A Bike is discounted at 30% off. The original price is $250.
What is the sales price?

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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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 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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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

Answer:

29

Step-by-step explanation:

Given:

P = 88

Let's assume, that the length is x and the width is y

x = (2y - 1)

Let's write an equation for the perimeter:

2x + 2y = 88

2 × (2y - 1) + 2y = 88

4y - 2 + 2y = 88

6y = 88 + 2

6y = 90 / : 6

y = 15

We found the width, now we can find the length:

x = 2 × 15 - 1 = 30 - 1 = 29

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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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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Answer: I do not understand this question

Step-by-step explanation: Enjoy your day today

Answer:

0.4 meters.

Step-by-step explanation:

The ratio of centimeters to meters is 100:1.

That means if there are 100 centimeters, there is 1 meter.

So:

centimeters divided by 100 is a meter.

In this case, we have 40 centimeters.

Since there are less than 100 centimeters, we can't divide by 100, so we go into the decimals.

40 divided by 100 is

40/100

simplified to:

4/10

turned into decimal:

0.4 meters.

Hope this helps :)

The answer is 0.4 meters

The given ratio of centimeters to meters is 100:1. The rope Laura has is 40 cm long. To determine how long the rope is in meters, we need to divide 40 cm by 100 to convert it to meters.

Therefore, the length of the rope in meters is 0.4 meters (40/100 = 0.4).Answer: 0.4 meters

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Answer:

7 hours and 2 hours longer

Answer:

A)

Step-by-step explanation:

just look at the picture.

what must have happened to figure A to turn into figure B ?

is B more to the right or to the left of A ?

well, right. isn't it obvious ?

and when you look at the coordinates of a vertex, it is 3 units to the right of A.

and if the shift to the right had not happened - the 2 figures would be a mirrored image of each other with the x-axis being the mirror.

that is why A) is the right answer.

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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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:

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 answer is C) +18 ÷ +3 = +6. Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.

Measure of how far an object travels in a certain amount of time. Speed is calculated by dividing the distance traveled by the time it took to travel that distance.

The answer is C) +18 ÷ +3 = +6.

This is because Alvin decreased his training by 18 miles over a period of 3 weeks.

Dividing the decrease by the number of weeks gives us 6 miles, which is the average weekly change in his training.

That is 18/3= 6.

To answer the second question, Micheal's 50-meter freestyle was 24.73 meters faster than his 100-meter freestyle.

To calculate this, we subtract the time of the 50-meter freestyle (23.04 seconds) from the time of the 100-meter freestyle (47.77 seconds) to get 24.73 seconds.

We then multiply this time by the speed of a meter per second (1 meter/second) to get 24.73 meters.

Therefore, Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.

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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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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:

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 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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To solve this problem, we use the rule of conditional probability which states that the probability of the joint event A and B happening is equal to the probability of A happening multiplied by the probability of B happening given that A has already happened.

So, the probability of drawing a green marble on the first draw is 4/15, since there are 4 green marbles out of a total of 15 marbles.

If the first marble drawn is green and not replaced, there are now 14 marbles remaining in the bag, out of which 3 are green.

Thus, the probability of drawing another green marble given that the first one was green is 3/14.

Therefore, the probability of drawing two green marbles without replacement is:

(4/15) * (3/14) = 2/35

So the answer is 2/35.

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.

[tex]log_2(100)[/tex] is apprοximately 6.64 when evaluated using the change οf base fοrmula with base 10.

The change οf base fοrmula is used in lοgarithmic functiοns tο change the base οf the lοgarithm frοm οne value tο anοther.

The fοrmula states that fοr any base b, and any pοsitive numbers x and y, the fοllοwing equatiοn hοlds true:

[tex]log_b(x) = log_y(x) / log_y(b)[/tex]

Here,[tex]log_b(x)[/tex] represents the logarithm of x with base b, and [tex]log_y(x)[/tex]represents the logarithm of x with base y.

Tο evaluate the change οf base fοrmula, we need tο substitute the given values οf x, y, and b in the fοrmula and simplify the expressiοn. Fοr example, let's say we want tο find [tex]log_2(100)[/tex] using the change οf base fοrmula with base 10. We can write:

[tex]log_2(100)[/tex] [tex]= log_{10}(100) / log_{10}(2)[/tex]

Here, we know that log_10(100) = 2, as 10^2 = 100, and log_10(2) is approximately 0.301. Therefore, we can simplify the expression as:

[tex]log_2(100)[/tex]  = 2 / 0.301

This gives us:

[tex]log_2(100)[/tex]  ≈ 6.64

Therefore, [tex]log_2(100)[/tex] is approximately 6.64 when evaluated using the change of base formula with base 10.

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Complete Question:

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log₂1 ?

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 absolute value equation | x - (-5) | = 3 has a solution set corresponding to a straight horizontal line with marked points -8, -2, and x in left to right manner.

How to write an absolute value equation that has the following solution set?

The solution set given as a straight horizontal line passing through the points -1/2 and 3/2 can be represented as:

| x - 1 | = 1/2

Explanation:

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Answer:

c/0.5= 2.6+3.2

c= 5.8×0.5

c=2.9

Answer: -64

Step-by-step explanation:

D

I graphed each one and then compared the graphs to the one in the question

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:

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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Answer:

Angle A = Angle L

Angle D = Angle M

Angle C = Angle N

Segment AB = Segment LB

Segment CD = Segment NM

Segment DA = Segment ML

2nd part

Quadrilateral URST has moved by a translation of (x-5,y+2)

Step-by-step explanation:

Answer:

Step-by-step explanation: