Answer:
Step-by-step explanation:
Answer:
1. The volume of water in the tank in cubic yards can be calculated by multiplying the length, width, and depth of the tank in feet by the conversion factor of 0.037037 yds3/ft3:
87 ft x 36 ft x 15 ft x 0.037037 yds3/ft3 = 997.78 yds3
2. To treat the water, the aquarium must purchase 998 bags of salt, as 1.1 yds3 of water requires one bag of salt.
3. The aquarium must pay $4,835.30 for the salt to treat the water in the new shark tank. This is calculated by multiplying the number of bags of salt (998) by the cost of one bag of salt ($4.85).
a) Choose two vectors vw in R2 and a third vector b also in R2, and express b as a linear combination of v,w by finding scalars c₁,c2 such that c₁v + c₂w = b. Sketch the situation in R2 with an illustration that uses the parallelogram rule. (b) Repeat part (a) with vectors in R3 such that the augmented matrix [v w | b] gives a consistent system, again illustrating by graphing but this time in R3. (c) Why is it harder to find a consistent system for part (b) compared to part (a)? Explain your idea clearly using complete sentences.
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a) The linear combination of v, w by finding scalars c₁, c₂ such that c₁v + c₂w = b is [v w | b]
b) The graph of the equation is attached below.
c) The matrix representation is a useful tool for finding linear combinations of vectors, but it becomes more complex as the number of dimensions increase.
A linear combination of two vectors is when a third vector is expressed as a sum of the two vectors multiplied by scalars.
In R2, this can be represented using a parallelogram, where the vectors are drawn and the third vector is the diagonal of the parallelogram.
To find the scalars, we use the matrix representation [v w | b]. If the matrix gives a consistent system, it means that the third vector b can be expressed as a linear combination of the two vectors v and w.
In R3, the matrix representation is still used but it becomes more challenging to find a consistent system because there are more variables involved.
The vectors are graphed in 3D, and the third vector is found as the diagonal of a parallelogram that is now a parallelepiped.
However, it may not always be possible to find a consistent system in R3, as the third vector may not lie in the plane formed by the two vectors.
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What is g(x)?
O A g(x)=-x
OB. g(x)=-lxi
OC. g(x)=-2*
O D. g(x)=-x²
Answer:
c.
Step-by-step explanation:
this graph is exponential equation
Part 1 of 2
Evaluate the function f(x)=x-7 at the given value of the variable.
a. f(13)
b. f(3)
Answer:
a)
b)-4
Step-by-step explanation:
a) f(13) = 13-7=
b) f(3)= 3-7= -4
Margie has 64 rectangular steppingstones to arrange in an array in her backyard . How many arrays can Margie make with the 64 steppingstones
If Margie has 64 rectangular steppingstones to arrange in an array in her backyard. The number of arrays that Margie can make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.
How to find the number of array:Given data:
Rectangular steppingstones to arrange in an array =64
In order to determine the number of arrays we have to find the number that will give us 64 when multiply.
The number that will gives us 64 as the answer when multiply are:
2 × 32 = 64
4 ×16 = 64
8 × 8 = 64
The arrays are 3 which are:
2 × 32
4 ×16
8 × 8
Therefore we can conclude that the number of array that Margie can make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.
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Identify the coefficient of each term of the polynomial
Answer:
7 and 4/9
Step-by-step explanation:
18 is the diameter , 9 is the radius , what is the area
Answer: The area of the circle with a radius of 9 is approximately 253.94 square units.
Step-by-step explanation:
The area of a circle is given by the formula A = πr^2, where A is the area, r is the radius, and π is approximately 3.14.
Given that the radius of the circle is 9, we can substitute this value into the formula to find the area:
A = πr^2 = π(9)^2 = 3.14 * 81 = 253.94
So the area of the circle with a radius of 9 is approximately 253.94 square units.
Note that the diameter of the circle is 18, which is twice the radius. If you knew the diameter you could also use the formula A = (π/4)*D^2 to calculate the area, where D is the diameter.
