How long a line can you make using all the 5/8 inch strips?

For instance: Let f(x) = 2x + 1 and g(x) = x^2. Find (f ∘ g)(3). First, we need to find g(3) which is 3^2 = 9. Then we plug this value into f: f(g(3)) = f(9) = 2(9) + 1 = 19. Therefore, (f ∘ g)(3) = 19.

Function composition is a mathematical concept that is used to combine two or more functions into a single function. This concept is widely used in real life situations, such as in computer programming, engineering, and physics.

For example, in computer programming, function composition is used to break down complex programs into smaller, more manageable parts. By using function composition, programmers can create complex programs that are easier to read and maintain. Therefore, function composition is a powerful tool that is used in various fields to simplify complex problems and create more accurate models of the world around us.

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The proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

What is proportion?

A proportion is a statement that two ratios or fractions are equal. It is commonly written in the form of two fractions separated by an equal sign, such as a/b = c/d.

To write a proportion comparing the rise to the run for each of the similar slope triangles, we can use the fact that the ratio of corresponding sides of similar triangles is the same.

Let's say we have two similar triangles with corresponding sides of length a, b, and c, and a', b', and c', respectively. Then we can write the following proportion:

a / a' = b / b' = c / c'

Now, let's apply this to finding the proportion of the rise to the run for each of the similar slope triangles.

In a right triangle, the slope is defined as the ratio of the rise (vertical change) to the run (horizontal change). Let's say we have two similar right triangles with slopes m and m', respectively, and the rise and run of the first triangle are h and b, respectively. The rise and run of the second triangle are then mh and mb', respectively.

We can write the proportion of the rise to the run for each triangle as:

h / b = mh' / mb'

Simplifying this proportion, we can cancel out the common factor of b:

h / b = mh' / mb'

h / 1 = mh' / m'

h = bmh'

Therefore, the proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

The numeric value of this proportion will depend on the specific values of the rise and run for each triangle and the slope of the triangles.

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The first five terms of the sequences are 2, 3, 5, 9, 17. and 1, 4, 7, 10, 13

Using the formula, an = 2an-1 - 1 where a1 = 2, we can find the first few terms of the sequence as follows:

a2 = 2a1 - 1 = 2(2) - 1 = 3

a3 = 2a2 - 1 = 2(3) - 1 = 5

a4 = 2a3 - 1 = 2(5) - 1 = 9

a5 = 2a4 - 1 = 2(9) - 1 = 17

Therefore, the first five terms of the sequence are: 2, 3, 5, 9, 17.

For the second sequence, the first five terms are

1, 4, 7, 10, 13

Because the common difference is 3

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We need to find the perimeter of the shape given by the coordinates. Let's start by drawing a Cartesian coordinate system and identifying the points. This will give us information about the geometric shape.

A Cartesian coordinate system is given in the photos below and the indicated points [(2,3), (2,8), (6,3) and (6,8)] are marked.

We can see that this shape is a rectangle. A rectangle is home to two sides of different lengths, long and short. To find the perimeter of a rectangle, we add the length of the long side and the length of the short side and multiply the result by [tex]2[/tex]. (Because a rectangle must have [tex]2[/tex] long sides and [tex]2[/tex] short sides).

The rectangle in the figure has a long side length of [tex]5[/tex] feet and a short side length of [tex]4[/tex] feet.

Perimeter: [tex]2(L+S) = 2(5+4)=18ft.[/tex]

Answer: Part A:

To find the x-intercepts of the graph of f(x), we need to set f(x) equal to zero and solve for x:

-16x2 + 60x + 16 = 0

Divide both sides by -4 to simplify:

4x2 - 15x - 4 = 0

We can use the quadratic formula to solve for x:

x = (-b ± sqrt(b2 - 4ac)) / 2a

Where a = 4, b = -15, and c = -4.

x = (-(-15) ± sqrt((-15)2 - 4(4)(-4))) / 2(4)

x = (15 ± sqrt(385)) / 8

Therefore, the x-intercepts are approximately 0.256 and 3.194.

Part B:

The coefficient of the x2 term in f(x) is -16, which is negative. This means that the graph of f(x) opens downward, so the vertex is a maximum.

The x-coordinate of the vertex can be found using the formula:

x = -b / 2a

Where a = -16 and b = 60.

x = -60 / 2(-16) = 1.875

To find the y-coordinate of the vertex, we can plug in this value of x into the equation for f(x):

f(1.875) = -16(1.875)2 + 60(1.875) + 16 = 80.25

Therefore, the coordinates of the vertex are (1.875, 80.25).

Part C:

To graph f(x), we can use the information we obtained in Part A and Part B. We know that the x-intercepts are approximately 0.256 and 3.194, and the vertex is at (1.875, 80.25).

We can also find the y-intercept by plugging in x = 0:

f(0) = -16(0)2 + 60(0) + 16 = 16

Therefore, the y-intercept is (0, 16).

Using all of this information, we can sketch the graph of f(x) as a downward-opening parabola with x-intercepts at approximately 0.256 and 3.194, a vertex at (1.875, 80.25), and a y-intercept at (0, 16).

Step-by-step explanation:

Reasons to include an interaction term in our model include (1) to estimate context-specific effects of some predictor variable on the outcome (y) and (2) if the joint effect of two variables on the outcome cannot be correctly modeled as the sum of the main effects associated with each variable. So, the correct answers are (1) and (2).

Including an interaction term can be useful to estimate the context-specific effects of some predictor variable on the outcome (y) when the effect of that predictor on the outcome may depend on the value of another predictor variable.

Additionally, including an interaction term can be necessary if the joint effect of two predictor variables on the outcome cannot be correctly modeled as the sum of the main effects associated with each variable.

This is because the effect of one predictor variable on the outcome may depend on the value of the other predictor variable, and this dependency cannot be captured by the main effects alone.

So, the correct options are (1) and (2).

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According to the problem, the amount of petrol in the second tank is twice that in the first tank, which means the amount of petrol in the second tank is 2x liters.

If we draw out 25 liters from the first tank and add it to the second tank, the amount of petrol in both tanks will be the same. Therefore, the total amount of petrol in both tanks after the transfer is (x - 25) + (2x + 25) = 3x.

Since the amount of petrol in both tanks is the same after the transfer, we can set up an equation:

x - 25 = (2x + 25) / 2

Simplifying this equation, we get:

2x - 50 = 2x + 25

2x - 2x = 25 + 50

x = 75

Therefore, the amount of petrol in the first tank is 75 liters, and the amount of petrol in the second tank is 2x = 2*75 = 150 liters.

Net WPM is a better formula than Gross WPM to calculate typing speed because it provides a more comprehensive and accurate measure of a person's typing abilities

Speed is a measure of how fast an object or person is moving. It is usually expressed in units of distance per unit of time, such as miles per hour (mph), kilometers per hour (km/h), or meters per second (m/s).

Net WPM is a better formula than Gross WPM to calculate typing speed because it takes into account the number of errors made during typing.

Gross WPM (Words Per Minute) is calculated by dividing the total number of characters typed by 5 (the average number of characters in a word) and then dividing the result by the time taken to type those characters in minutes.

However, Gross WPM does not account for any mistakes made during typing.

On the other hand, Net WPM calculates the typing speed by subtracting the number of errors made during typing from the total number of words typed and then dividing the result by the time taken to type.

This formula provides a more accurate measure of the typing speed, as it takes into account the accuracy of typing as well as the speed.

Therefore, Net WPM is a better formula than Gross WPM to calculate typing speed because it provides a more comprehensive and accurate measure of a person's typing abilities

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To find the probability that the average of 25 randomly selected claims exceeds 20,000, we need to first determine the mean and standard deviation of the sample distribution.

Given:
- Mean of the population (μ) = 19,400
- Standard deviation of the population (σ) = 5,000
- Sample size (n) = 25

Step 1: Calculate the mean of the sample distribution (μ_sample)
Since the sample mean is an unbiased estimator of the population mean, μ_sample = μ = 19,400.

Step 2: Calculate the standard deviation of the sample distribution (σ_sample)
σ_sample = σ / √n = 5,000 / √25 = 5,000 / 5 = 1,000

Now, we need to find the probability that the sample mean exceeds 20,000. We can do this using the Z-score formula:

Z = (X - μ_sample) / σ_sample

where X is the sample mean we want to find the probability for (20,000 in this case).

Step 3: Calculate the Z-score
Z = (20,000 - 19,400) / 1,000 = 600 / 1,000 = 0.6

Step 4: Find the probability
Now, we need to find the area to the right of the Z-score in the standard normal distribution table or use a calculator/software that provides the probability.

The area to the right of Z = 0.6 is approximately 0.2743. So, the probability that the average of 25 randomly selected claims exceeds 20,000 is approximately 0.2743 or 27.43%.

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The value of the indicated sides of the shape given above are as follows:

Scale factor = 1.67

X = 15

Y = 9

Z = 9

To call the scale factor of a given shape the formula used is given below;

Scale factor = Dimension of new shape(bigger)/dimension of the old shape(smaller).

