T(n) = n^3 + 2n^2 + 8n + 16

The dominant term is n^3, so the big-O notation is O(n^3).

b) T(n) = (nlog(n) + n^2)(n^3 + 3)

Expanding the expression:

T(n) = n^4log(n) + 3n^3 + n^2log(n) + 3n^2

The dominant term is n^4log(n), so the big-O notation is O(n^4log(n)).

c) T(n) = 3n(5 + 2log(n^2))

Simplifying the expression:

T(n) = 3n(5 + 4log(n))

The dominant term is 12nlog(n), so the big-O notation is O(nlog(n)).

d) T(n) = log(2n) + 2n + n^2

The dominant term is n^2, so the big-O notation is O(n^2).

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Part 1

There are many ways to go about this, but one possibility is the following:

You are building a tree house. Your ladder is 10 feet long and the portion in the tree you're trying to get to is 8 feet off the ground. How far should the base of the ladder be from the tree so you can reach that portion?

==========================================================

Part 2

The drawing is shown below. The diagram is shown in 2D to keep things as simple as possible. Adding a third dimension greatly complicates everything.

We have a right triangle, so it has a 90 degree angle as shown by the square marker. The vertical leg is 8 feet. The horizontal leg is unknown. The hypotenuse (longest side) is 10 feet long to indicate the ladder.

==========================================================

Part 3

Use the pythagorean theorem to get...

a^2 + b^2 = c^2

x^2 + 8^2 = 10^2

x^2 + 64 = 100

x^2 = 100-64

x^2 = 36

x = sqrt(36)

x = 6

The base of the ladder should be 6 feet away from the tree, so that you can reach 8 feet off the ground.

Answer:

The answer is 8 cm .

Step-by-step explanation:

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