Lena's penny bank is 1/2 full. After she removes 200 pennies, it is 3/10 full. How many pennies can Lena's bank hold?

Answer with Step-by-step explanation:

Let there be r rows and s seats in every row.

An audience of 450 people is seated in an auditorium and each seat is occupied.

i.e. rs=450

or s=450/r

With three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats.

i.e. (s-3)(r+5)=450

s(r+5)-3(r+5)=450

rs+5s-3r-15=450

450+5s-3r-15=450

Subtracting both sides by 450,we get

5s-3r-15=0

i.e. 5s-3r=15

5(450/r)-3r=15

Dividing both sides by 3 and multiplying by r, we get

750-r²=5r

r²+5r-750=0

r² + 30r - 25r - 750 = 0  

r(r + 30) - 25(r + 30) = 0  

(r + 30)(r - 25) = 0

either r+30=0 or r-25=0

either r= -30 or r=25

r can't be negative

Hence, number of rows in auditorium are:

25

The practical domain of the function f(p) = 12p + 5 is all integers from 1 to 9, inclusive.

The practical domain of the function f(p) = 12p + 5 refers to the set of all possible values that p, the number of packages of rolls, can take given the constraints of the situation described. Since the caterer cannot order partial packages and can order up to 9 packages, p must be an integer from 1 to 9 inclusive.

Moreover, these are the only values that make sense in the context of this problem since ordering 0 packages will not change the quantity of rolls they already have and ordering more than 9 packages is beyond the caterer's limit.

Solving an equation is likened to unwrapping a present because in both cases, you aim to uncover what's within by dealing with the outer layers systematically. Through an inverse process, you isolate the equation's variable and solve for it, just as the step-by-step unwrapping of layers reveals the gift within the package.

Unwrapping a present is a great way to understand the process of solving an equation. If you consider the equation itself as being 'wrapped' in different operations such as multiplication, division, addition, and subtraction, you can begin to 'unwrap' it by systematically dealing with these operations in reverse from the order of operations. This would be like when you unpack the present by undoing the tape, then the paper, then the box, or whatever other layers might be present.

To use a direct example, let's consider the equation 3x + 7 = 22. You start unwrapping by isolating for the term with the variable. This means you handle the operation that does not involve the variable first. So, subtract 7 from both sides of the equation to get 3x = 15. Next, you handle the multiplication operation by dividing both sides by 3 and solving for x, which would be 5 in this case. Just like unwrapping a present, we aim to get to the 'inside' or the root of the equation.

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Answer:

3/4

Step-by-step explanation:

I got it right.

Answer:

[tex]x=\frac{-2\pm \sqrt{(2)^{2}-4(4)(-1)}}{2(4)}[/tex] is the answer.

Step-by-step explanation:

Given quadratic equation is 4x²+ 2x - 1 = 0

To find the solution of the equation we use the quadratic formula

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]

Now we put the values of a = 4, b = 2 and c = (-1)

Therefore, quadratic formula for the equation given will be

[tex]x=\frac{-2\pm \sqrt{(2)^{2}-4(4)(-1)}}{2(4)}[/tex]

The average rate of change of the function f(x)=120(0.1)^x from x=0 to x=2 is calculated as (f(2) - f(0)) / (2 - 0), which gives -59.4.

Average Rate of Change

The average rate of change of a function over an interval is calculated by the difference in function values at the endpoints divided by the difference in input values. For the function f(x) = 120(0.1)^x, we want to find this rate from x = 0 to x = 2. First, we find the function values:

f(0) = 120(0.1)⁰ = 120

f(2) = 120(0.1)² = 120(0.01) = 1.2

Then we use the formula for average rate of change:

Average rate of change = (f(2) - f(0)) / (2 - 0) = (1.2 - 120) / 2 = -118.8 / 2 = -59.4

Therefore, the average rate of change of the function on the interval from x = 0 to x = 2 is -59.4.

Answer:

D) 15

Step-by-step explanation:

The value of the function f(x) = 5x + 40 at x = -5 will be 15. Then the correct option is D.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = 5x + 40

The value of the function f(x) = 5x + 40 at x = -5, then the value of the function will be

f(-5) = 5 (-5) + 40

f(-5) = - 25 + 40

f(-5) = 15

Then the value of the function f(x) = 5x + 40 at x = -5 will be 15.

Then the correct option is D.

More about the function link is given below.

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Invest in more than one type of investment.

After buying stock at $83.60, the price increased by $15.35 the next day, followed by a 4.75% decrease the day after. The final stock price was therefore $94.25, and this is a reasonable fluctuation in the stock market.

Luis purchased stock at an initial price of $83.60. On the next day, the stock price increased by $15.35, resulting in a new price of $83.60 + $15.35 = $98.95. The following day, the stock price experienced a decrease by 4 and 3/4 percent. To find the change in price, we multiply $98.95 by 4.75% (or 0.0475 in decimal form), which equals approximately $4.70. So, the final stock price after the decrease would be $98.95 - $4.70 = $94.25.

Is this answer reasonable? Yes, a price fluctuation in stock is common, and a change of $15.35 followed by a percentage decrease the following day is a typical scenario in the stock market.

Answer:

they spend $ 5.88 to buy a gift but there is not enough money left to buy a card of $3.25

Step-by-step explanation:

The earnings form Wednesday of Samuel and Jason are:

   Samuel earnings = 12.5x0.40 = $5

   Jason earnings = 7.1x0.40 = $ 2.84

The combined earnings form Wednesday are:

   Combined earnings = Samuel earnings + Jason earnings

   Combined earnings= $5 + $ 2.84 = $ 7.84

The spended earnings are:

    Spended earnings = combined earnings x ¾

    Spended earnings = 7.84 x ¾ = $ 5.88

The left over is:

    Left over = combined earnings – spended earnings

    Left over = 7.84 – 5.88 = $ 1.96

So, they spend $ 5.88 to buy a gift but there is not enough money left to buy a card of $3.25

Tarriq must use "2" as the Multiplication Property of equality.

The Multiplication Property of Equality for any numbers a, b, and c, If we multiply both sides of an equation by the identical number, we always have equivalency.

Rearrange unfamiliar terms to the left side of the equation then

2x = -190 - 50

Calculate the sum or difference

2x = -240

Divide both sides of the equation by the coefficient of variable 2, and we get

x = -240 [tex]$ \div[/tex] 2

Calculate the product or quotient then we get

x = -120

Therefore, the correct answer is option D) 2.

To learn more about Multiplication Property of equality

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Tarriq must use factor C) 1/2, as this represents dividing both sides of the equation by 2 to isolate x, resulting in x = –120.

To finish solving the equation 2x = –240 using the multiplication property of equality, Tarriq must divide both sides of the equation by 2, which is the coefficient of x.

This step can be shown as:

2x / 2 = –240 / 2

The division property of equality allows us to simplify by canceling out the 2s on the left, resulting in:

x = –240 / 2

Therefore, x equals:

x = –120

This shows that the factor Tarriq must use to finish solving the equation is C) 1/2 since that represents the inverse operation of multiplying by 2.

Answer:

No, the answer is not $ 336

The interest that she will pay is $ 504.

Step-by-step explanation:

Given : Andrea borrowed 2,240 at 15% apr for 18 months.

We have to calculate  the interest will she pay.

Using formula for Simple interest.

[tex]SI =P\times r\times t[/tex]

Where P is principal amount

r is rate of interest

t is time period.

Given : P = $ 2240

t = 18 months

In years , [tex]\frac{18}{12}[/tex]

r = 15% = 0.15

Substitute, we have,

[tex]SI=2240\cdot0.15\cdot\frac{18}{12}[/tex]

Simplify, we have,

SI = 504

Thus, The interest that she will pay is $ 504.

No, the answer is not $ 336

Andrea will pay $504 in interest on a loan of $2,240 at 15% APR over 18 months, not $336. The calculation involves converting the loan duration into years and applying the formula for simple interest.

To determine how much interest Andrea will pay on a loan of $2,240 at 15% APR for 18 months, we first need to understand that APR (Annual Percentage Rate) is the interest rate for a whole year (annual), rather than just a monthly fee or rate. Since APR is annual but our loan term is in months, we convert the duration into years to match the APR's annual nature. 18 months is equivalent to 1.5 years. Therefore, the interest calculation would be as follows:

Principal (the amount borrowed) = $2,240

Rate (APR) = 15%

Time = 1.5 years

Interest = Principal × Rate × Time

Interest = $2,240 × 15% × 1.5 = $2,240 × 0.15 × 1.5

Interest = $504

Therefore, Andrea will pay $504 in interest, not $336 as presumed. It's essential to accurately convert the time to years when dealing with APR to ensure the calculation is correct.

The correct answer is that there are 2000 people in the school.

To solve this problem, we can set up a proportion based on the information given. We know that 9% of the school's population is in the band, and the band has 180 members. We want to find the total population of the school, which we will denote as [tex]\( P \)[/tex].

The proportion can be written as:

[tex]\[ \frac{9}{100} = \frac{180}{P} \][/tex]

Now, we can solve for [tex]\( P \)[/tex] by cross-multiplying:

[tex]\[ 9P = 180 \times 100 \][/tex]

Divide both sides by 9 to isolate [tex]\( P \)[/tex]:

[tex]\[ P = \frac{180 \times 100}{9} \][/tex]

Simplify the right side of the equation:

[tex]\[ P = \frac{18000}{9} \][/tex]

[tex]\[ P = 2000 \][/tex]

Therefore, the total population of the school is 2000 people. This matches the correct answer given in the options.

An equation for a line in the plane allows you to find the x- and y-coordinates of any point on that line.

The statement is True.

An equation for a line in the plane, such as y = mx + b, allows you to find the x- and y-coordinates of any point on that line. The x-coordinate can be found by substituting a given y-value into the equation and solving for x. Similarly, the y-coordinate can be found by substituting a given x-value into the equation and solving for y.

Answer: TRUE!!!!!

Step-by-step explanation:

trust me

The slope of the line that passes through the points (1, -19) and (-2, -7) is calculated to be -4.

The slope of the line through the pair of points (1, -19) and (-2, -7), you can use the slope formula: slope (m) = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using the points given:

x₁ = 1, y₁ = -19

x₂ = -2, y₂ = -7

Substitute these values into the formula:

m = (-7 - (-19)) / (-2 - 1)

m = (12) / (-3)

m = -4

Therefore, the slope of the line through the points (1, -19) and (-2, -7) is -4.

Lee Wong's annual salary raise of $3,000 represents a 4.6% increase from his original salary of $65,000 when rounded to the nearest tenth of a percent.

To calculate the percentage increase of Lee Wong's salary, we use the formula for percentage change: Percentage Change = (Change in Quantity / Original Quantity) × 100%. In this case, the change in quantity is the raised amount of $3,000, and the original quantity is the original salary of $65,000.

Percentage Increase = ($3,000 / $65,000) × 100% = 0.04615 × 100% = 4.615%. Rounded to the nearest tenth of a percent, Lee Wong's salary increase is 4.6%.

Sam and Jesse wash a total of 70 cars over two days, by washing five cars each hour for seven hours each day.

Sam and Jesse work together to wash cars. They can wash five cars each hour, and they work for seven hours each day. Since they do this over the course of two days, we need to calculate the total number of cars they wash in this period.

First, we find out how many cars they can wash in one day by multiplying the number of cars they can wash in an hour by the number of hours they work:

Next, since they work for two days, we multiply the number of cars washed in one day by two:

Sam and Jesse wash a total of 70 cars over the two days.

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