To multiply the given radicals, first simplify the radicals to get like terms, then multiply coefficients and like radicals separately. The result of multiplying 4√3 × 10√12 × √6 × √2 is 480√3.
The task is to multiply the following radical expressions: 4√3 × 10√12 × √6 × √2.
First, let's simplify the radicals where possible. We know that √12 can be broken down into √4×√3, because 4 is a perfect square and 4×3=12. Thus, √12 simplifies to 2√3. Now, our expression looks like: 4√3 × 10×2√3 × √6 × √2.
Next, we multiply the coefficients (numbers outside the radicals) and the like radicals separately:
Coeficients: 4 × 10 × 2 = 80Radicals: √3 × √3 × √6 × √2 Multiplying the radicals, we get (√3)^2 × √6 × √2. Since the square of a square root equals the number itself, (√3)^2 = 3. Therefore, we have 3 × √6 × √2.Simplifying further, we can pair √6 and √2 to get √12, which we already simplified earlier into 2√3. Thus, 3 × 2√3 = 6√3.
Finally, we multiply the coefficient we got from our first step (80) by the simplified radical (6√3) to get the final answer: 480√3.
12 is 30% of blank plz give the right answer
Y -2 > -11 what is the answer to this
What is an equation of the line in slope-intercept form? m = 2 and the y-intercept is (0, 3)
Please do not make into a fraction because I can’t use a fraction as an answer. Rewrite using a negative exponent.
1/(xy)^1
David bought a used car for $3,000 and later sold it for $1,000. What was the approximate percent decrease in the price of the car?
what is 63 as the product of prime factors in ascending order?
for the function:
f(x) = -3x^4
complete the table of values using at least 5 points.
x -2 -1 0 1 2
f(x)
The blade of a circular saw rotates at a rate of \2500 revolutions per minute. what is the linear velocity in miles per hour of a point on the tip of the outer edge of a 7 and one fourth7 1 4 inch diameter blade?
The linear velocity of a point on the tip of the outer edge of the circular saw blade is 0.429 miles per hour.
Explanation:To find the linear velocity of a point on the tip of the outer edge of the circular saw blade, we can use the formula:
Linear velocity = 2 * π * radius * angular velocity
Where the radius is half of the diameter. Given that the diameter is 7 1/4 inches, the radius is 7 1/4 / 2 = 3 5/8 inches or 3.625 inches. Converting this to feet, we get 3.625 / 12 = 0.302 feet. To convert the angular velocity from revolutions per minute to radians per second, we multiply by 2 * π / 60. Substituting these values into the formula, we get:
Linear velocity = 2 * π * 0.302 * (2500 * 2 * π / 60) = 37.699 feet per minute.
To convert this to miles per hour, we divide by 5280 (since there are 5280 feet in a mile) and multiply by 60 (since there are 60 minutes in an hour):
Linear velocity = (37.699 / 5280) * 60 = 0.429 miles per hour.
What is 2(6+5•2)=5(4-2•5)
Answer: Not true
Step-by-step explanation: 2(16)=5(-6)
32=-30
This is not true
While catching fireflies, you and a friend decide to have a competition. after mm minutes, you have (3m+13)(3m+13) fireflies and your friend has (4m+6)(4m+6) fireflies.
a. how many fireflies are caught each minute during the competition?
To find for the number of fireflies caught in a minute, we simply look at the equation. The equation is linear and takes the form y = slope * x + b
where slope is also equivalent to the fireflies caught each minute.
So the equation of you and your friend is: (where y is the total fireflies caught)
you:
y = 3 m + 13
your friend:
y = 4 m + 6
So the fireflies caught each minute is:
you: 3
your friend: 4
So a total of 7 fireflies each minute combined
When four basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name.
P(shoot free throws in alphabetical order) = _____
The total number of possibilities of drawing their names is given by permutation.
4P4 = 24
The total possibility of drawing their names in alphabetical is only 1.
Therefore the probability is:
P = 1 / 24
P = 0.0417
Therefore there is about 4.17% chance that it will be in alphabetical order
Dani is working a sample booth at the national soda and beverage convention. She is paid $1.50 for each of the first ten tastings $2.50 for each of the next twenty tastings and $4.00 for each tasting beyond thirty she conducts each day. Today Dani conducted 36 tastings. How much total pay did Dani earn today?
Luis makes $23.10 per hour at his job for the first 40 hours he works each week. if he works more than 40 hours, then luis makes $34.65 per hour. if luis works 46 hours in one week, how much does he earn?a.$1,062.60b.$1,097.25c.$1,131.90d.$1,593.90
Answer:
correct answer is C. Just took the test.
willie wants to save for a new racing bike. if he deposits $250 in a saving account at 4% simple annual interest, what willis balance be after 3 years?
A.15
B.30
C.265
D.280
The length of a rectangle is 4 inches more than its width. the perimeter of the rectangle is 32 inches. what is the length of the rectangle
Lets find F^(-1) if
y=-2x+1
I’m not sure if the F^(-1)=1+x/2
The graph of a line goes up and to the right when
Answer: When the coefficient of X is positive!
bh+hr=25
solve for h and r
To solve for h and r in the equation bh + hr = 25, isolate one variable, solve for h using division, and solve for r by expanding the equation. There is no unique solution for h and r in terms of each other.
Explanation:To solve for h and r in the equation bh + hr = 25, we need to isolate one variable on one side of the equation. Let's solve for h first:
bh + hr = 25
Factor out h from the left side of the equation:
h(b + r) = 25
Divide both sides by (b + r) to solve for h:
h = 25 / (b + r)
Now, let's solve for r. Replacing h in the original equation:
bh + hr = 25
b(25 / (b + r)) + r(25 / (b + r)) = 25
Multiply both sides by (b + r) to get rid of the denominators:
25b + 25r = 25(b + r)
Expand the equation:
25b + 25r = 25b + 25r
As we can see, the equation is an identity, meaning any value of r will satisfy it. Therefore, there is no unique solution for r in terms of h, and vice versa.
Learn more about Solving equations here:https://brainly.com/question/14410653
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Write 3 ½% as a fraction
Answer:
7/200
Step-by-step explanation:
3.5% = 3.5/100 = (3.5/100)×(2/2) = 7/200
_____
The % symbol is a shorthand way to write "/100", so 3.5% = 3.5/100.
Marla has a pet hamster. The hamster makes 3 laps around her cage every minute.
What line represents the situation?
Line a
Line b
Line c
Line d
Let
x-------> the time in minutes
y------> the number of laps
we know that
In this problem the linear equation represent a direct variation and the slope is equal to
[tex]m=3\frac{laps}{minute}[/tex]
so
the equation of the line is
[tex]y=3x[/tex]
For [tex]x=1\ minute[/tex]
the value of y is equal to
[tex]y=3*1=3\ laps[/tex]
Plot the point [tex](1,3)[/tex] in the graph
therefore
the answer is
The solution is the line b
see the attached figure to better understand the problem
Staci is attending a music festival. The ticket to the festival costs 87.96. Staci plans to purchase 30.00 t-shirts from the event for close friends. She is taking 200.00 to the festival . What is the maximum number of t-shirts Staci can purchase?
Final answer:
Staci can purchase a maximum of 3 T-shirts after buying her festival ticket, given she brings $200.00 and each T-shirt costs $30.00.
Explanation:
To calculate the maximum number of T-shirts Staci can purchase at the music festival, we can follow these steps:
Subtract the cost of the festival ticket from the total amount of money Staci is taking to the festival. This will give us how much money she has left for the T-shirts.
Divide the remaining amount by the cost of one T-shirt to find out the maximum number of T-shirts she can buy.
So for the first step:
Staci has $200.00 and the ticket costs $87.96, leaving her with $200.00 - $87.96 = $112.04.
For the second step:
Each T-shirt costs $30.00, so we divide $112.04 by $30.00, which gives us 3.734.
Since Staci cannot buy a fraction of a T-shirt, we round down to the nearest whole number, which is 3.
Therefore, the maximum number of T-shirts Staci can purchase is 3.
(99 POINTS AVAILABLE)
When three or more lines intersect at one point, the point of intersection is called the ____________.
What type of angles are 6 and 8?
(y3 - 4y2 + 7y - 6) ÷ (y - 2)
A scatter plot has been created with a line of best fit that matches the equation y = 11x + 340. Using this line of best fit, determine the output value when the input is 10. Do you think this matches a point on the scatterplot? Why or why not?
The formula for the area of a triangle is a=1/2bh. solve the formula for h. a triangle has a base of 7cm and an area of 28cm squared. what us it's height
Answer: 8 cm
Step-by-step explanation:
Given : The formula for the area of a triangle is [tex]a=\dfrac{1}{2}bh[/tex]
If a triangle has a base of 7 cm and an area of 28 cm squared.
The substitute the values of b = 7 and a = 28 in the above formula, we get
[tex]28=\dfrac{1}{2}(7)h[/tex]
Divide 7 and multiply 2 on on both sides, we get
[tex]h=\dfrac{28\times2}{7}=4\times2=8\ cm[/tex]
Hence, the height of triangle = 8 cm
A vertical plane intersects the three-dimensional object in the image and divides the object into equal halves. What is the shape of the cross section?
Thank you :)
Answer:
Option 4 is correct .
Step-by-step explanation:
Given : A three dimensional figure
To Find : What is the shape of the cross section?
Solution :
If we intersects the three-dimensional object in the image and divides the object into equal halves by vertical plane then we can see the attached figure what the output will be .
We can see that if we see the cross section from the side then it looks like the fourth one
So, Option 4 is correct .
Alberto, Carlos and Maria share an inheritance of $54000 in the ratio of 3: 4: 5
What fraction of the the money does Alberto get?
Alberto gets [tex]\( \frac{1}{4} \)[/tex] of the inheritance.
To find out the fraction of the money Alberto gets, we first need to find out how much of the total inheritance each part of the ratio represents.
The total parts in the ratio are [tex]\(3 + 4 + 5 = 12\)[/tex].
Alberto's share is [tex]\(3\)[/tex] parts out of [tex]\(12\)[/tex].
So, Alberto's share of the inheritance is [tex]\( \frac{3}{12} \)[/tex] of the total amount.
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is [tex]\(3\)[/tex]:
[tex]\( \frac{3}{12} = \frac{1}{4} \)[/tex]
Therefore, Alberto gets [tex]\( \frac{1}{4} \)[/tex] of the inheritance.
A friend creates an IRA (Individual retirement account) with an APR of 6.25%. She starts the IRA at the age of 25 and deposits $50 at the end of each month. How much will her IRA contain when she retires at the age of 65?
C(x) = 0.5x+70 find the domain and range