Answer:
3x^2 + 10x
Step-by-step explanation:
Evaluate the expression 1^4+3(10-2)^2show your work
Answer: 193
Step-by-step explanation:
1^4 + 3(10 - 2)^2
1^4 + 3(8)^2
1^4 + 3(64)
1^4 +192
1 + 192
193
The volume of fuel in a tank changes at a rate given by the equation:
V′(t)=4t/√(t^2+33_, t≥0. At t=√7 hours the tank holds 9.3 gallons. What is the volume of fuel in the tank after 6 hours?
Round answer to one decimal place.
The volume of fuel in the tank after 6 hours is 97.5 gallons.
To find the volume of fuel in the tank after 6 hours, we need to integrate the rate of change of the volume, given by V′(t)=4t/√(t^2+33), with respect to time from the initial time of t=√7 hours to t=6 hours.
The integral of V′(t) with respect to t is V(t)= 2/3 (t^3 + 33t) + C
We know that when t = √7 hours, the volume of fuel in the tank is 9.3 gallons. So we can use that information to find the value of the constant C.
9.3 = 2/3 (√7^3 + 33√7) + C
C = 9.3 - 2/3 (7^3/2 + 337^1/2)
C = 9.3 - 2/3 (343/2 + 337^1/2)
C = 9.3 - 2/3 (343/2 + 231)
C = 9.3 - 2/3 (574)
C = 9.3 - 382 = 5.5
Now we can substitute t = 6 into the equation for V(t) to find the volume of fuel in the tank after 6 hours.
V(6) = 2/3 (6^3 + 33*6) + 5.5
V(6) = 2/3 (216 + 198) + 5.5
V(6) = 2/3 (414) + 5.5
V(6) = 276/3 + 5.5
V(6) = 92 + 5.5 = 97.5
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a man jumps from a great height and falls freely to the earth. another man jumps from the same height 1 second later. how’s much are the two men separated by, 2 seconds after the second man jumps
Answer:
24.53
Step-by-step explanation:
d = (1/2)gt²
First man travels 1 sec + 2 sec = 3 sec
d = (1/2)(9.81 m/s²)(3 s)² = 44.15 m
Second man travels 2 sec
d = (1/2)(9.81 m/s²)(2 s)² = 19.62 m
Distance between the 2 men:
44.15 m - 19.62 m = 24.53 m
For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. {[ 6a-2c -5b-5c -6a+ 5b+ 2c -6a+ 2c]:a b c in R]
(a) A basis for a subspace is a set of linearly independent vectors that span the subspace. To find a basis for this subspace, we can use the following steps:
Write the given set of vectors as the rows of a matrix, with each vector as a row.
Use row-reduction (Gaussian elimination) to put the matrix in row-echelon form.
The non-zero rows of the row-echelon form matrix form a basis for the subspace.
So, we get the matrix:
| 6a - 2c | -5b - 5c | -6a + 5b + 2c | -6a + 2c |
Using row-reduction, we can simplify the matrix to:
| 1 - 1/3 | 0 | 1/3 | -1/3 |
The non-zero rows are {[ 1 - 1/3 0 1/3 -1/3 ]}
So, a basis for the subspace is:
{[ 1 - 1/3 0 1/3 -1/3 ]}
(b) The dimension of a subspace is the number of linearly independent vectors in a basis for the subspace. In this case, the basis for the subspace has only one vector, so the dimension of the subspace is 1.
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(1 point) Let T be a matrix transformation from R" to R" . Determine whether or not T is one-to-one in each of the following situations: C 1. n = m A 2. n > m B. 3. n < m A. T is not a one-to-one transformation. B. T is a one-to-one transformation. C. There is not enough information to tell. (Enter "A", "B", "C"; not "A.", "B.", "C.")
The answer is:
1. n = m ........ .There is not enough information to tell.
2. n > m .........T is a one-to-one transformation.
3. n < m ......... There is not enough information to tell.
The transformation matrix is a matrix that transforms one vector into another vector. The positional vector of a point is changed to another positional vector of a new point, with the help of a transformation matrix.
he transformation matrix transforms a vector into another vector, which can be understood geometrically in a two-dimensional or three-dimensional space. The frequently used transformations are stretching, squeezing, rotation, reflection, and orthogonal projection.
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how many groups of 1/5 are in4
Answer:
20 groups
Step-by-step explanation:
There are 20 groups of 1/5 in 4 because you have to divide (4)/(1/5) so aplying the ear law you obtain 20.
If BAC=70, and ABC=60 and CE bisects BCD. then find BCE thanks
On solving the provided question we can say that the solution required angle bisector ∠BCE=50°.
What is angle bisector?An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts. For example, if a ray AX divides an angle of 60 degrees into two equal parts, then each measure will be equal to 30 degrees. Every angle has an angle bisector.
The sum of all the three angles of the triangle is 180°.
∠BAC=70° and ∠ABC=60°.
We know that in a triangle there are three angles and the sum of all the three angles is 180°.
∠ABC+∠BAC+∠BCE= 180°
Putting the values of the given angles we have,
60°+70°+∠BCE=180°
on adding the angles,
130°+∠BCE=180°
aking 130° to the right-hand side,
∠BCE=180°-130°
on solving we have,
∠BCE=50°
Therefore, the required angle is 50°.
The required angle ∠BCE=50°.
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On solving the provided question we can say that the solution required angle bisector ∠BCE=50°.
What is angle bisector?An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts. For example, if a ray AX divides an angle of 60 degrees into two equal parts, then each measure will be equal to 30 degrees. Every angle has an angle bisector.
The sum of all the three angles of the triangle is 180°.
∠BAC=70° and ∠ABC=60°.
We know that in a triangle there are three angles and the sum of all the three angles is 180°.
∠ABC+∠BAC+∠BCE= 180°
Putting the values of the given angles we have,
60°+70°+∠BCE=180°
on adding the angles,
130°+∠BCE=180°
aking 130° to the right-hand side,
∠BCE=180°-130°
on solving we have,
∠BCE=50°
Therefore, the required angle is 50°.
The required angle ∠BCE=50°.
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Zoe sells handmade jewelry at craft fairs. She bought a package of c charms. She used all the charms in the package to make 12 bracelets, and each bracelet had 8 charms.
Which diagram models the story?
The diagram that models the story is given as follows:
Right diagram.
The equation that models the story is given as follows:
c = 12 x 8.
How to model the story?The story is modeled applying the proportions from the units given in the context of the problem.
We have that the parameters are given as follows:
Zoe bought c charms.She made 12 bracelets.Each bracelet is composed of eight charms.Hence the total number of charms that she purchased is given as follows:
c/12 = 8.
c = 12 x 8. (which is the equation that models this situation).
c = 104.
The diagram that represents a multiplication of 12 by 8 is the diagram that is composed by a successive addition of twelve times the number 8, hence it is the right diagram.
Missing InformationThe complete problem is given by the image presented at the end of the answer.
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5c - 4c + c; = 2, = 5, and =– 3
Answer: 0
Step-by-step explanation:
c2+2c−24=0
PLEASE HELP!!!!
Find the greatest common factor. 5x^2a+5xa^2
The greatest common factor of the expression 5x²a + 5xa² is 5xa
How to find greatest common factor of 5x²a + 5xa²?To find the greatest common factor (GCF) of the expression 5x²a + 5xa², we need to find the greatest term that can divide into both terms in the expression.
In this case, the GCF is 5xa, as it can divide into both 5x²a and 5xa².
We can check this by dividing both terms with 5xa:
5x²a + 5xa² = (5xa)(x) + (5xa)(a) = 5xa (x + a)
Thus, the GCF of 5x²a + 5xa² is 5xa.
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The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
Using the general depreciation calculation, y = A(1 - r)^t, the car will be worth $12528.15 after 4 years.
How to calculate the car's value in four yearsY = A(1 - r)^t, is the general depreciation formula, which is used to solve the car's worth.
Description of the variables
y is the current value and where =?
Original cost was $24,000,
rate of depreciation was 15%, and
time was measured in years. = 4 years
plugging in the values
current value, y = A(1 - r)^t
current value, y = 24000 * (1 - 0.15)^4
current value, y = $12528.15
The car has been depreciated to $12528.15
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complete question
The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years?
1 2 3 4 5 6 7 8 9 10 A graph has quantity on the x-axis and price on the y-axis. Demand curve points are at (20, 70), (40, 40), (60, 10).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (20, 70), (40, 80), (60, 90). Based on the demand graph and the supply graph shown above, what is the price at the point of equilibrium? a. 100 b. 70 c. 40 d. There is not enough information given to determine the point of equilibrium. Please select the best answer from the choices provided A B C D Mark this and return
Answer:
B) 70
Step-by-step explanation:
2.1 8cm B. a 10cm D b 2.1.1 Calculate the length of a. 2.1.2 Calculate the length of b. 9cm C
need working out
Answer:
a = 6 , b = 17
Step-by-step explanation:
using Pythagoras' identity.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
using right triangle ABD , then
a² + 8² = 10²
a² + 64 = 100 ( subtract 64 from both sides )
a² = 36 ( take square root of both sides )
a = [tex]\sqrt{36}[/tex] = 6
using right triangle ABC
note that BC = a + 9 = 6 + 9 = 15
b² = 8² + 15² = 64 + 225 = 289 ( take square root of both sides )
b = [tex]\sqrt{289}[/tex] = 17
A rectangle has a length tht is five times longer than its width. If the perimeter of the rectangle is 12 inches what is the width
The width of the rectangle is 1 in.
What is rectangle?A rectangle is a type of parallelogram, having each angle right angle and equal diagonal.
Given that, A rectangle has a length that is five times longer than its width. and the perimeter of the rectangle is 12 inches
Perimeter of a rectangle = 2(length+width)
Let the width be w then length will be (5w)
Therefore,
(w+5w)2 = 12
6w = 6
w = 1
Hence, the width of the rectangle is 1 in.
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The amount of water in the tank is decreasing at 600 gallons per hour.
True
False
Answer:
True.
Step-by-step explanation:
Answer:
True.
The statement "The amount of water in the tank is decreasing at 600 gallons per hour" is true. It means that the water level in the tank is going down by 600 gallons per hour, which means that the water is being used or drained out of the tank at a rate of 600 gallons per hour.
Step-by-step explanation:
A student lifts up a spring scale attached to a block on a table. While the block is still resting on the table, compare the effort force to the force of gravity
The relation between effort force and the force of gravity can be represented as, Fₐ < Fₙ
What is Force ?The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.
Given that,
A student lifts up a spring scale attached to a block on a table
The block is still resting on the table
The relation between effort force to the force of gravity = ?
Suppose,
The effort force = Fₐ
The force of gravity = Fₙ
block is still resting on the table,
it means effort force is less than the force of gravity,
To move upward, it is required to apply more effort force,
but, here effort force is less
So, It can be written as,
Fₐ < Fₙ
Hence, the relation between both the forces is Fₐ < Fₙ
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Which rule represents the relationship in the table above?
Oy=x
Oy = 2.54x
Oy=x+1.54
Oy=x²
The rule that is used for the relationship in the table is
B. y = 2.54xHow to find the rule as used for the tableThe relationship between x in inches and y in centimeters as represented can be solved by directly on the table or using the knowledge of conversion of inches to centimeter
Another procedure to solve this is to try the equations as in the options;
The first option is y = x, this is obviously wrong as the values in the y and the values in the x are not equal.
The second option, is y = 2.54x
for x = 1, y = 2.54 * 1 = 1
for x = 2, y = 2.54 * 2 = 5.08
and continuing for other values shows that this is the correct option
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I NEED HELP ON THIS PART
Because a cubic function is a polynomial function, which are continuous curves, the domain of a cubic function is all real numbers.
Do cubic functions possess three roots?All odd-degree polynomials have at least one real root; a cubic function has one to three real roots, which may or may not be distinct. A cubic function's graph always has one inflection point. It might have a local minimum and local maximum as its two critical points.
What are the cubic function's minimum and maximum?The cubic function [tex]f(x) = x^3 + x^2 + x + 1[/tex] has a local maximum at x = 1 and a local minimum at x = 1/3. A cubic function can also have two local extreme values (1 max and 1 min).
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Estimate sum of 1 1/3 and 2 3/4
Answer:
estimation: 4
real: 4 1/12
Step-by-step explanation:
Estimation: 1+2=3 1/3+3/4= around 1 3+1=4
Real= 4/3+ 11/4 = 4 1/12
Please need help with A) B) and C)
a) The y-intercept of the line is 25.66, which represents the predicted number of wins when yards allowed is 0.
b) The Seattle Sea hawks, the observed number of wins (10) is 4.12 less than the predicted number of wins based on the least-squares regression line.
c) It will increase the R-Sq and R-Sq(adj) and decrease the S.
What is the equation of least-squares regression and calculation for above answer?The equation of the least-squares regression line is given by:
Number of wins = 25.66 - 0.003131 * (Yards_allowed)
This equation shows the relationship between the number of wins for a team (the dependent variable) and the number of yards allowed by the team (the independent variable).
The slope of the line is -0.003131, which means that for every 1 yard increase in yards allowed, the number of wins decreases by 0.003131. The y-intercept of the line is 25.66, which represents the predicted number of wins when yards allowed is 0.
b) To calculate the residual for the Seattle Seahawks, we can use the equation of the least-squares regression line and the data for the team:
Residual = Observed value - Predicted value
Residual = 10 - (25.66 - 0.003131 * 4668)
Residual = 10 - (25.66 - 14.12)
Residual = -4.12
This means that for the Seattle Seahawks, the observed number of wins (10) is 4.12 less than the predicted number of wins based on the least-squares regression line.
c) The point representing the Carolina Panthers (5167 yards allowed, 15 wins) has a positive effect on the equation of the least-squares regression line because it is above the line.
This means that the team performed better than expected based on the number of yards allowed. Since this point is an outlier, it will increase the R-Sq and R-Sq(adj) and decrease the S.
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Write a function rule for "The output is three less than the input x y=
The statement "The output is three less than the input x" as an expression is y = x - 3
How to determine the function rule statement as an equationFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
The output is three less than the input x
Less than here means minus
So, we have the following representation
The output is three less than the input x = x - 3
The question does not require that we solve the expression
So, we leave it at x - 3
Introduce the output varianle
y = x - 3
Hence, the required expression is y = x - 3
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please help asap!! I'm doing a semester test! 16 points + brainly for correct answer!!
A regular-size box of cereal measures 3 1/2 inches by 8 1/2 inches by 15 inches. The manufacturer also sells an individual-size box that has a volume that is 1/10 of the volume of the regular-size box.
What is the volume of the individual-size box of cereal?
Enter your answer as a MIXED NUMBER IN SIMPLEST FORM by filling in the boxes.
Answer: 44 5/8
Step-by-step explanation:
Regular Volume: (3.5)(8.5)(15)= 446.25
Individual Volume (1/10 of regular): 446.25/10= 44.625
44.625 as Fraction: 44 5/8
cos(x)= square root of 3 over 2
The measure of angle x is 30°
How to find the measure of angle x?Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is concerned with the measurement of angles and the calculation of sines, cosines, and tangents of those angles.
These ratios are known as trigonometric functions and they are used to relate the ratios of the sides of a right triangle to the angles opposite or adjacent to the right angle.
cos(x) = (√3)/2
x = cos⁻¹((√3)/2) = 30°
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1+1+1-5+2+2+2+4-8 x 100 +1
Answer:
-792
Step-by-step explanation:
According to PEMDAS, you would multiply 8 x 100 first making the equation
1+1+1-5+2+2+2+4-800+1
then combine like terms, 8-800+1
Since 8 is smaller than 800, you would get a negative number, -792
then you add 1, making your answer -792
What’s the next number 3,-4,-11,-18,-25
Answer:-7
Step-by-step explanation:
3 to -4 the difference is -7
The answer is -7
the mean of 2,10,9 is what
Answer:
7.
Step-by-step explanation:
Mean = (2+10+9)/3
= 21/3
= 7.
Answer:
the mean is 7
Brief explanation:
To find the Mean of a set we add all the numbers first.
Remember that the Mean relies on a sum.
So we just add up 2 + 10 + 9 = 21
Then divide 21 by 3 (3 because there are 3 numbers in this set) :
21 : 3 = 7
so how do we find the Mean?We take all the numbers in the set, and divide by how many numbers we have in this set.
--
help me answer a. b. c. d. e. and f
Answer:
The correct answer is F hope you have a hood day
During the month of June 2022, the average price per gallon of gas was $4.42. During August of 2022, the average price per gallon of gas dropped to $3.75. What was the percent decrease from June of 2022 to August of 2022? Round to the nearest percent. The percent decrease from June of 2022 to August of 2022 was ___________ %
The percent decrease from June 2022 to August 2022 was 15%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
During the month of June 2022, the average price per gallon of gas was $4.42.
During August of 2022, the average price per gallon of gas dropped to $3.75.
As per the question, the required solution would be as:
100 × (4.42 - 3.75) / 4.42
= 15.1583
Rounding to the nearest percent, we get
= 15%
Thus, the percent decrease was 15%.
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12 ÷ (4 − (6 × 2 − ((3 + 3) × 2 − 1)))
Answer:
Step-by-step explanation:
12 ÷ (4 − (6 × 2 − ((3 + 3) × 2 − 1)))
12 ÷ (4 − (12 − ((3 + 3) × 2 − 1)))
12 ÷ (4 − (12 − ((6) × 2 − 1)))
12 ÷ (4 − (12 − (12 − 1)))
12 ÷ (4 − (12 − 11)))
12 ÷ (4 − (1))
12 ÷ (4 − 1)
12÷3
4
If the social security tax is 6.2% and the Medicare tax is 1.45% and Murr annual salary is 57,285.50 then what is murrs annual social security deduction
Answer: Murr's annual social security deduction is the amount of money he pays in social security taxes. Social security tax is 6.2% of Murr's annual salary. To find the annual social security deduction, we can multiply Murr's annual salary by the social security tax rate:
57,285.50 x 6.2% = 3,541.829
Murr's annual social security deduction is 3,541.829
Note that Medicare tax is 1.45% and it's calculated separately, if you want to calculate it you can use the same formula:
57,285.50 x 1.45% = 829.4078
So the total Social security and Medicare tax is 3,541.829 + 829.4078 = 4,371.2368
It's important to note that these are the federal Social Security and Medicare taxes, there might be additional state taxes or deductions that are not included.
Step-by-step explanation: