Type the correct answer in each box. Use numerals instead of words. What is the inverse of this function? f -1(x) = x2 − , for x ≤.

The equation of the line is shown as y = ax + p, where a and p are actual numbers. The slope-intercept form of a line is given as y = mx + b, where m is the slope of the line and b is the y-intercept. The line slope-intercept form can be compared with the equation of the line given as y = ax + p.

We know that the equation of a line in slope-intercept form is given as y = mx + b. Here, we are given the equation of the line as y = ax + p, where a and p are real numbers. Thus, the following is true about a and p.The slope of the line in the slope-intercept form is m = a. Therefore, a is the slope of the given line. The y-intercept of the line in the slope-intercept form is b = p.

p is the y-intercept of the given line. Hence, we conclude that in the equation of the line, y = ax + p, where a and p are real numbers, a is the slope of the line and p is the y-intercept of the line.

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The statement that must be true when calculating the effective rate of a loan with n = 1 is: III. The interest is compounded annually. Therefore, the answer is d. III only.

When n equals 1, it means that the interest is compounded once per year. In this case, the effective rate of the loan is equal to the nominal rate since there are no additional compounding periods within the year.

This is because when n equals 1, there is no need to consider the length of the loan (statement II) since it is already implied that the loan is for one year.

However, statement I, which states that the nominal rate equals the effective rate, may not necessarily be true for loans with other values of n. Hence, only statement III is required to be true when n equals 1 to calculate the effective rate of a loan.

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Paul earned a total of $1,368 during his summer vacation. To calculate how much money Paul earned during his summer vacation, we need to determine his hourly rate and the total number of hours he worked.

Given that Paul earned $8.55 per hour and worked 20 hours per week for 8 weeks, we can calculate his total earnings.

First, let's find the total number of hours Paul worked:

20 hours/week * 8 weeks = 160 hours.

Next, we multiply the total number of hours by his hourly rate to find his total earnings:

160 hours * $8.55/hour = $1,368.

Therefore, Paul earned a total of $1,368 during his summer vacation.

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To simplify the given expression, we can first simplify the height and width separately.

The height is 4w^3 - 4w. This expression does not have any common factors, so it cannot be simplified further.

The width is 5w^2 - 3w - 4. This expression can be factored as (5w + 1)(w - 4).

Now we can substitute these simplified expressions into the formula for the area of a rectangle, which is A = length × width. The length in this case is the height.

Area = (4w^3 - 4w) × (5w^2 - 3w - 4)

To multiply these expressions, we can use the distributive property:

Area = 4w^3(5w^2 - 3w - 4) - 4w(5w^2 - 3w - 4)

Expanding the multiplication:

Area = 20w^5 - 12w^4 - 16w^3 - 20w^3 + 12w^2 + 16w

Combining like terms:

Area = 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w

Therefore, the simplified expression for the area of the rectangle is 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w.

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After 5 years, the population is expected to double if the growth pattern continues.

To determine after how many years the population will double, we need to consider the growth rate and the initial population.

If the population is increasing every year, it indicates exponential growth. In this case, we can use the formula for exponential growth:

P(t) = P(0) * (1 + r)^t

Where:

P(t) is the population at time t,

P(0) is the initial population,

r is the growth rate per year, and

t is the number of years.

In this scenario, we know that the initial population (P(0)) is 1200. We want to find the value of t when the population (P(t)) doubles, which means it will be 2 * P(0).

2 * P(0) = P(0) * (1 + r)^t

Dividing both sides by P(0):

2 = (1 + r)^t

Now, let's check the given options to determine which one satisfies the equation:

01: (1 + r)^1 = 2 (Not satisfied)

02: (1 + r)^2 = 2 (Not satisfied)

03: (1 + r)^3 = 2 (Not satisfied)

05: (1 + r)^5 = 2 (Satisfied)

So, after 5 years, the population is expected to double if the growth pattern continues.

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Using a line of best fit with the equation Y equals negative 3X +21 to predict the value of Y when X equals 10 is an example of a linear regression.

A linear regression is a statistical technique used to model the relationship between two variables by fitting a linear equation to the observed data. It is used to determine the strength and direction of the relationship between the two variables .Linear regression is widely used in business, finance, economics, and other fields to predict future trends and make informed decisions.

The equation Y equals negative 3X +21 represents the slope and intercept of the line of best fit for the given data set with integer X-values One through six. By substituting X equals 10 in the equation, we can predict the value of Y when X equals 10 as follows :Y = -3(10) + 21 = -30 + 21 = -9Therefore, the predicted value of Y when X equals 10 is -9.

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Therefore, the amount of money in the CD after 6 years is $200.76.

Given that Loretta was 18 years old when she deposited $100 into a 20-year certificate of deposit (CD) account that earns interest at a better rate than her standard savings account and she must leave the money in the account for 20 years, without making any withdrawals or deposits.

Six years later, she had $132 in the account.The formula for the growth of money at a compounded rate is given by

y =[tex]a (1 + r/n)^_(nt)[/tex]

Where

y = the amount of money at the end of the period.

a = the initial amount of money.

r = the annual interest rate in decimal form.

n = the number of times compounded per year.

t = the number of years.

The initial deposit was $100, and the total amount after 20 years would be $132. So, we have

$132 =[tex]$100(1 + r/n)^_(nt)[/tex]

Taking the natural logarithm of both sides,ln 132

= [tex]ln(100) + ln(1 + r/n)^{(nt)}ln 132 - ln 100[/tex]

= nt ln (1 + r/n)ln (132/100)

= nt ln (1 + r/n)ln (1.32)

= nt ln (1 + r/n)ln (1.32)

= t ln (1 + r/n)ln (1 + r/n)

= ln (1.32)ln (1 + r/n)

= 0.2877

Since the number of times compounded per year is not given, it can be assumed that it is compounded annually.i.e., n = 1

Therefore,ln (1 + r/1)

= 0.2877ln (1 + r)

= 0.2877r

= [tex]e^{(0.2877)} - 1r[/tex]

= 0.3338

So, the rate of interest is 33.38%.

Therefore, the equation for the amount of money in the CD after t years is

y = [tex]100(1 + 0.3338)^t[/tex]

Thus, the amount of money at the end of 6 years is

y = [tex]100(1 + 0.3338)^6[/tex]

= $200.76

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The required simplified expression  for the sum of the two algebraic expressions modeled by the algebra tiles  is 3x - 1.

To write the sum of two algebraic expressions, we need the specific expressions or equations. Since you mentioned using algebra tiles, assuming  to simplify an expression using visual representation.

Let's consider an example expression: (x + 3) + (2x - 4).

To simplify this expression using algebra tiles, we can represent x using a green tile, a positive constant term using a yellow tile, and a negative constant term using a red tile. Each x represents one green tile, each positive constant term represents one yellow tile, and each negative constant term represents one red tile.

(x + 3) can be represented as one green tile (x) and three yellow tiles (+3).

(2x - 4) can be represented as two green tiles (2x) and four red tiles (-4).

To find the sum, we can combine like terms by putting the tiles together. We combine the green tiles and the yellow tiles separately:

Green tiles: x + 2x = 3x (Three green tiles)

Yellow tiles: +3 - 4 = -1 (One yellow tile and four red tiles)

Therefore, the simplified expression  for the sum of the two algebraic expressions modeled by the algebra tiles  is 3x - 1.

Using algebra tiles, we can visually represent and manipulate expressions, helping in understand the concepts of combining like terms and simplifying expressions.

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Josephine made an error in Step 1 of solving the quadratic equation (2+6)^2 = 49. The mistake occurred when she took the square root of both sides and incorrectly simplified the square root of 49 as V49.

The correct simplification should be 7. The error in Step 1 led to subsequent incorrect steps and an incorrect final answer.

Josephine's error can be identified in Step 1, where she attempted to take the square root of both sides of the equation. The square root of (2+6)^2 is correctly simplified as |2+6|, which equals 8. However, Josephine incorrectly wrote it as V(2+6)^2 or V49.

The square root of 49 is actually 7, not V49. This mistake carried forward into Step 2, where Josephine incorrectly equated V(2+6)^2 to 7, resulting in the equation x + 6 = 7. Consequently, the subsequent steps (Step 3 and Step 4) were performed based on this incorrect equation, leading to an incorrect solution of x = 1.

Therefore, Josephine's error occurred in Step 1 of the solution process for the quadratic equation.

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The speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.

The speed of the kayak can be represented in component form, which consists of two perpendicular components: one in the east-west direction (x-component) and the other in the north-south direction (y-component).

Given that the kayak is traveling at a speed of 8 meters per second in the direction of S 67 degrees W, we can use trigonometry to determine the x-component and y-component of the speed.

The x-component represents the east-west direction and can be calculated using the cosine function. The y-component represents the north-south direction and can be calculated using the sine function.

To calculate the x-component:

x-component = speed * cosine(angle)

x-component = 8 * cosine(67 degrees)

x-component ≈ 8 * 0.389

x-component ≈ 3.112 meters per second (rounded to three decimal places)

To calculate the y-component:

y-component = speed * sine(angle)

y-component = 8 * sine(67 degrees)

y-component ≈ 8 * 0.921

y-component ≈ 7.368 meters per second (rounded to three decimal places)

Therefore, the speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.

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the train's average speed was approximately 68 miles per hour.

To calculate the average speed of the train, we need to divide the distance traveled by the time taken.

Given:

Distance: 170 miles

Time taken: 4:18 PM - 1:48 PM = 2 hours and 30 minutes

To calculate the average speed, we first need to convert the time taken to hours. Since there are 60 minutes in an hour, we have:

Time taken = 2 hours + 30 minutes / 60 = 2.5 hours

Now we can calculate the average speed:

Average speed = Distance / Time taken

Average speed = 170 miles / 2.5 hours

Average speed = 68 miles per hour (rounded to the nearest whole number)

Therefore, the train's average speed was approximately 68 miles per hour.

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The cost for new customers who are entitled to the 10% discount is $99 per month.

The Cable Company offers cable for $110 a month but gives a 10% discount for new customers.

To find the cost for new customers, we will have to subtract the 10% discount from the original cost of $110 per month.

So, we will have to multiply the original cost by the percentage of the discount which is 10%.10% of 110 = (10/100) * 110= 11

Therefore, the discount offered by the company is $11.

Now, we will have to subtract the discount from the original cost:

Cost for new customers = $110 - $11 = $99

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The time it takes for the rock to hit the ground can be determined using the equation h(t) = -4.9t^2 + 150, where h(t) represents the height of the rock in meters and t represents time in seconds. By setting h(t) to 0 and solving for t, we can find the time it takes for the rock to hit the ground.

Set the equation h(t) = -4.9t^2 + 150 to 0, since the rock hits the ground when the height is 0.

-4.9t^2 + 150 = 0

Solve the quadratic equation for t by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c:

t = (-0 ± √(0^2 - 4(-4.9)(150))) / (2(-4.9))

Simplify and calculate the value of t:

t = (√(2940)) / (-9.8) ≈ ±7.23

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The length of BC in the rectangle ABCD is 16 units.

To find the length of BC in the rectangle ABCD, we can use the properties of rectangles and the intersecting diagonals.

Let's consider the given information:

AC = 16 (given)

ABD = 30° (given)

In a rectangle, the diagonals are equal in length. Therefore, AO = CO and BO = DO.

Since ABD is a right triangle, we can use trigonometric ratios to find the length of AO. In triangle ABD, the angle ABD is 90°, and we know ABD = 30°. Therefore, the remaining angle BDA is 180° - 90° - 30° = 60°.

Using the trigonometric ratio for a right triangle:

sin(BDA) = AO / AB

sin(60°) = AO / AB

√3 / 2 = AO / AB

Since AB is the length of the diagonal of the rectangle, we can represent it as d:

√3 / 2 = AO / d

Now, we can find AO:

AO = (√3 / 2) * d

Since AO = CO and BO = DO, we can conclude that BO and CO also have lengths of (√3 / 2) * d.

Now, let's consider triangle AOC. We know that AC = 16, and AO = CO = (√3 / 2) * d. We can use the Pythagorean theorem to find OC:

OC^2 = AC^2 - AO^2

OC^2 = 16^2 - [(√3 / 2) * d]^2

OC^2 = 256 - (3/4) * d^2

OC = √(256 - (3/4) * d^2)

Similarly, in triangle BOC, we have BO = (√3 / 2) * d and OC = √(256 - (3/4) * d^2). We can again use the Pythagorean theorem to find BC:

BC^2 = BO^2 + OC^2

BC^2 = [ (√3 / 2) * d ]^2 + [ √(256 - (3/4) * d^2) ]^2

BC^2 = (3/4) * d^2 + 256 - (3/4) * d^2

BC^2 = 256

Taking the square root of both sides:

BC = √256 = 16

Therefore, BC = 16.

