Rodney opens a savings account with $75 and also deposits $40 each month. Morgan opens an account with $50 and also deposits $40 each month. Will they have the same amount in their account at any point? If so, after how many months? Explain.


FAST RESPONSE ALSO EQUATION AND STEPS

Answer: [tex]y < \frac{1}{3}x+2, y < -2x+2[/tex]

Step-by-step explanation:

The equations of the lines are [tex]y=\frac{1}{3}x+2[/tex] and [tex]y=2-2x[/tex].

Since the line [tex]y=\frac{1}{3}x+2[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < \frac{1}{3}x+2[/tex].

Since the line [tex]y=2-2x[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < 2-2x[/tex].

Equation for the line in point-slope form is 5x + 6y = 6.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Given Data

P(6, -3)

y =1/2 x + 2

When the equation has been solved for y, the line in slope intercept form with slope = m = 1/2 = the coefficient of the x term is represented by the equation y= (1/2)x + 2. 2 represents the y coordinate of the location (0, 2) where the line intersects the y axis as the y intercept.

So, the points are (6,-3) and (0,2)

Formula

y₂ - y₁ = m(x₂ - x₁)

slope of the line (m) = [tex]\frac{x-x}{y-y}[/tex]₁¹

m= [tex]\frac{2-(-3)}{0-6}[/tex]

m = -[tex]\frac{5}{6}[/tex]

Equation

y- (-3) = -[tex]\frac{5}{6}[/tex](x- 6)

y +5 = -[tex]\frac{5}{6}[/tex]x + 6

y + 5 = -[tex]\frac{5+36 }{6}[/tex]

6y + 30 = -5x + 36

5x + 6y = 6

Equation for the line in point-slope form is 5x + 6y = 6.

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Answer:

the probability is 2/8

Step-by-step explanation:

From the graph below, the domain is

Answer:

 65 pairs

Step-by-step explanation:

Black makes up 5/(5+8) = 5/13 of the total order, so ...

 (5/13)(169 pairs) = 65 pairs

Vinny will order 65 pairs of black high tops.

First step, derivative of the constant:

Second step, the chain rule:

Where we applied that the derivative of tangent is the secant^2.

Hence the answer is:

Answer:

See below

Step-by-step explanation:

Rotate rectangle A 90 ° clockwise with the center being the lower right hand corner.  Then translate down and right until rectangle A in over rectangle B

To answer this question, it is a good practice to order the data in ascending order as follows:

We need to check for the total number of data. In this case, we have 30 observations.

To find the mean, we need to find the sum of all the observations and then divide this result by the total of observations (30). Then, we have:

Then, the value for the mean is:

The range is the result of subtracting the greatest number and the lowest number in the data:

The mode is the observation that is repeated the most (appears the most).

We can see that we have two values that appear six times in the list: 11 and 15.

Therefore, we can see that there is not a unique element, so there is no mode.

In summary, we have:

• Mean = 12.73333...

• Range = 8

• Mode = None.

Answer:

70

Step-by-step explanation:

14 x 10 is 140.

Since a triangle is just half a square, we multiply the two sides we have and then divide it.

140 ÷ 10 = 70.

Answer = 70.

P.S If it is correct, pls give Brainliest, thanks!

The given algebraic expression would be equivalent to the expression [tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex] which is the correct answer would be an option (B)

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given algebraic expression is:

[tex](64x^{\frac{2}{3} })^{-\frac{1}{3} }[/tex]

Apply the property of a⁻ˣ = 1/aˣ in the above term,

[tex]\dfrac{1}{ (64x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Here 64 = 4×4×4 = 4³

[tex]\dfrac{1}{ (4^3x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Apply the cube root property and Multiply the exponent of the variable x to 1/3

[tex]\dfrac{1}{ 4x^{\frac{2}{3} }^\times^{\frac{1}{3} }}[/tex]

Apply the multiplication operation to the exponent of the variable x to get the solution.

[tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex]

Hence, the correct answer would be an option (B)

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Step-by-step explanation:

i don't know if this is right

8x - 34 and 5x + 2 are corresponding angles and, by the Corresponding Angles Theorem, are congruent.

8x - 34 = 5x + 2
8x - 34 + 34 = 5x = 2 + 34
8x = 5x + 36
8x - 5x = 5x + 36 - 5x
3x = 36
3x/3 = 36/3
x = 12

Using a regression calculator, the line of best fit for the given set of data is:

where y = mass of the rope and x = length of the rope.

To estimate the length of the rope if its mass is 4.25 kilograms, let's replace "y" in the equation above with 4.25, and then solve for x.

Subtract 0.168088 on both sides of the equation.

Then, divide both sides of the equation by 0.34121.

Therefore, the length of the rope having a mass of 4.25 kilograms is approximately 11.96 meters.

Answer:

$194.69

Step-by-step explanation:

The best way to predict the amount of tips is using this formula:

[tex]100(\frac{Tips(total)}{Customers(total)} )[/tex]

This finds the average tip per customer with all of the data, and multiplies it by 100 to get the predicted amount of tips for 100 customers.

Plugging in the data from the table gives you this equation:

[tex]100(\frac{1174}{603} )[/tex]

This equals $194.69.

It will take 80 seconds for both tank 1 and tank 2 to have the same amount of water

Water in the tank 1 = 120 gallons

Drainage rate of tank 1 = 1/2 gallon each second

Water in tank 2 = 100 gallons

Drainage rate of tank 2 = 1/4 gallon each second

Let x represent the number of seconds it will take for both tanks to have the same amount of water

Formulating the equation we get the following:

Water in tank 1 - Drainage rate of tank 1*x = Water in tank 2 - Drainage rate of tank 2*x

120 - 1/2x = 100 - 1/4x

20 = 1/2x - 1/4x

20 = 1/4x

x = 80

So, it will take 80 seconds

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Answer:

Step-by-step explanation:

V = 4/3.pi.r^3

36 = 4/3 pi r^3

8.6 = r^3

r = 2 in

---------------------

Area of sphere :

A = 4.pi.r^2

A = 4 . Pi . 2^2

A = 16 Pi

A = 50.26 in

For 18000 units the calculated sum is $150,000.

The following are the company's production and period costs:

The product costs $ 350,000 for 20,000 units.

20,000 units = $150,000 in cost period

The product costs $ 385,000 for 22,000 units.

18,000 units each period = $ 135,000

The corporation incurs two major costs while creating an item: production costs and period costs.

Production costs are expenses directly connected to the manufacturing process. These expenses include labor, raw materials, and overhead.

While period costs are expenses incurred for the company's activities such as administrative and selling/sales charges,1. The cost of making 20,000 units is

Existing unit manufacturing costs are as follows:

Direct labor costs $7.00. Manufacturing variable overhead of $4.00 Fixed manufacturing overhead of $1.50 $ 5.00

Total product cost per unit = $7.00 + $4.00 + $1.50 + 5.00 = $17.5

So, for 20,000 units, the calculation is: 20,000 x $17.5 = $350,000

The time required to produce 20,000 units is

Each unit's cost period is as follows:

$ 3.50 in fixed selling expenses, $ 2.50 in fixed administration expenses, and $ 1.00 in variable administrative expenses.

Total period cost per unit = $ 3.5+ $ 2.5+ $ 1.00+ $ 0.5 = $ 7.5

So, for 20,000 units, the calculation is: 20,000 x $ 7.5 = $150,000

The cost of making 22,000 units is

Existing manufacturing costs per unit: $ 17.5

So, for 20,000 pieces, the cost is 22,000 x $17.5 = $ 385,000

The total period cost / unit for generating 18,000 units is $ 7.5.

So, for 18,000 units, the calculation is: 18,000 x $ 7.5 = $ 135,000

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Answer: x < -4

Step-by-step explanation:

➜ First thing we notice is the open circle. This means we will use either < or >

➜ The next thing we notice is that the values are pointing to the left of the circle, this means we will be using <

➜ The last part we notice is that the dot is on -4. This is the value we'll use to write our inequtliy.

    The last thing to do is to write the inequality using the parts we pointed out above:

x < -4

4x -2 = 3(x-3)

4x - 2 = 3x - 9

bring like terms together

4x-3x = -9 +2

x = -7

The finance charge on Daniyar's May statement is $4.45.

What is finance charge?

The cost of consumer credit expressed as a dollar amount is the financing charge. It includes any fee imposed by the creditor as an incident to or a requirement of the credit extension that is directly or indirectly payable by the customer. It excludes any fee that would be paid in an equivalent cash transaction.

The finance charge is equal to the product of the average daily balance and the monthly periodic rate.

So,

$270.31 x 1.65%

= $270.31 x 0.0165

= $4.45

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Let t be the time, in hours, elapsed till the buses are 791 miles apart, then we can set the following equation:

Solving the above equation for t we get:

Answer: 7 hours.

Step-by-step explanation:

6×(4 + x) = 7

24 + 6x = 7

6x = -17

x = -17/6 = -2.833333333... = -2 5/6

Answer: Linear

Step-by-step explanation:

Each time [tex]x[/tex] increases by [tex]1[/tex], [tex]y[/tex] decreases by [tex]8[/tex]. Since the value of y changes at a constant rate, the relationship is linear.

Answer:

This is an isosceles right triangle, so

x = 45°.

The stock witness an total average decrease in stock of $80 in the 8 weeks

The given parameters are:

Average decrease per week = 10 dollars

Also, we have the number of weeks to be

Number of  Weeks = 8 weeks

So, the total average decrease in the stock is calculated using the following equation

Total = Average decrease per week x Number of weeks

Substitute the known values in the above equation

So, we have the following equation

Total = 10 x 8

Evaluate the products in the above equation

So, we have the following equation

Total = 80

Hence, the total average decrease in the stock is $80

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Every other multiple of 3 is even.

The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7

The digits in multiples of 3 add up to a multiple of 3 (36 = 3 + 6, 111 = 1 + 1 + 1, etc.) All EVEN multiples of 3 are also a multiple of 6 (the even multiples of 3 are the 6 “count by's”).

The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7. To find out which one is a factor of 7, we should divide each of them by 7. 1/7 will be a decimal number and 7/7 = 1, which is a whole number. Thus, 7 will be a multiple of 7 and also a factor of 7.

A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components.

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Given:

• AD = 3

• DC = 27

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:

Where BD is the altitude.

Cross multiply:

Plug in the values and solve for x:

Take the square root of both sides:

Therefore, the value of x is 6 .

ANSWER:

d. 6

1) Looking at that table, we can pick the points

(1,9) (3,23)

2) Note that every time x increases by 2 units y increases by 14

3) Considering this a linear function we can find the rule by plugging in

23-9/3-1=14/2 = 7

9=7(1)+b

9=7 +b

2 =b

So we can write the rule as y =7x+2

The expression which is equivalent to the given expression; (ab²)³/b⁵ as given in the task content is; a³b.

It follows from the task content that the expression which is equivalent to; (ab²)³/b⁵ be determined.

Hence, since the given expression is; (ab²)³/b⁵.

By first applying the power of power law of indices; we have;

(ab²)³/b⁵ = a³b⁶/b⁵.

Also, by applying the quotient of powers rule of indices; we have;

a³ b^(6 - 5)

= a³b¹

= a³b

Ultimately, the expression which is equivalent to; (ab²)³/b⁵ as required in the task content is; a³b.

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