Terrance and his three friends earned $359 in August, $522 in July, and $420 in September selling lemonade. How much would they each earn if they divided their earnings equally?

it will take approximately 22.56 years for the amount to triple.

The given information for this problem is that there is an initial investment of $600 in an account with an annual interest rate of 4%. The task is to determine after how many years the amount will triple.Using the compound interest formula, we can find the amount in the account after t years:A = P(1 + r/n)nt Where,A = final amount in the account, P = initial amount in the account r = annual interest rate ,n = number of times the interest is compounded per year ,t = time in years.

From the problem statement, we know that the initial amount, P, is $600 and the annual interest rate, r, is 4%. Let's assume that the interest is compounded annually, i.e., n = 1.Substituting these values in the formula, we get:A = $600(1 + 0.04/1)1t Simplifying this expression,A = $600(1.04)t.

Taking the ratio of the final amount to the initial amount, we get: 3P = $600 × 3 = $1800. Therefore,A/P = 3 = (1.04)t.Dividing both sides by P, we get:3 = (1.04)t ln(3) = ln(1.04)t. Using the logarithmic property, we can bring down the exponent to the front:ln(3) / ln(1.04) = t Using a calculator, we get ≈ 22.56. Therefore, it will take approximately 22.56 years for the amount to triple.

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Since the triangles are similar, the value of x is equal to: C. 18 units.

In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;

AC/RS = AB/RT

By substituting the given side lengths into the above equation, we have the following:

x/24 = 24/32

By cross-multiplying, we have the following;

32x = 24(24)

32x = 576

x = 576/32

x = 18 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The solution of the system of equtaions:

Y = 5x + 1

Y = -x - 5

is (-1, -4), look at the graph at the end.

To solve a system of equations graphically just graph both of the equations, in this case are the lines y = 5x + 1 and y = -x - 5, in the same coordinate axis and then identify the point where these two lines intersect.

That point will be the solution of the given system of equations.

Said graph can be seen in the image at the end. There you can see two lines, one orange and one blue, and the lines intersect at the point (-1, -4), so that is the solution of the system.

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Answer:

(5x+40)+x+2(2x+20)=360

5x+40+x+4x+40=360

10x+80=360

10x=360-80

10x=280

x=28°

substitute x=28° into (5x+40)

=140+40= 180

therefore line Ac is the diameter of a he circle because a diameter divides a circle into 2 equal part and the angle on the line is 180° showing that the circle is on a straight line

The average rate of change of the function as x varies from 2 to 5 is 22.

Given function: g(x) = 1 – 2x + [tex]3x^2[/tex]

To find the average rate of change of the function as x varies from 2 to 5.

Solution: We are given a function: g(x) = 1 – 2x + [tex]3x^2[/tex]

The average rate of change of the function as x varies from a to b is given by:

Average rate of change = f(b) - f(a) / b - a

Let a = 2 and b = 5

We have to find the average rate of change of g(x) as x varies from 2 to 5.

So, the average rate of change of g(x) is given by:

Average rate of change = g(5) - g(2) / 5 - 2

= [1 - 2(5) + 3([tex]5^2[/tex])] - [1 - 2(2) + 3([tex]2^2[/tex])] / 3

= [1 - 10 + 75] - [1 - 4 + 12] / 3= 66 / 3= 22

Therefore, the average rate of change of the function as x varies from 2 to 5 is 22.

An average rate of change is the amount that the function changes on average over a specified interval.

The formula for average rate of change is given as the change in the function value divided by the change in x value for two distinct points on the function.

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The cost to ship a box containing 5 laptops, weighing a total of 11 kg (including the empty box), is $58.90, with a cost of $40.00 for the first 5 kg and $3.15 for each additional kilogram.

The total mass of the packed shipping box can be found by adding the mass of the laptops (5 * 1.65 kg = 8.25 kg) to the mass of the empty box (2.75 kg) for a total mass of 11 kg.

Since the cost to ship the box is $40.00 for the first 5 kg and $3.15 for each additional kilogram over 5 kg, we can split the total mass into two parts: the first 5 kg and the additional weight above 5 kg.

The cost to ship the first 5 kg is $40.00, and the remaining weight is 11 kg - 5 kg = 6 kg.

The cost to ship the additional 6 kg is $3.15 per kilogram, so the total cost to ship the packed box is:

$40.00 + $3.15 * 6 kg = $58.90

Therefore, the cost to ship the packed box is $58.90.

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Using the area formula for the rectangle, we can find that 2752 in² of plastic is needed to line the trough.

To determine the area a rectangle occupies within its perimeter, apply the formula for calculating a rectangle's area. Multiplying the length by the width yields the area of a rectangle (breadth).

As a result, the area of a rectangle with the length and breadth l and w, respectively, is calculated as follows. L × W = the rectangle's area. Hence, the area of a rectangle is equal to (length width).

Now in the given question,

We have 5 faces of the cuboid.

Now to find the total area of the required space we have to find the area of all the rectangles.

Area of rectangle with dimensions, l = 40inches and b = 14 inches.

Area = l × b

= 40 × 14

= 560in²

Now there are 2 rectangles with the same dimensions, so the total area = 560 + 560 = 1120in².

Now area of rectangles with dimensions, l = 14 inches and b = 24 inches.

Area = l × b

= 14 × 24

= 336in².

There are 2 rectangles with the same dimensions, so area = 336 + 336 = 672in².

Area of the final rectangle = l × b

= 40 × 24

= 960in².

So, the total required area = 1120 + 672 + 960 = 2752in².

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Yes

The logarithm function is continuous for all x>0. Its derivative is 1/x and r12 ln x dx = x ln x - x + c.

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Answer: 16x+3x^3−8

Please mark me brainliest :)

To increase £88 by 14%, we can use the multiplication method, which involves multiplying the original amount by the decimal equivalent of the percentage increase.

The multiplication method is a mathematical technique used to solve problems involving multiplication. It involves breaking down numbers into their constituent parts and then multiplying those parts together to arrive at the final answer.

To find the decimal equivalent of 14%, we divide the percentage by 100:

14% ÷ 100 = 0.14

This tells us that a 14% increase is equivalent to multiplying the original amount by 1.14 (1 + 0.14).

To increase £88 by 14%, we can multiply it by 1.14:

£88 x 1.14 = £100.32

Therefore, the increased amount is £100.32.

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Answer:

√1.5

Step-by-step explanation:

As a fraction, the square root of 3/2 can be expressed as √1.51 or just as √1.5.

The class intervals are given as:

0 - 15   15-30  30-45

2            3          2

A histogram is a graphical representation of the distribution of numerical data. It is a way of summarizing the shape and spread of a set of continuous data values into a series of bins or intervals.

The histogram is a bar graph-like representation of the data, where the data is grouped into intervals or bins on the horizontal axis and the frequency or count of observations falling into each bin is represented by the height of the bar on the vertical axis.

Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.

The class intervals are given as:

0 - 15   15-30  30-45

2            3          2

The histogram is provided below:

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The associative property works with expressions that use multiplication and addition. The correct option is (D).

The associative property is a rule in mathematics that allows us to change the grouping of the numbers or variables in an expression without changing the result. This property only applies to addition and multiplication, and not to subtraction and division.

The associative property of addition tells us that we can add a group of numbers in any order, and the result will be the same. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). The associative property of multiplication tells us that we can multiply a group of numbers in any order, and the result will be the same. For example, (2 × 3) × 4 is the same as 2 × (3 × 4).

However, the associative property does not work with subtraction and division. For example, (10 - 3) - 2 is not the same as 10 - (3 - 2). Similarly, (12 ÷ 2) ÷ 3 is not the same as 12 ÷ (2 ÷ 3). Therefore, the correct answer to the question is D - the associative property works with expressions that use multiplication and addition.

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The height is either 10 cm,12 cm,14 cm.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The base of the parallelogram has a length of 10 cm.

Here, area is not given so the height may be anything.

suppose h = 10

Hence, We get;

Area = base * height

      = 10 * 10

       = 100 cm²

if h = 12

area = 10 * 12

       = 120 cm²

if h = 14

area = 10 * 14

        = 140 cm²

Therefore, the height is either 10 cm,12 cm,14 cm.

