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The expression  [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] is equivalent to 0 when x=0.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

If x=0, then the expression [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] becomes:

And we are given that x=0. So, we can substitute x=0 into the expression:

[tex]^3\sqrt{ 27 * 0} + ^3\sqrt{0}[/tex]

= 0 + 0 = 0

The first term simplifies to ∛(0), which is 0, because any number raised to the 1/3 power and multiplied by 0 is equal to 0.

The second term also simplifies to ∛(0), which is 0, because any number raised to the 1/3 power and multiplied by 0 is equal to 0.

Therefore, the sum of the two terms is 0.

Hence, the expression  [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] is equivalent to 0 when x=0.

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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 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.

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]

$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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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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The area of the space devoted to paintings is: 600 ft²

The formula for the area of a triangle is expressed as:

A = ¹/₂ * b * h

where:

A is area

b is base

h is height

From the 7th grade painting, we see that each box of 1 unit represents 10 ft actually.

Thus, area of space devoted to paintings is:

Area = ¹/₂ * 40 * 30

= 600 ft²

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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.

Answer: I do not understand this question

Step-by-step explanation: Enjoy your day today

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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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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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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Answer:

The sisters will spend a total of $240 on their mom for Christmas.

Step-by-step explanation:

$60 x 4 (sisters) = $240

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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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.

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:

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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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.

Step-by-step explanation:

give atleast 2 situations,in which you would store the data on cloud storage

Relationship between the area and the circumference of the circle is that they are proportional to each other.

The relationship between the area and the circumference of a circle with a radius of 5 units that has an area of 78.5 units² and a circumference of 31.4 units can be expressed as follows:

Area = πr²

where r is the radius of the circle.

Area = π(5)² = 78.5 units²

Therefore, the area of the circle is 78.5 units².

Circumference = 2πr,

where r is the radius of the circle.

2πr = 31.4 units

Therefore, 2π(5) = 31.4 units

Therefore, the circumference of the circle is 31.4 units.

Since the radius is the same, the relationship between the area and the circumference of the circle is that they are proportional to each other.

Area : Circumference

πr² :  2πr

r : 2

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Angles are measured in degrees and radians, and can be created by joining the extremities of two rays. The joint vertex is the common terminal of the two beams. Thus, ∠SRT = 38.16°.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

According to our question,

6x-66°+5x-26°+70°+x+70°=360°

6x+5x+x+ 66°+140°=360°

12x+ 206°=360°

12x=360°-206°

12x=  154°

x= 154/12°

Hence, ∠SRT = 5x - 26°

                       = 5 * 154/12° - 26°

                       = 770/12° - 26°

                       = 64.16° - 26°

                       = 38.16°

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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: 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:

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 total distance of the trip is 600 km if a train meet with an accident and then proceed further with its former speed.

Normal time be x for remaining distance, but time taken = 4x/3

Difference in time = (1+1/2+4x/3)−(1+x)=72

x=9

2nd case of going further 90 km which lessens the difference by 1/2

If it loses 90 km in 1/2 hr.

Total difference was 3 + 1/2 out of which 1/2 was for repair

Difference in travelling is 3+1/2-1/2=3 hrs

It will lose 3 hrs in 90 x 6=540 km

Now it travelled for 10 hr hours, which is 1 hr + 540 km

So 540 in 9hr

So 60 km per hour

Total distance = 540+60=600km

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-- The given question is incomplete, the complete question is

"A train, an hour after starting, meet with an accident which delays it for half an hour and after this, it proceeds at 3/4th of its former rate and arrives 3.5 hrs late. Had the accident happened 90 km farther along the line, it would have arrived only 3 hour late. What is the length of trip in km?" --

Step-by-step explanation:

30% of 500 voted for Sycamore

30% x 500   =   .30  * 500 = 150  votes

Fox Glen got the most votes

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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