Dimension of new shape = BC = 30

Dimension of old shape = FE = 18

scale factor = 30/18 = 1.67

X = AD/1.67

X = 25/1.67

X = 15 (approximately)

Y = DC/1.67

Y = 15/1.67

Y = 9 (approximately)

Z = AB/1.67

Z = 15/1.67

Z = 9(approximately)

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The curve described by these parametric equations is the graph of the Cartesian equation: x = 2e^[(1 - y)/5]

To eliminate the parameter t, we need to find a way to express t in terms of x and y, and then substitute that expression into one of the equations to eliminate t.

x(t) = 2e^t

y(t) = 1 - 5t

Let's start by solving the second equation for t:

y = 1 - 5t

Adding 5t to both sides, we get:

5t = 1 - y

Dividing both sides by 5, we get:

t = (1 - y)/5

Now we can substitute this expression for t into the first equation:

x = 2e^t

x = 2e^[(1 - y)/5]

This is the Cartesian equation in terms of x and y. We have eliminated the parameter t and expressed the equation solely in terms of x and y.

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The probability that the married couple will have adjacent desks is 0.72.

Probability means how likely an event is to occur. In many real-life situations, we may have to predict the outcome of events. We may or may not be fully aware of the outcome of the event. In this case, we say it will happen or not. The result often has good applications in sports, business as a result of forecasting, and the result is also widely used in the field of new intelligence.

Mathematically, the number of ways to assign 6 desks to 6 employees is equal to 8!

Now,

the number of ways the couple can interchange their desks is just 2 ways

Thus,

the number of ways to assign desks such that the couple has adjacent desks is 2(6!)

The number of ways to assign desks among all six employees randomly is 7!

Thus, the probability that the couple will have adjacent desks would be ;

2(6!)/7! = 2/7

This means that the probability that the couple have non adjacent desks is 1-2/7 = 5/7 = 0.71428 ≈ 0.72

Which is 0.72 to the nearest tenth of a percent

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$30.21  is the total amount, in dollars, the customer pays for the discounted book.

If the original price of the book was $38, and it was discounted by 25%, then the discounted price of the book would be:

Discounted price = Original price - Discount

Discounted price = $38 - 0.25 x $38

Discounted price = $28.50

Now, the customer must pay a 6% sales tax on the discounted price of the book. The sales tax can be calculated as:

Sales tax = 0.06 x Discounted price

Sales tax = 0.06 x $28.50

Sales tax = $1.71

Therefore, the total amount the customer pays for the discounted book is the sum of the discounted price and the sales tax:

Total amount = Discounted price + Sales tax

Total amount = $28.50 + $1.71

Total amount = $30.21

So, the customer pays $30.21 for the discounted book

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The order from least to greatest is:

The number of possible license plates for each situation:

Neither the letters nor the numbers can be repeated: 26 x 25 x 9 x 8 x 7 = 327,600

The letters can repeat, but the numbers cannot repeat: 26 x 26 x 9 x 8 x 7 = 405,504

The number can repeat, but the letters cannot repeat: 26 x 25 x 9³ = 5,153,250

The letter "O" cannot be used, but there are no restrictions on repeating the other letters or numbers: 25 x 25 x 9 x 9 x 9 = 15,187,500

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Image transcribed:

Use the arrows to move each item into the correct order. Click the "up" arrow to move the item up, or click the "down" arrow to move the item down. Once all the items are in the correct order, submit your response.

A bike license consists of 2 letters, using any of the 26 letters in the alphabet, followed by 3 digits from 1 to 9. Calculate the number of possible license plates in each situation, then order them from least to greatest.

↑ ↓The letters can repeat, but the numbers cannot repeat.

↑ ↓The numbers can repeat, but the letters cannot repeat.

↑ ↓Neither the letters nor the numbers can be repeated.

↑ ↓The letter "o" cannot be used, but there are no restrictions on repeating the other letters or numbers.

Answer: I do not understand this question

Step-by-step explanation: Enjoy your day today

Answer:

c/0.5= 2.6+3.2

c= 5.8×0.5

c=2.9

Answer:

Point L

Step-by-step explanation:

Which point represent the ordered pair

(2, -[tex]\frac{7}{2}[/tex])

-7/2 = -3.5

Looking at it we see point L is the answer.

The areas of the two cross-sections would be proportional to k².

If a new cross-section was created in each solid, both at the same height using a scale factor k, the areas of the two cross sections would be proportional to k².

The reason for this is that when a scale factor is applied to a two-dimensional figure, the area of the resulting figure increases by a factor of k². This is because the linear dimensions of the figure (length and width) are multiplied by k, and since the area is calculated by multiplying length and width, the area of the figure is multiplied by k².

Therefore, if the two cross sections are created at the same height and are scaled by the same factor k, their areas will be proportional to k². For example, if k=2, the area of each cross-section will be four times the original area; if k=3, the area of each cross-section will be nine times the original area, and so on.

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Answer: We can use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients, and use this relationship to find the values of p and q.

Given the equation ²-13x - 30 = (x+p)(x+q), we can see that the coefficient of the x^2 term is 1, the coefficient of the x term is -13, and the constant term is -30.

By comparing the coefficients with the formula for the sum and product of the roots of a quadratic equation, we have:

p + q = -(-13)/1 = 13

p*q = -30/1 = -30

Since the absolute value of p is greater than the absolute value of q, we know that either p is positive and q is negative, or p and q are both negative. We can eliminate the possibility of p being positive and q being negative, since their product would be negative, and we know that p*q = -30. Therefore, both p and q must be negative integers.

We also know that the sum of p and q is 13, which means that the absolute value of q is less than the absolute value of p. Since p and q are both negative, this means that q has a larger absolute value (i.e., is farther from zero) than p. Therefore, q is the negative integer in this case.

Step-by-step explanation:

Answer:

Let's use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given that one leg (let's call it the shorter leg) is twice the length of the other leg. So, if we let x represent the length of the shorter leg, then the longer leg has a length of 2x.

We are also given that the length of the hypotenuse is √45 centimeters. We can simplify this by noticing that √45 = √(9 × 5) = √9 × √5 = 3√5. So the length of the hypotenuse is 3√5 centimeters.

Now we can write the Pythagorean Theorem equation:

x^2 + (2x)^2 = (3√5)^2

Simplifying, we get:

x^2 + 4x^2 = 45

5x^2 = 45

x^2 = 9

x = 3

So the shorter leg has a length of 3 centimeters, and the longer leg has a length of 2x = 2(3) = 6 centimeters.

The range wοuld stay the same value οf 8 inches.

Let's lοοk at the average fοrmula in mοre detail in this part and use sοme examples tο illustrate hοw it may be used. The fοllοwing is an example οf the average fοrmula fοr a specific set οf data οr οbservatiοns: Average = (Sum οf Observatiοns) ÷ (Tοtal Numbers οf Observatiοns).

In the οriginal data set, the maximum value is 22 inches and the minimum value is 14 inches, sο the range is:

22 - 14 = 8 inches

If anοther plant with a height οf 14 inches is added tο the data, the minimum value will still be 14 inches, but the maximum value will nοw be 22 inches (since there are twο plants with a height οf 22 inches).

Therefοre, the range will increase:

22 - 14 = 8 inches

Sο the cοrrect answer is: The range wοuld stay the same value οf 8 inches.

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a. The probability density function of the random variable generated using rand in Excel is:1:b. The probability of generating a random number between 0.2 and 0.8 can be found by calculating the area under the probability density function between those values:P(0.2 ≤ X ≤ 0.8) = ∫0.8 0.2 f(x) dxP(0.2 ≤ X ≤ 0.8) ≈ 0.6Therefore, the probability of generating a random number between 0.2 and 0.8 is approximately 0.6.c. The probability of generating a random number with a value less than or equal to 0.5 can be found by calculating the area under the probability density function up to that value:P(X ≤ 0.5) = ∫0.5 0 f(x) dxP(X ≤ 0.5) ≈ 0.5Therefore, the probability of generating a random number with a value less than or equal to 0.5 is approximately 0.5.d. The probability of generating a random number with a value greater than 0.8 can be found by calculating the area under the probability density function above that value:P(X > 0.8) = ∫1 0.8 f(x) dxP(X > 0.8) ≈ 0.1Therefore, the probability of generating a random number with a value greater than 0.8 is approximately 0.1.e. Using the given random numbers, we can calculate the mean and standard deviation as follows:Mean:μ = (0.931806 + 0.398110 + 0.216843 + ... + 0.545347 + 0.159312) / 50μ ≈ 0.464257Therefore, the mean of the given random numbers is approximately 0.464257.Standard deviation:s = sqrt([(0.931806 - μ)^2 + (0.398110 - μ)^2 + ... + (0.545347 - μ)^2 + (0.159312 - μ)^2] / (50 - 1))s ≈ 0.316221Therefore, the standard deviation of the given random numbers is approximately 0.316221.

a. The probability density function is 1.

b. The probability of generating a random number between 0.2 and 0.8 is 0.6.

c. The probability of generating a random number with a value less than or equal to 0.5 is 0.5.

d. The probability of generating a random number with a value greater than 0.7 is 0.3.

e. The mean is 0.472817 and the standard deviation is 0.316211.

