Box C has the smallest volume, followed by Box A, and Box B has the largest volume.
Explanation on how to get the least volumeFirst, we need to find the volume of each box.
Recall that the formula for volume of a box is given as:
V = length x height x width
For Box A,
V = 3 cm x 2 cm x 4 1/2 cm = 27 cm³
For Box B,
V = 2 1/3 cm x 3 cm x 5 cm = 7/3 cm x 3 cm x 5 cm = 35 cm³
For Box C,
V = 4 cm x 3 cm x 1 1/4 cm = 4 cm x 3 cm x 5/4 cm = 15 cm³
So, the order of the boxes by volume from least to greatest is: Box C, Box A, and Box B.
Learn more about order here:
https://brainly.com/question/27864906
#SPJ1
A car with a mass of 1200 kg and traveling 40 m/s east runs into the back of a parked truck with a mass of 2000 kg. After the collision the car and truck do not stick together, but the car is stopped. If momentum is conserved, what would the velocity of the truck be after the collision?
The velocity of the truck after the collision would be 24 m/s east.
The law of conservation of momentum states that the momentum of a closed system remains constant if no external forces act on it. In this case, we can assume that the car and the truck form a closed system.
The momentum of an object is given by its mass multiplied by its velocity, p = mv. Initially, the momentum of the system is:
p_initial = m_car * v_car + m_truck * v_truck
where m_car and v_car are the mass and velocity of the car, and m_truck and v_truck are the mass and velocity of the truck.
After the collision, the car is stopped, so its velocity is 0. The momentum of the system after the collision is:
p_final = m_car * 0 + m_truck * v'_truck
where v'_truck is the velocity of the truck after the collision.
Since momentum is conserved, we can set p_initial equal to p_final:
m_car * v_car + m_truck * v_truck = m_truck * v'_truck
Solving for v'_truck, we get:
v'_truck = (m_car * v_car + m_truck * v_truck) / m_truck
Substituting the given values, we have:
v'_truck = (1200 kg * 40 m/s + 2000 kg * 0 m/s) / 2000 kg
v'_truck = 24 m/s east
Therefore, the velocity of the truck after the collision would be 24 m/s east.
To know more about law of conservation of momentum refer here:
https://brainly.com/question/24131537
#SPJ11
A segment with endpoints A (2, 6) and C (5, 9) is partitioned by a point B such that AB and BC form a 3:1 ratio. Find B.
A. (2. 33, 6. 33)
B. (3. 5, 10. 5)
C. (3. 66, 7. 66)
D. (4. 25, 8. 25)
The coordinates of point B are (4.25, 7.5), which is closest to option D (4.25, 8.25).
To find the coordinates of point B, we need to use the concept of section formula which states that if a line segment with endpoints A(x1, y1) and C(x3, y3) is partitioned by a point B(x2, y2) such that AB:BC = m:n, then the coordinates of B are given by:
x2 = (mx3 + nx1)/(m + n)
y2 = (my3 + ny1)/(m + n)
Here, A has coordinates (2, 6) and C has coordinates (5, 9). Let the ratio AB:BC be 3:1, which means that m = 3 and n = 1. Substituting these values in the formula, we get:
x2 = (3*5 + 1*2)/(3 + 1) = 17/4 = 4.25
y2 = (3*9 + 1*6)/(3 + 1) = 30/4 = 7.5
Therefore, the coordinates of point B are (4.25, 7.5), which is closest to option D (4.25, 8.25).
To learn more about coordinates, refer below:
https://brainly.com/question/16634867
#SPJ11
3. Compute the integral JSS, udv, where U is the part of the ball of radius 3, centered at 0,0,0), that lies in the 1st octant. Recall that the first octant is the part of the 3d space where all three coordinates I, y, z are nonnegative. (Hint: You may use cylindrical or spherical coordinates for this computation, but note that the computation with cylindrical coordinates will involve a trigonometric substitution - 30 spherical cooridnates should be preferable.)
To compute the integral JSS, udv, where U is the part of the ball of radius 3, centered at 0,0,0), that lies in the 1st octant, we can use spherical coordinates. Since the region is defined as having all three coordinates nonnegative, we can set our limits of integration as follows: 0 ≤ ρ ≤ 3, 0 ≤ θ ≤ π/2, and 0 ≤ φ ≤ π/2.
Using the Jacobian transformation, we have:
JSS, udv = ∫∫∫U ρ²sinφ dρdθdφ
Substituting in our limits of integration, we get:
JSS, udv = ∫0^π/2 ∫0^π/2 ∫0³ ρ²sinφ dρdθdφ
Evaluating the integral, we get:
JSS, udv = (3³/3) [(sin(π/2) - sin(0))] [(1/2) (π/2 - 0)]
JSS, udv = 9/2 π
Therefore, the value of the integral JSS, udv, over the part of the ball of radius 3 that lies in the 1st octant is 9/2π.
To compute the integral JSS, udv, over the region U, which is the part of the ball of radius 3 centered at (0,0,0) and lies in the first octant, we will use spherical coordinates for this computation as it's more preferable.
In spherical coordinates, the volume element is given by dv = ρ² * sin(φ) * dρ * dφ * dθ, where ρ is the radial distance, φ is the polar angle (between 0 and π/2 for the first octant), and θ is the azimuthal angle (between 0 and π/2 for the first octant).
Now, we need to set up the integral for the volume of the region U:
JSS, udv = ∫∫∫ (ρ² * sin(φ) * dρ * dφ * dθ), with limits of integration as follows:
ρ: 0 to 3 (radius of the ball),
φ: 0 to π/2 (for the first octant),
θ: 0 to π/2 (for the first octant).
So, the integral becomes:
JSS, udv = ∫(0 to π/2) ∫(0 to π/2) ∫(0 to 3) (ρ² * sin(φ) * dρ * dφ * dθ)
By evaluating this integral, we will obtain the volume of the region U in the first octant.
Visit here to learn more about integral brainly.com/question/18125359
#SPJ11
X is a random variable with the probability function: f(x) = x/6 for x = 1, 2, or 3. the expected value of x is _____.
The expected value of X is 2.33.
To find the expected value of the random variable X, we need to use the given probability function f(x) and the formula for expected value: E(X) = Σ[x * f(x)]. Here's a step-by-step explanation:
1. Identify the possible values of x: 1, 2, and 3.
2. Calculate f(x) for each x value using the given probability function f(x) = x/6:
f(1) = 1/6
f(2) = 2/6 = 1/3
f(3) = 3/6 = 1/2
3. Apply the expected value formula by multiplying each x value by its corresponding f(x) and summing the results:
E(X) = (1 * 1/6) + (2 * 1/3) + (3 * 1/2) = 1/6 + 2/3 + 3/2
4. Simplify the expression to find the expected value:
E(X) = 1/6 + 4/6 + 9/6 = (1 + 4 + 9)/6 = 14/6 = 7/3
The expected value of the random variable X is 7/3 or 2.33.
Learn more about expected value,
https://brainly.com/question/30398129
#SPJ11
How many sides does a regular n-gon have if one interior angle measures 150°? Show all work!
Answer:
A regular n-gon with one interior angle of 150° has 12 sides.
Step-by-step explanation:
The formula for the measure of each interior angle of a regular n-gon is:
180(n-2)/nwhere:
n is the number of sidesWe are given that one interior angle measures 150°, so we can set up the equation:
180(n-2)/n = 150Multiplying both sides by n, we get:
180(n-2) = 150nDistributing, we get:
180n - 360 = 150nSubtracting 150n from both sides, we get:
30n - 360 = 0Adding 360 to both sides, we get:
30n = 360Dividing both sides by 30, we get:
n = 12Therefore, a regular n-gon with one interior angle of 150° has 12 sides.
Mariah is training for a sprint distance triathlon. She plans on cycling from her house to the library, shown on the grid with a scale in miles. If the cycling portion of the triathlon is 12 miles, will mariah have cycled at least 2/3 of that distance during her bike ride?
