Solve for the formula m
e=mc squared

We need to remove either (1, 4) or (1, 1) to create a function.

Relations are formed by two sets, an input set known as domain and an output set known as range and relationships between these sets. A relation is a function if and only if each element from domain is related to only one element of the range. Mathematically speaking, we must satisfy the following proposition:

x → f(x), x → f'(x) ⇒ f(x) = f'(x)

Based on this definition, there are two possibilities to create a function:

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1,3 is the answer I believe. :)

a) Shelly Lemony's down payment is $24,000.

b) The loan amount is $96,000.

c) The monthly payment is $8,350.89.

d) The finance charge is $4,210.68.

The down payment represents the initial up-front partial payment for the purchase of the equipment on loan.

The down payment reduces the cost of the equipment to the loan amount.  Finance companies demand a down payment to ascertain the buyer's willingness and ability to proceed with the loan arrangement.

It is a sign of commitment to meet the loan contract obligations.

Monthly Pay:   $8,350.89

Total Loan Amount = $96,000.00

Upfront Payment $24,000.00

Equipment loan = $120,000

Number of periods = 12 months

APR = 8%

Total of 12 Loan Payments = $100,210.68

Total Loan Interest = $4,210.68

Total Cost (price, interest, tax, fees) = $124,210.68

Thus, Shelly will make a down payment of $24,000 or 20% of the equipment loan.

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The number of bills received by brady family are 781.

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable with the form an x + b = 0 are solved utilizing basic algebraic operations.

Let x equal the number of letters obtained,

(x - 3) equal the number of bills obtained,

(x + 5) equal the number of advertisements received, and also

the number of magazines did receive is also given (x - 3).

The following equation can be derived:

x + (x - 3) + (x + 5) + (x - 3) = 3131

4x - 1 = 3131

4x = 3132

x = 784

Thus, number of bills received are-

(x - 3) = 784 - 3

number of bills received = 781.

Therefore, the number of bills obtained by brady family are 781.

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Answer:

193.0 mph

Step-by-step explanation:

The average is defined as the sum of the items divided by the number of items.  In this case the sum is 771.888.  If we divide that by the number of items (4) we get 192.972.  However, our answer typically cannot have more significant digits than the element having the least number of significant digits.  Since one of the numbers has only one digit to the right of the decimal point, we would usually want to round our answer to one place as well.  So 192.972 will round to 193.0.

DG = 60

Therefore,[tex]4x - 3 + 2x + 21 = 60[/tex]

→[tex]6x+18 = 60 \\ 6x = 60 - 18[/tex]

→[tex]6x = 42[/tex]

Divide both sides by 6

→[tex]x = 7[/tex]

DO =[tex]4x - 3 [/tex]

→[tex]4(7) - 3 \\ 28 - 3[/tex]

DO [tex]= 25[/tex]

OG [tex]= 2x + 21[/tex]

→[tex]2(7) + 21 \\ 14 +21[/tex]

OG [tex]= 35[/tex]

Therefore:

[tex]x = 7[/tex]

[tex]DO = 25 ft[/tex]

[tex]OG = 35 ft[/tex]

Answer:

18 gallons

Step-by-step explanation:

Start with x gallons of 70% juice and 18 gallons of 30% juice.

Result: x + 18 gallons of 50% juice

0.7x + 0.3 × 18 = (x + 18)(0.5)

0.7x + 5.4 = 0.5x + 9

0.2x = 3.6

x = 18

Answer: 18 gallons

The standard deviation is a measure of a collection of values' variance or dispersion. The correct option is C, standard deviation.

The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

Shifting data, by adding a constant to each data value, do not change the standard deviation. This is because the standard deviation is a measurement of how much a group of values varies or is dispersed.

Hence, the correct option is C, standard deviation.

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The indicated function value is f(6²) = -72

The function definitions are given as

f(x) = -2x

g(x) = 2x+ 5

h(x) = x^2 + 3x - 10

The function f(6²) means that x = 6² in f(x)

So, we have

f(6²) = -2(6²)

Evaluate

f(6²) = -72

Hence, the indicated function value is f(6²) = -72

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Answer:

4c + 35

Step-by-step explanation:

What every the monthly amount is (c) you would multiply that by 4 to find the cost for 4 months and then you have to add in the one time cost of 35

Answer:

There are 160 boys and 200 girls

Step-by-step explanation:

its a proportion

The solution of the equation for h is H = 2a/(B1 + B2)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

a=H(B1 + B2)/2

The above means that the variable h is represented by the variable H

Multiply both sides of the equation by 2

So, we have

2a = H(B1 + B2)

Divide both sides of the equation by (B1 + B2)

H = 2a/(B1 + B2)

Hence, the solution of the equation for h is H = 2a/(B1 + B2)

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Answer is

(a) She can buy 7 packages of plain coffee or 5 packages of coffee.

(b) f = [tex]\frac{T- 5.50 p}{7}[/tex]

(c) she can buy 3 packages of  flavoured coffee

(a) she spent on coffee is $ 40

amount of money she spends on coffee is 5.50

then, packages of plain coffee = [tex]\frac{40}{5.50}[/tex] ≈ 7.2

      so she buy 7 packages of plain coffee.

she spent on coffee is $ 40  and amount spends on flavoured coffee is 7

then , packages of flavoured coffee = [tex]\frac{40}{7}[/tex] ≈ 5.7

so she can buy 5 packages of flavoured coffee.

(b)According to question ,

T = 5.50 + 7f

so 7f = T - 5.50

then , f = [tex]\frac{T - 5.50}{7}[/tex]

(c) we get the value of f = [tex]\frac{T - 5.50}{7}[/tex]

given that , f is equal to 3

then,  f = [tex]\frac{T - 5.50}{7}[/tex]

           =   [tex]\frac{T - 5.50}{7}[/tex]×3

we get   =  [tex]\frac{T - 16.5}{7}[/tex]

when T is equal to 40

then , f = [tex]\frac{40 - 16.5}{7}[/tex] ≈ 3.35

so she can buy 3 packages of flavoured coffee.

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The scale used by Wyatt is; 11 inches : 4 yards.

Now, for the given values in question.

For the area of picnic is 84 yards.= long.

The length in the drawing is 31 inches.

Let the scale for yards is 'x'.

Then;

231 inches: 84 yards = 11 inches: x yards

Write in the fraction form,

231/84= 11/x

Cross multiplying;

x = (11×84)/231

x = 4

Thus, scale becomes; 11 inches : 4 yards.

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It is realistic that 3 owners spend $720 a year on their graph

Given that

To find

So, according to the question

We can say that,

3 owners are present and,

A pet's annual cost is $720.

So, the option C (Yes, it is realistic that 3 owners spend $720 a year on their pet(s) ) is correct explanation of it.

Because no fractional value can represent the number of owners. Therefore, having 7.2 owners is not feasible and other options showing only one value. So A, B, and D are wrong answer.

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The exponential smoothing forecast for next period is 63.2.

A time series forecasting technique called exponential smoothing can be expanded to support data with a systematic trend or seasonal component.

Now,

Given:

To find: Simple exponential smoothing forecast with α = 0.4 for next period.

Finding:

Now, by the concept of exponential smoothing, forecast for next period will be given by:

Ft + 1  = α Dt + (1 - α)F,

where,

Ft+1 = the next forecast,

α = weighing factor,

Dt = actual value for this period,

F = forecast value for the current period,

Substituting the values in the above expression:

=> Ft + 1 = 0.4 (65) + (1 - 0.4) 62

=> Ft + 1 = 26 + 37.2

=> Ft  + 1 = 63.2

Hence the exponential smoothing forecast for next period is 63.2.

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The rate of change for each set of ordered pairs is:

a. 1/2

b. 3

c. 7

The average rate of change = change in y / change in x.

Average rate of change for (2,3.5), (6,5.5):

Average rate of change = (5.5 - 3.5)/(6 - 2) = 2/4 = 1/2

Average rate of change for (-1,0), (0, 3):

Average rate of change = (3 - 0)/(0 - (-1)) = 3/1 = 3

Average rate of change for (3,-3), (4,4):

Average rate of change = (4 -(-3))/(4 - 3) = 7/1 = 7

Therefore, the rate of change for each set of ordered pairs is:

a. 1/2

b. 3

c. 7

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Answer:

Step-by-step explanation:

By rearranging the formula using algebraic operations, the value of x is [tex]\frac{y}{4}[/tex] - 1.

When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.

To find the value of x, use the same operations on both sides of the equation.

For making x the subject  

Divide by 4 on both sides

[tex]\frac{y}{4}[/tex] = (x-1)

On both sides of the equation, add 1.

[tex]\frac{y}{4}[/tex] - 1 = x

As a result, by rearranging the equations, the value of x is [tex]\frac{y}{4}[/tex] - 1.

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a. The expression of the amount of phosphorus-32 remaining as a function of time t is A(t) = [tex]6.6\left(\frac{1}{2}\right)^{t / 14}[/tex].

b. The time when 1 gram remaining is 38.1145 days.

The half-life is the amount of time it takes for half of a unstable nuclei to decay. Each substance has its own half-life.

Now, as per the question;

Exponential growth is given by the formula;

[tex]A(t)=A_0(1+r)^t[/tex]

Where,

A(t) = amount at time t.

A₀ = Initial amount of the nuclei (= 6.6)

r = rate of increasing( = -1/2; as decay is always negative)

t = time (= t/14)

Part a. Calculate the expression for the amount of phosphorus-32 remaining as a function of time t as-

Substituting all the values in the equation;

[tex]\begin{aligned}&A(t)=6.6\left(1+\left(-\frac{1}{2}\right)\right)^{t / 14} \\&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]

This is the requires expression.

Part b. Calculate the time there be 1 gram remaining as;

This time can be written as A(t) = 1.

Substitute the value in the equation.

[tex]\begin{aligned}&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14} \\&1=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]

[tex]\left(\frac{1}{2}\right)^{t / 14}=\frac{10}{66}[/tex]

Further solving;

t = 38.1145 days.

Thus, the time taken by phosphorus-32 to remain as 1 gram is 38.1145 days.

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Answer:

32

Step-by-step explanation:

There is nothing this but the answer is 32.

Answer:

Step-by-step explanation:

Look at the File I attached. The Question says that a car travels 76 km north then 25 km east. Now think of this as the Right angled triangle I attached in the file.

a) Bearing from the staring point to the means the degrees of the part i marked with a question mark.

Now SOH CAH TOA

76 km is the ADJACENT

25 km is the OPPOSITE

and x is the HYPOTENUSE

We have the values of the ADJACENT and the OPPOSITE.

Now see which rule has both, It is TOA(tan rule) which is:

tan(y) = OPPOSITE/ADJACENT     (y is the degrees we will get)

tan(y) = 25/76  ( opposite of the degree we need is 25 and adjacent is 76)

tan inverse(25/76) = y  (inverse will be given as to the power -1 on the calculator)

FINAL ANSWER OF (a) = 18.21°

b) This part is asking for the length of the hypotenuse, which i denoted as x in the attached file.

For this part, you will use the Pythagoras Theorem

Which is :

   a² + b² = c²

Where c is the hypotenuse and a and b are the opposite and adjacent.

So

    76² + 25² = x²

     6401 = x²

  √6401 = x

     x = 80.01

The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be

V = π r²h cubic units

Then the surface area of the cylinder will be

SA = 2πrh square units

Then the ratio of the volume of the cylindrical tank to its surface area will be

V / SA = π r²h / 2πrh

V / SA = r / 2

The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

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1234567890123456789012345678901234567890

Answer:

f(-7) = -15

g(-3) = 27

Step-by-step explanation:

We see that the functions defined are:

f(x) = 2x - 1

AND

g(x) = 2x^2 - 3x

This problem asks to find f(-7) and g(-3). To find this, we have to plug the respective numbers into the respective functions.

f(-7) = 2 (-7) - 1

f(-7) = - 14 - 1

f(-7) = -15

g(-3) = 2(-3^2) - 3(-3)

g(-3) = 2(9) + 9

g(-3) = 18+9

g(-3) = 27

FINAL ANSWER: f(-7) = -15, g(-3) = 27

160.55 is  the difference. i underlined each number i added on each line.

What is an linear equation in math?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The two numbers are 15.75 and 176.3

First we will compare the numbers.

1. A=176.3

2. B=15.75

one's place of A is greater than once place of B.

tens place of A is greater than tens place of B.

Hundred place of A is greater than hundred place of B.

So, A>B

So  we will subtract 15.75 from 176.3.

176.30 -15.75=

176.30     ----A

- 1 5.75     ----B

Hundreths place of A - Hundreths place of B =  0-5=10-5=5

Tenth place of A  - Tenth place of B =12-7=5

ones place of A - ones place of B=5-5=0

Tens place of A - Tens place of B =7-1=6

So the solution is 160.55

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The equation of the line is x = 25, in accordance with the given conditions.

Given:

To find: Equation of the line.

Finding:

Let the equation of the line be: (y - y') = m (x - x'),

where, (x',y') = point through which the line passes and m = slope of the line.

The slope of the first line = [tex]\frac{1}{0}[/tex] , i.e., the y-intercept of this line does not exist and it is a vertical line.

Hence, the equation of the line is 0 = 1 (x - x')

Thus, the equation of the line => 0 = 1 (x - 25)

=> x = 25.

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Answer:

1/48 should be added.

Step-by-step explanation:

If you add 9/16 to -7/12 you will get -1/48. Then do -7/12 + 1/48 and it will give you 9/16.

Considering the definition of an equation and the way to solve it, the cost of one hot wing is $0.6.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it and the equality must be true.

To solve an equation, keep in mind:

Being "x" the cost of one hot wing, and knowing that:

the equation in this case is:

First customer payment= Second customer payment

8x +4= 10x +2.80

Solving:

4 - 2.80= 10x - 8x

1.2= 2x

x= 1.2 ÷ 2

x=0.6

Finally, the cost of one hot wing is $0.6.

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The different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3

The mathematical statement is given as:

three groups of five

The statement three groups of five means

Three multiplied by 5

i.e. 3 * 5

This can also be written as

5 + 5 + 5

Also, it can be expressed as

3 + 3 + 3 + 3 + 3

Hence, the different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3

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