I need help. In MATH, (not science) i have an equation. The equation is E=mc^2 , solve for c. i am lost

The number of dots will be in each pattern in 4th step:

1. In pattern A: 16 dost

2. In pattern B: 18 dots

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

two patterns,

Pattern A:

number of dots,

step 0:  0

step 1: 4

step 2:  8

step 3:  12

So here it can be seen that,

4 dots are more in each step in compare with previous step,

So generalized expression can be written as:

Number of dots in nth step =  0 + 4n

In 4th step, there will be- 16 dots

Similarly, in Pattern B:

Number of dots in nth step = 2 + n²

In 4th step, there will be- 18 dots

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Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

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Answer:

The calf raiser uses 960 oz of milk replacer for 15 calves, so each calf gets 960 oz / 15 = 64 oz of milk replacer.

To convert this to quarts, we need to divide by 32 (since there are 32 oz in a quart)

64 oz / 32 oz/quart = 2 quarts

Each calf gets 2 quarts of milk replacer and the calf raiser needs to add 34 as much water as milk replacer

So the total amount of water she needs is 2*34 = 68 quarts

To convert the quarts of water to ounces we need to multiply by 32 (since there are 32 oz in a quart)

68 quarts * 32 oz/quart = 2176 oz of water.

So the calf raiser needs 2176 ounces of water to mix with the milk replacer for 15 calves.

Answer:

Step-by-step explanation:

Volume of cylinder:

Given:

Find the volume:

Answer:

KJslDKSLADJKLJALKJDLKDLKAsdmjklLkLKLKSLKSLKSKLSJSSJLKJLAJDJLDKJDLSJDLSAJALDLKASJLAS

Step-by-step explanation:

The line parallel to the x-axis passing through the points (5,5) and (-5,5) has a slope of 0, indicating a horizontal line with a constant y-coordinate value of 5.

To determine the slope of the line that represents this relationship, we can use the formula for slope, which is given by:

slope = (change in y-coordinates) / (change in x-coordinates)

In this case, we are given two points on the line: (5,5) and (-5,5).

The change in y-coordinates is 5 - 5 = 0, as the y-coordinate remains constant.

The change in x-coordinates is -5 - 5 = -10.

Substituting these values into the slope formula, we get:

slope = 0 / -10 = 0

Therefore, the slope of the line that represents this relationship is 0.

A slope of 0 indicates that the line is parallel to the x-axis. This means that the line has a constant y-coordinate value for all x-coordinate values. In this case, the line passes through the point (5,5) and (-5,5), and it remains at y = 5 for all x-values.

Visually, a line with a slope of 0 would be a horizontal line on the coordinate plane. It does not have an upward or downward slope but remains parallel to the x-axis.

It's important to note that the slope of 0 indicates a relationship where the dependent variable (y) does not change with respect to the independent variable (x). In this case, no matter the value of x, the corresponding y-value remains constant at 5.

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The fraction in its lowest terms for 7 1/2 percent is 3/40.

To express the mixed number 7 1/2 percent as a fraction in its lowest terms, we need to convert it to a fraction and simplify.

First, we convert the mixed number to an improper fraction:

7 1/2 percent = 7 1/2 / 100

To simplify this fraction, we find the least common multiple (LCM) of the denominator (2) and the percent denominator (100), which is 200.

Now, we can rewrite the fraction with the common denominator:

7 1/2 / 100 = (7 * 2 + 1) / 200 = 15/200

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 200 is 5.

15/200 = (15 ÷ 5) / (200 ÷ 5) = 3/40

Therefore, the fraction in its lowest terms for 7 1/2 percent is 3/40.

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F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Answer: 54

Step-by-step explanation: coz I juss know

Answer: d.12

Step-by-step explanation:

Nearest whole number will be 782318.

Nearest ones whole number is the first digit before the decimal point of a number.

For example nearest ones of 9.6 is equal to 10.

If the tenth digit (first number before decimal point) of the number is greater than or equal to 5 we round up and add 1 to ones of number, If the tenth digit of the number is less than 5 we remove the decimal part. Example:

124.6

The first number of right of decimal point is 6

6 is greater than 5, so we add 1.

Result = 125

Now given number is 782317.772

since the  first digit after decimal is 7 which is greater than 5 thus the nearest whole number will be 782318.

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Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 represents the correct relationship.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The proportional relationship for 6 cups of grape juice for every three-fourths cup of rainbow sherbet.

So, the ratio of grape to rainbow sherbet is 3/4 : 6 = 3 : 24.

Which is (24/3) = 8 times.

Now checking the options Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 is the correct relationship.

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The value of a = 2

Product of roots = -29

From formula of quadratic equation:

Answer:

below

Step-by-step explanation:

A) 3x+2y=31 is line perpendicular with 2x-3y=12, slope= -3/2 vs 2/3 and intersect at (9 ,2)

B) 6x-9y=11 parallel to 2x-3y=12, has same slope of 2/3, no intersect

C) they have "positive type of slopes" to form parallel lines

9514 1404 393

Answer:

  A) (x, y) = (9, 2)

  B) no solution

  C) the same slope

Step-by-step explanation:

A) In the attached, the given equation is graphed in red. The paired equation is shown in blue. They intersect at the point (9, 2), which is the solution to this system of paired equations.

__

B) The line is parallel to its paired line, so there is NO SOLUTION.

__

C) Parallel lines have the same slope.

_____

Additional comments

A graphing calculator provides a quick and easy solution to a system of equations. There are many calculators and apps and on-line sites that can solve a system of equations for you.

For the pair of equations in part A, you can eliminate the y-variable by adding 2 times the first equation to 3 times the second equation:

  2(2x -3y) +3(3x +2y) = 2(12) +3(31)   ⇒   13x = 117   ⇒   x = 9

Substituting in the first equation gives ...

  2(9) -3y = 12   ⇒   6 -y = 4   ⇒   y = 2

__

For the paired equation in part B, the ratio of the x- and y-coefficients is 6/-9 = -2/3, the same as it is for the given equation. The constants are different (even after dividing the second equation by 3), so the lines are parallel (not coincident). This means the system of paired equations has no solution.

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

1.9 liters

Step-by-step explanation:

Answer:

(i) To compute the value of the fund based on the withdrawals required, we can use the formula for the future value of an annuity due:

FV = P * ((1 + r)^n - 1) / r) * (1 + r)

where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, n is the total number of periods, and the extra (1 + r) factor is because the payments are made at the beginning of each period.

In this case, P = €25,000, r = 0.065, n = 20. We want to find the future value at the end of the 20-year period:

FV = 25000 * ((1 + 0.065)^20 - 1) / 0.065) * (1 + 0.065)

FV ≈ €743,704.96

Therefore, the value of the fund based on the withdrawals required is approximately €743,704.96.

(ii) To compute the amount of each deposit needed in order to maintain the fund, we can use the formula for the present value of an ordinary annuity:

PV = P * ((1 - (1 + r)^(-n)) / r)

where PV is the present value of the annuity, P is the annual payment, r is the interest rate per period, and n is the total number of periods.

In this case, PV = €743,704.96, r = 0.065, n = 20. We want to find the annual payment:

PV = P * ((1 - (1 + 0.065)^(-20)) / 0.065)

P ≈ €22,630.53

Therefore, the amount of each deposit needed in order to maintain the fund is approximately €22,630.53.

(iii) To compute the total interest earned over the entire 50 years, we can subtract the total deposits from the total withdrawals, and then subtract the initial balance. The total deposits are the annual deposit amount times the number of years (30), and the total withdrawals are the annual withdrawal amount times the number of years (20). The initial balance is the present value of the annuity that we calculated in part (ii).

Total deposits = €22,630.53 * 30 = €678,915.90

Total withdrawals = €25,000 * 20 = €500,000

Initial balance = €743,704.96

Total interest earned = Total withdrawals - Total deposits - Initial balance

Total interest earned = €500,000 - €678,915.90 - €743,704.96

Total interest earned ≈ -€922,620.86

Note that the negative sign indicates that the insurance company actually earned interest on this annuity, rather than the couple earning interest on their investment. This is because the withdrawals are greater than the deposits, and the interest rate earned by the insurance company is greater than the interest rate paid to the couple.

Step-by-step explanation:

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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The solution of the given expression is 9*\(x^{4}\)/100.

GIven an expression equal to 27\(x^{12}\)/300\(x^{8}\).

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27\(x^{12}\)/300\(x^{8}\).

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27\(x^{4}\)/300

Now divide numerator an denominator by 3.

=9\(x^{4}\)/300

Hence the expression 27\(x^{12} /300x^{8}\) will look like \(9x^{4} /100\) after simplifying.

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Answer:

\(Simplify:\sqrt\frac{27x^{12} }{300x^{8} }\)

\(O \frac{9}{100}x^{4}\)

✔ \(\frac{3}{10} x^{2}\)

\(O \frac{27}{300} x^{4}\)

\(O\frac{9}{10} x^{2}\)

Answer:

u = 7\/10

Step-by-step explanation:

Answer:

16 1/2 as a decimal is 16.5.

We convert it to an improper fraction which, in this case, is 33/2 and then we divide the new numerator (33) by the denominator to get our answer.

