Mary took out a student loan for $15000 at 4% simple interest. How much interest will she pay in 10 years? suppose she paid it off in 8 years instead of 10 years. how much would she save in interest?

Answer:

[tex]\delta=\frac{\epsilon}{3}[/tex]

The proof is in the explanation.

Step-by-step explanation:

Compare [tex]\lim_{x\rightarrow 7}(3x-2)=19[/tex] to [tex]\lim_{x\rightarrow a}f(x)=L[/tex].

We want to find  [tex]\delta[/tex] such that whenever [tex]0<|x-a|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].

We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|3x-2-19|<\epsilon[/tex].

[tex]|3x-2-19|<\epsilon[/tex]

Simplify:

[tex]|3x-21|<\epsilon[/tex]

Factor on left side inside the | |:

[tex]|3(x-7)|<\epsilon[/tex]

|ab|=|a||b|:

[tex]|3||x-7|<\epsilon[/tex]

|3|=3:

[tex]3|x-7|<\epsilon[/tex]

Divide both sides by 3:

[tex]|x-7|<\frac{\epsilon}{3}[/tex]

So we will need to choose [tex]\delta=\frac{\epsilon}{3}[/tex].

We want to prove there exists a [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].

Proof:

Let [tex]\epsilon>0[/tex]. We will choose [tex]\delta=\frac{\epsilon}{3}[/tex] such that [tex]0<|x-7|<\delta[/tex] will give us [tex]|f(x)-L|<\epsilon[/tex].

[tex]|f(x)-L|=|(3x-2)-19|[/tex]

        [tex]=|3x-21|[/tex]

        [tex]=|3||x-7|[/tex]

        [tex] =3|x-7|<3\delta=3\frac{\epsilon}{3}=\epsilon[/tex].

Therefore, we have for all [tex]\epsilon>0[/tex], [tex]\delta=\frac{\epsilon}{3}[/tex] is the number that satisfies the definition.

conducting the survey as visitors leave the park

The park manager wants to figure out how people like the park so she will conduct the survey as people leave the park.

Final answer:

The most representative sample for a survey on park facilities satisfaction would be obtained by conducting the survey as visitors leave the park, ensuring a broad and unbiased cross-section of park users are included.

Explanation:

The question asks which method would provide the most representative sample for a survey about how people like the park facilities. The most representative sample would be achieved by conducting the survey as visitors leave the park. This method ensures a wide cross-section of park users are surveyed, capturing various interests and usage patterns of the park facilities, from those who come for leisure activities at the softball diamond or playground to those seeking quiet contemplation or exercise.

Conducting the survey in other locations like a shopping mall or specific areas within the park, such as the softball diamond or playground, would likely bias the results. Surveying at a shopping mall doesn't guarantee participants have visited or are familiar with the park, and focusing solely on one area within the park would not capture the diverse usage and opinions of all park visitors. Therefore, surveying as visitors leave the park is the most inclusive and unbiased approach to understanding how the facilities meet the needs of the community.

Answer:

175% increase

Step-by-step explanation:

(3.5 / 2) * 100 = 175%

Use this formula to get the total angle measurement of the figure:

T=180(n-2)

Since there are 7 sides, the total measurement must be:

180(7-2)

180(5)

900 degrees

Set up an equation and solve for x:

123+121+127+128+139+125+x=900

763+x=900

x=137

So the missing angle is 137 degrees.

Hope this helped!

Answer:

Debt

Step-by-step explanation:

Let's say someone uses debit instead of credit and they don't have any money in their account. If used multiple times you could potentially end up owing the bank (be in debt) .

Negative numbers are used in real-world contexts to describe temperatures below zero, financial debts, or elevations below sea level, helping to clearly indicate quantities that are less than a referenced zero point.

You would use a negative number to describe a real-world amount when talking about temperatures below zero, debts, or elevations below sea level, among other scenarios. For example, if the temperature is 5 degrees below zero, it could be represented as -5°C. This indicates that it is 5 degrees colder than the point at which water freezes (0°C). Another example is financial: if you owe $100, you could represent your account balance as -$100, indicating a debt. Similarly, a town located 100 meters below sea level could have its elevation represented as -100 meters.

These examples show how negative numbers can effectively convey quantities less than zero in various real-world contexts, providing a clear understanding of situations where values are lacking or in deficit compared to a reference point.

Answer:

(x, y) =(-6,4)

Step-by-step explanation:

3x-y=-28

-5x-4y=-10

y=3x+28

-5x-4(3x+28)=-10

y=3x+28

-5x-12x-112=-10

y=3x+28

-17x=-10+112

y=3x+28

-17x=102

y=3x+28

x=102/(-17)

y=3x+28

x=-6

y=3*(-6)+28

x=-6

y=-24+28

x=-6

y=4

x=-6

(x,y)=(-6,4)

To find the numbers, we can set up a system of equations and solve for the variables.

Let's represent the numbers as x and y. According to the problem, one number is 6 more than the other. This can be written as:

x = y + 6

The sum of the numbers is 30. This can be written as:

x + y = 30

We can solve this system of equations by substituting the value of x from the first equation into the second equation:

(y + 6) + y = 30

Combining like terms:

2y + 6 = 30

Subtracting 6 from both sides:

2y = 24

Dividing by 2:

y = 12

Now, we can substitute the value of y back into the first equation to find the value of x:

x = 12 + 6

x = 18

Therefore, the two numbers are 12 and 18.

Answer:

k = 4

Step-by-step explanation:

-8|4k-10|=-48

|4k-10|=-48/-8

|4k-10|= 6

4k = 6+10

4k = 16

k = 4

If you add 10 and then subtract 1, you get the same result as if you just added 9.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have to add 24+9 by making 10s.

As per the given question, the required solution would be as:

24 + 10 - 1 = 33

Therefore, if you add 10 and then subtract 1, you get the same result as if you just added 9.

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Final answer:

To add 24 and 9 using tens, break 9 into 6 and 3, add 6 to 24 to get 30, and then add the remaining 3 to reach 33.

Explanation:

To add 24 and 9 by making 10s, you can first break down the number 9 into 6 and 3.

Add 6 to 24 to make a round number, which is 30.

Now you have made a '10' because 30 is a multiple of 10.

Next, add the remaining 3 to get 33.

So, 24 + 9 = 33.

Answer:

-10k-28

Step-by-step explanation:

-19+4k-15k+k-9

-28-11k+k

-10k-28

Answer:

12k+ -10

im not truely sure if this is correct... but i went off my knowlage

You will need 119 cups to sell all of the lemonade.

Step-by-step explanation:

Given,

Diameter of cups = 9 cm

Radius of cup = [tex]\frac{Diameter}{2}=\frac{9}{2}=4.5\ cm[/tex]

Height of cups = 12 cm

We will find volume of cup.

[tex]Volume = \frac{1}{3}\pi r^2h\\[/tex]

Putting all the values

[tex]Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3[/tex]

Therefore;

Each cup can hold 254.34 cubed centimeter of lemonade.

Number of gallons = 8

1 gallon = 3785 cm³

8 gallons = 3785*8 = 30280 cm³

Let,

x = Number of cups

Volume of lemonade in one cup * Number of cups = Volume of 8 gallons

254.34x=30280

Dividing both sides by 254.34

[tex]\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05[/tex]

Rounding off to nearest whole number

x = 119

You will need 119 cups to sell all of the lemonade.

Keywords: volume, division

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Answer:

35+65+80=180

Step-by-step explanation:

the total interior angle of a triangle is 180

Answer:

its the third answer

[tex]35 \: \: 65 \: \: 80[/tex]

Step-by-step explanation:

because the addition of a interior angles has to be 180.'

Option C: [tex]$148 \mathrm{in}^{2}$[/tex] is the area of the trapezoid.

Explanation:

The image of the trapezoid having these descriptions is attached below:

Now, we shall determine the area of the trapezoid using the formula,

[tex]$A=\frac{a+b}{2} h$[/tex] where a and b are the base of the trapezoid and h is the height of the trapezoid.

Thus, we shall find the value of a and b from the diagram given below.

[tex]a= AB=14in[/tex]

[tex]b=DC\\b=DF+FE+EC\\b=3+14+6\\b=23in[/tex]

It is given that the height of the trapezoid [tex]h=8in[/tex]

Thus, substituting the values of a,b and h in the formula [tex]$A=\frac{a+b}{2} h$[/tex], we get,

[tex]A=\frac{14+23}{2}(8)\\ A=\frac{37}{2} (8)\\A=148in^2[/tex]

Thus, the area of the trapezoid is [tex]$148 \mathrm{in}^{2}$[/tex]

Hence, Option C is the correct answer.

Answer:

245=2.45

7/50=0.14

Step-by-step explanation:

divide by 100

USE MATHAWAY DOT COM!!

The answer is B, 7i.

sqrt(-49)

Pull out an i.

i*sqrt(49)

Take the square root to get 7i.

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Answer:

5/1, 25/5

Step-by-step explanation:

Final answer:

The expression (9-3)+4(6-7)-7 is calculated following PEMDAS, resulting in a value of -5 after simplifying the operations within the expression.

Explanation:

The value of the expression (9-3)+4(6-7)-7-1720 seems to have a typo, and it should probably read (9-3)+4(6-7)-7. To evaluate this expression, you follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, calculate the parentheses: (9-3) = 6 and (6-7) = -1.

Next, perform the multiplication: 4 * (-1) = -4.

Finally, add and subtract from left to right: 6 + (-4) - 7 = 6 - 4 - 7 = 2 - 7 = -5.

The value of the expression is -5.

Answer:

Explanation:

The average cost is found dividing the total cost by the number of hot dogs:

         [tex]Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs[/tex]

The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:

[tex]Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog[/tex]

           [tex]Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15[/tex]

Where x is the number of hot dogs.

         [tex](15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000[/tex]

Which shows you how you can find that the answer is 30,000 hot dogs.

Final answer:

To find the number of hot dogs needed to achieve an average cost of $1.15, including a fixed investment of $15,000 and a variable cost of $.65 per hot dog, the calculation reveals that 30,000 hot dogs must be sold to reach this target.

Explanation:

The question asks how many hot dogs must be sold before the average cost per hot dog is $1.15, given an initial investment of $15,000 and a production cost of $.65 per hot dog. To find the break-even point in terms of units sold to reach the target average cost, we use the formula to calculate average cost: Average Cost = (Fixed Costs + Variable Costs) / Quantity. Here, the fixed cost is the initial investment of $15,000, and the variable cost is $.65 per hot dog.

To find the number of hot dogs needed to achieve an average cost of $1.15, we set up the equation: $1.15 = ($15,000 + $.65Q) / Q. Solving for Q gives us 30,000 hot dogs as the break-even point where the average cost per hot dog would be $1.15.

This calculation allows the business owner to understand how many units need to be sold to overcome the initial investment and start making a profit on each hot dog sold at or above $1.15.

Evaluate the inside absolute values first:

17-|16*9|

17-|144|

17-144

-127

Hope this helped!

70 adults and 100 children attended the carnival.

Step-by-step explanation:

Given,

Cost of each adult ticket = $10

Cost of each child ticket = $5

Total tickets sold = 170

Total revenue generated = $1200

Let,

Number of adults = x

Number of children = y

According to given statement;

x+y=170      Eqn 1

10x+5y=1200    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=170)\\10x+10y=1700\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](10x+10y)-(10x+5y)=1700-1200\\10x+10y-10x-5y=500\\5y=500[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{500}{5}\\y=100[/tex]

Putting y=100 in Eqn 1

[tex]x+100=170\\x=170-100\\x=70[/tex]

70 adults and 100 children attended the carnival.

Keywords: linear equation, elimination method

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Answer:

-80

Step-by-step explanation:

The answer is -80 because 80 feet below sea level would be a negative number. So you just add a negative sign to 80 and voila! You get the answer. Your welcome, by the way!

Elevation 80 feet below sea level can be represented by the negative number -80 in mathematics. This is because negative numbers are used to represent depths or locations below sea level.