So, the length of BC in the rectangle ABCD is 16 units.

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We know that congruence is a geometric transformation that preserves angles and lengths.

A representation of a transformation on a coordinate grid that does not preserve congruence is option G, which is (x,y) → (17x,17y).

This transformation enlarges the shape by a scale factor of 17 and changes the distance between each pair of points in the transformed shape.

Option F represents a translation of a shape on a coordinate grid, which means that it preserves congruence because the distance and angles between each pair of points remain the same.

Option H represents a rotation of a shape on a coordinate grid, and option J represents a reflection of a shape across the x-axis.

These transformations also preserve congruence because they do not change the length or angles between each pair of points in the transformed shape.

Therefore, the correct answer is G, (x,y) → (17x,17y).

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The x-intercepts for the function f(x) = x^2 + 2x - 15 are x = -5 and x = 3.

To find the x-intercepts, we set the function equal to zero and solve for x. In this case, we have the equation:

x^2 + 2x - 15 = 0

To factor this quadratic equation, we look for two numbers that multiply to -15 and add up to 2. The numbers that satisfy this condition are -5 and 3.

Therefore, the factored form of the equation is:

(x - 3)(x + 5) = 0

Setting each factor equal to zero, we find the x-intercepts:

x - 3 = 0 --> x = 3

x + 5 = 0 --> x = -5

Hence, the x-intercepts for the function f(x) = x^2 + 2x - 15 are x = -5 and x = 3.

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The average relative humidity in the afternoon in New Orleans is 61.6%, rounded to the tenths place.The problem states that New Orleans has 77% humidity in the mornings and it decreases by 20% in the afternoon.

To determine the average relative humidity in the afternoon in New Orleans, we can follow these steps:

Step 1: Find the decrease in humidity from morning to afternoon.

In the afternoon, the humidity decreases by 20%. To find out what 20% of 77 is, we can use the formula:

decrease = percent decrease × original value decrease = 20% × 77 decrease = 0.2 × 77 decrease = 15.4

Step 2: Subtract the decrease from the original value.To find the average relative humidity in the afternoon, we need to subtract the decrease from the original value (morning humidity):

afternoon humidity = morning humidity − decrease afternoon humidity = 77 − 15.4 afternoon humidity = 61.6.Therefore, the average relative humidity in the afternoon in New Orleans is 61.6%, rounded to the tenths place.

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Here's an example of possible measurements for Sharon's liquid ingredients:

Ingredient A: 8.53 L (liters) - This could represent a larger quantity of a liquid ingredient that needs to be added in liters, such as water or broth.

Ingredient B: 1.5 L (liters) - This measurement could represent another liquid ingredient that needs to be added in liters, like oil or a sauce.

Ingredient C: 3500 mL (milliliters) - This measurement represents a smaller quantity of a liquid ingredient that is measured in milliliters, such as a flavoring extract or a concentrated ingredient.

Ingredient D: 250 mL (milliliters) - This measurement could represent another liquid ingredient measured in milliliters, like a specific sauce or a liquid seasoning.

In this example, Sharon uses a combination of liter and milliliter measurements to accurately measure different volumes of liquid ingredients for her recipe. The liter measurements (Ingredient A and Ingredient B) are used for larger quantities, while the milliliter measurements (Ingredient C and Ingredient D) are used for smaller amounts. This combination allows for precise measurement and flexibility in handling both large and small quantities of liquid ingredients.

It's important to note that the specific measurements can vary depending on the recipe and the desired quantities of each ingredient.

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So the ratio of the first measurement to the second measurement is approximately 73.33%.

The diameter of ball A is 33 mm.

The diameter of ball B is 4.5 cm.

1 cm = 10 mm

4.5 cm = 4.5 × 10 mm

= 45 mm

To find the ratio of the first measurement (ball A) to the second measurement (ball B), we divide the diameter of ball A by the diameter of ball B.33 mm ÷ 45 mm = 0.7333...

We can simplify this fraction by multiplying both the numerator and denominator by 100 to get a percentage:

0.7333... × 100% = 73.33...%

Ratio of the first measurement to the second measurement = 73.33%.

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The chance that it will not rain tomorrow can be found by subtracting the probability of rain from 100% or 1 in decimal form. Therefore, if there is a 70% chance of rain, there is a 30% chance it will not rain.