4x-3 =3x + y. 3x+y =2y+5x-12
simultaneous equation
pls help
Answer: To solve these simultaneous equations, we can substitute one equation into the other.
4x-3 = 3x + y.
3x+y =2y+5x-12
If we substitute the first equation into the second equation, we get:
3(4x-3) + y = 2y+5x-12
12x -9 + y = 2y+5x-12
Now we can solve the system of equations by isolating one of the variables and then substituting it back in one of the equations.
12x - 9 + y = 2y + 5x - 12
y = -9 + 2y + 5x -12
y = 2y + 5x -21
y - 2y = 5x -21 -9
-y = 5x -30
y = -5x + 30
Now we can substitute the value of y back into one of the original equations, we have:
4x-3 = 3x + (-5x + 30)
4x-3 = -2x + 30
4x-3+2x = 30
6x -3 = 30
6x = 33
x = 5.5
Now we can substitute the value of x back into one of the original equations to find the value of y:
4x -3 = 3x + y
4(5.5) -3 = 3(5.5) + y
22 - 3 = 16.5 + y
19 = 16.5 + y
y = 2.5
So the solution to the system of equations is x = 5.5 and y = 2.5.
Step-by-step explanation:
Ahigh-speed train travels 25 feet in 1/3 second. In 4 seconds, the train will have traveled ? feet
Answer: 300 ft
Step-by-step Explanation: You start by multiplying 4 by 3 to get 12 because each second is split into 3 parts. From there you just have to multiply 12 by 25 for foot per second to get 300.
A track runner counted the number of races he had during a season. The graph shows the relationship between the number of track meets, x, and the number of races, y.
coordinate plane with the x axis labeled number of track meets and the y axis labeled number of races with a line that passes through the points 0 comma 5 and 1 comma 7
Part A: Calculate the slope of the linear equation shown in the graph. Show all necessary work. (3 points)
Part B: What does the slope mean for the relationship between the number of races and the number of track meets? (3 points)
Part C: Interpret the y-intercept in the situation. (3 points)
Part D: Write the equation of the line shown on the graph in slope-intercept form. (3 points)
A. The slope of the linear function is given as follows: m = 2.
B. The slope means that the number of races increases by two when the number of track meets increases by one.
C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.
D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x assumes a value of zero.The input and output variables for this problem are given as follows:
Input x: number of track meets.Output y: number of races.Two points in the function are given as follows:
(0,5) and (1,7).
Hence the slope and the intercept are given as follows:
Slope of 2, as when x increases by one, y increases by two.Intercept of 5, as when x = 0, y = 5.Meaning that the function is defined as follows:
y = 2x + 5.
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Fiona is purchasing hammers and wrenches for her workshop, and she would like to
spend under $120. Each hammer costs $5, and each wrench costs $6. Let x be the
number of hammers and y be the number of wrenches.
Select the inequality that describes the situation.
O 6x + 5y< 120
5x + 6y> 120
O6x + 5y 120
5x + 6y< 120
Answer:
The inequality that describes the situation is 5x + 6y < 120
Step-by-step explanation:
This inequality states that the total cost of purchasing x hammers and y wrenches must be less than $120. Each hammer costs $5 and each wrench costs $6, so the total cost is represented by the expression 5x + 6y.
The inequality states that 5x + 6y < 120 which means for any number of hammers and wrenches she buys it should be less than 120.
The other options:
6x + 5y < 120: the coefficient of x is 6 instead of 5 and that of y is 5 instead of 6.
5x + 6y > 120: the inequality is greater than instead of less than, which means that the total cost should be greater than $120 which is not the case.
6x + 5y ≥ 120 : the inequality is greater than or equal to instead of less than, which means that the total cost should be greater than or equal to $120 which is not the case.
How would you do this problem on a ti-84 calculator? Or could you do this by hand and get the answer.
The answer is supposed to be -64/17, but I don't know how to get that answer.
Step-by-step explanation:
(R○R)(x) = (5 - 2((5 - 2x)/x))/((5 - 2x)/x)
we simply put the original R function into the places of x.
so,
(R○R)(-6) = (5 - 2((5 - 2×-6)/-6))/((5 - 2×-6)/-6) =
= (5 - 2((5 + 12)/-6))/((5 + 12)/-6) =
= (5 - 2×17/-6)/(17/-6) =
= (5 + 17/3)/(17/-6) = (15/3 + 17/3)/(17/-6) =
= 32/3 / 17/-6 = -6×32 / (3×17) =
= -2×32 / 17 = -64/17
Answer:
-64/17
Step-by-step explanation:
Same person here who answered previous question.
(R · R)(-6)
This basically means R(R(-6))
Now, R(-6) = (5 + 12)/-6 = -17/6
Put that value again, in (5 - 2x)/x = (5 + 34/6)/(-17/6)
= (64/6)/(-17/6) = -64/17
So, the answer is correct.
If you have any questions, please leave a comment.
Otherwise, cheers
Pls help me solve this!! It’s due today!!
f(x) and g(x) are inverses using composition
How to use composition to prove that f(x) and g(x) are inverses?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
To confirm the inverse relationship using composition.
For valid inverse f(g(x)) must be equal to g(f(x))
f(x) = ∛(x) + 13; g(x) = (x - 13)³:
f(g(x)) = f((x - 13)³)
f(g(x)) = ∛((x - 13)³) + 13
f(g(x)) = x - 13 + 13
f(g(x)) = x
g(f(x)) = g(∛(x) + 13)
g(f(x)) = (∛(x) + 13 - 13)³
g(f(x)) = (∛(x))³
g(f(x)) = x
Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse
f(x) = x³ + 1; g(x) = ∛(x - 1):
f(x) = x³ + 1; g(x) = ∛(x - 1)
f(g(x)) = f(∛(x - 1))
f(g(x)) = (∛(x - 1))³ + 1
f(g(x)) = x - 1 + 1
f(g(x)) = x
g(f(x)) = g(x³ + 1)
g(f(x)) = ∛((x³ + 1) - 1)
g(f(x)) = ∛(x³)
g(f(x)) = x
Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse
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7.4% of what number is $3.33?
Answer:
Step-by-step explanation:
A $5000 loan at 5% dated July 5 is due to be paid on November 10.calculate the amount of interest. assuming ordinary interest
Answer:
$250
Step-by-step explanation:
because we have to do 5,000 of 5% = 250 in sale's tax or interest.
The solution is, $250 is the amount of interest.
What is interest?Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.
here, we have,
Explanation:
given that,
A $5000 loan at 5% dated July 5 is due to be paid on November 10.
Since the borrower is to pay 5% of the money by November 10(Due time)
so, we get,
5% of the principal is simply
(5/100)* 5000
= $250
Hence, The solution is, $250 is the amount of interest.
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find a and b if the points (3, 1) and
(0,2) lie on the grabh of ax-by=6
Answer:
[tex]a=1, b=-3[/tex]
Step-by-step explanation:
[tex](3,1) \implies 3a-b=6 \\ \\ (0,2) \implies -2b=6 \implies b=-3 \\ \\ \therefore 3a-(-3)=6 \implies a=1[/tex]
Solve the system by substitution.
y= x 9x−2y= −49
Answer:-7,-7
Step-by-step explanation:
Solve for a. Help please!
Answer:
a = √63
Step-by-step explanation:
Pre-SolvingWe are given a right triangle (notice the right angle).
We know that the hypotenuse (the side opposite of the right angle) is 12.
We also know that one leg (a side that makes up the right angle) is 9, and that the other one is a.
We want to find what a is.
SolvingWe can use the Pythagorean Theorem to help us find a.
The Pythagorean Theorem says a² + b² = c², where a and b are the legs and c is the hypotenuse.
Since we already know the values of the legs and hypotenuse, we can substitute these values in the theorem, but let's first label the values of everything to avoid confusion / mistakes.
a = a
b = 9
c = 12
Now, plug into the formula.
a² + 9² = 12²
Simplify:
a² + 81 = 144
Subtract 81 from both sides
a² = 63
Square root both sides to get the value of a.
a = √63
one number is 2 less than another. their sum is 16
Multiply both sides: multiply both sides by what?
-10w ( ) = -9 ( )
[tex]-10w=-9[/tex]
Divide both sides by -10(to isolate the variable):
[tex]\dfrac{-10w}{-10} =\dfrac{-9}{-10}[/tex]
[tex]=0.9[/tex]
You can hire someone without experience for $13 per hour or someone with experience for $19 per hour. You believe the
experienced person increases the sales per customer by $3. Each person handles about 12 customers per hour. Should you hire the
experienced person?
a) Yes
b) No
Answer:
a) Yes
The experienced person costs more per hour, but also increases sales per customer. To determine if it is more cost-effective to hire the experienced person, you would need to calculate the net gain or loss from hiring them.
You can do this by multiplying the increase in sales per customer by the number of customers per hour, and comparing that to the difference in hourly wages.
(12 customers/hour * $3/customer) - ($19/hour - $13/hour) = $36/hour - $6/hour = $30/hour
Since the net gain is positive, it is more cost-effective to hire the experienced person.
Could you please answe this immediately
The area of the triangle KLM is found using Heron's formula as:
A = 60 in².
Explain the Heron's formula.The semi-perimeter of such a triangle, wherein area needs to be calculated, is represented by the letter s in Heron's formula. The total of the triangle's three sides, divided by two, is the semi-perimeter.S = (a+b+c)/2
where a, b, and c are the triangle's three sides.
The sides of the triangle KLM are:
Let KL : a = 13 in.Let LM : b = 13 in.Let KM : c = 10 in.Then,
Semi perimeter s = a + b + c / 2
s = (13 + 13 + 10)/ 2
s = 18 in
Thus,
s - a : 18 - 13 = 5
s -b : 18 - 13 = 5
s - c : 18 - 10 = 8
By Heron's formula;
area of triangle KLM = √(s - a)(s -b)(s - c)
A = √18*5*5*8
A = 60
Thus, the area of triangle KLM is found using Heron's formula as:
A = 60 in².
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Lauren walks to work. She walks 112
miles in 38
hour. What is her unit rate?
Answer: Lauren's unit rate is 2.95 Miles per hour (MPH)
Step-by-step explanation:
divide the distance Lauren traveled by the time it took to travel said distance
112/38 hours=2.95 mph
Answer:
2.95 miles/hour or 2.95mph
Step-by-step explanation:
112/38 = 2.94736842 ⇒ 2.95 miles/hour
. The cylinder shown below
has a diameter of 5.2 cm on
the base and a height of 7.1
cm. Label the
measurements and find the
volume of the cylinder.
15/b=24/11
Round the answer to 1 decimal digit
Answer:
[tex]\huge\boxed{\sf b = 6.9}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle \frac{15}{b} =\frac{24}{11} \\\\Cross \ Multiply\\\\15 \times 11 = b \times 24\\\\165 = 24b\\\\Divide \ both\ sides\ by\ 24\\\\165/24=b\\\\6.9=b\\\\b = 6.9\\\\\rule[225]{225}{2}[/tex]
Find the measurement indicated in each parallelogram
(PLEASE ANSWER THIS IS DUE SOON!!!!!!! WILL MARK BRAINLIEST!!!)
15. Rahj owns a hardware store. For every increase of 10¢ in the price A of a package of batteries, he estimates that sales decrease by 10 packages per day. The store normally sells 700 packages of batteries per day, at $5.00 per package. a) Determine an equation for the revenue, y, when x packages of batteries are sold. b) What is the maximum daily revenue that Rahj can expect from battery sales? How many packages of batteries are sold when the revenue is at a maximum? also,how to get the zeros and the equation
Answer:
a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.
Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.
b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.
Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.
It means that the store will sell a maximum number of batteries when the price is at $5.00
And the maximum daily revenue will be $5 * 700 = $3500.
So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.
The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.
The zeroes of the equation are the points at which the function crosses the x and y-axis.
The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)
The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)
Step-by-step explanation:
3 + y = 18 for y help with problem
Answer: y = 15
Step-by-step explanation:
Subtract both sides by 3
3 + y = 18
y = 15
The rule of a function changes from
f(x) = x² − 4 to g(x) = -x² + 4 when it is dilated.
Which statement best describes how this dilation affects the graph of f(x)?
A. The graph is reflected across the x-axis.
B. The graph is reflected across the y-axis.
C. The graph moves up 8 units.
D. The graph moves down 8 units.
The rule for the graph changes form of the function is A)The graph is reflected across the x-axis.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Function is a relation that connects members of one set in a certain way to those of another set. Formally speaking, a function from to is an object such that each is specifically linked to an object. Therefore, a function is a many-to-one (or occasionally, one-to-one) relation.
Here Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let h(x) = f(x)-c Shifting downward c units yields this graph of h from the graph of f.
We know that if the function reflected over x-axis then
g(x) = -f(x)
Here the given function f(x) = [tex]x^2-4[/tex] then reflection over x-axis then
=> g(x) = -f(x)
=> g(x) =-( [tex]x^2-4[/tex])
=> g(x) = [tex]-x^2+4[/tex]
Hence the correct option is A)The graph is reflected across the x-axis.
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Classify each of the following attributes as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous.
(a)
number of students in a class of 32 who turn in a term paper before the due date
categorical
numerical (discrete)
numerical (continuous)
(b)
gender of the next baby born at a particular hospital
categorical
numerical (discrete)
numerical (continuous)
(c)
amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop
categorical
numerical (discrete)
numerical (continuous)
(d)
thickness of the gelatin coating of a vitamin E capsule
categorical
numerical (discrete)
numerical (continuous)
(e)
birth order classification (only child, firstborn, middle child, lastborn) of a math major
categorical
numerical (discrete)
numerical (continuous)
The correct classifications for these variables are a = numerical discrete, b= categorical, c= numerical continuous, d= numerical continous, e= categorical.
What is the difference between a numerical and a categorical variable?As indicated by their name, numerical variables can be measured using numbers; here are some examples:
Weight of a person: 170 poundsDistance between two cities: 645 kilometersNumber of students in a class: 25 studentsOn the other hand, categorical variables fit into categories, for example:
Female vs Male
Dog vs cat
What is the difference between discrete and continuous?Discrete variables differ from continuous variables because they are obtained by counting, for example, the number of students in a classroom, while continuous variables need to be measured, for example, the distance.
Based on this the correct classification is:
A. Numerical (discrete) = the number of students in a class of 32B. categorical =gender of the next baby born at a particular hospitalC. Numerical (continuous) =amount of fluid (in ounces)D. Numerical (continuous) =thickness of the gelatin coating of a vitamin E E. Categorica, =birth order classification (only child, firstborn, middle child, lastborn)Learn more about variables in: https://brainly.com/question/17344045
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if wx = 14 and wr= 8, find RZ
The length of RZ is obtained as follows:
RZ = 11.5.
How to obtain the length of RZ?From the kite given by the image at the end of the answer, the segment lengths are given as follows:
WX = 14.WR = 8.Segments WX and WZ are congruent, hence segment WZ has the length given as follows:
WZ = 14.
Then the length of RZ is obtained considering a right triangle, for which:
RZ = x and WR = 8 are the side lengths.WZ = 14 is the hypotenuse.The Pythagorean Theorem states that the length of the hypotenuse squared is equals to the sum of the lengths squared of the sides.
Considering the Pythagorean Theorem, the length RZ is obtained as follows:
x² + 8² = 14².
[tex]x = \sqrt{14^2 - 8^2}[/tex]
x = 11.5.
RZ = 11.5.
Missing InformationThe problem is given by the image presented at the end of the answer.
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