What is the standard notation for the following expression?
4.62 × 10⁻³

The gravitational potential energy is 2940 Joules

The formula for gravitational potential energy is expressed as;

Gravitational Potential energy = m g h

Where;

Substitute the values into the formula;

⇒ 20 × 9. 8 × 15

Multiply through

⇒ 2940 Joules

Thus, the gravitational potential energy is 2940 Joules

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Answer:

2m+4 is the answer

Step-by-step explanation:

the answer to the given question is 11.3 cm

Side = 13 cm

Height of triangle = root3/2  * 13

= 11.25 cm

Therefore, the Height of the triangle is 11.3 cm

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On solving linear equation 1.05x=12.60, we get that Emma has 48 quarters.

Let x be any variable then ax + b = c  b is an linear equation in one variable.

where a, b, c are constants  then we get solution for x as

x=(b-c)/a

Given as Emma has 4 times as many as quarters as nickels

Let the no of nickels be x

Then as there are 4 times as many as quarters as nickels

then no quarters be = 4x

Value of one nickel = 5 cents= $0.05

Value of one quarter = 25 cents = $0.25

Therefore x nickels and 4x quarters worth is = x(.05)+4x(.25)

Total worth of given nickels and quarters = $12.60

Then 0.05x+x = 12.60

This is an linear equation in one variable

1.05x=12.60

x= 12.60/1.05

x=12

Therefore ,Emma has 12 nickels

and 4(12)= 48 quarters

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Answer:

1 is a function

2 and 3 is not

Step-by-step explanation:

the first one doesn't have anything repeating but 2 and 3 both do

Answer:

1. Yes, it's a function.

2. No, it's not a function.

3. No, it's not a function.

Step-by-step explanation:

A function is a relation in which each element of the domain (input) corresponds with exactly one element of the range (output).

Hope this helps.

Answer: 2 and 0/7

MATH

For the given data, x1 = (8 + 12)/2 = 10;

Mean = Sum of frequencies*components/Sum of frequencies = 590 / 30 = 19.6667

A histogram roughly depicts the distribution of numerical data. Karl Pearson is credited with coining the phrase. To create a histogram, you must first "bin" (or "bucket") the data range, divide it into a series of intervals, and then count how many values fall into each interval. The bins are often defined as discrete intervals that don't overlap. The bins (intervals) must be next to each other and are frequently (but not necessarily) of the same size.

When the bins are the same size, a rectangle is constructed across each bin, with the height being proportional to the frequency—that is, the number of cases in each bin.

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The approximation of the trigonometry ratio cot(5) is 11.43

The trigonometry ratio expression is given as

cot(5)

In trigonometry ratio, we have the following equation

cot(x) = 1/tan(x)

This means that x = 5

Substitute 15 for x in the equation cot(x) = 1/tan(x)

So, we have

cot(5) = 1/tan(5)

Using a calculator, we have:

cot(5) = 1/0.0875

Evaluate the quotient

So, we have

cot(5) = 11.4286

Approximate the above result

So, we have

cot(5) = 11.43

Hence, the approximation of the trigonometry ratio cot(5) is 11.43

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Answer:

x = 0

Step-by-step explanation:

Hello!

Solve for x by isolating the variable.

The value of x should be 0, as any number multiplied by 0 is 0.

According to the standard deviation rule, 99.7% of people have an IQ between 55 and 145.

The standard deviation rule which is the empirical rule in statistics tells us that for distributions that have the normal shape, approximately 99.7% of the observations will fall within 3 standard deviations of the mean.

Now, In this question the mean is 100, and the standard deviation is 15. Thus, we can say that approximately 99.7% of the observations (IQ scores) fall between 100 − (3 * 15) and 100 + (3 * 15) or between 55 and 145.

Now, approximately 100% − 99.7% = 0.3% of the observations fall outside this interval. Since the normal shape is symmetric, approximately 0.15% of the observations fall above 145.

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The Simplification of the expression 6(3x-17) + 2x -18 = 9(4x+7) -9 + 17 and value for the unknown x, is approximately 11.94

6(3x-17) + 2x -18 = 9(4x+7) -9 + 17

18x - 102 + 2x - 18 = 36x + 63 - 9 + 17

18x + 2x - 36x = 63 - 9 + 17 + 102 + 18

- 16x = 191

x = 191 / - 16

x = 11.9375

Approximately,

x = 11.94

Therefore, the Simplification of the expression 6(3x-17) + 2x -18 = 9(4x+7) -9 + 17 and value for the unknown x, is approximately 11.94

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Domain: {x-9 ≤x ≤9},  Range:{x-9 ≤x ≤9},  Intercepts points : (-9, 0), (0, -9), (0, 9), (9, 0) and Symmetry: x-axis and y-axis the correct answer would be option (C).

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

We have been given that the graph is that of a function.

To determine its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin

The domain of the given function would be {x-9 ≤x ≤9}

The range of the given function would be : (y-9 y ≤9)

The intercepts points of the given function would be : (-9, 0), (0, -9), (0, 9), (9, 0)

And the graph is symmetric about the x-axis and y-axis.

Hence, the correct answer would be option (C).

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Calculate the absolute value: 52

Substitute  into :: {a =2 ,b = -4} into Va³ 7+1b| =| [tex]2^{3}[/tex] 7 +1*-4|

Determine the sign for exponential or radical expressions:  |[tex]2^{3}[/tex] 7 +1*-4|

Calculate the power: |56-4|

Calculate the sum or difference: |52|

Calculate the absolute value: 52

In mathematics, the absolute value or modulus of a real number {x}x, denoted { |x|}|x|, is the non-negative value of { x}x without regard to its sign. Namely, { |x|=x}{ |x|=x} if x is a positive number, and {|x|=-x}{ |x|=-x} if { x}x is negative (in which case negating { x}x makes { -x}-x positive), and { |0|=0}{ |0|=0}.The absolute value of a number may be thought of as its distance from zero.

For example, an absolute value is also defined for the complex numbers, the  ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical  that is divisible by both 5 and 2, it is the least common multiple of 5 and 2.

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Answer:

3

Step-by-step explanation:

27 tickets = 9 prizes

Since they are all equal, it would be 27 divided by 9 = 3

Answer:

The standard form is: (x−h)2+(y−k)2=r2where (h,k) is the center and r is the radius.Your center is at (0,0) and the radius, r=3(x−0)2+(y−0)2=32

Step-by-step explanation:

The standard deviation is approximately 1.825

The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. A low standard deviation means that the values tend to be near to the established mean, whereas a large standard deviation shows that the values are distributed throughout a broader range.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is equal to the square root of that variable's variance. It is more algebraically straightforward than the average absolute deviation, but being less reliable in actual use.

The standard deviation is calculated by the formula :

[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]

where N= n-1(n=size of sample) , [tex]\mu[/tex]= mean of the data , [tex]x_i[/tex]= each data value.

Now the given data for the question are {6,5,9,8}

mean of the data ([tex]\mu[/tex])=(6+5+9+8)÷4=28÷4=7

Standard deviation:

[tex]{\displaystyle \sigma ={\sqrt{{\frac {(6-7 )^{2}+(5-7 )^{2}+(9-7 )^{2}+(8-7 )^{2}}{N}}}}[/tex]

[tex]{\displaystyle \sigma ={\sqrt{{\frac {(-1 )^{2}+(-2)^{2}+(2)^{2}+(1 )^{2}}{N}}}}\\[/tex]

[tex]{\displaystyle \sigma =\sqrt{\frac{1+4+4+1}{4-1}}\\[/tex]

[tex]{\displaystyle \sigma =\sqrt{\frac{10}{3}}\\[/tex]

[tex]{\displaystyle \sigma =\sqrt{1.333}[/tex]

[tex]{\displaystyle \sigma =1.825[/tex]

The standard deviation is approximately 1.825.

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Answer:

Yes, the ratios are equivalent.

Step-by-step explanation:

The equation 8 * 0 is similar to 0 * 3, the correct option is the first.

In mathematics, zero has unique properties, one of the properties is seen in multiplication. The unique property of zero in multiplication is that, zero has the power to return itself to any number that multiplies it, or when zero multiplies the number. The order does not matter.

For instance, as used in the equation 8 multiplying zero will return zero as the solution. Bearing in mind this unique feature zero multiplying any number gives zero too hence 0 * 3 = 0.

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The difference between a tax rebate and a discount is For a rebate the tax, the tax is calculated on the full price, and the customer receives the rebate later. For a discount, the tax is calculated on the reduced price after the discount is applied.

A tax rebate is also known as a tax refund and the purpose of it is to pay back a tax payer when they paid more taxes than they were meant to pay. It is therefore calculated on the full amount of tax.

This is different from a tax discount which works by using the discount to reduce the amount of tax owed and then you can pay off the discounted amount as tax.

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the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3) are (1/2, 1, 3/2).

Equidistant is a synonym for "equally distant," which is the state of two points being at the same distance from one another. Equidistant implies at the same distance from a location. The term "equidistant" is commonly used in reference to circles, perpendicular bisectors, parallel lines, and other geometrical concepts .Equidistant refers to the relationship between two or more objects or points that are situated at the same distance from one another. A point is considered to be equidistant from two other points when they are both located at the same distance from it. In the middle of the two starting points is a midway. The distance formula or the halfway formula can be used to demonstrate this.

Equation of sphere passes through origin is given by

x2 + y2 + z2 + ax + by+ cz =0

Given, it also passes through (1,0,0), (0,2,0),(0,0,3)

1+ a = 0,                                a = -1

4+2b =0,                             b=-2

And, 9+3c = 0,                       c= -3

The equation of the sphere becomes x2 +y2+ z2 -x -2y -3z = 0

Comparing with x2 +y2+ z2+ 2gx +2fy +2kz +C =0

Therefore the point that is equidistant from all the given points will be the centre of the sphere passing through all these points.

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Answer:

132p

Step-by-step explanation:

if 7 pens cost 84 total then you need to find the cost of each to know how much 11 pens would cost in total

84/7=12

now you know it's 12 each so just multiply 12 by 11 and you know how much for 11 total!

12*11=132p

Answer:

132 is correct

Step-by-step explanation:

84÷7=12

12×11= 132

1) El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

1) En este problema tenemos el caso de un vehículo que se desplaza a rapidez constante. Aquí tenemos que la rapidez (v), en kilómetros por hora, es inversamente proporcional al tiempo invertido (t), en minutos.

[(40 km /h) / (50 km / h)] = t / 20 min

4 / 5 = t / 20

t = 80 / 5

t = 14 min

El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) El porcentaje correspondiente a la rapidez reportada se calcula mediante porcentajes:

r = [(50 km / h) / (90 km / h)] × 100 %

r = 55.556 %

La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

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The length and width of the rectangle are: 42 feet and 11 feet.

Rectangle refers to a plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Given:

To find: the length and width of the rectangular field.

Finding:

Let the width of the rectangular field be 'x'

Then the length of the field = 4x - 2

Perimeter of rectangle = 2 (width + length)

=> 106 = 2 ( x + 4x -2)

=> 53 = 5x - 2

=> 55 = 5x

=> 11 = x, i.e., the width of the field = 11 feet

The length of the field = 11(4) - 2 = 42 feet.

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