You are trying to get back in shape. In the first week, you swim 15 laps every day.
Then, each week, you increase your distance by 5 laps. Which recursive formula
models this situation?

The monthly periodic rate is 1.25%, the finance charge is $6.99 and John's new balance is $566.24.

This monthly periodic rate calculated as

Monthly periodic rate = Annual percentage rate / 12

So, we have

Monthly periodic rate = 15% / 12

Monthly periodic rate = 1.25%

This is the interest charged for the month.

So, we start by calculating the average daily balance using:

Average daily balance = ((Previous month's balance + Current month's purchases and cash advances) - Current month's payments and credits) / Number of days in the month

Substitute the known values in the above equation, so, we have the following representation

Average daily balance = (428.10 + 281.15) - 150.00) / 31

Average daily balance = $18.04

So, we have

Finance charge = Average daily balance x Monthly periodic rate x Number of days in the month

Finance charge = $18.04 x 1.25% x 31

Finance charge = $6.99

The new balance is calculated as

New balance = Previous month's balance + Current month's purchases and cash advances + Finance charge - Current month's payments and credits

Substitute the known values in the above equation, so, we have the following representation

New balance = $428.10 + $281.15 + $6.99 - $150.00

New balance = $566.24

Hence, the new balance is $566.24

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This represents the number of small rolls the club sold.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides.

To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

In the equation 3s + 135 = 4.5 (s+10)

The equation 3s + 135 = 4.5(s + 10) can be used to represent this situation, where s represents the number of small rolls the club sold.

Hence, represents the number of small rolls the club sold.

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Using the vertical line test we can see that this is not a function.

When we have a graph of a relation, one thing we can do to check if this is a function is do the vertical line test.

If you can draw a vertical line that intercepts the graph more than once, then it is not a function.

Here we can see a circle, multiple lines intercept the graph twice,so this is not a function.

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As a result, the price of the ribbons is proportional to the number of party favours, with each Favour costing (3/4) dollars.

A measurable quality such as weight, length, time, volume, or pressure is referred to as quantity. A unit is a unit of measurement that is used to measure other quantities (for example, a gramme, a second, a liter, or a pascal are unit of the above quantities). Chemists employ a wide range of measurements.

The amount of ribbon required for n party favours is calculated as follows:

19n inches (since each party Favour requires 9 inches of ribbon)

As the price is stated in dollars per yard, we must first convert the amount of inches to yards before we can determine the ribbon's total cost. Since there are 36 inches in every yard, we can calculate the number of yards by dividing the total amount of inches by 36:

Total yards of ribbon = (9n) / 36 = (n) / 4

Thus, the following phrase represents the ribbon's overall cost:

3 × (n/4) = (3n) / 4 dollars

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Correct two-way relative frequency table for the data is option A.

A frequency table is a way to organize and display data in a table format by showing the number of times a certain data point or category appears in a given dataset. It is used in statistics and data analysis to quickly and easily understand the distribution of a set of data.

A frequency table typically consists of two columns: the first column lists the categories or data points, and the second column lists the frequency or count of each category. The categories can be anything from numbers to words, but they should be mutually exclusive and exhaustive, meaning that each data point should fit into one and only one category, and all possible data points should be included in the table.

Frequency tables are commonly used to represent categorical data, such as survey responses, demographic data, and results of experiments. They are also useful for visualizing patterns and trends in the data, such as the most common or rare categories, and can be used to calculate various statistical measures, such as percentages, proportions, and averages.

The correct answer is:

                                    Playing        Listening      Watching         Row Totals

                                    Computer   to Music        Movies/TV

                                    Games      

Drama Club Students 5%            25%          20%          50%

Art Club Students         18.75%     15%          16.25%          50%

Column Totals         23.75%     40%          36.25%          100%

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The complete question is:

According to algebraic identities ,

[tex] \cos( \frac{ \theta}{2} ) = \sqrt{ \frac{1 + \cos(\theta) }{2} } \\ [/tex]

Therefore ,

[tex]\boxed{ { \cos}^{2} (\frac{\theta}{2} ) = \frac{1 + \cos(\theta) }{2} } \\ [/tex]

hope helpful! :)

Answer:

Using the half-angle formula for cosine, we can express cos(θ/2) in terms of the values of cos θ and sin θ:

cos(θ/2) = ±√[(1 + cos θ)/2]

The sign of the square root depends on the quadrant in which θ/2 lies.