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Answer: what do you mean? I need more info-

Step-by-step explanation:

I can answer it with more info :)

Answer:

30 feet

Step-by-step explanation:

Coordinates of Ann: (-4,3)

Coordinates of bottle caps: (4,-10)

Distance from Ann to bottle caps can be found out using the distance formula:
[tex]x_2=4, x_1=-4\\y_2=-3,y_1=-10\\Distance=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 } \\=\sqrt{(4-(-4))^2 + ((-10)-3)^2} \\=15.26\\15\text{ is the answer}[/tex]

The probability that 2 red balls and 2 blue balls are taken from the box is 3/7. This can be expressed mathematically as [tex](8C2 * 8C2) / (16C4) = 3/7[/tex].

To better understand this probability, let's look at an example. Say there are 8 red balls and 8 blue balls in the box. This can be represented as:

R = 8, B = 8

We want to determine the probability of taking 2 red balls and 2 blue balls out of the box. To do this, we need to calculate the total number of ways of selecting 4 balls from the box (16 balls in total) and then calculate the total number of ways of selecting 2 red and 2 blue balls out of the box.

The total number of ways of selecting 4 balls from the box can be expressed as (16C4). This is calculated by dividing the number of ways of selecting 4 balls out of 16 (16!) by the number of ways of arranging those 4 balls in any order (4!):

[tex](16C4) = 16! / 4! = 1820[/tex]

The total number of ways of selecting 2 red and 2 blue balls out of the box can be expressed as (8C2 * 8C2). This is calculated by multiplying the number of ways of selecting 2 red balls out of 8 (8C2) by the number of ways of selecting 2 blue balls out of 8 (8C2):

[tex](8C2 * 8C2) = 8C2 * 8C2 = 28[/tex]

The probability of taking 2 red balls and 2 blue balls out of the box is then the ratio of the number of ways of selecting 2 red and 2 blue balls out of the box (28) to the total number of ways of selecting 4 balls from the box (1820):

P(2 red balls, 2 blue balls) = 28 / 1820 = 3/7

In conclusion, the probability of taking 2 red balls and 2 blue balls out of a box containing 8 red balls and 8 blue balls is 3/7.

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Answer: Should be standard form.

Step-by-step explanation: Just cause the others don't really make sense and the equation looks basic.

Variable b represents the number of hours Kevin spends watching television each week.

A statement proving the equality of two mathematical expressions is known as an equation.

Given equation a + b = 15 relates the number of hours.

If here Kevin spends doing homework each week (represented by the variable "a") and the number of hours he spends watching television each week (represented by the variable "b").

Since the total number of hours Kevin spends doing homework and watching television each week is 15, we can write:

homework + watching television = 15 hours

a + b = 15

To find out what b represents, we can rearrange the equation to solve for b:

b = 15 - a

This means that b represents the number of hours Kevin spends watching television each week, given that he spends a hours doing homework each week and the total number of hours spent on both activities is 15.

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Complete question-

The equation is a + b = 15

Answer:

O I, II & III

Step-by-step explanation:

(2, 3) and (1, 1)

m = (3 - 1)/(2 - 1) = 2

y = 2x + b

1 = 2(1) + b

b = -1

The equation of the line is

y = 2x - 1

I) y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1   Yes

II) y = 2x - 1   Yes

III) y = 2(x - 1) + 1 = 2x - 2 + 1 = 2x - 1   Yes

Answer: O I, II & III

Answer:

what's your exact question

Answer:

can u pls type the full question

Two plus x divided by twelve equals one divided by three

Case 1 :

Rewrite into numbers : 2 + x /12 = 1/3

-> x/12 = 1/3 - 2 = -5/3

-> x = -5/3 x 12 = -20

Case 2 :

Rewrite into numbers : (2 + x)/12 = 1/3

-> 2 + x = 1/3 x 12 = 4

-> x = 4 - 2 = 2

i dont know if you meant it the right way or the wrong way but ill just put them both

x=2

Step-by-step explanation:

(2+x)/12=1/3

3(2+x)=12

2+x=4

x=4-2

x=2

Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.