In mathematics, when we talk about locations below sea level, we represent them with negative numbers. So, an elevation of 80 feet below sea level will be represented as -80. This numerical representation helps us have an accurate and easy understanding of above and below sea level elevations. Such as, 0 represents sea level, positive numbers represent elevations above sea level, and negative numbers represent depths below sea level.

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Answer:

16

Step-by-step explanation:

(3x - 1) + 2

(3(5) - 1) + 2

(15 - 1) + 2

14 + 2

16

Answer:

16

Step-by-step explanation:

Start by plugging in 5 for x in the equation.

(3 x 5 - 1) + 2

Next do the multiplication.

15 - 1 + 2

Add and subtract.

16

You have your answer.

Hope this helped.

Answer:

d

Step-by-step explanation:

Answer:

24 hours

24 hours is the solution to 300=10(2)^t/15

Answer:

Step-by-step explanation:

8(6-k)+2k ≥-15-(-3k)

Opening bracket

48 - 8k + 2k ≥ -15 + 3k

-8k - 3k + 2k ≥ -15 - 48

-9k ≥ -63

k ≤ -63/-9

k ≤ 7

Answer:

k ≤ 7

Step-by-step explanation:

8 (6 - k) + 2k ≥ - 15 -(-3k)

Let's simplify this by solving each side.

First side:

8 (6 - k) + 2k ≥ - 15 -(-3k)

48 - 8k + 2k ≥ - 15 -(-3k)

48 - 6k ≥ - 15 -(-3k)

Second side:

48 - 6k ≥ - 15 -(-3k)

48 - 6k ≥ -15 + 3k

DONE SIMPLIFYING!

Now solve for "k" algebraically (transitions are in bold):

48 - 6k ≥ -15 + 3k

-6k ≥ -15 - 48 + 3k

-6k ≥ -63 + 3k

-6k - 3k ≥ -63

-9k ≥ -63

-k ≥ -63 ÷ 9

-k ≥ -7

k ≤ 7

Answer:

C

Step-by-step explanation:

Total number of rolls = 96

There are three even numbers: 2, 4 and 6.

Number 2 was rolled 13 times

Number 4 was rolled 17 times

Number 6 was rolled 20 times

Hence, even number was rolled [tex]13+17+20=50[/tex] times.

The experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

Therefore,

[tex]P=\dfrac{50}{96}=\dfrac{25}{48}[/tex]

Answer:

X = 0

Y = 2

so Option A (0,2) IS CORRECT

Step-by-step explanation:

Y = -1/3 x + 2 equation 1

Y = x+ 2 equation 2

from equation 2 we have

y = x+ 2 Put in equation 1

x + 2 = -1/3 x + 2

x +1/3x = 2 -2

0.67 x = 0

X = 0

so put x =0 in equation 2 then we have

y = x +2

Y = 0+ 2

Y = 2

Answer:

Circumference of circle= 37.68 units

Circumference of sector= 6.28 units

Step-by-step explanation:

The given figure is a circle with given radius OB= 6 units.

The circumference of a circle is the total length of its boundary.

For the complete circle its circumference can be calculated by;

           Circumference= [tex]2\pi r[/tex]

                                 [tex]=2*3.14*6\\=37.68[/tex] units

For the circumference of the Sector with 60° in the figure, the circumference can be calculate by:

                              [tex]=\frac{60}{360}* 2*\pi*6\\\\=\frac{1}{6}*12*3.14\\\\ =2*3.14\\\\=6.28[/tex] units

So, the circumference of the full circle is 37.68 units and the circumference of the sector is 6.28 units.

Answer:

Step-by-step explanation:

18x+8=14

18x=6

x=1/3

When ƒ(x) is equal to 14, the value of x is 1/3.

To find the value of x when f(x) is equal to 14, we can set up the equation:

f(x) = 18x + 8

We know that f(x) is equal to 14, so we substitute that into the equation:

14 = 18x + 8

We isolate the variable x by subtracting 8 from both sides of the equation:

14 - 8 = 18x

6 = 18x

To solve for x, we divide both sides of the equation by 18:

6/18 = x

1/3 = x

Therefore, when f(x) is equal to 14, the value of x is 1/3.

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Answer:

-2x-5

Step-by-step explanation: