what is the probability that a standard normal random variable will be between .3 and 3.2?

A map is scale at one inch to fifteen miles. On a map, if two cities are 3.4 inches apart, They are actually apart 15.

A scale is a collection of values, such as levels or numbers, that are applied to a particular system of measurement or comparison. Scale is the ratio that establishes the relationship between the model and the actual figure. The real figures in smaller units are shown by it on maps. As an illustration, a scale of 1:5 means that 1 on the map is equivalent to the size of 5 in the real world. A framework or application can manage heavier loads if it scales properly.

Based on the given conditions, formulate:: 3.4*15/1

3.4 in  x 15mi/1in = 51 mi

Calculate the product or quotient: 51

They are actually apart 15

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Answer:

[tex]\textsf{A)} \quad \cos 2 \theta=\dfrac{9}{25}[/tex]

[tex]\textsf{B)} \quad \sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]

Step-by-step explanation:

Given:

[tex]\sin \theta=\dfrac{2\sqrt{2}}{5},\quad \dfrac{\pi}{2} < \theta < \pi[/tex]

[tex]\hrulefill[/tex]

To determine the exact value of cos 2θ, we can use the Cosine Double-Angle formula:

[tex]\large\boxed{\cos^2\theta = 1 - 2 \sin^2 \theta}[/tex]

Substitute the given value of sin θ into the formula:

[tex]\begin{aligned}\cos 2 \theta&=1-2\left(\dfrac{2\sqrt{2}}{5}\right)^2\\\\\cos 2 \theta&=1-2\left(\dfrac{8}{25}\right)\\\\\cos 2 \theta&=\dfrac{25}{25}-\dfrac{16}{25}\\\\\cos 2 \theta&=\dfrac{9}{25}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

To determine the exact value of sin (θ/2), we can use the half-angle formula for sine:

[tex]\large\boxed{\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\cos \theta}{2}}}[/tex]

First, find the value of cos θ by substituting the given value of sin θ into the trigonometric identity sin²θ + cos²θ = 1:

[tex]\begin{aligned}\left(\dfrac{2\sqrt{2}}{5}\right)^2+\cos^2\theta&=1\\\\\dfrac{8}{25}+\cos^2\theta&=1\\\\\cos^2\theta&=1-\dfrac{8}{25}\\\\\cos^2\theta&=\dfrac{17}{25}\\\\\cos\theta&=\pm \sqrt{\dfrac{17}{25}}\\\\\cos\theta&=\pm \dfrac{\sqrt{17}}{5}\end{aligned}[/tex]

As cos θ is negative on the interval π/2 < θ < π, we take the negative square root. Therefore:

[tex]\cos\theta&=-\dfrac{\sqrt{17}}{5}[/tex]

Now, substitute the found value of cos θ into the half-angle formula:

[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\left(-\dfrac{\sqrt{17}}{5}\right)}{2}}[/tex]

Therefore:

[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5}{5}+\dfrac{\sqrt{17}}{5}}{2}}[/tex]

[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5+\sqrt{17}}{5}}{2}}[/tex]

​​

​[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]

As sin θ is positive on the interval π/2 < θ < π, we take the positive square root. Therefore:

[tex]\sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]

Using  probability, the possible PINs with 5 digits if digits can be repeated are 3125.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. The fundamental ingredient of probability theory is an experiment that can be repeated, at least hypothetically, under essentially identical conditions and that may lead to different outcomes on different trials.

Given that, The PIN has 5 digits, the digits can be repeated.

The number of possible PINs are 5⁵

= 5 * 5 * 5 * 5 * 5

= 3125

the possible PINs with 5 digits if digits can be repeated are 3125.

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The solution is Option D.

The quotient of the coordinates will be a coefficient in the equation

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 0 )

Let the second point be Q ( 4 , 7 )

Now , the slope of the line between the points is ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 7 - 0 ) / ( 4 - 0 )

On simplifying the equation , we get

Slope m = 7/4

Therefore , the quotient of the coordinates will be a coefficient in the equation

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

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

On simplifying the equation , we get

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

Adding 7 on both sides of the equation , we get

y = ( 7/4 )x

Hence , the equation of line is y = ( 7/4 )x

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Answer:d

Step-by-step explanation:

The approximate distribution (give distribution name and parameters) of the total length will be =  450 minutes

The estimated distribution of the total length of Tina's simulation study is a triangular distribution with a base worth of 2 minutes, a greatest worth of 4 minutes, and a mode (most reasonable worth) of (2+4)/2 = 3 minutes.

