Use the values of a₁ and Sn to find the value of a n a₁=4 and S₄₀=6080 ; a₄₀

Einstein's mass energy relation, and the formula for finding the percentage error gives;

7) a) 9.0 × 10¹⁶ Joules

b) The bulb could be powered for approximately 47533146.96 years

8) 16.46%

9) The possible values are;

61.093 Joules and 96.77 Joules

Percentage error is the ratio of the difference between estimated value and the actual value to the actual value expressed as a percentage.

7) a) The Einstein mass energy relation is presented as follows;

E = m•c²

The speed of light, c = 3×10⁸ m/s

The mass, m = 1 kg, gives;

E = 1 kg × (3×10⁸ m/s)² = 9.0 × 10¹⁶ Joules

b) Energy consumption of the light bulb = 60 J/sec

The duration, t, the light bulb will remain lit is therefore;

8) Percentage error, %error, is found as follows;

%error = ((Approximate value - Actual value)/(Actual value)) × 100

Appreciate value = 46,620 km

Actual value = 40,030.2 km

Which gives;

%error = ((46,620 - 40,030.2)/(40,030.2))×100 ≈ 16.46%

9) The calculated value of the kinetic energy = 74.9 J

The observed error in the calculation = 22.6%

Required; The two possibilities for the correct kinetic energy

Solution;

E% = ((Approximate value - Actual value)/(Actual value)) × 100

Taking the calculated value as the approximate value, and the correct value as the actual value, we have;

22.6% = ((74.9 - Actual value)/(Actual value)) × 100

(22.6/100)×Actual value = 74.9 - Actual value

Actual value + 0.226×Actual value = 74.9

1.226 × Actual value = 74.9

Which gives;

The actual value can also be given as follows;

22.6% = ((Actual value - 74.9)/(Actual value)) × 100

Actual value - 0.226×Actual value = ,74.9

Actual value = 74.9 J/(1-0.226) ≈ 96.77 J

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The term "total moles of a solute contained in a kilogram of a solvent" exists utilized to define molality. The amount of water required exists 252ml.

Given: Mass of urea = 25 g

Required Molality = 1.65m

Density of water = 1000 kg/m³

Formula for urea = CH₄N₂O

Mass of Carbon atom = 12 u

Mass of Oxygen atom = 16 u

Mass of Nitrogen atom = 14 u

Mass of Hydrogen atom = 1 u

Molecular Mass of Urea

= (1)12 + (4)1 + (2)14 + 16

= 12 + 4 + 28 + 16

= 60 u

Molar mass = 60 g

No of moles = Given mass/Molar mass

No of moles = 25/60 = 5/12

Molality = Mass of solute / Mass of solvent(g)

Let the weight of water be x kg

1.65 = (5/12)/x

simplifying the above equation, we get

1.65 x = (5/12)

x = (5/12) / 1.65

x = 5 / 1.98

x = 0.2525

Mass of water = 0.252 kg.

Volume of water = 0.252 ÷ 1000 kg/m³

= 0.000252 m³

= 0.252 liters

= 252 ml

Therefore, the require amount of water is 252 ml.

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The given statement exists true that "The orthocenter of a right triangle is always found at the right angle's vertex".

The orthocenter is the point at which the triangle's three altitudes cut or intersect. The altitude is the line drawn from the triangle's vertex that is perpendicular to the opposite side. There are three altitudes because the triangle has three vertices and three sides.

The given statement exists true that "The orthocenter of a right triangle is always located at the vertex of the right angle".

The altitudes from the two non-right vertices (A and B) will always be the legs of the triangle, which intersect at the vertex containing the right angle, as shown in the right triangle below (C). Because the altitude to the triangle's hypotenuse originates at the vertex, the three altitudes (the red rays) intersect there. As a result, the vertex of a right triangle is always the orthocenter.

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It should be noted that the place the square root of 75 minus 13 would be plotted on a number line is C. Between −4 and −5, but closer to −4.

It should be noted that a square root simply means the numbers that can be multiplied by itself that will give the original number.

It should be noted that the square root of 75 is 8.66. Therefore, square root of 75 minus 13 would be:

= ✓75 - 13

= 8.66 - 13

= -4.3397

Therefore, it should be noted that the place the square root of 75 minus 13 would be plotted on a number line is vetween −4 and −5, but closer to −4

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Answer:

inequality form would be x<-6 or x>-6

21x⁵-3x³+3x²+4 will be the solution for x for the given equation 17x⁵+3x²+2-(-4x⁵+3x³-2) so option (D) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear b. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given the equation,

17x⁵+3x²+2-(-4x⁵+3x³-2)

⇒ 17x⁵+3x²+2 + 4x⁵- 3x³+ 2

⇒ 17x⁵ + 4x⁵ - 3x³ + 3x² + 4

Hence "21x⁵-3x³+3x²+4 will be the solution for x for the given equation 17x⁵+3x²+2-(-4x⁵+3x³-2)".

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The function that models the horizontal shink of f(x) by a scale factor k = 3 is:

g(x) = |3*x| + 5

Here we want to apply a transformation to a given function where the transformation is a shrink.

For a function f(x), a horizontal shrink (or compression) of scale factor K is written as:

g(x) = f(k*x)

In this case we have the absolute value function:

f(x)= |x| + 5

And we want to apply an horizontal shrink of scale factor k = 3, so we will have a new function defined as:

g(x) = f(3*x)

If we replace f(x) by the function above we will get:

g(x) = f(3*x) = |3*x| + 5

So we conclude that the transformed function is just:

g(x) = |3*x| + 5

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A four seat Cessna airplane does an average of 5.84 miles per gallon of fuel traveling from Olympia to Hoquiam

Given that a four seat Cessna airplane uses an average of 11 gallons of avgas per hour, and it traveled from Olympia to Hoquiam for 28minutes, then we can solve for the amount of fuel it consumed for that flight.

amount of fuel = average consumption x time

amount of fuel = 11 gallons of avgas per hour x 28 minutes

amount of fuel = 11 gallons of avgas per hour x (28/60)h

amount of fuel = 77/15 gallons

If the flight from Olympia to Hoquiam is 30 miles and the amount of fuel used by the Cessna airplane is 77/15 gallons, then

average number of miles per gallon of fuel = distance traveled / amount of fuel consumed

average number of miles per gallon of fuel = 30 miles / (77/15 gallons)

average number of miles per gallon of fuel = 450/77

average number of miles per gallon of fuel = 5.84 miles / gallon of fuel

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Answer:

64 - 2g

Step-by-step explanation:

64 decreased by twice Greg's saving (given)

↓               ↓            ↓        ↓

64              -              2        g  (final equation)

64 - 2g

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

2(3-8y)=

6-16y

Step-by-step explanation:

The expression that is equivalent to 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 is D. 9^8

It should be noted that this is a question relating to indices.

It should be noted that we have to count the number of 9s that we gave in this case.

Therefore, 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 will be equivalent to 9^8.

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Which expression is equivalent to 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9? A. 9 B. 9 C. 99,999,999 D. 9^8

Answer:

C

Step-by-step explanation:

there are 8 of 9s so it is 99,999,999 tricky question!

The weight of Christensen's family's kitten is 9 pounds 3 ounces.

The imperial unit of mass or weight measurement is the pound. The symbols for pounds are lb and lbm. A kilogram weighs 0.4535 pounds. The term "pound" has Germanic roots.

In the conventional system of measurement, a pound is a unit of weight. 16 ounces make up one pound.

Therefore,

We know that 1 pound = 16 ounces

16 ounces = 1 pound

Dividing each side by 16.

( 16 / 16) ounces = ( 1/16 ) pound

1 ounce = ( 1/16 ) pound

Multiplying each side by 147,

1 ounce × 147 = ( 1/16 ) × 147 pound

147 ounces = ( 147 / 16 ) pounds

147 ounces = 9.1875 pounds

147 ounces = 9 + 0.1875 pounds

147 ounces = 9 pounds 3 ounces

The weight of the kitten is 9 pounds 3 ounces.

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Answer:

This is a survey

Step-by-step explanation:

The equivalent expression for the given expression is 4² or 16.

The given expression is [tex]\frac{-4^{4} }{-4^{2}}[/tex].

We need to write the equivalent expression for the given expression.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Now, [tex]\frac{-4^{4} }{-4^{2}}[/tex] can be simplified as follows:

=[tex]4^{4} \times4^{-2} =4^{4-2}[/tex]   (∵[tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex])

=4²=16

Therefore, the equivalent expression for the given expression is 4² or 16.

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Taking into account the definition of a system of linear equations, she sold 102 student tickets.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

Knowing that:

the system of equations to be solved is

[tex]\left \{ {{A+S=145} \atop {5A+3S=521}} \right.[/tex]

Of the multiple methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable A from the first equation:

A= 145 - S

Replacing this expression in the second equation:

5(145 - S) + 3S= 521

5×145 - 5S + 3S= 521

725 - 5S + 3S= 521

-5S + 3S= 521 - 725

-2S= -204

S= (-204)÷(-2)

S= 102

Finally, she sold 102 student tickets.

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Answer:

[tex] - 1 \geqslant x \geqslant 2[/tex]

Absolute value equality entered:

|x-3|+2 = 7

Another term is moved/added to the right-hand side.

|x-3| = 7 - 2

|x-3| = 5

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |x-3|

For the Negative case, we'll use -(x-3)

For the Positive case, we'll use (x-3)

-(x-3) = 5

Multiply

-x+3 = 5

Rearrange and add up

-x = 2

Multiply both sides by (-1)

x = -2

Which is the solution for the Negative Case

(x-3) = 5

Rearrange and add up

x = 8

Which is the solution for the Positive Case

x=-2

x=8

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Answer:

Section formula for external division:

[tex]P(x,y)=(\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]

By drawing two comparable right triangles, the evidence for this result is similar to the proof for internal divisions.

If we know the ratio of the internal distances of any two points from the provided location, we may use the section formula to obtain the coordinates of that point.

If we were to determine the coordinates of the point P, we might use the formula below by knowing the coordinates of the points A and B and the ratio of their distances to the provided point P. (section formula).

Since all other values must be provided, any formula with two or more variables can be used to determine the value of any variable. Therefore, the formula also include the other quantities.

Another well-known coordinate geometry formula exists and is a specific instance of the section formula.

If a point is equally spaced from the provided points, the mid-point formula may be used to get its coordinates. (where the ratio of m to n is 1:1)

Thanks,

Eddie

The equation that can be written to represent this situation is 15 + 25h = 115.

Let the number of hours be represented by h.

The equation will be:

(3 × 5) + (25 × h) = 115

15+ 25h = 115

It should be noted that 15 represents the cost of jackets

Therefore, the equation that can be written to represent this situation is 15 + 25h = 115.

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Alejandro stated -4/3 instead of -3/4 as the slope of the perpendicular line in step 2, therefore, his first error is in step 2.

For any two given perpendicular lines, they must have slope (m) values that are negative reciprocals of each other. The equation of any line can be written in slope-intercept form as, y = mx + b, where m is the slope of the line.

Given the equation, 4x - 3y = -8, rewrite in slope-intercept form:

-3y = -4x - 8

-3y/-3 = -4x/-3 - 8/-3

y = 4/3x + 8/3

This means that the line has a slope of 4/3. Thus, the slope of the line that is perpendicular to the given line would be the negative reciprocal of 4/3, which is: -3/4.

Thus, we can see that Alejandro stated -4/3 instead of -3/4 as the slope of the perpendicular line in step 2, therefore, his first error is in step 2.

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Answer:

10

Step-by-step explanation:

5 outside the star 5 inside the star

The geometric mean of two positive numbers can be determined by multiplying the numbers and taking their square root.

Geometric mean is the mean or average value which expresses the central tendency of the set of numbers by taking root of the product of their values. In other words, we multiply the n values and take the nth root of the numbers. Geometric mean can also be expressed as the nth root of the product of n numbers.

The formula for finding geometric mean is:

GM = n√ x1*x2*x3…xn

Let the two terms be 2 and 8. Hence, x1=2, x2=8 and n=2.

GM = √2*8=√16=4

Hence, the geometric mean of the two chosen positive number 2 and 8 is 4.

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6 of 20 cents there if they add up to a total of 13.2 euros.

The area of mathematics known as discrete mathematics deals with objects that can only take into account individual, unique values. The basic ideas of Sets, Relations, and Functions, Mathematical Logic, Group Theory, Counting Theory, Probability, Mathematical Induction, and Recurrence Relations, as well as Graph Theory, Trees, and Boolean Algebra are covered in this course.

X=coins t 1 euro

18-x coins 20 cents

X+0,20*(18-x)= 13,2

X+3,6- 0,20x= 13,2

0,8x=96

X=9,6/0,8= 12 coins  1-euro

18-12=6 coins 20 cents

Hence, 6 of the 20 cents here add up to a total of 13.2 euros.

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Hector outperformed the challenge rate as he exercised 2.88 hours a week.

It is best to convert the mixed fraction to decimals for easier calculation.

The students are encouraged to exercise 2¹/₂ hours per week. In decimals this is:

= 2 + ¹/₂

= 2 + 0.5

= 2.5 hours per week

In the 4 week period, Hector exercised 11¹/₂ hours which is:

= 11 + ¹/₂

= 11 + 0.5

= 11.5 hours

The number of hours he exercised per week is:

= Number of hours in total / Number of weeks

= 11.5 / 4

= 2.88 hours per week

When compared to the fitness challenge rate, we can conclude that Hector outperformed the challenge rate

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Answer:

v= cube root of 12 or 2. 2894 or 2.3

Step-by-step explanation:

cube root of v³ = v

cube root of 12 = ³√12

Answer:

Step-by-step explanation:

The equation best represents the population, y, of Midtown .x years after 1990 is x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)    

Based on the given conditions, stated: x *(1+2%) (199-1990) = 2050

Calculate the sum or difference: x*1.02-1791 = 2050

Divide both sides of the equation by the coefficient of variable: Inferentially, when you divide, you assume that the number you are dividing by is not equal to zero. By dividing, you rule out the chance that the given number is zero, which may result in the elimination of the right answers. x = 2050 / 1.02-1791    

Simplify using negative exponent rule: For every number “a” with negative exponents “-n”, take the reciprocal of the base number and multiply the value according to the value of the exponent number.  For every number “a” in the denominator with negative exponent “-n” (i.e.,) 1/a-n, the result can be written in the form of a × a ×.. n times.

a-n = 1/an : x= 2050*1.021791

Convert decimal to fraction: x = 2050* (102/100)1791

Cross out the common factor: x = 2050 * (51/50)1791

Simplify using exponent rule with same exponent: (ab) n = an. bn  

x= 2050 * 511791 / 501791

Write a single fraction: x= 2050 * 511791 /501791

Hence, the equation represents the population is,  x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)  

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