If there is a 70% chance of rain tomorrow, the chance it will not rain can be found by subtracting the probability of rain from 100% (or 1 in decimal form):

Chance of not raining = 100% - Chance of raining

Chance of not raining = 1 - 0.7

Chance of not raining = 0.3 or 30%

Therefore, the chance it will not rain is 30%.

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To represent how much more Company X charges than Company Y for n minutes, we can subtract the total cost of Company Y from the total cost of Company X. The expression that represents this is (35 + 5n) - (20 + 4n) cents. Simplifying this expression yields 15 + n cents.

To find how much more Company X charges than Company Y for n minutes, we need to calculate the difference in their total costs. For Company X, it costs 35 cents to connect and an additional 5 cents for each minute, resulting in a total cost of (35 + 5n) cents for n minutes. For Company Y, it costs 20 cents to connect and an additional 4 cents for each minute, giving a total cost of (20 + 4n) cents for n minutes.

To find the difference, we subtract the total cost of Company Y from the total cost of Company X: (35 + 5n) - (20 + 4n) cents. Simplifying this expression, we combine like terms and get 15 + n cents. Therefore, the expression (15 + n) represents how much more Company X charges than Company Y for n minutes.

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The correct function for Adrianne's purpose, where the growth is calculated every 3 months instead of every year, is f(x) = 467(5^(x/4)).

To calculate the growth every 3 months instead of every year, we need to modify the original function by adjusting the exponent of 5.

Step 1: The original function is f(x) = 467(5)^x, where x represents the number of years.

Step 2: To calculate the growth every 3 months, we divide x by 4, as there are 12 three-month periods in a year.

Step 3: Adjust the exponent of 5 to (x/4), representing the growth over each three-month period.

Step 4: The modified function becomes f(x) = 467(5^(x/4)), which calculates the growth every 3 months.

Therefore, the correct function for Adrianne's purpose is f(x) = 467(5^(x/4)).

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Brian's computer will be worth £1408 in 3 years if it depreciates at a rate of 4% per year. Depreciation is a measure of how much the asset has lost in value over a period of time.

Depreciation refers to a decrease in the value of an asset over time due to its wear and tear or obsolescence. When an asset is purchased, it has an original value that is its initial worth. After some time, the asset will lose its value and become less valuable. Depreciation is a measure of how much the asset has lost in value over a period of time.

In this problem, Brian bought a computer for £1600, and it depreciates at a rate of 4% per year. To find out how much it will be worth in 3 years, we need to use the formula for depreciation which is:

Depreciation = Original value × rate of depreciation (as a decimal) × time (in years)

To calculate the depreciation, we have:

Depreciation = 1600 × 0.04 × 3= £192.

The depreciation value is what the computer will be worth in 3 years. Therefore, we can find the current value of the computer by subtracting the depreciation value from the original value. Hence, we have:

Current value = Original value - Depreciation= £1600 - £192= £1408.

Therefore, the computer will be worth £1408 in 3 years.

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The data in both classes represents the ages of students in the respective photography classes, showing variation in ages, some common ages, and instances of repeated ages within each class. Additionally, Class B exhibits a slightly wider range of ages compared to Class A.

The data in both Class A and Class B can be described as follows:

The data represents the ages of students enrolled in two separate photography classes.

The data in both classes shows a range of ages, spanning from the youngest age to the oldest age observed in each class.

There is variation in the ages within each class. For example, in Class A, the ages range from 16 to 30, while in Class B, the ages range from 15 to 32.

Both classes have some common ages. For instance, there are students in both classes who are 16, 17, and 18 years old.

The data in both classes includes students of different ages, indicating a diverse group of students in each class.

There are instances of repeated ages within each class, suggesting that multiple students share the same age. For example, in Class A, there are multiple students who are 18 years old.

The range of ages in Class B appears to be slightly wider than in Class A, as Class B includes students as young as 15 and as old as 32, while Class A ranges from 16 to 30.

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(a) 5:8 < 7:10

To compare the ratios, we can find their equivalent fractions. For 5:8, the equivalent fraction is (5/8), and for 7:10, it is (7/10).

Comparing the fractions, (5/8) is less than (7/10) because the denominator of (8) is larger than the denominator of (10), and the numerators (5 and 7) are the same.

To compare ratios, we can convert them into equivalent fractions. In the first case, 5:8 and 7:10 can be written as fractions (5/8) and (7/10), respectively. To determine which fraction is larger, we compare their numerators and denominators. In this case, both fractions have the same numerator (5 and 7). However, the denominator of (5/8) is 8, which is larger than the denominator of (7/10), which is 10. Since the numerators are equal and the denominator of (5/8) is larger, we can conclude that 5:8 is less than 7:10.

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To write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.

Step 1: Write the percentage as a fraction by dividing it by 100.For example, let's say we want to write 25% as a fraction in its simplest form.

25% is equivalent to 25/100 or 0.25 as a decimal.

Step 2: Simplify the fraction by finding a common factor between the numerator and denominator.

For example, let's simplify 25/100.

Both the numerator and denominator can be divided by 25, giving us 1/4.

Therefore, 25% as a fraction in its simplest form is 1/4.

Another example: let's write 60% as a fraction in its simplest form.

60% is equivalent to 60/100 or 0.6 as a decimal.

The numerator and denominator can both be divided by 20, giving us 3/5.

Therefore, 60% as a fraction in its simplest form is 3/5.

In summary, to write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.

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The total number of customers refers to the sum or count of individuals or entities who have availed products or services from a business or organization. It represents the overall customer base of a company.

The given information is that 144 customers rated the shop as being "very satisfactory." This number represented 50% of the total number of customers who took the survey.

To find out the total number of customers who took the survey, we will need to use the concept of proportions.The proportion can be set up as follows:

[tex]\frac{x}{100} = \frac{144}{50}[/tex]

Here, x represents the total number of customers who took the survey.Cross-multiplying,

50x = 14400

[tex]x = \frac{14400}{50}[/tex]

x = 288

Therefore, the total number of customers who took the survey is 288.

Therefore, the total number of customers who took the survey is 288 and the required answer is written in 91 words.

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The angle of the quadrilateral z is 50°

We have the four angles of a quadrilateral.

The  vertices of the four angles are:

w, x, y , z

The angles of the vertices are:

w = 110

x = 120

y = 80

We have to find the angle of z.

Now, According to the question:

Since, sum of angles of a quadrilateral is 360∘ .

Then, w + x + y + z = 360°

Plug all the values:

110 + 120 + 80 + z = 360

310 + z = 360

z = 360 - 310

z = 50°

Hence, The angle of the quadrilateral z is 50°.

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The farmer sold 2.42 kilograms of apples at the farmer's market.

To solve the problem, first, we need to find out how much weight the farmer sold in pears.

We are given that 3/4 of the weight is pears and 1/4 of the weight is apples.

We can use this information to set up an equation that represents the weight of the pears sold.

Let the weight of pears sold be "x":

Weight of pears sold + Weight of apples sold = Total weight of fruit sold

3/4x + 1/4x = 7.3 kg

Simplifying this equation, we get:

x = 4.88 kg

This means that the farmer sold 4.88 kg of pears.

To find out how many kilograms of apples she sold, we can subtract this weight from the total weight of fruit sold:

Weight of apples sold = Total weight of fruit sold - Weight of pears sold

Weight of apples sold = 7.3 kg - 4.88 kg

Weight of apples sold = 2.42 kg

Therefore, the farmer sold 2.42 kilograms of apples at the farmer's market.

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The weight of 60 nuts and 50 bolts would be 9.25 kg.

We have to given that,

An order of 50 nuts and 60 bolts weighed 10.6kg.

And, An order of 40 nuts and 30 bolts weighed 6.5kg.

Let us assume that,

Weight of one nut = x

And, Weight of one bolt = y

Hence, We get;

50x + 60y = 10.6  .. (i)

And, 40x + 30y = 6.5  .. (ii)

We want to find the weight of 60 nuts and 50 bolts, which we can denote as:

60x + 50y = ?

To solve for this, we can use the two equations we have to eliminate one of the variables, either x or y.

Let's start by eliminating x:

Multiply equation 1 by 4 and equation 2 by 5, to get:

200x + 240y = 42.4 (equation 3)

200x + 150y = 32.5 (equation 4)

Subtract equation 4 from equation 3:

90y = 9.9

y = 0.11

Now we can substitute y = 0.11 into equation 2 to solve for x:

40x + 30(0.11) = 6.5

40x = 2.5 x = 0.0625

Therefore, the weight of 60 nuts and 50 bolts would be:

60(0.0625) + 50(0.11) = 3.75 + 5.5 = 9.25 kg

So 60 nuts and 50 bolts would weigh 9.25 kg.

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