Since the simulation time is generally consistently distributed somewhere in the range of 2 and 4 minutes, the total simulation time will be the sum of 150 free random variables each with a triangular distribution.

Hence, the total simulation time will also have a triangular distribution with a base worth of 2 minutes x 150 = 300 minutes, a greatest worth of 4 minutes x 150 = 600 minutes, and a method of (300+600)/2 = 450 minutes.

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The complete question is:

Tina is running a simulation study on her laptop. The duration of each simulation is roughly uniformly distributed between 2 and 4 minutes. She needs to run 150 simulations and she runs all her simulations back-to-back. - What is the approximate distribution (give distribution name and parameters) of the total length of Tina's simulation study? Explain your answer

Answer: A. 2.7

Step-by-step explanation:

Answer: 2.7

2 7/10 = 27/10 = 2.7

= Hence, Proved that 2.7 = 2 7/10

Answer:

The standard form is  [tex]\boxed{3n^4m^2}[/tex] .

The coefficient is [tex]\boxed{3}[/tex]

Step-by-step explanation:

What is Standard Form of Polynomial?

The standard form of a polynomial is a way of writing a polynomial such that the term with the highest power of the variables comes first followed by the other terms in decreasing order of the power of the variable

We are given the expression

[tex]\dfrac{2}{3}m^2n \cdot 4.5 n^3\\\\[/tex]

and we have to convert to standard form

First multiply the constants together to get the coefficient:

[tex]\dfrac{2}{3} \cdot 4.5 = \dfrac{2 \cdot 4.5}{3} = \dfrac{9}{3} = 3[/tex]

There is only one m term which is m²

Multiply the two n terms to get [tex]n \cdot n^3 = n^(1 + 3} = n^4[/tex]

Therefore in standard form we get ( in decreasing order of exponents)
[tex]3n^4m^2[/tex]

The coefficient is 3

3) Ascending order of numbers are, 3/100 , 1/10, 0.8, 0.91.

4) Ascending order of numbers are, 11/100, 0.21, 0.35, 0.6, 7/10, 0.9

5) Ascending order of numbers are, 8/100, 1/10, 0.2, 36/100, 0.44, 0.5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

3) Numbers are,

⇒  0.8, 1/10, 3/100, 0.91

It can be written as;

⇒ 0.8, 0.1, 0.03, 0.91

Hence, Ascending order of numbers are,

⇒ 0.03, 0.1, 0.8, 0.91

⇒ 3/100 , 1/10, 0.8, 0.91

4) Numbers are,

⇒ 0.9, 0.35, 11/100, 7/10, 0.6, 0.21

It can be written as;

⇒ 0.9, 0.35, 0.11, 0.7, 0.6, 0.21

Hence, Ascending order of numbers are,

⇒ 0.11, 0.21, 0.35, 0.6, 0.7, 0.9

⇒ 11/100, 0.21, 0.35, 0.6, 7/10, 0.9

5) Numbers are;

⇒ 36/100, 0.2, 1/10, 8/100, 0.5, 0.44

It can be written as;

⇒ 0.36, 0.2, 0.1, 0.08, 0.5, 0.44

Hence, Ascending order of numbers are,

⇒ 0.08, 0.1, 0.2, 0.36, 0.44, 0.5

⇒ 8/100, 1/10, 0.2, 36/100, 0.44, 0.5

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Answer:

(−3.6)y − 4

Step-by-step explanation:

2/5 y − 0.2y − 6 + (−2)

= (2/5 y − 0.2y) − (6 + (−2))

= (2/5 y − 0.2y) − 4

= (2/5 y − 4) − 0.2y

= (2/5 y − 0.2y) − 4

= (2/5 − 0.2)y − 4

= (−3.6)y − 4

The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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Answer:

y = 20x +22

Step-by-step explanation:

The probability of getting 1 spade card when we take two cards out randomly of a deck of cards is 1/4.

By dividing the entire number of possible outcomes by the total number of possible events, the probability is determined.

Probability and odds are two distinct ideas.

To calculate chances, divide the likelihood of an event by the likelihood that it won't occur.

Mathematicians investigate probability, which may be broken down into four primary categories: axiomatic, classical, empirical, and subjective.

So, we know that:
There are 13 spades in the deck of 52 cards.

Then use the probability formula which is as follows:

P(E) = Favourable events/Total events

P(E) = 13/52

P(E) = 1/4

Therefore, the probability of getting 1 spade card when we take two cards out randomly of a deck of cards is 1/4.

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tricia wants to install a decorative wall paper border around the top of the wall in her master bedroom. the room measures 14ft by 17ft. then perimeter 62 feet of the border will will she need

For the installation of a decorative wall paper Tricia will need 70 ft of the border to decorate the wall of her master bedroom.

The measures of the room is 17 ft by 14 ft.

So, the length of the room (l) = 17 ft

The width of the room(w) = 14 t

As we know that, perimeter of rectangle is 2(l×w).

We will get perimeter of he room = 2l × 2w

                                                   = 2(17) × 2(14)

                                                   = 62 ft.

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The value of 8 in the number is 800million

Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one's position.

For example the place place value of 4 in 400 is 4 hundred. Place value starts with unit, tens hundreds, thousands, ten thousands, hundred thousands , million, ten million, 100million e.t.c

The place value of 8 in the number is 8 hundred million. This means 800,000.

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The actual distance between the two cities is 288 miles.

A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio.  This means that the scale drawing of the two cities would be smaller than the actual cities.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.

The actual distance between the two cities = (3 x 24) ÷ 1/4

= 3 x 24 x 4 = 288 miles

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The general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].

The general solution of the following differential equation is [tex]$\quad 3 x^2 y^{\prime}+6 x y=15 y^3$[/tex].

The differential equations which are represented in terms of (x,y) such as the x-terms and y-terms can be ordered to different sides of the equation (including delta terms). Thus, each variable after separation can be integrated easily to find the solution of the differential equation. The equations can be written as:

solution: [tex]$\quad y^{\prime}=\frac{d y}{d x}$[/tex]

So rewritten question as

[tex]$$\begin{aligned}& 3 x^2 \frac{d y}{d x}+6 x y=15 y^3 \\& \frac{d y}{d x}+\frac{6 x y}{3 x^2}=\frac{15 y^3}{3 x^2} \\& \frac{d y}{d x}+\frac{2 y}{x}=\frac{5}{x^2} y^3\end{aligned}$$[/tex]

compare equation (1) with Bernoulli's Equation

[tex]$$\begin{aligned}& \frac{d y}{d x}+P(x) y=Q(x) y^n \\& P(x)=\frac{2}{x} \quad Q(x)=\frac{5}{x^2} \\& n=3\end{aligned}$$[/tex]

Substitute:

[tex]v & =y^{1-n} \\v & =y^{1-3} \\v & =y^{-2} \\y \quad y & =v^{(-1 / 2)}-(2) \\\frac{d y}{d x} & =-\frac{1}{2}\left(v^{-\frac{1}{2}-1}\right) \frac{d v}{d x}\end{aligned}$$[/tex]

[tex]\frac{d y}{d x}=-\frac{1}{2} v^{-3 / 2} \frac{d v}{d x}[/tex]

substitute value of y and [tex]$\frac{d y}{d x}$[/tex] from 4 (2) and (3) respectively in equation (1)

⇒[tex]& \frac{-1}{2} v^{-3 / 2} \frac{d v}{d x}+\frac{2}{x} \cdot v^{-1 / 2}=\frac{5}{x^2} \cdot v^{-3 / 2}[/tex]

⇒[tex]& \frac{d v}{d x}-\frac{4}{x} v=\frac{-10}{x^2} \\[/tex]

⇒ Integrating factor[tex]=e^{\int-4 / x d x} \\[/tex]

[tex]& =e^{-4 \ln x} \\& =e^{\ln x^{-4}} \\& =x^{-4} \\& =\frac{1}{x^4} \\[/tex]

⇒[tex]\frac{1}{x^4} v=\int \frac{1}{x^4} \times \frac{-10}{x^2} d x \\[/tex]

[tex]& =-10 \int x^{-6} d x \\[/tex]

[tex]& =+10 \frac{x^{-6+1}}{(-6+1)}+C=\frac{+10^2}{+8} x^{-5}+C \\&[/tex]

⇒[tex]\frac{1}{x^4} \cdot v & =\frac{2}{x^5}+c \\[/tex]

⇒[tex]v & =\left(\frac{2}{x^5}+c\right) x^4 \\[/tex]

⇒[tex]v & =\left(\frac{2}{x}+c x^4\right)[/tex]

Now replace v=y-2

⇒[tex]& y^{-2}=\frac{2}{x}+c x^4 \\[/tex]

⇒[tex]& y=\left[\frac{1}{\left(\frac{2}{x}+\left(x^4\right)\right.}\right]^{1 / 2} \\[/tex]

⇒[tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex]

Therefore, the general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].

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Answer:

a and c

Step-by-step explanation:

The lines on the graph cross over those two points. Hope this helps.

The 7th term of the geometric sequence is -0.0021 .

What is geometric progression?

If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the sequence is called a geometric progression. (GP), whereas the constant value is called the common ratio.

For example, 2, 4, 8, 16, 32, 64, … is a GP, where the common ratio is 2.

Given :

first term : -2100

common ratio : -0.1

7th term =-2100 *-0.1^(7 - 1)

                =-2100 * -0.1^6

                =-2100 * 0.000001

                =- 0.0021

Hence , the 7th term of the geometric sequence is -0.0021 .

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In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. the 90% confidence interval for the levels of lead is between (0.4958, 0.7422).

p is 26/42=0.6190

rootp(1-p)/n=root0.6190(1-0.6190)/42=0.0749

satisfies that above this and under the standard normal density there is an area of 0.05. In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. the 90% confidence interval for the true population proportion of water specimens that contain detectable levels of lead is between (0.4958, 0.7422).

Density is the number of things—which could be people, animals, plants, or objects—in a certain area. To calculate density, you divide the number of objects by the measurement of the area. The population density of a country is the number of people in that country divided by the area in square kilometers or miles.

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Based on the word problem "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." Eric's fraction is 12/30.

Generally speaking, a fraction comprises two (2) main parts and these include the following:

Next, we would translate the word problem "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." into an algebraic expression as follows;

n/(n + 18) = 2/5

By cross-multiplying, we have:

5n = 2(n + 18)

5n = 2n + 36

5n - 2n = 36

3n = 36

n = 36/3

n = 12.

Now, we can determine the fraction as follows;

n/(n + 18) = 12/(12 + 18)

n/(n + 18) = 12/30.

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Complete Question:

Eric has a riddle: "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." what is his fraction?

The time when the concentration of the chemical in the tank is 0.8 lb/gal is 36.31 minutes.

Let C be the concentration of the chemical in the tank and V be the volume of the tank.

Initially, V = 100 gal and C = 40 lb/100 gal = 0.4 lb/gal.

Let t be the time in minutes.

The rate of change of C is given by:

dC/dt = (5*3.5 lb/gal - 7*C)/V

Solving the differential equation, we get:

C = 0.4 + 0.6e^(-7t/100)

Setting C = 0.8 lb/gal, we get:

0.8 = 0.4 + 0.6e^(-7t/100)

=> 0.6e^(-7t/100) = 0.4

=> e^(-7t/100) = 0.67

=> -7t/100 = ln 0.67

=> t = 100*ln0.67/-7

=> t = 36.31 minutes

Therefore, the time when the concentration of the chemical in the tank is 0.8 lb/gal is 36.31 minutes.

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The Sum of interior angles is, 2160°.

The sum of the exterior angles of a 14-sided polygon is 360°

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:

A polygon with 14 sides.

The Sum of interior angles = (n - 2) × 180°

= 12 x 180

= 2160°

The sum of the exterior angles of a 14-sided polygon is 360°

Therefore, all the required values are given above.

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The mean absolute deviation is 3.4

Option D is the correct answer.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

2, 2, 1, 6, 6

Mean = (2 + 2 + 1 + 6 + 6) / 5 = 17/5 = 3.4

Thus,

The mean is 3.4

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The arc length of the partial circle is, 28.26 units.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Radius of semicircle = 9 units

Now, We know that;

Arc length of semicircle = (2πr) × 180°/360°

Here, Radius of semicircle = 9 units

Hence, We get;

Arc length of semicircle = (2πr) × 180°/360°

Arc length of semicircle = (2 × 3.14 × 9) × 180°/360°

Arc length of semicircle = 28.26 units.

Thus, The arc length of the partial circle is, 28.26 units.

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Answer:

To find the distance around a hat, you need to find the circumference of a circle with a diameter of 4.7 inches.

The formula for the circumference of a circle is C = π * d, where d is the diameter.

Plugging in the values and using π = 3.14, we have:

C = 3.14 * 4.7 = 14.758

Rounding to the hundredths place, the circumference of the hat is 14.76 inches.

So, the answer is 14.76 inches.

Answer:it is correct the awnser is d 14.76

Step-by-step explanation:did the test

The value of x is 21.

The question above can be written:

2x-6=36, then simplified the equation

2x=36+6

2x=42

x= 21

Mathematical models are used to simplify problems so that they are easy to understand. Therefore, a mathematical model is a model that represents a problem with a system that reflects relationships between symbols or mathematical relationships.

A mathematical model is a form of human interpretation in translating or formulating existing problems into mathematical forms, so that these problems can be solved using mathematics.

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The new price of the item after a deduction of 80% from the original price is $14

Percentage discount = 80%

Original price of the item = $70

New price of the item= Original price of the item - (Percentage discount × Original price of the item)

= 70 - (80% × 70)

= 70 - (0.8 × 70)

= 70 - 56

= $14

In conclusion, the item now cost $14 after deducting discount.

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Resolviendo un sistema de ecuaciones, veremos que que la piedra estuvo 7 segundos en el aire y 5 en el agua.

Sabemos que:

En el aire tuvo una velocidad promedio de 16 m/s. En el agua tuvo una velocidad promedio de 3 m/s antes de tocar el fondo del mar.

Definamos las variables:

x = tiempo que la piedra estuvo en el aire.

y = tiempo que la piedra estuvo en el agua.

Sabemos que el trayecto completo duro 12 segundos, entonces podemos escribir:

x + y = 12

Y la caida total fueron 127 metros, entonces:

x*16 + y*3 = 127

Entonces tenemos un pequeño sistema de ecuaciones:

x + y = 12

x*16 + y*3 = 127

En la primera podemos aislar x:

x = 12 - y

Reemplazar eso en la otra ecuacion:

(12 - y)*16 + y*3 = 127

192 - 13y = 127

192 - 127 = 13y

65 = 13y

65/13 = y

5 = y

Entonces la piedra esta 5 segundos en el agua y los otros 7 segundos en el aire.

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The correct answer is option 1. The version of the sample variance where you divide by n is biased.

This is because dividing by n will produce a biased downward population variance estimate. We must divide by n-1 rather than n to correct this bias. Mathematically, this can be expressed as:

Population Variance = s2 = ∑ (x - μ)2 / n Sample Variance = s2 = ∑ (x - x(bar))2 / (n-1)

In other words, we must subtract 1 from the sample size in the denominator when calculating the sample variance. This is due to the fact that the sample variance and the sample mean are both unbiased estimators of the population variance, respectively.

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Complete Question:

which of the following statements is true?

group of answer choices

The ratio of the area of circle A to the area of circle B is 9:1

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of the circumference of circle A to the circumference of circle B is 3:1. What is the ratio of the area of circle A to the area of circle B

The circumference of circle = 2π × radius

We have,

Circumference(A) / Circumference(B) = 3 / 1

Let the radius of A be R and that of B be r,

2πR / 2πr = 3/1

R/r = 3

R = 3r

Now, the area of a circle = π × radius²

Area(A) = πR²

= π(3r)² = 9πr²

Area(B) = πr²

Ratio of the area of circle A to Circle B = 9πr² / πr²

= 9/1

Hence, the ratio of the area of circle A to the area of circle B is 9:1

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