On a bicycle, Lomasi rides for 10 hours and is 22 miles from her house. After riding for 12 hours, she is 26 miles away. What is Lomasi's rate?

The recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs.

A recursive definition of a function is when the definition of the function involves the function itself. This type of definition is used to express complex operations in a simpler form. It is an effective way to break down a complicated problem into simpler, manageable parts. It allows us to define a set of rules in terms of smaller versions of itself, which can then be worked out using a series of steps.

A recursive definition for the function f is a process by which the value of f for a given input can be defined in terms of the values of f for smaller inputs. In other words, a recursive definition for f is a definition that describes how f can be calculated from its inputs.

In this case, the recursive definition for the function f is given by:

f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3

This means that the value of f for a given x can be calculated by multiplying 500 (the value of f for x = 1) by 1/5 raised to the power of x-1. This is because f(1) = 500, f(2) = 100 (1/5 * 500), and f(3) = 20 (1/5 * 1/5 * 500).

This recursive definition can also be expressed in a more general form as:

f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3

Where a and b are constants. In this case, a is 500 and b is 1/5.

In conclusion, the recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs. This definition can also be expressed in the more general form of f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3.

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We are given the expression √4x^2+100 and the substitution x/5=tan(θ). Our goal is to use the substitution to write the expression as a trigonometric expression and simplify as much as possible.

First, let's substitute x/5=tan(θ) into the expression:

√4(tan(θ)*5)^2+100

Next, let's simplify the expression:

√4(25tan^2(θ))+100

√100tan^2(θ)+100

Now, let's factor out 100 from the expression:

√100(tan^2(θ)+1)

10√tan^2(θ)+1

Finally, let's use the trigonometric identity 1+tan^2(θ)=sec^2(θ) to simplify the expression further:

10√sec^2(θ)

10sec(θ)

Therefore, the expression √4x^2+100 can be written as 10sec(θ) using the substitution x/5=tan(θ).

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The exact number for tan(t + 71) is -0.5846.

To find tan(t + 71), we can use the formula for the sum of two angles:
tan(t + 71) = (tan t + tan 71)/(1 - tan t * tan 71)

Given that tan t = 5, we can substitute this value into the formula:
tan(t + 71) = (5 + tan 71)/(1 - 5 * tan 71)

To find the exact number for tan 71, we can use a calculator or a table of trigonometric values. The exact value of tan 71 is approximately 2.9042.

Substituting this value into the formula, we get:
tan(t + 71) = (5 + 2.9042)/(1 - 5 * 2.9042)

Simplifying the expression, we get:
tan(t + 71) = (7.9042)/(1 - 14.521)
tan(t + 71) = (7.9042)/(-13.521)
tan(t + 71) = -0.5846

Therefore, the exact number for tan(t + 71) is -0.5846.

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Answer:

-0

Step-by-step explanation:

A blue token is worth 15 points and a yellow token is worth 5 points.

Two or more expressions with an Equal sign is called as Equation.

Let b  represent the point value of a blue token and

y represent the point value of a yellow token.

We can set up two equations:

4b + 7y = 95 (Jillian's score)

4b + 3y = 75 (Jacob's score)

Subtracting the second equation from the first, we get:

4b + 7y - (4b + 3y) = 95 - 75

Simplifying this, we get:

4y = 20

Dividing both sides by 4, we get:

y = 5

So a yellow token is worth 5 points.

Now we can substitute this value of "y" into one of the original equations and solve for "b".

4b + 7y = 95

4b + 7(5) = 95

4b + 35 = 95

4b = 60

b = 15

So a blue token is worth 15 points.

Therefore, a blue token is worth 15 points and a yellow token is worth 5 points.

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The width of the rectangle is 4 2/3 yards.

The area of a rectangle is the measure of the total region that the rectangle occupies in two-dimensional space.

It is calculated by multiplying the length of the rectangle by its width.

The formula for the area of a rectangle is:

Here we have

The area of a rectangular tablecloth is 8 3/4 square yards.  

The width of the tablecloth is 1 7/8 yards

For simple calculation convert given fractions into improper fractions

=> 8 3/4 = 35/4 yards

=> 1 7/8 = 15/8  yards  

Let 'x' be the breadth of the rectangle

As we know Area of the rectangle = Length ×  width

=> x × 15/8 = 35/4

=> x = 35/4 × 8/15

=> x = 14/3

Here, 14/3 = 4 2/3 yards  

Therefore,

The width of the rectangle is 4 3/2 yards.

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The length of DC is √102, which is the simplest radical form.

The proportion of corresponding sides in similar triangles is the same. This is known as the similar triangles theorem.

In other words, if two triangles are similar, then the ratio of the lengths of any two corresponding sides is the same.

Since DE is parallel to AB, we can use similar triangles to set up the following proportion:

DC/AC = DE/AB

Substituting the given values, we get:

DC/17 = 6/AB

Since AB is the same length as DC, we can replace AB with DC:

DC/17 = 6/DC

Cross-multiplying and simplifying, we get:

DC^2 = 17 * 6

DC^2 = 102

DC = √102 in simplest radical form

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The next three terms in the sequence are 1/81, -1/243, and 1/729.

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:

a, ar, ar^2, ar^3, ...

where a is the first term, r is the common ratio

To identify the next three terms in the sequence, we need to first determine the pattern. Looking at the sequence, we can see that each term is obtained by multiplying the previous term by -1/3, which means that this is a geometric sequence with a common ratio of -1/3.

Using this common ratio, we can find the next three terms in the sequence as follows:

-1/3 * (-1/27) = 1/81

1/81 * (-1/3) = -1/243

-1/243 * (-1/3) = 1/729

Therefore, the next three terms in the sequence are 1/81, -1/243, and 1/729.

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Answer:

20%

Step-by-step explanation:

Formula - multiply decimal by 100

0.2- Word form= two tenths

Fraction * 2/10 *

0.2 (multiply by 100)

0.2 x 100 = 20

20% is 0.2 as a percent

( hope this helps I’m online so ask any questions you need)

Answer:

x = -5.5

Step-by-step explanation:

-2x - 4 + 2x + 32 - 2x - 21 = 18​

-2x - 4 + 32 - 21 = 18

-2x + 7 = 18

-2x = 11

x = -5.5

So, the answer is x = -5.5

The statements that are true about the function when graphed on a coordinate plane include the following:

C. The relative minimum of the function is (3, 0)

E. When t > 3, the function is increasing.

In order to determine the minimum and maximum of this function, we would have to determine the critical points where the derivative of the function is equal to zero or undefined, and then evaluate the function at these critical points and at the endpoints of the interval.

By taking the first derivative of the given function and factorizing, we have:

f(t) = t³ - 6t² + 9t

f'(t) = 3t² - 12t + 9  

3t² - 12t + 9 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0

t = 3 and t = 1

Therefore, the critical points of the function are at t = 1 and t = 3.

By taking the second derivative of the given function and factorizing, we have:

f''(t) = 6t - 12

At point t = 1, we have:

f''(1) = 6(1) - 12 = -6 (it is less than zero).

Therefore, f(t) has a local maximum at t = 1.

At point t = 3, we have:

f''(3) = 18 - 12 = 6 (it is greater than zero).

Therefore, the function f(t) has a local minimum at t = 3.

At t = 4, f''(4) = 24 - 12 = 12

At t = 5, f''(5) = 30 - 12 = 18

In conclusion, the relative minimum of the function is (3, 0) and when t > 3, the function would increase.

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Answer:

Multiply the numerator and denominator by the conjugate.

a with a small 3 b with a small 5 and check under it will be a small a and small b

Step-by-step explanation:

The total amount will Perri need when she gets the keys for the house at closing is $41,860.

Perri is making a 7% down payment on the $364,000 purchase price of the condominium, so her down payment will be

0.07 x $364,000 = $25,480.

Perri estimates her closing costs to be 4.5% of the purchase price, which is 0.045 x $364,000 = $16,380.

Therefore, the total amount Perri will need when she gets the keys for the house at closing is the sum of the down payment and the closing costs, which is $25,480 + $16,380 = $41,860.

So the answer is (C) $41,860.

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Answer:

Second option

Step-by-step explanation:

Check the relationship between the x digits and compare with y digits. It must be the same all through

In the second option x =2y for all the digits

4:2, 7:3.5,8:4,10:5

The correct answer is O for some discrete probability distributions but not all.

This is because the probability of a random variable X being less than 8 can vary depending on the type of distribution it follows. For some discrete distributions, such as a binomial distribution, the probability of X < 8 can be calculated by summing the probabilities of all possible values of X that are less than 8. However, for other discrete distributions, such as a Poisson distribution, the probability of X < 8 may not be as straightforward to calculate. Therefore, the statement that P(X < 8) = P(X < 8) is true for some discrete distributions but not all.

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Simplifying the expression (2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27) will result to (x - 5)/(3x(x - 3)(x + 5)).

To simplify the given expression completely, we need to factor the numerator and denominator of each fraction, and then simplify by canceling out common factors.

(2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27)

= (2x(x² - x - 20))/(2x^2 + 5x - 12) ÷ (6x^2(x^2 - 25))/(8x^3 - 27)

= (2x(x - 5)(x + 4))/(2x² + 8x - 3x - 12) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (2x - 3)(4x² + 6x + 9)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (2x - 3)/(6x(x - 5)(x + 5))

= (x - 5)/(3x(x - 3)(x + 5))

Therefore, the simplified expression is (x - 5)/(3x(x - 3)(x + 5)).

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The transformation applied to the function f(x) is a translation of 4 units up.

Here we can see that:

f(x) = √(x + 3)

and g(x) is a vertical translation of k units:

g(x) = f(x) + k

To get the value of k, just look how many units the graph has been translated up ( remember that each of the smalls squares in the coordinate axis represents a single unit), we can see that it is 4 units up, then k = 4

We have a vertical translation of 4 units up.

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Thus, 2002 + 23 = 2025 is the year at which the populace hits 7 million.

The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

To find the year when the population reaches 7 million people, we need to solve the equation:

f(x) = 7

where f(x) represents the population, in millions of x years after 2002, and x is the number of years after 2002.

Substituting the given function f(x) = 6.7(1.0032)x into this equation, we get:

6.7(1.0032)x = 7

Dividing both sides by 6.7, we get:

1.0032x = 1.0448

When we take the natural log of both parts, we obtain:

ln(1.0032)x = ln(1.0448)

Using the logarithmic identity ln(aᵇ) = b ln(a), we can simplify this to:

x ln(1.0032) = ln(1.0448)

Dividing both sides by ln(1.0032), we get:

x = ln(1.0448) / ln(1.0032)

Using a calculator, we find:

x ≈ 22.6

Therefore, the population will reach 7 million people approximately 22.6 years after 2002. Rounding this to the nearest whole number, we get:

x ≈ 23

So the year when the population reaches 7 million people is 2002 + 23 = 2025.

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The coordinates of point B' after the translation are given as follows:

B'(1,-2).

A translation happens when either a figure or a function are moved horizontally or vertically.

The meaning of the translation for this problem is given as follows:

The coordinates of point B are given as follows:

B(5,1).

Hence the coordinates of point B' are given as follows:

Meaning that the last option is correct.

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Answer:

∠ A = 19.8°

Step-by-step explanation:

the 3 angles of the triangle sum to 180°

sum the 3 angles and equate to 180

5x - 18 + 4x + x = 180

10x - 18 = 180 ( add 18 to both sides )

10x = 198 ( divide both sides by 10 )

x = 19.8

Then

∠ A = x = 19.8°

Answer:

Step-by-step explanation:

Kelsie has written checks for a total of $46 + $82 + $264 + $127 = $519.

Since she only has $370 in her account, this means she has overdraft by $519 - $370 = $149.

Therefore, the bank will charge her $22 for each overdraft, which gives a total of $22 * 7 = $154.

Thus, Kelsie owes the bank a total of $519 + $154 = $673. Answer: \boxed{673}.

The cost of backpack is $38.97. The markup amount is $13.64. The regular unit selling price for the backpack is $52.61
Mountain Equipment Co-op will be $19.02.The profit will be $19.02, which is higher than the profit of $6.63 when selling at the regular unit selling price.

To find the cost, markup amount, regular unit selling price, and profit for the backpack, we need to use the following formulas:

1. Cost = List Price - Trade Discount - Quantity Discount
2. Markup Amount = Cost × Markup Percentage
3. Regular Unit Selling Price = Cost + Markup Amount
4. Profit = Regular Unit Selling Price - Cost - Expenses

Let's plug in the given values and calculate each of these:

1. Cost = $59.95 - ($59.95 × 0.25) - ($59.95 × 0.10) = $59.95 - $14.99 - $5.99 = $38.97
2. Markup Amount = $38.97 × 0.35 = $13.64
3. Regular Unit Selling Price = $38.97 + $13.64 = $52.61
4. Profit = $52.61 - $38.97 - ($38.97 × 0.18) = $52.61 - $38.97 - $7.01 = $6.63

Now, if MEC sells the backpack at the MSRP (Manufacturer's Suggested Retail Price), the profit will be different. The MSRP is typically higher than the regular unit selling price, so the profit will be higher as well. Let's say the MSRP is $65. The profit would be:

Profit = MSRP - Cost - Expenses = $65 - $38.97 - ($38.97 × 0.18) = $65 - $38.97 - $7.01 = $19.02

So, if MEC sells the backpack at the MSRP, the profit will be $19.02, which is higher than the profit of $6.63 when selling at the regular unit selling price.

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The sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.

A cοnnectiοn between twο expressiοns οr values that is nοt equal in mathematics is referred tο as inequality. Hence, inequity results frοm imbalance. In mathematics, an inequality establishes the cοnnectiοn between twο nοn-equal numbers. Equality and inequality are nοt the same.

Use the nοt equal symbοl mοst frequently when twο values are nοt equal (). Values οf any size can be cοntrasted using a variety οf inequalities.

By changing the twο sides until just the variables are left, many straightfοrward inequalities may be sοlved.

Nοnetheless, a variety οf factοrs suppοrt inequality: Bοth sides' negative values are split οr added. Exchange the left and the right.

5x - 15 + 15 > -65 + 15

5x > -50

5x/5 > -50/5

x > -10

Because the inequality is severe, the οpen circle at -10 shοws that it is nοt part οf the sοlutiοn set (i.e., x must be greater than -10, nοt greater than οr equal tο -10).

The right arrοw shοws that the sοlutiοn set gοes οn fοrever in that directiοn.

Hence, the sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.

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The total amount of merchandise that stores A and B sold is 21x²+5x+8

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, are two stores selling merchandise given by equation,

A = 13x²+8x-3 and B = 8x²-3x+11, we need to find the total amount of merchandise that stores A and B sold.

We add both the equations to find the same,

Total merchandise sold = 13x²+8x-3 + 8x²-3x+11

= 21x²+5x+8

Hence, the total amount of merchandise that stores A and B sold is 21x²+5x+8

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The area of a cross section that passes through the center of a sphere with a diameter of 7 centimeters will be 12.25π cm².

Three-dimensional objects with a sphere-like shape exist in all three dimensions. Three axes, the x-axis, y-axis, and z-axis, are used to define the sphere. The key distinction between a circle and a sphere is this. In contrast to other 3D shapes, a sphere lacks any vertices or edges.

The sphere's points are evenly spaced apart from one another on its surface. In light of this, the sphere's surface and core are always equally separated from one another. The sphere's radius is the measurement between these points. Ball, globe, planets, and other objects are all examples of spheres.

Given : Diameter of Sphere = 7 cm

∴ Radius = 7/2 = 3.5 cm.

Since It is a cross section in a sphere, so, it would be circle.

So, Area of the cross section = Area of circle

Hence, Area of Cross section = πr²

                                                 = π (3.5)²

                                                 =  12.25π cm²

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The 95% confidence interval for the population proportion of defective calculators is (0.0015, 0.0069).

Hence, (0.0015 < p < 0.0069).

According to the given information

we can use the formula for calculating the confidence interval for a population proportion,

⇒ P ± z√(P(1-P )/n)

Where,

P = sample proportion of defective calculators = 5/1200

                                                                              = 0.0042

n = sample size = 1200

z = z-score for 95% confidence level = 1.96 (from standard normal distribution table)

Substituting the values in the formula, we get,

⇒ 0.0042 ± 1.96√(0.0042(1-0.0042)/1200)

Simplifying the expression gives us the confidence interval,

⇒ (0.0015 < p < 0.0069)

Therefore,

The 95% confidence interval for the population proportion of defective calculators is (0.0015, 0.0069).

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The percentage of the attendees that had dessert at the football team banquet is 75%.

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

To find the percentage of attendees who had dessert, we can use the formula:

Percentage = (part/whole) x 100%

where:

Substituting the given values, we get:

percentage = (60/80) x 100%

percentage = 0.75 x 100%

percentage = 75%

Therefore, 75 perecent of the attendees had dessert.

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Answer:

4700=πr²×31

4700/31=πr²

151.6.../π=r²

√151.6.../π=

6.946933566=r

r=6.95mm

Explain:

Volume of cylinder=

πr²×height

The extra number of people that should be engaged to reap the field in 10 days is given by A = 21 people

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the extra number of people that should be engaged to reap the field in 10 days be represented as A

Now , the number of people that should be engaged to reap the field in 10 days = n

The number of people that can reap the field in 17 days = 30 persons

So , the proportion is

30 x 17 = n ( 10 )

On simplifying , we get

Divide by 10 on both sides , we get

n = ( 30 x 17 ) / 10

n = 3 x 17

n = 51

And , the number of extra persons A = n - 30

So , the extra number of people that should be engaged to reap the field in 10 days A = 21 people

Hence , the proportion is A = 21 people

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The concept time and work is used here to determine the number of people required to reap the same field in 10 days. The number of people required is 51.

The time and work represents the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the workdone by each of them.

If 30 persons can reap a field in 17 days

1 person can reap = 30 × 17 = 510 days

In 10 days, number of persons needed = 510 / 10 = 51 persons

Thus 51 persons can reap the field in 10 days.

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Answer:

ABD = 75 degrees

Step-by-step explanation:

ABD is the same as ABC + CBD

ABC = 30

CBD = 45

30+45 = 75 degrees

Therfore, ABD = 75 degrees