Mariah cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
What is a triathlon?A triathlon is described as an endurance multisport race consisting of swimming, cycling, and running over various distances.
The coordinates are given as follows:
Library (4,9).Mariah's House: (9, 2).Suppose that we have two points, and . The distance between them is given by:
distance = √(x2 - x1)² + (y2-y1)²
We substitute in the equation
Hence the distance between her house and the library is:
D = 8.6 miles.
She cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
Learn more about triathlon at:
https://brainly.com/question/30817420
#SPJ1
Javier's deli packs lunches for a school field trip by randomly selecting sandwich, side, and drink options. each lunch includes a sandwich (pb&j, turkey or ham and cheese), a side (cheese stick or chips), and a drink (water or apple juice)
1. what is the probability that a student gets a lunch that includes chips and apple juice?
2. what is the probability that a student gets a lunch that does not include chips?
Answer is: Probability of a student getting a lunch that does not include chips is 6/12 or 0.5.
1. To find the probability of a student getting a lunch that includes chips and apple juice, we need to first find the total number of possible lunch combinations. There are 3 options for sandwiches, 2 options for sides, and 2 options for drinks, so there are a total of 3 x 2 x 2 = 12 possible lunch combinations.
Out of those 12 combinations, there is only 1 combination that includes chips and apple juice: ham and cheese sandwich, chips, and apple juice.
Therefore, the probability of a student getting a lunch that includes chips and apple juice is 1/12 or approximately 0.083.
2. To find the probability of a student getting a lunch that does not include chips, we can count the number of possible lunch combinations that do not include chips and divide by the total number of lunch combinations.
There are 3 sandwich options and 2 drink options, so there are a total of 3 x 2 = 6 possible lunch combinations without chips.
Out of the total of 12 possible lunch combinations, 6 do not include chips, so the probability of a student getting a lunch that does not include chips is 6/12 or 0.5.
To know more about probability:
https://brainly.com/question/24756209
Please helpppp
side lengths, surface areas, and volumes fo...
a designer builds a model of a sports car. the finished model is exactly the same shape as the original, but smaller. the scale factor is 3:11
(a) find the ratio of the surface area of the model to the surface area of the original.
(b) find the ratio of the volume of the model to the volume of the original.
(c) find the ratio of the width of the model to the width of the original.
nrite these ratios in the format m:n.
surface area:
volume:
width:
The ratios are: surface area 9:121, volume 27:1331, width 3:11.
(a) The ratio of the surface area of the model to the surface area of the original can be found by using the scale factor to find the ratio of the corresponding side lengths. Since surface area is proportional to the square of the side length, we can use this ratio squared to find the ratio of the surface areas.
The ratio of the corresponding side lengths is 3:11, so the ratio of the surface areas is (3/11)^2, which simplifies to 9/121.
Therefore, the ratio of the surface area of the model to the surface area of the original is 9:121.
(b) The ratio of the volume of the model to the volume of the original can be found using the same method as above, but with volume instead of surface area. Since volume is proportional to the cube of the side length, we can use this ratio cubed to find the ratio of the volumes.
The ratio of the corresponding side lengths is 3:11, so the ratio of the volumes is (3/11)^3, which simplifies to 27/1331.
Therefore, the ratio of the volume of the model to the volume of the original is 27:1331.
(c) The ratio of the width of the model to the width of the original can be found directly from the scale factor, since width is one of the corresponding side lengths.
The ratio of the corresponding side lengths is 3:11, so the ratio of the widths is 3:11.
Therefore, the ratio of the width of the model to the width of the original is 3:11.
Overall, the ratios are: surface area 9:121, volume 27:1331, width 3:11.
Learn more about surface area here, https://brainly.com/question/76387
#SPJ11
what is the approximate length of the base of the triangle ? round to the nearest tenth if needed.
The approximate length of the base of the triangle is 5 units.
