Therefore, the expression that equals 3B - 3C in standard form is -21x² - 6x + 24.
What is expression?In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated or simplified to obtain a single value or another expression. In algebra, expressions are often used to represent mathematical relationships or formulas, and can be manipulated using various algebraic techniques such as factoring, expanding, simplifying, and solving for unknown variables. Expressions are also used in calculus, probability theory, and many other branches of mathematics to describe mathematical models and relationships.
Here,
We can start by substituting the expressions for B and C into the expression for 3B - 3C and simplifying:
3B - 3C = 3(-3x - 7x²) - 3(-x² - 8 - x)
= -9x - 21x² + 3x² + 24 + 3x
= -21x² - 6x + 24
To know more about expression,
https://brainly.com/question/30091997
#SPJ1
An angle in a circle with vertex on the circle itself___AngleCentral angleInscribed angleChord
Answer:
Inscribed angle
Step-by-step explanation:
Central angles have the vertex as the center of the circle, and chords are not angles
find the exact side values?
Answer:
[tex]a = \frac{5 \sqrt{2} }{2} [/tex]
[tex]c = \frac{3 \sqrt{3} }{2} [/tex]
Step-by-step explanation:
The first triangle is an isoceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. So we have:
[tex]a \sqrt{2} = 5[/tex]
[tex]a = \frac{5}{ \sqrt{2} } = \frac{5 \sqrt{2} }{2} [/tex]
The second right triangle is a 30°-60°-90° triangle, so the length of the shorter leg is one-half the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. Here, the length of the shorter leg is 3/2, or 1.5, and so we have:
[tex] {( \frac{3}{2}) }^{2} + {c}^{2} = {3}^{2} [/tex]
[tex] {c}^{2} = \frac{27}{4} [/tex]
[tex]c = \frac{3 \sqrt{3} }{2} [/tex]
What is H in the limit definition of a derivative?
The limit definition of the derivative is written as [tex]f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]. Here, h is defined as (x₂ – x₁) or ∆x or the change in x.
The limit definition of the derivative is also known as the difference quotient or increment definition of the derivative. This is a product of the input value difference, (x + h) - x, and the function value difference, f(x + h) - f(x). This can be calculated using the difference quotient formula as follows,
[tex]\begin{aligned}f '(x) &= \lim_{h \to 0}\;\text{(difference quotient)}\\f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\end{aligned}[/tex].
Here, f(x) represents (y₁), f(x+h) represents (y₂), x represents x₁, x+h represents x₂, h represents (x₂ – x₁) or ∆x or the change in x, Lim represents the slope M as h→0, and f (x+h) – f (x) – represents (y₂ – y₁).
This provides a measurement of the function's average rate of change over an interval. In other words, this provides the current rate of change.
To know more about the limit definition of derivative:
https://brainly.com/question/29144258
#SPJ4
On a world map, the distance between 2 cities is 7 inches. The scale on the map states that
every 500 miles is represented by each half-inch.
How many miles apart are the 2 cities?
The distance between two cities are 7000 miles apart.
What is distance ?
Distance is the amount of space between two points or objects. In the context of the question you asked earlier, "distance between two cities" refers to the actual physical distance between the two cities in terms of miles.
Given by the question:
On the map, 500 miles is represented by each 0.5 inches. Therefore, 1 inch represents 1000 miles.
So, the distance between the two cities on the map is 7 inches. This corresponds to a real-world distance of:
distance on map / scale on map = actual distance
7 inches * 1000 miles/inch = 7000 miles
Therefore, the two cities are 7000 miles apart.
To know more about Distance visit:
https://brainly.com/question/15256256
#SPJ1
Two pools are being filled with water. To start, the first pool contains 915 Liters of water and the second pool is empty. Water is being added to the first pool at a rate of 15.25 liters per minute. Water is being added to the second pool at a rate of 45.75 Liters per minute. After how many minutes will the two pools have the same amount of water? How much water will be in each pool when they have the same amount?
a) 30 minutes are taken to have the same amount of water.
b) Both pools have an amount of 1372.5 liters when 30 minutes have passed.
What is Linear Function?A linear function is one that produces a straight line when plotted. Generally, it is a polynomial function with a maximum degree of 1 or 0.
Now in the given question ,
a) Physically speaking, the capacity (Q) of each pool, in liters, is equal to the product of flow rate , in liters per minute, and time (t), in minutes. Hence, we derive the following functions :
First pool,
[tex]Q_1=915+15.25t\\[/tex] ...... (1)
Second pool,
[tex]Q_2=45.75t[/tex] ....... (2)
The following expression can be used to calculate how long it will take to find two pools with the same amount of water:
[tex]Q_1=Q_2[/tex] ........ (3)
By putting value of (1) and (2) in (3),
915 + 15.25 t = 45.75 t
30.5 t = 915
t = 915 ÷ 30.5
t = 30 minutes
30 minutes are taken to have the same amount of water.
b) By (2) and knowing that t = 30 , then we have the corresponding amount:
[tex]Q_2=45.75t\\\\Q_2=45.75*30\\\\Q_2=1372.5L[/tex]
Both pools have an amount of 1372.5 liters when 30 minutes have passed.
To learn more on linear functions, visit:
brainly.com/question/14165558
#SPJ1
what is defference continuous vs discrete variable?
A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers but a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers
Continuous and discrete variables are two types of quantitative variables in statistics.
A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers. Examples of continuous variables include height, weight, time, temperature, and distance. These variables can be measured using instruments with varying degrees of precision, but they can theoretically take on an infinite number of values.
On the other hand, a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers. Examples of discrete variables include the number of siblings a person has, the number of cars in a parking lot, and the number of points a basketball team scores in a game. These variables can only take on a limited number of values, and often represent counts or whole numbers.
The main difference between continuous and discrete variables is the way they can be measured and the number of possible values they can take. Continuous variables can take on an infinite number of values and can be measured with varying degrees of precision, while discrete variables can only take on specific values and are often measured with exact precision.
Learn more about discrete variable here
brainly.com/question/13339063
#SPJ4
PQRST is a solid regular pyramid on a square base QRST
where QR = 20 cm and edge PQ = 30 cm.
Find
a the height of P above the base QRST
b the angle that PS makes with the base QRST
c the total surface area of the pyramid including
the base.
Answer: a) To find the height of the pyramid, we can use the Pythagorean theorem. Let H be the height of the pyramid, and let M be the midpoint of QR. Then, PM is half of PQ, which is 15 cm. We can use the Pythagorean theorem to find H:
H^2 = PQ^2 - PM^2
H^2 = 30^2 - 15^2
H^2 = 675
H = sqrt(675) = 5 sqrt(3) cm
b) To find the angle that PS makes with the base QRST, we can use trigonometry. Let A be the foot of the perpendicular from P to the base QRST, and let B be the midpoint of PS. Then, we have:
tan(angle PSB) = AB / PB
Since triangle PAB is a right triangle, we can use the Pythagorean theorem to find AB:
AB^2 = AP^2 - PB^2
AB^2 = H^2 + (PQ/2)^2 - PB^2
AB^2 = (5 sqrt(3))^2 + (15/2)^2 - PB^2
AB^2 = 225/4 + 75 - PB^2
AB^2 = 375/4 - PB^2
Since triangle PBS is also a right triangle, we can use the Pythagorean theorem to find PB:
PB^2 = PS^2 - BS^2
PB^2 = (2 H)^2 - (PQ/2)^2
PB^2 = 4 (5 sqrt(3))^2 - (15/2)^2
PB^2 = 500 - 56.25
PB^2 = 443.75
Substituting these values into the equation for tan(angle PSB), we get:
tan(angle PSB) = sqrt(375/4 - 443.75) / sqrt(443.75)
tan(angle PSB) = -0.4385
Since angle PSB is in the second quadrant, we have:
angle PSB = 180 degrees + arctan(-0.4385) = 152.4 degrees (rounded to one decimal place)
c) To find the total surface area of the pyramid, including the base, we can divide the pyramid into four triangular faces and a square base. The area of each triangular face can be found using the formula:
area = (1/2) base * height
where the base is the length of one edge of the square base, and the height is the height of the pyramid. The area of the base is simply the area of the square QRST, which is (20 cm)^2 = 400 cm^2. Therefore, we have:
area of each triangular face = (1/2) (20 cm) (5 sqrt(3) cm) = 50 sqrt(3) cm^2
total surface area = 4 (50 sqrt(3) cm^2) + 400 cm^2 = 200 sqrt(3) cm^2 + 400 cm^2
total surface area = (200 + 200 sqrt(3)) cm^2 ≈ 532.4 cm^2 (rounded to one decimal place)
Step-by-step explanation:
Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the trapezoid.
Answer:
0.06
Step-by-step explanation:
Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle either is in the hexagon or in the circle
Area of rectangle = 26.2 * 13 = 340.6 sq inch
Area of Hexagon = 3√3(side)²/2 = 3√3 (1.8)²/2 = 8.42 sq inch
Area of circle = π(radius)² = 3.14 * (2)² = 12.56 sq inch
Area of hexagon + area of circle = 12.56 + 8.42 = 20.98 sq inch
Probability of selecting point inside the hexagon or in the circle = 20.98/340.6
= 0.06
how to convert microliter to ml
Answer:
1 Microliter = 0.001 Milliliter
Step-by-step explanation:
What are units?A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
Converting these units:
1 Microliter = 0.001 Milliliter1 Milliliter = 1,000 MicroliterTherefore, for every 1 microliter it is equivalent to 0.001 Milliliter.
Determine the type of distribution and the best measure of center and spread of the data set. 1, 7, 11, 14, 17, 17, 17, 21, 21, 23, 23, 26 The distribution is SO and (Type integers or decimals rounded to the nearest tenth as needed.) ... best represent the data set.
The mean of the data is 16.5 and the standard deviation is 7.28
What is the distribution of the dataThe given data set is a small sample of 12 observations.
To determine the type of distribution, we can first create a histogram or a boxplot of the data.
A histogram of the data shows that the distribution is unimodal and slightly right-skewed.
Alternatively, we can calculate the skewness of the data. If the skewness is close to zero, then the data is approximately symmetric. If the skewness is positive, then the data is right-skewed. If the skewness is negative, then the data is left-skewed.
Calculating the skewness of the data set, we get:
skewness = (n / ((n - 1) * (n - 2))) * Sum[(xi - x-bar)^3 / s^3]
where n is the sample size, x-bar is the sample mean, s is the sample standard deviation, and Sum is the sum of the values in the data set.
Using this formula, we get a skewness of approximately 0.456, which indicates that the distribution is slightly right-skewed.
Based on these findings, we can conclude that the distribution of the data set is approximately normal, but slightly right-skewed.
To find the best measure of center and spread, we can calculate the sample mean and sample standard deviation, respectively.
Sample mean:
mean = (1 + 7 + 11 + 14 + 17 + 17 + 17 + 21 + 21 + 23 + 23 + 26) / 12 = 16.5
Sample standard deviation:
s = sqrt((1/11) * [(1 - 16.5)^2 + (7 - 16.5)^2 + ... + (26 - 16.5)^2]) = 7.28
Therefore, the best measure of center for this data set is the sample mean of 16.5, and the best measure of spread is the sample standard deviation of 7.28.
Learn more on mean here;
https://brainly.com/question/14532771
#SPJ1
For a large order of brownies. Ms. Perry made 8/8 kg of fudge in her kitchen. She then got 1/6 kg from Mrs. Marshall. If she needs a total of 1 1/8kg for brownies, how much more fudge does she needs to make?
Answer:
Ms. Perry needs to make an additional 1/24 kg of fudge.
Step-by-step explanation:
Ms. Perry has a total of 8/8 + 1/6 = 13/6 kg of fudge. She needs 1 1/8 kg of fudge for the brownies, which is equivalent to 9/8 kg. To find how much more fudge she needs to make, we can subtract the amount of fudge she already has from the amount she needs:
9/8 - 13/6 = 27/24 - 26/24 = 1/24
Therefore, Ms. Perry needs to make an additional 1/24 kg of fudge.
The current exchange rate between Australia and the US is $AUD 1 = $USD 0.77.
How much $AUD can I get with $US 100,000?
Answer:
$129,870.13 AUD
Step-by-step explanation:
To find out what we need to solve, we can use these exchange rates:
1 AUD = 0.77 USD? AUD = 100,000 USDNow, we need to divide 100,000 by 0.77.
100,000 ÷ 0.77 = 129,870.13Why do we do this?We do this because we need to figure out how many times 0.77 must be multiplied to get 100,000. Then, we take that amount, and multiply that by however many AUD's you have.
129870.13 × 1 = 129870.13Therefore, for every $100,000 USD, there is $129,870.13 AUD.
what is -22 x -5 someone please helpppp
Answer:
110
Step-by-step explanation:
After a discount, the marked price of an article is 48$. Calculate the original price if a 20% discount was given
The original price of the article without the discount is %60.
What is discount?Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.
Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods.
Let us suppose original price = x.
Given that, after a discount, the marked price of an article is 48$ and the discount is 20%.
Thus,
48 = x(1 - 20/100)
48 = x(80/100)
x = 60
Hence, the original price of the article without the discount is %60.
Learn more about percentage here:
https://brainly.com/question/14695543
#SPJ1
how many sundays in a year
Usually there are 52 Sundays in a year approximately.
There are a total of 52 weeks in a year if we take a rough estimate.
Every week has one sunday in it. So, going by this logic, each year will have about 52 sundays in it.
Now, one thing that we should notice here is that is not certain that there will be definitely 52 sundays. This number of 52 can increase also by a number of one or two because it is possible that the year might not starting from sunday. Because when we do 365/7 we get 52.14 so, this decimal place might include one or two Sundays in it.
To know more about days in year, visit,
https://brainly.com/question/152631
#SPJ4
what is the exact decimal equivalent of 7/10
Answer:
Step-by-step explanation:
Decimals are out of 100.
7/10 = 70/100
Which equals to 0.70 or 0.7
So your answer is 0.70 (0.7)
Answer:
The exact decimal equivalent of 7/10 is 0.7
Step-by-step explanation:
The reason for this is because when you divide something by ten you move the decimal place one place to the left.
So then 7.0 becomes 0.7 because the decimal place is moved once divided by ten.
what is the seventh root of 128
Answer:
2
Step-by-step explanation:
The seventh root of a number is the number that would have to be multiplied by itself 7 times to get the original number so if you multiply 2 by itself 7 times you'd get 128
what is the 58 percentage conversion in decimal ?
The conversion value of the given quantity 58 percentage in decimals is equal to 0.58.
Percentage is that quantity of mathematics which represents the fraction of 100.One percentage converted to decimals is written as :
1 percentage = ( 1 / 100 )
= ( 0.01 )
Now Get the value in decimals for 58 percentage using conversion factor we have ,
= 58 percentage
= ( 58 / 100 )
= ( 0.58 ) in decimal form
Therefore, the value which we get after conversion of percentage to decimals is equal to 58 percentage = 0.58 in decimals.
Learn more about decimals here
brainly.com/question/29765582
#SPJ4
Can someone help me answer the second one
Answer:
[tex](u \circ \; w)(2) = \boxed{7}[/tex]
[tex](w \circ \;u)(2) = \boxed{3}[/tex]
Step-by-step explanation:
We have the two functions as
[tex]u(x) = x^2 + 3\\\\w(x) = \sqrt{x + 2}[/tex]
[tex](u \circ w)(x)[/tex] also written as [tex]u(w(x))[/tex] is the composite function; it means that
[tex]x = w(x)[/tex] should be substituted in [tex]u(x)[/tex]
To determine [tex](u \circ w)(x)[/tex], simply substitute the expression for [tex]w(x)[/tex] wherever there is an x in [tex]u(x)[/tex]
For a specific value of x, in this case x = 2,
first find w(x2)substitute this value for x in u(x)
Part 1
[tex](u \circ w)(2):\\\\w(2) = \sqrt{2 + 2} = 4(u \circ w)(2) = 2^2 + 3 = 4 + 3 = 7[/tex]
For [tex](w \circ u)(x),[/tex] we substitute the expression for [tex]u(x)[/tex] into [tex]w(x)[/tex] wherever an [tex]x[/tex] appears in [tex]w(x)[/tex]
For a specific value of x, say 2, find the value of u(2) and substitute it into [tex]w(x)[/tex]
[tex]u(2) = 2^2 + 3 = 7[/tex]
[tex](w \circ u)(2), = \sqrt{7 + 2} = \sqrt{9} = 3\\[/tex]
You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $60 per hour. Great Sounds Studio rents for $25 plus $80 per hour. Determine the number of hours for which the cost of 1 Step renting the studios is the same. Work needs to be showed btw
The solution is found by slope of the graph and the solution is 2,200.
Let x the amount of money per hour and y the total amount of money.
Studio A:-
Rents for 100 dollars plus 50 dollars per hour.
[tex]y= 100 + 50x[/tex]
So the slope is 50 and the y intercept is 100.
Studio B:-
rents for 50 dollars plus 75 dollars per hour.
[tex]y= 50 + 75x[/tex]
So the slope is 75 and the y intercept is 50.
ThrTh solution is 2200 , see the gragraphph.
To know more about Slope of graph go through:-
https://brainly.com/question/3493733
#SPJ4
Complete question:- You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $50 per hour. Great Sounds Studio rents for $50 plus $75 per hour. Solve the system by graphic method.
What is the conversion of 64kg in pounds?
The conversion of 64kg in pounds is equivalent to approximately 141.09568 pounds.
The kilogram (kg) is the SI unit of mass. It is equal to the mass of the international prototype of the kilogram. This prototype is a platinum-iridium international prototype kept at the International Bureau of Weights and Measures. One kg is approximately equal to 2.20462262184878 pounds.One pound, the international avoirdupois pound, is legally defined as exactly 0.45359237 kilograms.
To convert 64 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.
Therefore,64 kilograms = 64 x 2.20462 pounds
= 141.09568 pounds (rounded to 5 decimal places)
So, 64 kilograms is equivalent to approximately 141.09568 pounds.
For such questions on conversion,
https://brainly.com/question/30775068
#SPJ4.
ANSWER QUICKLY PLEASE
If XY = 24. XZ = 22, JQ = 9, and the radius of the circumscribed circle of AXYZ is 15, find QK.
The required, measure of QK is approximately 10.82.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.
First, we can use the Pythagorean theorem to find the length of side XZ:
[tex]XZ^2 = XY^2 - YZ^2[/tex]
[tex]YZ = \sqrt{(XY^2 - XZ^2) }[/tex]
[tex]= \sqrt(24^2 - 22^2) = 10[/tex]
The length of the perpendicular bisector of XY is half the distance between points A and the midpoint of XY. The midpoint of XY can be found by dividing the length of XY by 2:
midpoint of XY = (X + Y)/2
Since we are given the length of XY, we can find the coordinates of its endpoints X and Y. Let X be the origin (0,0) and let Y have coordinates (24,0) (since XY = 24). Then the midpoint of XY is the midpoint of XY
= (X + Y)/2
= (0 + 24)/2
= (12,0)
Now we can use the distance formula to find the distance between A and the midpoint of XY distance between A and the midpoint of XY
= [tex]= \sqrt((12 - 0)^2 + (0 - 15)^2)[/tex]
= [tex]\sqrt(12^2 + 15^2)[/tex]
=[tex]3 \sqrt(29)[/tex]
This is the length of the perpendicular bisector of XY, which passes through the center of the circumscribed circle. So the distance from Q to the center of the circle is the distance from Q to center = 15 - 9 = 6
Finally, we can use the Pythagorean theorem to find QK:
[tex]QK^2 = QJ^2 + JK^2 = QJ^2 + (distance \ from \ Q \ to\ center)^2[/tex]
[tex]QK^2 = 9^2 + 6^2 = 81 + 36 = 117[/tex]
[tex]QK = \sqrt(117)\\ = 10.82[/tex]
Therefore, QK is approximately 10.82.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ1
A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 9 inches has volume V = 3πx^2 + 42πx + 147π, what is the cone’s radius r in terms of x? (15 pts)
The radius of the cone in terms of x is: r = √(x² + 14x + 49). This can be solved by using volume of cone formula.
What is the Volume of a Cone?Volume of cone (V) = 1/3πr²h, where r is the radius and h is the height of the cone.
Given:
h = 9 in.
V = 3πx² + 42πx + 147π
r = ?
Substitute
3πx² + 42πx + 147π = 1/3(π)(r²)(9)
3π(x² + 14x + 49) = (π)(r²)(3)
Divide both sides by 3π
x² + 14x + 49 = r²
Square on both sides
√(x² + 14x + 49) = r
r = √(x² + 14x + 49)
Therefore, the radius of the cone in terms of x is: r = √(x² + 14x + 49).
To learn more about volume of cone on:
brainly.com/question/13677400
#SPJ1
randomization in an experiment is important because it ensures that
Select the addition problem that is shown by the fraction strips below.
Answer:2/8 + 2/8
Step-by-step explanation:
so, you start at 2/8
then, you add the extra 2/8
then, you add them together ( don’t forget: when the bottom numbers of the fraction are the same the stay at the same number ex: 3/8 + 3/8 = 6/8)
then after adding them up you get 4/8 which could also mean 1/2
A fruit seller had 2520 apples and oranges. There were 2/3 as many apples as oranges. He threw some rotten apples away and the ratio of apples to oranges became 1 : 4. How many rotten apples did he throw away?
If the fruit seller threw some rotten apples away and the ratio of apples to oranges became 1 : 4. The fruit seller threw away 630 rotten apples.
To find the number of rotten apples that the fruit seller threw away, we will need to use the given information and set up equations to solve for the unknown variable.
Let's start by using the given information that there were 2/3 as many apples as oranges. We can set up an equation to represent this relationship:
2/3 O = A
Where O is the number of oranges and A is the number of apples.
We are also given that the fruit seller had 2520 apples and oranges in total. We can set up another equation to represent this relationship:
O + A = 2520
Now, we can use the first equation to solve for one of the variables in terms of the other. Let's solve for A in terms of O:
A = (2/3)O
Now we can substitute this expression for A into the second equation:
O + (2/3)O = 2520
Simplifying this equation gives us:
(5/3)O = 2520
Now we can solve for O:
O = (3/5)(2520) = 1512
Now that we know the number of oranges, we can use the first equation to solve for the number of apples:
A = (2/3)(1512) = 1008
So the fruit seller originally had 1008 apples and 1512 oranges.
We are also given that after throwing away some rotten apples, the ratio of apples to oranges became 1:4. We can set up an equation to represent this relationship:
(A - X)/O = 1/4
Where X is the number of rotten apples that were thrown away.
Substituting the values we found for A and O into this equation gives us:
(1008 - X)/1512 = 1/4
Cross-multiplying and simplifying gives us:
4(1008 - X) = 1512
4032 - 4X = 1512
4X = 2520
X = 630
Therefore, the answer to the question is 630.
Learn more about ratio here:
https://brainly.com/question/26460724
#SPJ11
Find the volume of the complex figure below.
The volume of the rectangular prism in the image is 480 cubic units.
What is volume ?
Volume is a measurement of the amount of space occupied by a three-dimensional object. It is a physical quantity that is measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).
The image shows a rectangular prism with a length of 12 units, a width of 8 units, and a height of 5 units.
To find the volume of a rectangular prism, you need to multiply its length, width, and height.
So, the volume of the rectangular prism in the image is:
Volume = length x width x height
Volume = 12 units x 8 units x 5 units
Volume = 480 cubic units
Therefore, the volume of the rectangular prism in the image is 480 cubic units.
To learn more about Volume from given link.
https://brainly.com/question/1578538
#SPJ1
how to convert 20cm to in?
20 centimeter is approximately equal to 7.8740 inches ( rounded to four decimal places )
To convert 20 cm to inches, we can use the following formula:
1 cm = 0.393701 inches
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in inches = conversion factor × The length in centimeter
Substitute the values in the equation
20 cm = 20 x 0.393701
Multiply the numbers
= 7.8740 inches ( rounded to four decimal places )
Therefore, 20 centimeter is 7.8740 inches
Learn more about conversion factor here
brainly.com/question/5056146
#SPJ4
set up but do not evaluate the integral for the mass of a thin wire in the shape of a parabola density x^2 y^2
The integral for the mass of a thin wire in the shape of a parabola density is [tex]\int[-1,1]\int[0,x^2] x^2 y^2 dy dx[/tex]
To find the mass of the thin wire in the shape of a parabola with density function ρ(x, y) = [tex]x^2 y^2[/tex],
we can set up a double integral over the region that describes the parabola. The mass M is given by the following integral:
M = ∬ρ(x,y) dA
where dA represents the area element in the xy-plane. To set up this integral, we need to first determine the limits of integration for x and y.
The parabola can be described by the equation y =[tex]x^2[/tex], where x ranges from -1 to 1. Therefore, the limits of integration for x are -1 to 1.
For each value of x, the y-values range from the parabola to the x-axis, which is the region between y = 0 and y = [tex]x^2[/tex]. Therefore, the limits of integration for y are 0 to[tex]x^2[/tex].
Using these limits of integration, the integral for the mass of the thin wire is:
M = ∫∫ρ(x,y) dA
=[tex]\int[-1,1]\int[0,x^2] x^2 y^2 dy dx[/tex]
This integral can be evaluated using standard integration techniques.
To learn more about Parabola density :
https://brainly.com/question/15089285
#SPJ4
for a period of time, an island's population grows exponentially. If the population doubles every 34 years and the current population is 1233, what will the population be 6 years from now?
As a result, the island's population will be about 1397.33 persons in 6 years.
What is exponent?An exponent, also called a power or index, is a mathematical operation that indicates the number of times a base number is multiplied by itself. Exponents are written as a superscript number to the right of the base number. Exponents can be positive or negative, and they can be whole numbers or fractions. A positive exponent tells us to multiply the base number by itself, while a negative exponent tells us to divide the base number into 1. Exponents can be used to simplify and solve many mathematical problems, and they are an important part of many areas of mathematics, including algebra, calculus, and geometry.
Here,
If the population of the island doubles every 34 years, we can use the exponential growth formula to determine the population after a certain period of time:
P = P0 * 2ⁿ÷³⁴
where P is the population after time t, P0 is the initial population, and t is the time elapsed in years.
We know that the current population is 1233, so P0 = 1233. We want to find the population 6 years from now, so t = 6. Plugging these values into the formula, we get:
P = 1233 * 2⁶÷³⁴
P ≈ 1397.33
Therefore, the population of the island will be approximately 1397.33 people 6 years from now.
To know more about exponent,
https://brainly.com/question/11709654
#SPJ1