The hertz (Hz) is a unit of frequency that represents the number of complete cycles per second. It is used to measure repeating events, both scientific and general. For instance, a clock ticks at 1 Hz. One scientific application is the electromagnetic spectrum, or the range of all possible frequencies of electromagnetic waves. The spectrum includes frequencies from everyday contexts, such as radio and TV signals, microwaves, light (infrared, visible, and ultraviolet), and X-raysThe hertz (Hz) is a unit of frequency that represents.
For each question, use powers to write a mathematical expression. Then evaluate each expression.
Express your answer as a power.
a. How many hertz are in 1 gigahertz? 1 terahertz?
b. A television channel has a frequency of 60 megahertz. What is the channel’s frequency in hertz?
c. The frequency of a microwave is 30 gigahertz. What is the microwave’s frequency in hertz?
d. The frequency of a visible ray of light is 1000 terahertz. A radio station has a frequency of
100 megahertz. How many times greater is the frequency of the light than the frequency of the
radio station?

The description of the route of the limousine is

First, the limousine drives 18 blocks right and 8 blocks down and then it drives 17 blocks left and 2 blocks up

From the question, we have the following parameters that can be used in our computation:

T<18, -8> o T<-17, 2>

The above parameters represent the transformation and the positions of the limousine

The above statement represents the direction in words

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Complete the pyramid with the corresponding values

Since each number is the product of the two numbers directly below it. Then the pyramid can be completed as follows:

Check the attached image for labeling.

j = -1 × -1 = 1

h = -2 × j = -2 × 1 = -2

y = h × -1 = -2 × -1 = 2

j × n = -1

1 × n = -1

n = -1

n × m = 2

-1 × m = 2

m = -2

w = -1 × 2 = -2

t = y × w = 2 × -2 = -4

-1 × k = n

-1 × k = -1

k = 1

k × l = m

1 × l = -2

l = -2

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The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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x = 1

Answer:

-----------

3x + 1 = 4x

4x = 3x + 1

4x - 3x = + 1

x = 1

The total 7 two-player games and 6 six-player games were played.  

Here the total games = 13

And the total number of athletes participated = 50

Let us assume that x represents the total 2-player games played and y represents the total 6-player games played.

The neighborhood holds 13 total games.

So, we get an equation,

x + y = 13                    ................(1)

There are 50 athletes signed up for a neighborhood basketball competition.

So, we get an equation,

2x + 6y = 50                 .............(2)

From equation (1)

x = 13 - y                   ..........(3)

substitute above value of x in equation (2)

2(13 - y) + 6y = 50

26 - 2y + 6y = 50

4y = 24

y = 6

Substitute above value of y in equation (3)

x = 13 - 6

x = 7      

Thus, we can conclude that the total 7 two-player games and 6 six-player games were played.  

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Yes, Chris has enough money to buy 30 folders and 30 pens.

The cost of the stationaries Chris bought are as follows:

Chris wants to buy 30 pens and 30 folders and he has only £60.

Let's check If he has has enough money to buy the products.

Therefore,

3 pens cost £2.25

1 pen  = ?

cost of 1 pen = 2.25 / 3 = 0.75 dollars

5 folders cost £5.80

1 folder = ?

cost of 1 folder = 5.80 / 5 = 1.16 dollars

Hence,

30(0.75) + 30(1.16) = 22.5 + 34.8 = 57.3 dollars

Therefore, he has enough money to buy 30 folders and 30 pens

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Answer:15 nickels per minute (I believe)

Step-by-step explanation:

First, we want to know how much she got paid in total dollar amount, we'll break it up into nickels later. We know Jackie was paid $45 per hour, but we want to figure out how much per minute she makes. There are 60 minutes in an hour, so divide 45 by 60 ( 45/60 in a calculator).

The answer for 45/60 would then be 0.75. This means Jackie gets paid 75 cents a minute. Since a nickel is worth 5 cents, we just need to divide 75 by 5. Then, we get 15.

Now we know Jackie gets paid 15 nickels per minute. I assume this would be put in aspect ratio form by saying "Jackie gets paid 15 nickels per every one minute of work." but that may depend on how your teacher wants you to word your answer. I hope this helps :)

Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of a wave with a frequency of 4.11×10⁴ Hz is 7299.27 m.

Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).

Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).

The propagation speed is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.

The propagation speed relate the wavelength (λ) and the frequency (f) using the following equation:

v = f×λ

In this case, you know:

v= 3×10⁸ m/s

f= 4.11×10⁴ Hz

λ= ?

Replacing:

3×10⁸ m/s= 4.11×10⁴ Hz× λ

Solving:

λ= 3×10⁸ m/s ÷ 4.11×10⁴ Hz

λ=7299.27 m

In summary, the wavelength of the wave is 7299.27 m.

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This polynomial represents the area of the platform.A = w(w + 2)^2. the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width

A = w(w + 2)^2

A = Area of the platform

w = width of the platform

Since the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width, we can represent this statement mathematically as:

A = w(w + 2)^2

This polynomial represents the area of the platform.

A = w(w + 2)^2

A = w^2 + 2w^2

A = 3w^2

A = 56

3w^2 = 56

w^2 = 56/3

w = √56/3

A = w(w + 2)^2, area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width.

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If the force is changed to 50N, the acceleration of the object becomes 10m/s²

From the information given, we have that force is directly varies as the acceleration.

Given that;

This is represented as;

F ∝ a

Then, the constant is

F= ka

Now, make 'k' the subject of the formula, we get;

k = F/a

substitute the values to determine the value of k

k = 40/8 = 5

If the value of the force, F of the object changes to 50N, then the acceleration is given as;

a = F/k

Substitute the values into the formula

a = 50/5

Divide the values

a = 10m/s²

Hence, the value is a = 10m/s²

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The probability that Andre, Olivia, and Zach all win gift cards that are at least $25 is 0.

Since the value of the gift cards is determined by chance, it is impossible to calculate the probability of this exact outcome. Instead, we can calculate the probability of any one person winning a gift card that is at least $25, which is 0.5.

The probability of them all winning would be the product of the individual probabilities, which is 0.5 x 0.5 x 0.5 = 0.125. However, since this is impossible, the probability of this exact outcome is 0.

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(x - h)^2 + (y - k)^2 = r^2 is the equation for a circle with center (h, k) and radius (r).

What exactly is a math equation?

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."

So, an equation that represents a circle with center (5, -1) and radius of 16 units is:

(x - 5)^2 + (y + 1)^2 = 16^2

or

(x - 5)^2 + (y + 1)^2 = 256

The graph of this equation will be a circle centered at the point (5,-1) with a radius of 16 units.

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W = 6 is a solution to the inequality.

In mathematics, Inequality is an unequal comparison between two or more algebraic terms or expressions. The solution of an inequality is a numerical value that will satisfy the given expression.

The signs that we use in Inequality expression are  

'>' - greater than

'<' - less than

'≥' - greater than or equal to

'≤' - less than or equal to

Here we have

Inequality 8 > W

Where the symbol '>' less than indicates 8 is greater than W

or the value of W is less than 8  

As we can see that 6 < 8

Therefore,

W = 6 is a solution to the inequality.

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The acute angle formed by the hands of a clock at 4:20a.m is 10°.

For the minute hand, we can compute that, for its every move, it covers 6 degrees. And for the hour hand, each move covers 30 degrees.

A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees.

The angle between the hour's hand and the minute hand when the clock shows 4:20 pm can be calculated by using the formula:

Angle=|11/2 M-30H|

where M= minute H= hour's

Here M=20 H=4

Therefore we get the angle |11/2(20)- 30*4|=|110-120|=|-10°|=10°

Hence, 10° is the correct answer.

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The approach used to solve equations with integer coefficients & constants can also be used to solve equations with fractional / decimal coefficients and constants.

An equation is a mathematical statement that expresses the equality of two expressions. It is a relationship between two or more variables, such as x + y = z. Equations are used to solve a wide variety of problems in mathematics, physics, chemistry, engineering and other scientific fields.

The main difference is that when solving equations with fractional or decimal coefficients and constants. For example, if you have an equation with a decimal coefficient, divide both sides by the coefficient to make the coefficient 1 before you can use the same steps to solve the equation.

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Answer:

Hi, my name is Za'Riah! I will gladly help you with your problem. (see explanation)

Step-by-step explanation:

There really isn't much to explain or step out with this problem.

60% of 150 is 90

150 + 90 = 240 inches

The truck is 240 inches long.

Answer:

240

We will add 2 ml of klotrix to the orange juice for a 20.5kg patient.

We know that , 1 kg=2.20462 pounds

Therefore, 20.5kg=20.5x2.20462 pounds= 45.195 pounds or 45.195 lb

Additionally we have, 1 lb = 0.35 mEq

Therefore, 45.195 lb=  0.35 mEq × 45.195 = 15.818 mEq.

Also, 8mEq=1 mL

By using unitary method,

1 mEq=1/8 mL

Converting 15.818 mEq to mL, we get

15.818mEq = 15.818 ÷ 8 = 1.9 mL

Thus, 15.818mEq  = 1.9 mL

Rounding off the answer we get,

The amount of klotrix required to add to the orange juice for a 20.5 kg patient is 2mL

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The equation of the line, given the ordered pair and the y - intercept, is y = -2 x + 2

The slope ( m ) is - 2

The equation for a linear model takes the form :

y = mx + b

m =  slope

b = y - intercept

As we have the ordered pair, and the y - intercept, we can find the slope:

y = mx + b

- 4 = 3 x slope + 2

3 x slope = - 4 - 2

Slope = - 6 / 3

Slope = - 2

The equation is therefore:

y = -2 x + 2

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The class midpoint of the first class in the case of table of quantitative data is 0-4 and the second class is 5-9 is 2.5

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When the line of slope of 3 passes through two points, the value of y is -8.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

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

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of y is -8 when the line of slope of 3 is passing through 2 points as given.

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Answer:x<1

Step-by-step explanation:

move constant -5x>-2-3

Add alike numbers (-2 and -3)

-5x>-5

Divide both sides by -5

Then flip the inequality sign

x<1

Answer:

Step-by-step explanation:

Add 3 to the -2

-5x > 1

Divide by -5 the sign switches because of the negative

x < - 1/5 or X < -0.2

An equation in point slope form for the line that passes through (-4, 3) and whose slope is 3 is equal to y - 3 = 3(x + 4).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-4, 3) and has a slope of 3 by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 3(x - (-4))

y - 3 = 3(x + 4)

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Answer: The dependent variable is the time it takes to come to a complete stop. The independent variable is the speed at which you drive your car.

The dependent variable is the amount of food there will be. The independent variable is the number of students who attend the fiesta lunch.

Step-by-step explanation:

The eigenvectors of AAH are called the left-singular vectors of A and the eigenvectors of AHA are the right-singular vectors of A . They are called this way because of their use in singular value decomposition. Say A=UΣVH , then the columns of U are the left-singular vectors and the columns of V are right-singular vectors.

We know that the non-zero eigenvalues of AAH  and AHA are the same, they are the squares of the singular values of A . A singular of value of A is a value σ such that Av=σu   AHu=σv where u is a left-singular vector and vs a right-singular vector. This can be taken as the definition of singular value, left-singular vector (which is an eigenvector of AAH) and right-singular vector (which is an eigenvector of AHA).the left-singular and right-singular vector pair works with AAH and AHA

AAHu=σAv=σ2u

AHAv=σAHu=σ2v

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Q: What is the relationship between the eigenvectors of AAT and ATA?

The ratios 6:16 and 21:56, 9/11 = 27/15, and y=5x do not form a true proportion. Hence, options A, C, and, D are the correct options.

A true proportion is when both the ratios presented are equal. This can be verified by putting them in their respective fractional form. For example, let's take the ratios in the second option -

= 2/10 and 15/75

Here, we can see that 2*5 = 10 and 15*5 = 75

Hence these can be written as

= 2/2*5 and 15/15*5

Hence, these fractions are the same and as a result, the ratios form a true proportion.

As for the other ratios in question -

A) 6/16 is not equal to 21/56

C) 9/11 is not equal to 27/15

D) y= 5x are not proper ratios and are not equal

Thus, options A, C, and, D are the correct options.

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The multiplication of the numbers given to the reduced form is 10/7.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

The given expression is 5 × 2/7

One of the number is a whole number and the other is a fraction.

We can write 5 as 5/1 in terms of fraction and then multiply the numerators and the denominator.

(5/1) × (2/7) = (5×2) / (1 × 7) = 10/7, which is in the lowest form.

Hence the solution of the multiplication is 10/7.

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The SAS congruency is applied here.

Hence,

[tex] \frac{TR}{JK} = \frac{RS}{JL} = \frac{TS}{KL} \\ \frac{24}{x} = \frac{12}{6} = \frac{y}{15} \\ \frac{24}{x} = 2 \\ x = 48 = JK[/tex]

[tex] \frac{y}{15} = 2 \\ y = 30[/tex]

Perimeter =

[tex]6 + 30 + 48 \\ 36 + 48 \\ = 84[/tex]