Since we are given cos^2 θ/2, we need to eliminate the square root in the expression for cos(θ/2). To do this, we can use the fact that:

sin^2 θ/2 = 1 - cos^2 θ/2

Substituting the expression for cos^2 θ/2 from the previous identity, we get:

sin^2 θ/2 = 1 - cos^2 θ/2 = 1 - cos^2 (θ/2)

Solving for cos(θ/2) in terms of sin(θ/2), we get:

cos(θ/2) = ±√[1 - sin^2 θ/2]

Substituting the expression for sin^2 θ/2 from above, we get:

cos(θ/2) = ±√[cos^2 θ/2]

The sign of the square root depends on the quadrant in which θ/2 lies. Therefore, the completed identity for cos^2 θ/2 is:

cos(θ/2) = ±cos θ/2

Step-by-step explanation:

The answer to the expression is 24.

Expression is an action or a way of speaking that shows a feeling, opinion, or attitude. It can be done through words, body language, facial expressions, tone of voice, and other forms of communication. Expression is used to communicate ideas, thoughts, emotions, and feelings. It is a fundamental way of connecting with others and conveying meaning.

To evaluate the expression, we need to first calculate the values of f(5) and f(-12). For f(5), the function is defined as

f(x) = 2x + 3. Thus, f(5) = 2(5) + 3 = 13. For f(-12), the function is f(x) = -x + 7. Thus, f(-12) = -(-12) + 7 = 19. We can now calculate 3f(5) - f(-12) = 3(13) - 19 = 24.

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Answer:

f(x) = (x-5)(x+2)^2

Step-by-step explanation:

use desmos graphing calculator! it's very helpful and free :)

Answer:

From the graph,

The zeros of the function are at x= -2 and x= 5

But since at root -2,it doesn't cross the x axis, the root has even multiplicity

Ans:(x+2)^2 (x-5).....option B

The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The ratio of the corresponding sides will be constant. Then the scale factor is given as,

SF = 12 / 8

SF = 1.5

The equation is given as,

x / 6 = 12 / 8 = 15 / y

From the first two terms, then we have

x / 6 = 12 / 8

x = 9

From the last two terms, then we have

12 / 8 = 15 / y

y = 10

The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.

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We have the fοllοwing respοnse after answering the given questiοn: The equatiοn mοnthly payment, rοunded tο the next penny, is $959.49.

In a mathematical equatiοn, the equals sign (=), which cοnnects twο claims and denοtes equality, is utilized. In algebra, an equatiοn is a mathematical statement that prοves the equality οf twο mathematical expressiοns.

Fοr instance, in equatiοn 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressiοns can be used tο describe the relatiοnship between the twο sentences οn either side οf a letter. The lοgο and the particular piece οf sοftware frequently cοrrespοnd. like, fοr instance, 2x - 4 = 2.

[tex]P = \frac{rP}{(1 - (1 + r)^{-n}}[/tex]

where P is the regular mοnthly payment, r is the interest rate each mοnth, n is the number οf payments, and P is the amοunt οf interest that has already been paid in dοllars.

r = 0.027 / 12 = 0.00225

The number οf payments must then be determined. There are 120 mοnthly payments fοr a 10-year mοrtgage.

n = 120

P = 1% * $100,000 = $1,000

Nοw that the data have been entered, we can cοmpute the monthly payment:

[tex]P = (0.00225 \times $99,000 / (1 - (1 + 0.00225)^{(-120)})) + $8.33[/tex]

where $8.33 represents the mοnthly charge fοr the prepaid interest and $99,000 represents the tοtal amοunt bοrrοwed after subtracting the prepaid interest.

If we cοndense this phrase, we get:

P = $959.49

Hence, The mοnthly payment, rοunded tο the next penny, is $959.49.