Given that, the area of a hexagon is about 65 square units. You decompose the figure into 6 triangles.
A regular hexagon can be decomposed into 6 equal triangles,
So, the area of each triangle is 65/6 = 10.8 square units
The height of one triangle is about 4.3 units.
We know that, the area of a triangle is 1/2 ×Base×Hieght
Now, 10.8=1/2 ×Base×4.3
21.6=Base×4.3
Base=21.6/4.3
Base=5.02
Therefore, the approximate length of the base of the triangle is 5 units.
Learn more about the area here:
https://brainly.com/question/27683633.
#SPJ1
Since 2005, the amount of money spent at restaurants in a certain country has increased at a rate of 6% each year. In 2005, about $410 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2017? About $ billion will be spent at restaurants in 2017 if the trend continues
About $786 billion will be spent at restaurants in 2017 if the trend continues.
To solve this problemWe can use the formula for compound interest:
A = P(1 + r)^n
where:
A is the final amount
P is the initial amount
r is the annual interest rate
n is the number of years
In this instance, we're looking to determine how much will be spent at restaurants in 2017, which is 12 years from now, in 2005. The initial amount was $410 billion in 2005, and the yearly interest rate is 6%. We thus have:
A = 410(1 + 0.06)^12
A ≈ 786.34
Therefore, about $786 billion will be spent at restaurants in 2017 if the trend continues.
Learn more about compound interest here : brainly.com/question/2455673
#SPJ1
15/51+16/27-(-2/27-2/51)
Answer:
1
Step-by-step explanation:
USE PEMDAS OR ORDER OF OPERATIONS
1. Evaluate parenthesis.
-2/27 - 2/51 = - 52/459.
2. Add
15/51 + 16/27 = 407/459
3. Subtract to get the final answer
407/459 - -52/459 = 407/459 + 52/459 = 1
So, 15/51+16/27-(-2/27-2/51) = 1
Transformations and Congruence:Question 3 Triangle ABC is reflected over the x-axis. Which is the algebraic rule applied to the figure? Select one:
Hi! I'd be happy to help you with your question about transformations and congruence. When Triangle ABC is reflected over the x-axis, the algebraic rule applied to the figure is:
Your answer: (x, y) → (x, -y)
This rule states that the x-coordinate remains the same, while the y-coordinate is multiplied by -1, resulting in a reflection over the x-axis. This transformation preserves congruence, as the size and shape of Triangle ABC remain the same, only its position changes.
The algebraic rule applied to the figure when Triangle ABC is reflected over the x-axis is (x,y) → (x,-y), where x represents the x-coordinate and y represents the y-coordinate. This is because reflecting a figure over the x-axis involves keeping the x-coordinate the same while changing the sign of the y-coordinate. This preserves the congruence of the original and reflected triangles.
To know more about congruence refer here
https://brainly.com/question/31992651#
#SPJ11
Evaluate the integral. 8 Vi s dt Vi 8V1 ſ Vi dt=U Help me solve this Ca
The integral evaluates to (16/3)s³/² + C.
What is power rule of integration?The power rule of integration is a method for finding the indefinite integral of a function of the form f(x) = x^n, where n is any real number except for -1. The rule states that the indefinite integral of f(x) is (x^(n+1))/(n+1) + C, where C is an arbitrary constant of integration.
To evaluate the integral 8√(s) ds, follow these steps:
1. Rewrite the integral with a rational exponent: ∫8s¹/² ds
2. Apply the power rule for integration: ∫sⁿ ds = (sⁿ⁺¹/(n+1) + C, where n ≠ -1
3. Substitute n=1/2: (s³/²)/(3/2) + C
4. Multiply by 8: 8*(s³/²)/(3/2) + C
5. Simplify the expression: (16/3)s³/² + C
To know more about power rule click on below link:
https://brainly.com/question/23418174#
#SPJ11
How many possible outcomes are in the sample space if the spinner shown is spun twice?
There are 225 possible outcomes in the sample space if the spinner is spun twice
How many possible outcomes are in the sample spaceFrom the question, we have the following parameters that can be used in our computation:
Spinner
The number of sections in the spinner is
n = 15
If the spinner shown is spun twice, then we have
Outcomes = n²
Substitute the known values in the above equation, so, we have the following representation
Outcomes = 15²
Evaluate
Outcomes = 225
Hence, the possible outcomes are in the sample space are 225
Read more about sample space at
https://brainly.com/question/30206035
#SPJ1
The talk-time battery life of a group of cell
phones is normally disributed with a mean of 5
hours and a standard deviation of 15 minutes.
a)what percent of the phones have a battery life of at least 4 hours and 45 minutes? b)what percent of the phones have a battery life between 4. 5 hours and 5. 25 hours? c)what percent of the phones have a battery life less than 5 hours of greater than 5. 5 hours?
a) Approximately 79.38% of the phones have a battery life of at least 4 hours and 45 minutes.
b) Approximately 34.13% of the phones have a battery life between 4.5 hours and 5.25 hours.
c) Approximately 50% of the phones have a battery life less than 5 hours or greater than 5.5 hours.
a) What percentage battery life of 4 hours and 45 minutes?
a) For phones with a mean battery life of 5 hours and a standard deviation of 15 minutes, we can calculate the percentage of phones with a battery life of at least 4 hours and 45 minutes. By converting 4 hours and 45 minutes to minutes (4*60 + 45 = 285 minutes) and using the z-score formula, we find that the z-score is (285 - 300) / 15 = -1. Hence, the percentage is approximately 1 - 0.8359 = 0.1641, which is about 16.41%.
b) What percentage battery life between 4.5 hours and 5.25 hours?
b) To determine the percentage of phones with a battery life between 4.5 hours and 5.25 hours, we need to calculate the z-scores for both values. Converting the hours to minutes, we have 4.5 hours = 270 minutes and 5.25 hours = 315 minutes. The z-scores are (270 - 300) / 15 = -2 and (315 - 300) / 15 = 1. By referring to the standard normal distribution table, we find that the area between -2 and 1 is approximately 0.6141. Thus, the percentage is 0.6141 * 100 = 61.41%.
c) What percentage battery life less than 5 hours?c) For the percentage of phones with a battery life less than 5 hours or greater than 5.5 hours, we need to calculate the z-score for both cases. The z-score for 5 hours is (300 - 300) / 15 = 0, and the z-score for 5.5 hours is (330 - 300) / 15 = 2. By referring to the standard normal distribution table, we find that the area to the left of 0 is 0.5 and the area to the right of 2 is 1 - 0.9772 = 0.0228. Adding these percentages, we get 0.5 + 0.0228 = 0.5228, which is approximately 52.28%.
Learn more about battery life
brainly.com/question/10355447
#SPJ11
Find the area of the shaded region
The area of the shaded region of the circle is 89.75 mi².
What is the area of the shaded region?The area of a sector of a circle, you can use the formula:
A = (θ/360) × π × r²
Where A is the area of the sector, θ is the central angle of the sector, r is the radius of the circle, and π is a constant approximately equal to 3.14.
From the diagram, angle of the unshaded sector equals 150 degree.
Angle of the shaded region = 360 - 150 = 210 degree
Radius r = 7 miles.
We can substitute these values into the formula and solve for the area A.
A = (θ/360) × π × r²
A = ( 210/360 ) × 3.14 × 7²
A = ( 210/360 ) × 3.14 × 49
A = 89.75 mi²
Therefore, the area of the sector is approximately 89.75 mi².
Learn more about area of sector here: https://brainly.com/question/16367606
#SPJ1
A can of soda can be modeled as a right cylinder. Nicole measures its height as 11.4 cm and volume as 144 cubic centimeters. Find the can’s diameter in centimeters. Round your answer to the nearest tenth if necessary.
We can start by using the formula for the volume of a cylinder, which is:
V = πr^2h
where V is the volume, r is the radius (half of the diameter), and h is the height.
In this problem, we are given the height and volume of the can, but we need to find the diameter (which is twice the radius). We can rearrange the formula above to solve for the radius:
r = √(V/πh)
Substituting the given values, we get:
r = √(144/π x 11.4) ≈ 1.5 cm
Finally, we can find the diameter by doubling the radius:
d = 2r ≈ 3 cm
Therefore, the can's diameter is approximately 3 centimeters.
please help me on this question
Based on the data, we can infer that Kallie needs 6 teaspoons of water conditioner for the 12 fish tanks.
How to calculate how many teaspoons of water conditioner Kallie needs?To calculate how many teaspoons of water conditioner we must take into account the information on the capacity of each tank:
Each tank is equivalent to 20 quarts, that is, 5 gallons.There are 12 tanks in total.For every 10 gallons, you need 1 teaspoon of water conditioner.In accordance with the above, we do the following logical procedure.
We multiply the capacity of each tank by the number of tanks.
5 * 12 = 60So we need 60 gallons of water to fill the tanks, and we divide by 10 to find how many teaspoons we need to fill all 12 tanks.
60 / 10 = 6Based on the above, we need 6 teaspoons to condition the water in the 12 tanks.
Learn more about teaspoons in: https://brainly.com/question/25928464
#SPJ1
What’s the answer I need help pls?
Katie started with $40. how much money did she have left after purchases the supplies.
If Katie started with $40, the remaining balance after purchasing the supplies is $20.
To determine how much money Katie had left after purchasing the supplies, we'll consider the fraction "1/5" for the storybook and "3/10" for the calculator.
1: Calculate the amount spent on the storybook.
Katie spent 1/5 of her initial $40 on the storybook. To find this amount, multiply the fraction by the total amount:
(1/5) x $40 = $8
2: Calculate the amount spent on the calculator.
Katie spent 3/10 of her initial $40 on the calculator. To find this amount, multiply the fraction by the total amount:
(3/10) x $40 = $12
3: Add the amounts spent on both the storybook and calculator.
$8 (storybook) + $12 (calculator) = $20
4: Subtract the total amount spent from Katie's initial amount of money to find the remaining balance.
$40 (initial amount) - $20 (total spent) = $20
After purchasing the supplies, Katie had $20 left.
Note: The question is incomplete. The complete question probably is: Katie started with $40. He spent 1/5 of the money on a storybook and 3/10 on a calculator. how much money did she have left after purchases the supplies.
Learn more about Fraction:
https://brainly.com/question/78672
#SPJ11
Help
Look at the picture it says what it needs.
The value of x and y for the angles are 4 and 9 respectively.
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
10x - 4 = 6(x + 2) (opposite angles are equal to each other)
10x - 4 = 6x + 12
4x = 16
x = 4
Also:
18y - 18 = 16y
2y = 18
y = 9
The value of x and y are 4 and 9 respectively.
Find out more on equation at: https://brainly.com/question/22688504
#SPJ1
Is 2352 a perfect square? If not, find the smallest number by
which 2352 must be multiplied so that the product is a perfect
square. Find the square root of new number.
No, 2352 is not a perfect square.
To find the smallest number by which 2352 must be multiplied so that the product is a perfect square, we need to factorize 2352 into its prime factors.
2352 = 2^4 x 3 x 7^2
To make it a perfect square, we need to multiply it by 2^2 and 7, which gives us:
2352 x 2^2 x 7 = 9408
Now, we can take the square root of 9408:
√9408 = √(2^8 x 3 x 7) = 2^4 x √(3 x 7) = 16√21
Therefore, the smallest number by which 2352 must be multiplied so that the product is a perfect square is 2^2 x 7, which gives us the square root of 9408 as 16√21.
Answer:
The smallest number by which 2352 must be multiplied so that the product is a perfect square = 3
The square root of the new number = 84
Step-by-step explanation:
√2352 ≈ 48.5 so not a perfect square
Prime factorization of 2352 yields
2352 = 2 x 2 x 2 x 2 x 7 x 7 x 3
In exponential form this is
2⁴ x 7² x 3¹
So
[tex]\sqrt{2352} = \sqrt{2^4 \cdot 7^2 \cdot 3}\\\\= \sqrt{2^4} \cdot \sqrt{7^2} \cdot \sqrt{3}\\\\= 2^2 \cdot 7 \cdot \sqrt{3}\\\\= 28 \sqrt{3}[/tex]
To get rid of the radical in the square root and get a whole number, all you have to do is multiply [tex]\sqrt{2352}[/tex] by √3
[tex]28 \sqrt{3} \cdot \sqrt{3} = 28\cdot 3 = 84\\\\84^2 = 7056 = 2352 \cdot 3\\[/tex]
This means that if you multiply 2352 by 3 it will become a perfect square
Check:
[tex]2352 \cdot 3 = 7056\\\\\sqrt{7056} = 84[/tex]
Chase was on his school’s track team and ran the 2400m race. He has been working on his pace and can run 1600m in 5. 5 minutes. If he keeps this pace through the entire race, how long will it take him to finish the 2400m race?
A. 8. 25 minutes
B. 7. 75 minutes
C. 8. 5 minutes
D. 8. 42 minutes
If f(x) = 2x2 - 6x² + 4x – 8 and g(x)= 0, find (fog)(x) and (gof)(x).
The final values is (fog)(x) = f(g(x)) = f(0) = -8.
In the given problem, we are given two functions, f(x) and g(x). The function f(x) is a polynomial function, and g(x) is a constant function equal to 0. We are asked to find the composition of these two functions, that is, (fog)(x) and (gof)(x).
The composition of two functions f(x) and g(x) is denoted by (fog)(x) and is defined as follows:
(fog)(x) = f(g(x))
This means that we first evaluate g(x) and then use the output of g(x) as the input of f(x) to get the final output of (fog)(x).
In this case, since g(x) = 0, we have:
(fog)(x) = f(g(x)) = f(0)
To evaluate f(0), we substitute x = 0 in the expression for f(x):
[tex]f(x) = 2x^2 - 6x^2 + 4x - 8[/tex]
[tex]f(0) = 2(0)^2 - 6(0)^2 + 4(0) - 8[/tex]
f(0) = -8
Therefore, (fog)(x) = f(g(x)) = f(0) = -8.
Now, to find (gof)(x), we need to evaluate g(f(x)). Since f(x) is a polynomial function, we can find its value for any value of x. However, since g(x) is a constant function equal to 0, its output is always 0 for any input x. Therefore, g(f(x)) = 0 for all values of f(x).
This means that (gof)(x) = g(f(x)) = 0 for all x.
In summary, we found that (fog)(x) = -8 and (gof)(x) = 0.
To learn more about functions visit: https://brainly.com/question/12431044
#SPJ11
Find a quadratic function that models the
number of cases of flu each year, where y is years since 2012. What is the coefficient of x? Round your answer to the nearest hundredth
The quadratic function that models the number of cases of flu each year, where y is years since 2012 is y = -0.02x^2 + 0.5x + 10. The coefficient of x is 0.5.
Suppose the number of cases of flu each year initially increases rapidly, but then starts to level off and eventually decline. We can model this behavior with a quadratic function of the form:
y = ax^2 + bx + c
where y is the number of cases of flu, and x is the number of years since 2012. Estimate the coefficients a, b, and c.
Assume the number of cases of flu was initially very low in 2012, so the y-intercept c is small value, say 10.
Next, assume that the number of cases of flu initially increased rapidly, but then started to level off around 2018.
y = ax^2 + bx + 10
where a is negative and b is positive.
Suppose the coefficient of the linear term is small, since we expect the trend to level off rather than continue to increase at a constant rate.
So, a possible quadratic function that models the number of cases of flu each year is:
y = -0.02x^2 + 0.5x + 10
The coefficient of x in this function is 0.5, which represents the rate of change of the number of cases of flu each year after 2012.
Know more about quadratic here:
https://brainly.com/question/1214333
#SPJ11
is this a linear function
See image for the work
Answer:
For 10 sections you would need 60 rails
The rule for posts is to multiply the section by 3
the rule for rails is to multiply the post by 2
Using composition of functions, determine if the to functions are inverses of each othr. f(x)= square root of x, +4, x>0. g(x) x2-4, x>2.
Using the composition of functions, if the two functions are inverses of each other, therefore, we cannot conclude if f(x) and g(x) are inverses of each other.
To check if the two functions f(x) and g(x) are inverses of each other, we need to verify if their composition f(g(x)) and g(f(x)) results in the identity function f(x) = x.
Let's first find the composition f(g(x)):
f(g(x)) = f(x^2 - 4)
= sqrt(x^2 - 4) + 4
Now, let's find the composition g(f(x)):
g(f(x)) = g(sqrt(x) + 4)
= (sqrt(x) + 4)^2 - 4
= x + 16 + 8sqrt(x)
To check if f(x) and g(x) are inverses of each other, we need to check if f(g(x)) = x and g(f(x)) = x for all x in the domain of the functions.
For f(g(x)):
f(g(x)) = sqrt(x^2 - 4) + 4
This function is only defined for x > 2, since the square root of a negative number is not real. Therefore, the domain of f(g(x)) is (2, infinity).
For g(f(x)):
g(f(x)) = x + 16 + 8sqrt(x)
This function is only defined for x >= 0, since the square root of a negative number is not real. Therefore, the domain of g(f(x)) is [0, infinity).
Since the domains of f(g(x)) and g(f(x)) do not overlap, we cannot check if they are inverses of each other. Therefore, we cannot conclude if f(x) and g(x) are inverses of each other.
To learn more about “function” refer to the https://brainly.com/question/11624077
#SPJ11
How do you find square roots??
PLEASE HELP ME I AM SO LOST GIVE ME A STEP BY STEP
Step-by-step explanation:
Finding the square root of a number is simply jist dividing the given number by 2 till you get to the last number which should be 1 then you pair up the number of two's and multiply. For example you have 6 two's when you pair them in two's you get 3 two's left then you multiply the remaining two's which would then be 2×2×2 which is 6
Answer:
Step-by-step explanation:
so basically, a square root is just the number that is multipled together to equal that, so sq rt of 64 is 8. This is because 8x8= 64. If you were to take a weird number like sq rt of 112, it would be a little bit more difficult, however its pretty easy to do this through thinking of your multiplication charts. if you think about it 11x10 but thats 110, it would have to be a number around there. 11x11 is too high but 10x10 is too low. SO it would have to be a number around there. if you did 10.5x10.5 it would give 110.25. so if you try to do 10.6x10.6 it would equal 112.36. (The actual answer is 10.58300524425836) So that is how you determine how close you can get. It is very tedious to do this process and very time consuming. However, i would just advise you try to use a calculator (??)
this may be helpful if the videos aren't working for you :))
tice Problems
Scientists have calculated that recycling 10 pounds of paper, results in 8 fewer gallons of
water being required to produce an equivalent amount of new paper. If a school begins a
recycling program and is able to increase the amount of paper they recycle by 500 pounds
per month, calculate number of gallons of water this conserves over an entire year.
By increasing their recycling by 500 pounds per month, the school conserves 4,800 gallons of water in a year.
Determine the ratio of water conserved per pound of paper recycled:
8 gallons of water are saved for every 10 pounds of paper recycled.
Calculate the water saved for each pound of paper:
8 gallons/10 pounds = 0.8 gallons/pound.
Find the increase in paper recycled per month:
500 pounds/month.
Calculate the water saved per month:
[tex]500 $ pounds/month \times 0.8 $ gallons/pound = 400 $ gallons/month.[/tex]
Calculate the water saved in a year:
[tex]400 $ gallons/month \times 12 months = 4,800 $ gallons/year.[/tex]
For similar question on recycling.
https://brainly.com/question/2055088
#SPJ11