Answer:

16.5% and 16.5

Step-by-step explanation:

-3√45 + 3√20 = -3√(9 · 5) + 3√(4 · 5) =

= -3√(3² · 5) + 3√(2² · 5) =

= -3 · 3√5 + 3 · 2√5 =

= -9√5 + 6√5 = -3√5 ← the end

Sample standard deviation = 51.03

Sample variance = 2604.33

Mean (average):

\(= (107.5 + 108.2 + 133.6 + 151.4 + 155.8 + 149 + 106.11 + 16.1 + 181 + 165.7 + 130.6 + 126.5 + 109.5 + 139.6 + 139.4 + 140.8 + 143.2 + 132.7 + 171 + 115.7) / 20\\= 1894.28 / 20\\= 94.714\)

Squared differences from the mean:

\((107.5 - 94.714)^2 = 161.39\\(108.2 - 94.714)^2 = 182.14\\(133.6 - 94.714)^2 = 1507.99\\(151.4 - 94.714)^2 = 3217.15\\(155.8 - 94.714)^2 = 3750.18\\(149 - 94.714)^2 = 2922.18\\\)

\((106.11 - 94.714)^2 = 130.46\\(16.1 - 94.714)^2 = 6659.49\\(181 - 94.714)^2 = 7334.04\\(165.7 - 94.714)^2 = 5041.45\\\\(130.6 - 94.714)^2 = 1281.47\\(126.5 - 94.714)^2 = 1007.35\\(109.5 - 94.714)^2 = 217.75\\(139.6 - 94.714)^2 = 1997.15\\(139.4 - 94.714)^2 = 1990.18\\(140.8 - 94.714)^2 = 2108.42\\(143.2 - 94.714)^2 = 2353.86\\(132.7 - 94.714)^2 = 1425.68\\(171 - 94.714)^2 = 5852.45\\(115.7 - 94.714)^2 = 441.51\)

Sum of squared differences:

= 161.39 + 182.14 + 1507.99 + 3217.15 + 3750.18 + 2922.18 + 130.46 + 6659.49 + 7334.04 + 5041.45 + 1281.47 + 1007.35 + 217.75 + 1997.15 + 1990.18 + 2108.42 + 2353.86 + 1425.68 + 5852.45 + 441.51

= 49482.29.

Sample variance:

s^2 = Sum / (n-1)

= 49482.29 / (20-1)

= 2604.33105263

= 2604.33

Sample standard deviation:

s = sqrt(s^2)

s = sqrt(2604.33)

s = 51.0326366162

s = 51.03

Fulls:

An author is doing research on an upcoming book on skyscrapers in America. The author gathers data for 20 skyscrapers throughout America and decides to focus on the height data, given in meters, which are reproduced below.

Height of skyscraper (meters)

107.5

108.2

133.6

151.4

155.8

149

106.1

116.1

181

165.7

130.6

126.5

109.5

139.6

139.4

140.8

143.2

132.7

171

115.7

Calculate the sample standard deviation and the sample variance.

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Answer:

The estimate of the mean proportion of failures for these instructors is 0.2.

Step-by-step explanation:

In this question:

50 students from each instructor, so total of 50*4 = 200 students.

13 + 11 + 16 = 40 students failed.

What is the estimate of the mean proportion of failures for these instructors?

40/200 = 0.2

The estimate of the mean proportion of failures for these instructors is 0.2.

Answer:

0.43*0.43

Step-by-step explanation:

The pressure on the snow if the area of the footwear is 400 in² is 0.0645 pounds per square inch.

The force applied perpendicular to an object's surface per unit area across which that force is spread is known as pressure.

\(P= \dfrac{W}{A}\)

As it is given that the pressure is inversely proportional to the area of the footwear. Therefore, the relation can be written as,

\(P\propto \dfrac{1}{A}\\\)

Now, introducing a constant to remove the proportionality symbol, w that is the weight of the person, therefore,

\(P= \dfrac{W}{A}\)

Now, as the area of the shoe is 60in²,  the pressure on the snow is  0.43 pounds per square inch. Therefore, the value of w can be written as,

\(0.43= \dfrac{W}{60}\\\\W = 25.8\rm\ pounds\)

Now, the pressure on the snow if the area of the footwear is 400 in².

\(P= \dfrac{W}{A}\\\\P= \dfrac{25.8}{400}\\\\P = 0.0645 \rm\ pounds\ per\ inch^2\)

Hence, the pressure on the snow if the area of the footwear is 400 in² is 0.0645 pounds per square inch.

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Answer:

c

Step-by-step explanation:

2 x 2=4

2 x 2 =4
2 x 2 = 4

4 ^3 = 64

48 x 3 =192
Or:
192/2 = 96
96/2=48
48/2 = 24

24/2= 12
12/3=4

4/2=2
2 x 2 x 2 x 2 x 2 x 2 x 3

The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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