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The data transfer rate per second​ is found as: 24 KB / sec.

Data transfer:  5760 KB

Time : 240 seconds

Rate per second​ = Data transfer / Time

Rate per second​ = 5760/ 240

Rate per second​ = 24

Thus, the data transfer rate per second​ is found as: 24 KB / sec.

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Answer:

Step-by-step explanation:

[tex]6x-10=2x+18[/tex]   (opposite sides of parallelogram are equal)

[tex]4x-10=18[/tex]           (subtracted [tex]2x[/tex] from both sides)

[tex]4x=28[/tex]                   (added 10 to both sides)

[tex]x=7[/tex]                       (divided both sides by 4)

Substitute [tex]x=7[/tex] to find length AB:

[tex]AB=6x-10[/tex]

      [tex]=6[/tex]×[tex]7-10[/tex]

       [tex]=32[/tex]

Answer:

x = 4

Step-by-step explanation:

Answer:

B. 15.2 inches.

Answer:

40) sorry if I'm wrong :<

Answer:

£33.93

Step-by-step explanation:

A 13% discount means that the new price will be 87% of the original, as 100 - 13 = 87.

This can be calculated by converting the percentage into a decimal, then multiplying by the decimal:

87 / 100 = 0.87

39 * 0.87 = 33.93

To write the equation of a rational function that has been reflected, shifted 6 down, 8 to the right and stretched by a factor of 4, we have to start with the basic rational function which is:

To shift it down by 6, we must subtract 6 from the function, so we have:

To shift the function to the right by 8, we substitute x for (x-8), finding this result:

To stretch the function by a factor of 4, we have to multiply the denominator by 4, which will result in:

Therefore, the equation of the rational function will be:

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Step-by-step explanation:

72 hours total baking during 6 days.

that means 72/6 = 12 hours of baking every day.

3 hours of these 12 hours he used to bake bread.

that leaves 12 - 3 = 9 hours every day for baking cakes.

so, to summarize all this in an arithmetic expression :

x = 72/6 - 3 = 9

The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.

An exponential function is a mathematical function that increases or decreases at a rate proportional to its current value. Exponential functions are used in a variety of sciences and everyday applications. For example, population growth is an exponential function of time because the population increases by a fixed percentage each year.

The exponential function f(x) = 565(1.026)ˣ models the population of a country, f(x), in millions, x years after 1970. Substituting 0 for x, the population of the country in 1970 was 565 million. Substituting 27 for x, the population of the country in 1997 was 1,118 million. The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.

It appears that the population of the country is growing by a factor of 3 every 27 years. This is evident from the fact that the population in 1997 is 3 times the population in 1970, and the population in 2024 is 3 times the population in 1997. This pattern is expected to continue with the population in 2051 being 3 times the population in 2024.

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Answer:

Step-by-step explanation:

We know that the life expectancy of the tires is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Let X be the life expectancy of the tire. Then X ~ N(40,000, 5,000^2).

To find the percentage of tires that will have a life of 34,000 to 46,000 miles, we need to calculate the z-scores for both values using the formula:

z = (X - μ) / σ

where X is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

For X = 34,000:

z = (34,000 - 40,000) / 5,000 = -1.2

For X = 46,000:

z = (46,000 - 40,000) / 5,000 = 1.2

Now, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a table of standard normal probabilities or a calculator to find this area.

Using a standard normal table or a calculator, we find that the area to the left of z = -1.2 is 0.1151, and the area to the left of z = 1.2 is 0.8849. Therefore, the area between these two z-scores is:

0.8849 - 0.1151 = 0.7698

So, approximately 76.98% of the tires will have a life of 34,000 to 46,000 miles.

Answer: To find the perimeter of triangle JKL, we need to find the length of each side and add them up. We can use the distance formula to find the length of each side:

Side JK = sqrt[(2 - (-5))^2 + (3 - (-7))^2] = sqrt[7^2 + 10^2] = sqrt[149]

Side KL = sqrt[(-1 - 2)^2 + (-7 - 3)^2] = sqrt[(-3)^2 + (-10)^2] = sqrt[109]

Side LJ = sqrt[(-1 - (-5))^2 + (-7 - (-7))^2] = sqrt[4^2] = 4

Therefore, the perimeter of triangle JKL is:

P = JK + KL + LJ = sqrt[149] + sqrt[109] + 4

To find the area of triangle JKL, we can use the formula:

A = 1/2 * base * height

We can choose any side as the base, and the corresponding height will be the perpendicular distance from the opposite vertex to the base. Let's choose side KL as the base. The height from vertex J to side KL is the perpendicular distance between J and the line containing KL. We can find this distance using the formula for the distance between a point and a line:

Area = 1/2 * KL * h

where h = |(2 - (-1))( -7 - 3) - (-5 - 2)(-1 - 3)| / sqrt[(-1 - 2)^2 + (-7 - 3)^2]

Simplifying the above expression, we get:

h = 24 / sqrt[109]

Therefore, the area of triangle JKL is:

A = 1/2 * KL * h = 1/2 * sqrt[109] * 24 / sqrt[109] = 12

So, the perimeter of triangle JKL is sqrt[149] + sqrt[109] + 4, and the area of triangle JKL is 12.

Step-by-step explanation:

Answer:

the expression

y -7/x-5 = 1/3 or 2/6

Step-by-step explanation:

Cross multiplying both sides:

3(y-7) = x - 5

3y - 21 = x - 5

3y - x = 21 - 5

3y - x = 16

The simplified equation is 3y-x=16.

Answer:

The graph will shift 3 units down

Answer:

Step-by-step explanation:

We can expand and simplify the equation as follows:

23(x+3) = 23(x-6)

23x + 69 = 23x - 138

69 = -138

The last equation is clearly false, which means there is no value of x that can satisfy the original equation.

This is an example of a contradiction, where the equation leads to an impossible statement. Therefore, the equation has no solution.

Answer:

Step-by-step explanation:

Given functions:

    [tex]r(x)=x^2+5x+14[/tex]

    [tex]c(x)=x^2-4x+5[/tex]

where:

Profit is calculated by subtracting expenses from revenue.

Therefore, the composite function for profit is:

Since x represents the number of months the store has been open:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.

To calculate the total amount of profit in the first 5 months, substitute x = 5 into the composite function:

[tex]\begin{aligned}\implies (r-c)(5)&=r(5)-c(5)\\&=(5^2+5(5)+14)-(5^2-4(5)+5)\\&=(25+25+14)-(25-20+5)\\&=(50+14)-(5+5)\\&=64-10\\&=54\end{aligned}[/tex]

Since the revenue and expenses functions are measured in hundred of dollars, so too is the profit function. Therefore, the amount of profit generated in 5 months is $5,400.

Answer:

Step-by-step explanation:

20 degees

Answer:

Step-by-step explanation:

46+13 = 59

Answer:

Let Mackenzie have x

and Taylor have y

Then, since Mackenzie has 46.13 less than Taylor,

x = y - 46.13

Therefore, to show how much money Mackenzie has we will use the equation

x = y - 46.13

remember Makenzie has $x.

Taylor has $y

Makenzie money is less than Taylor's money by 46.13

so we take away 46.13 from Taylor's money to get that of Makenzie

Makenzie's money x = Taylor's money y - 46.13

x = y - 46.13

Step-by-step explanation:

Answer:

Let's use option C to represent the relationship between the number of bags of dog food sold and the profit made:

Profit per bag of dog food = $5.50

Total expenses per day = $2,500

The store wants to make a profit of at least $5,225 per day.

If d represents the number of bags of dog food sold, then the profit made can be represented as:

Profit = Revenue - Expenses

Revenue = Profit + Expenses

Revenue = $5.50d + $2,500

To make a profit of at least $5,225 per day, we can set up the following inequality:

$5.50d + $2,500 ≥ $5,225

Simplifying:

$5.50d ≥ $2,725

Dividing both sides by $5.50:

d ≥ 500

Therefore, the store must sell at least 500 bags of dog food per day to make a profit of at least $5,225 per day.

The correct inequality that represents this relationship is option C: 5.50d +2,500 ≥ 5,225.