Find the area of the surface generated when the given curve revolved about the x -axis. y = 8 √ x on [ 9 , 20 ]

This is because rotations preserve angles. The angle measures won't change. That's why angle BCD is the same as angle B'C'D'. This applies to any rotation (regardless how much you rotate), any translation, any reflection, and any dilation.

Note: dilations will change the side lengths

The smallest positive integer that begins with the digit 1 when written in base 10 and is tripled when the 1 is transferred to the end is 12.

To solve this problem, we need to use some algebraic equations. Let's represent the positive integer as "x" and write it in base 10 as 10a+b, where a and b are digits. We know that x begins with the digit 1, so a must be 1.

Now we transfer the digit 1 to the end of the number, making it 10b+1. We also know that when we triple this number, we get 3(10b+1) = 30b+3x.

Setting this equal to our original number, 10a+b=x, we get the equation 30b+3x=10a+b. Substituting a=1, we can simplify this to 27b=7+x.

We want to find the smallest integer that satisfies this equation, so we start by setting x=1 and solving for b. We get b=2, which means our original number was 12.

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Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

The product of the two functions is:

\((f \times g)(x) = 10x\)

So the correct option is A.

Remember that the square root has the property.

\(\sqrt{a}*\sqrt{b} = \sqrt{a*b}\)

Here we have:

\(f(x) = \sqrt{2x} \\\\g(x) = \sqrt{50x}\)

Then the product is:

\((f \times g)(x) = 10x = f(x)*g(x) = \sqrt{2x}*\sqrt{50x} = \sqrt{(2x)*(50x)} \\\\(f \times g)(x) = 10x = \sqrt{100x^2} = \sqrt{100}*\sqrt{x^2} = 10*x\)

the correct option is A.

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Ava and Kelly will be 3/4 mile apart after 22.5 minutes.

To determine when Ava and Kelly will be 3/4 mile apart, we can consider their relative speed. The relative speed is the difference between their individual speeds.

Ava's speed = 6 miles per hour

Kelly's speed = 8 miles per hour

The relative speed of Ava and Kelly is:

Relative speed = Kelly's speed - Ava's speed

= 8 miles per hour - 6 miles per hour

= 2 miles per hour

This means that Ava and Kelly are moving away from each other at a rate of 2 miles per hour.

To calculate the time it takes for them to be 3/4 mile apart, we can use the formula:

Distance = Speed × Time

In this case, the distance they need to cover is 3/4 mile, and the relative speed is 2 miles per hour.

3/4 mile = 2 miles per hour × Time

Simplifying the equation:

3/4 = 2 × Time

Dividing both sides by 2:

3/4 × 1/2 = Time

3/8 = Time

Therefore, it will take Ava and Kelly 3/8 hours (or 22.5 minutes) to be 3/4 mile apart.

Thus, Ava and Kelly will be 3/4 mile apart after 22.5 minutes.

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Answer:

Add up all the scores and divide by the number of assignments.

Step-by-step explanation:

That would be the "Mean" or the average score

Answer:

32h and a

Step-by-step explanation:

Answer:

First choice

Step-by-step explanation:

The '2' coefficient represents the 'per hour ' fee   .... '32 ' is the fixed fee.

Answer:

Step-by-step explanation:

Graph in the picture represents,

y = qˣ

a). Point of intersection of the curve with the y-axis → (0, 1)

b). Since, this graph passes through (1, 4)

    By substituting values in the equation,

    4 = q¹

    q = 4

c). Value of y when x = 10,

   \(y=4^{10}\)

   y = 1048576

The theoretical probability =\(\dfrac{5}{9}\),  The experimental probability  = \(\dfrac{5}{12}\)

The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.

The sample will be ={1,2,3,4,5,6,7,8,9}=9

favourable outcomes={1,3,5,7,9,}=5

The theoretical probability of spinning and odd number = \(\dfrac{5}{9}\)

As she spends the spinner 12 times

The experimental probability = \(\dfrac{5}{12}\)

Hence the theoretical probability =\(\dfrac{5}{9}\),  The experimental probability  = \(\dfrac{5}{12}\)

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Answer:

The theoretical probability of spinning an odd number is equal to 5/9 The experimental probability of spinning an odd number is equal to 2/3. Therefore, the theoretical probability of spinning an odd number is less. than the experimental probability of spinning an odd number.

if you could give me brainliest i would greatly appreciate it.

The percentage of 100 square quadrilateral grid shaded is 96%.

since there are 4 unshaded grids and rest 96 are shaded then the percentage will be

shaded percentage = 96 × 100/100 = 96%

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Al-Khwarizmi made significant contributions to the world of mathematics, particularly in the field of algebra. His major accomplishment was the development of algebra as an independent mathematical discipline.

Al-Khwarizmi, a Persian mathematician and scholar, wrote the book titled "Kitab al-Jabr wal-Muqabala," which laid the foundation for modern algebra. In this influential work, he introduced systematic methods for solving linear and quadratic equations. Al-Khwarizmi's algebraic techniques, including the use of variables and equations, greatly advanced mathematical understanding and problem-solving. His work also contributed to the development of algorithms and mathematical notation, such as the concept of the "zero" and the decimal system. Overall, al-Khwarizmi's contributions revolutionized mathematics and had a profound impact on subsequent generations of mathematicians and scientists.

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Answer:

531441

the answer is A because

Step-by-step explanation:

3*3*3*3*3*3*3*3*3*3*3*3=531441

Answer:

-1/3

write it out.........

Answer:

410 is the outlier.

What is an outlier?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.

In simpler words, it is the number that is significantly bigger or smaller than the rest of the numbers, and 410 is it.

Step-by-step explanation:

Hope it helps! =D

For a catering company, which used the linear function for calculating the total cost of parties, the cost to cater a dinner party with 90 guests is equals to the $42750.

We have a table form data of total cost of parties for a catering company. There is use of linear function to determine total cost of parties. Table look like as below,

Cost for dinner parties | number of guests

(each guest)

$315 30

$555 60

We have to determine the cost to cater a dinner party with 90 guests. For this we use simple multiplication arithmetic method. As we see in table, cost of cater a dinner party with 30 guests = $315 for each , that is cost for one guest = $315

so, cost of cater a dinner party with 30 guests = 30 × $315 = $ 9450

Similarly, when number of guests is 60 in count, cost of cater a dinner party = $555 for each one

So, total cost of cater a dinner party with 60 guests = 60× $555 = $ 33300

Now, we have total guest = 90

The cost to cater a dinner party with 90 guests

= cost to cater a dinner party with 30 guests + cost to cater a dinner party with 60 guests = $9450+ $33300

= $42750

Hence, required value is $42750.

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The value of the function f(x)-g(x)-h(x) is -5x^2+6x+6. Option D

It is important that we know functions are expressions showing the relationship between two variables.

These variables are called;

From the information given, we have the functions as;

f(x)=3x+5 g(x)=4x^2-2 h(x)=x^2-3x+1

Now, to determine the function, f(x)-g(x)-h(x). substitute the expressions, we get;

f(x)-g(x)-h(x) =3x + 5 - 4x² + 2 - x² + 3x - 1

Now, collect the like terms, we get;

f(x)-g(x)-h(x) = -4x² - x² + 3x+ 3x + 5 + 2 - 1

Add or subtract the like terms, we get;

f(x)-g(x)-h(x) = -5x² + 6x + 6

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To find the number of triangles with vertices of three different colors, we need to consider the combinations of colors we can choose from the given set of points.

We have 8 red points, 4 green points, and 6 blue points. To form a triangle with vertices of three different colors, we need to choose one point from each color group.

First, let's choose one red point. We have 8 options for this.

Next, let's choose one green point. We have 4 options for this.

Finally, let's choose one blue point. We have 6 options for this.

To determine the total number of triangles, we need to multiply the number of options for each color:

Total number of triangles = Number of options for red points × Number of options for green points × Number of options for blue points

                      = 8 × 4 × 6

                      = 192

Therefore, there are 192 triangles with vertices of three different colors.

It's worth noting that the order in which we choose the points does not matter because we are counting the number of distinct triangles. So, we are not considering permutations but rather combinations of colors.

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The remainder when x³ - 1 is divided by (x + 3) is  -28

The functions are given as

x 3 1 is divided by x 3

Rewrite them as

f(x) = x³ - 1 is divided by (x + 3)

Set the divisor to 0

So, we have

x + 3 = 0

Determine the value of x

This gives

x = -3

By the remainder theorem

Substitute x = -3 in the function f(x)

So, we have

f(-3) = (-3)³ - 1

Evaluate the expression

f(-3) = -28

By the remainder theorem, this represents the remainder

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In the given sample space of the outcomes of spinning a fair four-sided spinner and flipping a fair coin is 8 possible outcome.

What about sample space?

In probability theory, a sample space is the set of all possible outcomes of a random experiment or process. It is the collection of all possible outcomes that could occur when an experiment is performed.

For example, when rolling a six-sided die, the sample space would be {1, 2, 3, 4, 5, 6}, as those are the possible outcomes of the experiment. Similarly, when flipping a coin, the sample space would be {heads, tails}.

Define spinner:

A spinner is a circular device used in games and other activities to randomly select an outcome or determine a probability. It typically consists of a flat disk or wheel with different colored sections or markings, each representing a possible outcome. The spinner is spun, and the outcome is determined by the section or marking that comes to rest at the top of the spinner.

According to the given information:

The possible outcomes that we get from the given sample is,

\((H,1) (H,2) (H,3) (H,4) (T,1) (T,2) (T,3) (T,4)\)

So, the possible outcomes for the given condition is = 8 possible outcome.

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The number of students who watch between 1 - 2 hours is 9.

We have,

From the table,

Number of students who watch tv for 1 hour = 5

Number of students who watch tv for 1.5 hours = 3

Number of students who watch tv for 2 hours = 1

Now,

The number of students who watch between 1 - 2 hours.

= Number of students who watch tv for 1 hour + 1.5 hours + 2 hours

= 5 + 3 + 1

= 9

Thus,

The number of students who watch between 1 - 2 hours is 9.

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To simplify a complex fraction expression, first identify the numerator and denominator of each fraction.

A complex fraction is a fraction that contains one or more fractions in the numerator, denominator, or both. This type of fraction requires additional steps to simplify and can often be reduced to a simpler fraction or a whole number. Complex fractions are also known as compound fractions or nested fractions.

Then, factor each fraction into its simplest form by dividing each numerator and denominator by their greatest common factor. Finally, combine the fractions by multiplying the numerators and denominators. This will result in a simplified expression.

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The probability of the given security code is as follows:

C. 1/30,240.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

5 digits are taken from a set of 10, and the order is relevant, hence the total number of passwords is given as follows:

P(10,5) = 10!/(10 - 5)! = 30240.

Hence the probability is given as follows:

C. 1/30,240.

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The problem provides the information:

3 x + 5 y = 11

and x y = 2

Asking to find the value of 9 x^2 + 25 y^2

so we proceed to recall what the square of a binimial of the following form is:

So, we see that the square of the quantity: (3 x + 5 y) which from the information given equals 11^2 = 121, must equal the expression:

9 x^2 + 25 y^2 + 30 x y.

then we write the following equation making both parts equal:

Therefore the value of 9 x^2 + 25 y^2 = 61

Answer:

15% increase

Step-by-step explanation:

to find the percent increase from an initial value to a final value, first find the difference:

2070-1800=270

then divide the difference by the initial value:

270/1800= 0.15

and multiply by 100

0.15*100=15

so there is a 15% increase

Answer:

please see photo attached for detailed analysis.

The even function, among the options presented, is given as follows:

f(x) = 7.

The classification of even and odd functions is dependent on the relation f(x) and f(-x), as follows:

To prove that a function is not even, we have to find a contradiction, that is, a value of x for which f(-x) is different of f(x). In this problem, these contradictions are given as follows:

Hence the even function in this problem is given as follows:

f(x) = 7.

As it assumes a constant value no matter the input.

The options are given by the image at the end of the answer.

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Answer:

-sin Ф

Step-by-step explanation:

sin( O + 180) = sinФ cos180 + sin180 cosФ

                     =  sin Ф * -1 + 0 * cos Ф

                     =   -sin Ф

So

Answer:

2x + 3y = 42

Step-by-step explanation:

Standard form should be like:

=> ax + by = c

To make an equation like the above one, we need to do the point-slope form first.

=> y - y1 = slope (x - x1)

Slope = -2/3

Y-intercept -> to find the y-intercept, we need to make the 'x' as 0.

=> y = -2/3 * 0 + 7

=> y = 7

X-intercept -> to find the x-intercept, we need to make 'y' as 0.

=> 0 = -2/3x + 7

=> -7 = -2/3x

=> -21/2 = -x

=> -10.5 = -x

=> 10.5 = x

So, x and y intercepts are 10.5 and 7.

We can now write the point-slope form:

=> y - 7 = -2/3 (x - 10.5)

=> y - 7 = -2/3x + 21/3

=> y = -2/3x + 7 + 7

=> y = -2/3x + 14

=> 2/3x + y = 14

=> Multiply all numbers by 3

=> 2x + 3y = 42