At the middle school, 900 students ride the bus, and 300 students do not ride the bus. What percent of the students do not ride the bus?

Answer:

66.48% of full-term babies are between 19 and 21 inches long at birth

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean length of 20.5 inches and a standard deviation of 0.90 inches.

This means that \(\mu = 20.5, \sigma = 0.9\)

What percentage of full-term babies are between 19 and 21 inches long at birth?

The proportion is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19. Then

X = 21

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{21 - 20.5}{0.9}\)

\(Z = 0.56\)

\(Z = 0.56\) has a p-value of 0.7123

X = 19

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{19 - 20.5}{0.9}\)

\(Z = -1.67\)

\(Z = -1.67\) has a p-value of 0.0475

0.7123 - 0.0475 = 0.6648

0.6648*100% = 66.48%

66.48% of full-term babies are between 19 and 21 inches long at birth

These solutions can be further simplified, but they are all complex numbers. x = y - 2/3 = (8/9)√(5)/2 - 2/3

How to find?

To find the solutions of the cubic equation x²3 + 2x²2 + 3x + 6 = 0, we can use a combination of synthetic division and the quadratic formula.

First, we can use synthetic division to check if the equation has any rational roots. Since the coefficient of the highest degree term is 1, the possible rational roots are all factors of the constant term, 6. These are ±1, ±2, ±3, and ±6. We can use synthetic division to check if any of these values are roots of the equation:

-1 | 1   2   3   6

  |    -1  -1  -2

  |-------------

  | 1   1   2   4

-2 | 1   2   3   6

  |    -2  -2

  |------------

  | 1   0   1   4

-3 | 1   2   3   6

  |    -3  -3

  |------------

  | 1  -1   0   3

-6 | 1   2   3   6

  |    -6  24

  |-------------

  | 1  -4  27   0

None of the possible rational roots is a root of the equation. Therefore, the equation has no rational roots, and all the solutions are either irrational or complex.

Next, we can use the quadratic formula to find the solutions of the depressed cubic x²3 + 2x²2 + 3x + 6 = 0, which is obtained by substituting x = y - 2/3:

y²3 + py + q = 0

where p = 2 - (2/3)²2 = 4/9 and q = 6 - 4/3 = 16/3.

The quadratic formula gives:

c

y = [-p ± √(p²2 - 4q)]/2

Plugging in the values of p and q, we get:

y = [-4/9 ±√((4/9)²2 - 4(16/3))]/2

Simplifying:

c

y = [-4/9 ± √(16/81 - 64/9)]/2

c

y = [-4/9 ± √(-320/81)]/2

go

y = [-4/9 ± (8i/9)√(5)]/2

Therefore, the solutions of the cubic equation x²3 + 2x²2 + 3x + 6 = 0 are:

x = y - 2/3 = (-4/9 + (8i/9)√(5))/2 - 2/3

x = y - 2/3 = (-4/9 - (8i/9)√(5))/2 - 2/3

x = y - 2/3 = (8/9)√(5)/2 - 2/3

These solutions can be further simplified, but they are all complex numbers.

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-5 4/9 is one way.

-5 = -45/9, so -45/9 + 4/9. -41/9 is another way.

-41/9 = -4.5555.... , so -4.5555... is another way.

The three ways of writing \(- 5\frac{4}{9}\) is - 49/9 and  - 5.44.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, \(- 5\frac{4}{9}\).

One way of writing is - (45 + 4)/9 = - 49/9.

Another way of writing this is in a decimal form which is,

= - 5.44

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Answer:

which one substitution or elimination

Step-by-step explanation:

Substitution: (-1,-3 )

Elimination: (-1,-3)

i hope this helps you :)

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Two quantities x and y are proportional if they are related by:

Where a is known as the proportionality factor. In this case the quantities related are the length and the weight of a steal beam so the first two question would be:

- What's the length of the beam?

- What's its weight?

Then it is also important to know the proportionality factor so knowing that the length and the weight are proportionally related I would ask:

- What's the proportionality factor?

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

Answer:

No and No

Step-by-step explanation:

Squaring a odd, whole, number results in a even number 99% of the time with the only exception being 1 (1^2 equals 1). If m is 3 and n is 5, mn would be 15, so if both m and n are odd they don't always equal a even number.

Answer:

Step-by-step explanation:

If we are dealing with whole real numbers.

Both answers are based on the same idea.

The product of two numbers is even only if at least one of the two multiplicands is even.

The square of an odd number can only result in an odd number. The reverse is true as well. The square root of an odd number can only be an odd number.

This comes from number theory where multiplication is the repeated addition of one number a certain number of times.

If the first number is even, then every time you add itself again results in an even number, It does not matter if you add an even or odd number of times.

If the first multiplicand is odd, the sum of two odd numbers is always even, adding a third odd multiplicand again results in an odd number, the fourth is even, the fifth is odd, the pattern continues forever. The summation of an even number of odd multiplicands results in an even number. The summation of an odd number of odd multiplicands results in an odd number.

Answer:

(0,2)

Step-by-step explanation:

Answer: $32.74

Is your answer

Glad I could help!

Step-by-step explanation:

Answer:

The square of a negative number is a positive number as 2 negatives cancel when multiplied.

In this case the negative sign stays as is because it is not affected by a square.

Answer:

2x+2=58

2x=58-2=56

divide both sides by 2

x=28

The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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Answer is \(2\sqrt{2}\) mi

Given,

Kaylib’s eye-level height is 48 ft

Addison’s eye-level height is 85 and one-third ft above sea level.

From the formula d= \(\sqrt{3h/2}\),

get the difference as:

\(d=\sqrt{(3*(85+1/3))/2} - \sqrt{(3*48)/2}\)

=\(\sqrt{256/2} - \sqrt{3*24}\)

=\(\sqrt{128} - 6\sqrt{2}\)

=\(8\sqrt{2} - 6\sqrt{2}\)

d=\(2\sqrt{2}\)

Therefore, Addison sees \(2\sqrt{2}\)mi to the horizon

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Answer:

dilation with respect to the origin by a scale factor of 1/3 followed by a translation of 2 units down

Step-by-step explanation:

The sides of the △ HIJ are:

IH = 6

IJ = 3

Applying the scale factor we obtain the sides of △ H'I'J '.

The scale factor is k = 1/3.

Therefore, we have:

I'H '= 2

I'J '= 1

Then, we move the △ H'I'J 2 units down.

Answer:

441.66667 pounds

Step-by-step explanation:

divide 350/42 then multiply the quotient by 53

Answer:

3.5g/ml or 3.5g/cm³

Step-by-step explanation:

1cm³=1ML

Volume of the irregular shaped stone = New Volume of water in cylinder -initial Volume of water in cylinder

Volume of irregular shaped stone = 8ml-2ml

Volume of irregular shaped stone =6ml

Denisty =Mass/Volume

Density = 21g/6ml

Density = 3.5g/ml

Answer:

a. 49°

Step-by-step explanation:

x + 41 = 90

x = 90 - 41

x = 49°

The equation of a direct proportion is A. y=8x.

It should be noted that a direct proportion is also a direct variation. It is one when the relation between the two quantities have a value that's constant.

In this case, it's illustrated as y = 8x.

Let's say x = 1 y will be = (8 × 1) = 8

When x = 2, y = (8 × 2) = 16

In this case, it should be noted that the constant of 8 is illustrated.

In conclusion, the correct option is A.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Please help me important question in image

Step-by-step explanation:Please help me important question in image

Please help me important quePlease help me important question in image

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Please help me important question in image

Please help me important question in image

Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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To find the decimal form of 1/3, we just divide 1 by 3 in the following way:

We can continue but the residue will always be 1, therefore, the decimal form of 1/3 is 0.3333....

The trigonometric function that models the temperature T in the South Pole in March t hours after midnight is given as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

The lowest temperature is of -54ºC, while the highest is of -50ºC, with a difference of 4ºC, hence the amplitude is given as follows:

2a = 4

a = 2.

A function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -54 and -50, hence the vertical shift is given as follows:

d = -50.

The period is of 24 hours, hence:

2π/B = 24

24B = 2π

B = π/12.

The highest value of the cosine function should be assumed at t = 0, but it is assumed at t = 14(2 p.m.), hence the phase shift is given as follows:

c = 14.

Thus the function is defined as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

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It will take 5.189 hours to get doubled the size of Sample.

A relation of the form y = \(a^x\), with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

Growth rate = 5.8%

The continuous exponential growth model for populations is given by:

P(t)= \(P_0 e^{rt\)

So, r= 5.8%

r = 0.058

Now, the time taken to double the sample then P(t) = 2P(0).

So, P(t)= \(P_0 e^{0.058t\)

2P(0) = \(P_0 e^{0.058t\)

\(e^{0.058t\) = 2

Taking log on both side

log \(e^{0.058t\) = log 2

0.058 t = 0.301

t= 0.301/ 0.058

t = 5.189

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Answer: \(133\frac{9}{13}\) or \(\frac{1738}{13}\) or 133.7 (any three are correct)

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

Step 1: 5214 / 39 = 133 with a remainder of 27.

133 with a remainder of 27

Because 39 is what we will be dividing it by, it will be our denominator.

Step 2: Express as a mixed fraction.

\(133\frac{27}{39}\)

Step 3: Simplify by dividing the denominator/numerator by 3.

\(133\frac{9}{13}\) or \(\frac{1738}{13}\) or 133.7

~I hope I helped you! :)~

Answer:

14 square centimeters

Step-by-step explanation:

You gotta add the area of the first and second triangle.

First Triangle:

(1/2)x 4 x 4= 8cm

Second Triangle:

(1/2)x 4 x 3= 6cm

FINAL ANSWER: 6+8= 14cm

Answer:

Step-by-step explanation:

In this question, we need to use the formula of means to solve the. We can set the number of beads Rajiv brings as X, and use the formula of mean to get the total number of beads that the Four(4) children have and the total number of beads that the Five(5) children have.

Four(4) children each have some beads, the mean number of beads is: 8

        4 * 8 = 32

We set the number of beads Rajiv brings as:

x, so the total number of beads that the Five(5) children have is:

32  +  x

The mean number of the Five(5) children is now: 9

      5  *  9   =  45

     32 +  x    =    45

      x  +  32  =    45

           -  32  =   -32

       x            =     13

By solving the above equation, you can get:

x  =  13

       13

Hope this helps!

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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