The percentage of flights that do not arrive on time is 6%.

If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the

percentage means, a part per hundred. The word per cent means per 100.

An air line reports the 94% of its flights arrive on time.

The complement of the flight arriving on time would be the percentage of flights that do not arrive on time.

To calculate the complement, you can subtract the percentage of flights arriving on time from 100%.

The complement of the flight arriving on time = 100% - 94% = 6%

Therefore, the percentage of flights that do not arrive on time is 6%.

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The number of hours for the tortoise to walk 1 mile will be 1.5 hours.

Speed:

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration. The pie divides the dimension of distance by time. The SI unit of speed is meter per second (m/s), but the most common unit of speed in everyday use is kilometer per hour (km/h), or in the US and UK United, the mile per hour (mph). air And for sea travel, knots are commonly used.

We know that the speed formula

Speed = Distance/Time

A tortoise takes 1 1/4​ hours to walk 5/6 miles.

Convert the mixed fraction number into a decimal number.

1 ¹/₄ = 1.25 hours

Then the speed of the tortoise will be calculated as,

⇒ Speed = (5/6) / 1.25

⇒ Speed = 0.667 miles per hour

The number of hours for the tortoise to walk 1 mile will be calculated as,

⇒ T = 1 / 0.667

⇒ T= 1.5 hours

The number of hours for the tortoise to walk 1 mile will be 1.5 hours.

Complete Question:

A tortoise takes 1 1/4​ hours to walk 5/6 miles. At this rate, how long does it take her to walk 1 mile?

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Answer:

Samuel will need 614 2/3 feet of material to build eight of his standard fences. To find this answer, we simply need to multiply 76 2/3 feet (the perimeter of one fence) by 8 (the number of fences he wants to build). Thus, 76 2/3 feet x 8 = 614 2/3 feet.

Answer: it is going to be 1/100

The scale factor is basically like saying ratio.

60 millimeters is 60/1000 of a meter.

since there are 6 meters multiply by 6

60/6000

6/600

1/100

The movie was played in a scale factor of 1/100

Step-by-step explanation:

Answer: -64

Step-by-step explanation:

The surface area of the frustum is approximately 68.49 cm^2 and the volume is approximately 105 cm^3.

To calculate the surface area and volume of the frustum of a pyramid, we first need to determine the slant height of the frustum, which we can do using the Pythagorean theorem.

Calculate the slant height of the frustum:

Let s1 and s2 be the side lengths of the top and bottom squares, and h be the height of the frustum.

The slant height (l) can be calculated using the Pythagorean theorem:

l = sqrt(h^2 + ((s2 - s1)/2)^2)

l = sqrt(5^2 + ((6 - 3)/2)^2)

l = sqrt(25 + 1.5^2)

l = sqrt(25 + 2.25)

l = sqrt(27.25)

l ≈ 5.22 cm

Calculate the surface area of the frustum:

Surface area = top square area + bottom square area + lateral surface area

Top square area = s1^2 = 3^2 = 9 cm^2

Bottom square area = s2^2 = 6^2 = 36 cm^2

Lateral surface area = 0.5 * (s1 + s2) * l = 0.5 * (3 + 6) * 5.22 ≈ 23.49 cm^2

Total surface area ≈ 9 + 36 + 23.49 = 68.49 cm^2

Calculate the volume of the frustum:

We can use the following formula to calculate the volume of a frustum:

Volume = (h/3) * (A1 + A2 + sqrt(A1 * A2))

Where A1 and A2 are the areas of the top and bottom squares, respectively:

A1 = 3^2 = 9 cm^2

A2 = 6^2 = 36 cm^2

Volume = (5/3) * (9 + 36 + sqrt(9 * 36))

Volume = (5/3) * (45 + sqrt(324))

Volume = (5/3) * (45 + 18)

Volume = (5/3) * 63

Volume ≈ 105 cm^3

So, the surface area of the frustum is approximately 68.49 cm^2 and the volume is approximately 105 cm^3.

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Answer: 4.50

Step-by-step explanation: first of start with simple multiplacation to find wich adds up to 17.5 first you multiplye 4.50x3=13.5  then  1.72x2=3.5

add them together to get 13.5+3.5= 17.5 therfor the Answer will be 4.50