What is a free operant preference assessment? Free operant preference assessment refers to a behavior analysis process used to determine the preferred stimulus of an individual in a naturalistic environment. This method measures the potential and meaningful reinforcers through the observation of a child's free time. A reinforcement is a consequence that strengthens a behavior.The free operant preference assessment is frequently utilized in the autism field to identify reinforcing stimuli. It is a process of assessing a child's preferred items and actions in a naturalistic setting.The free operant preference assessment is conducted in three different stages: Stage 1: involves observation of preferred items and items that are likely to become potential reinforcers, Stage 2: involves assessing for a hierarchy of items and stage 3 involves using the data gathered to plan the student’s schedule, including reinforcement and non-contingent time periods.

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FREE OPERANT PREFERENCE ASSESSMENT. Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.

A free operant preference assessment is a measure of the attractiveness or preference for various stimuli by measuring an individual's time spent with them.

Free access to different stimuli is given to the individual to determine their preferences, which are subsequently used to reinforce the desired behavior or work on behavior modification through behavior analysis.

The steps to conducting a Free Operant Preference Assessment: Prepare the list of stimuli: Initially, you have to prepare a list of stimuli that you believe may act as a reinforcer for the individual, which may include toys, foods, or other things that the person likes.

Prepare the environment: Arrange the stimuli in a room, and let the individual enter it.

Make sure that there is sufficient space to move around and that the person has free access to all of the stimuli.  

Record the time the individual spends with each stimulus. You can observe the person, either directly or through video recording.

 Based on the data obtained, the most preferred and least preferred stimuli can be identified. Then, these preferred stimuli can be used as potential reinforcers.

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Answer:

it is a triangle bc it has angles of points

Step-by-step explanation:

Answer:

  4/33

Step-by-step explanation:

You want to write 0.1212...(repeating) as a simplified fraction.

A repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.

Here, there are 2 repeating digits, so the basic fraction is ...

  12/99

This can be reduced by removing a factor of 3 from numerator and denominator:

  [tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]

__

Additional comment

Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.

  0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99

Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.

You can also approach this by writing the number as a continued fraction. The basic form is ...

  [tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]

where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.

A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.

To estimate a population proportion with a margin of error of 1% and a 99% confidence interval, we would need a sample size of at least 6644 individuals.

The formula to calculate the sample size is:

n = [z² x p(1-p)] / e²

where:

n is the sample size

z is the z-score corresponding to the desired confidence level (in this case, 2.576 for a 99% confidence level)

p is the planning value for the population proportion, which we don't know in this case, so we will assume the worst-case scenario of p=0.5 (which gives us the maximum sample size needed)

e is the desired margin of error

Plugging in the values, we get:

n = [(2.576)² x 0.5(1-0.5)] / (0.01)²

n = 6643.04

Since we need to round up to the next whole number, the minimum sample size needed is 6644.

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Total number of  cups of berries does the school cafeteria have is 600

Addition is a basic mathematical operation that involves combining two or more numbers or quantities to find a total or sum. In other words, it is the process of finding the total amount when two or more numbers are added together.

To find the total number of cups of berries in the school cafeteria, you can add the number of cups of strawberries and blackberries.

The school cafeteria has 150 cups of strawberries and 450 cups of blackberries, so

Total cups of berries = cups of strawberries + cups of blackberries

Total cups of berries = 150 + 450

Total cups of berries = 600

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The following conditions must be met to conduct a two-proportion significance test:

the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.

The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.

To conduct the two-proportion significance test, the following conditions must be met:

Populations must be independent.

Sample sizes are greater than 30.

The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.

The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.

In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.


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Answer: 1250 miles

Step-by-step explanation:

50 miles in 1/5 of an hour = 250 miles in 1 hour = 1250 miles in 5 hours

Answer:

1,250

Step-by-step explanation:

50 divided by 1/5 equals 250.

Multiply 250 by 5.

250*5= 1,250