The expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.
We are given that there are 2 types of seating in an airplane which are economy and first class seating.
Also,
We are given that:
There are s seats in economy in each row and there are t seats in first class in each row.
Now, there are 24 rows in economy class seating.
So, number of seats in economy class = 24 × s = 24 s
And, there are 9 rows in first class seating.
So, number of seats in first class = 9 × t = 9 t
The total number of seats then will be = 24 s + 9 t
Therefore the expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.
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12y + 48 - 4y= 8(y - 6)
An Internet store charges a base fee plus $1.50 per pound to ship items. The table shows samples of their shipping rates.
Shipping Rates
Weight of Package
(pounds)
Shipping Cost
(dollars)
2
8.00
5
12.50
7
9
18.50
10
17
30.50
Derek wants to ship items that weigh a total of 7 pounds, and Keisha wants to ship items that weigh a total of 10 pounds. How much more does Keisha pay for shipping than Derek?
Answer:
Derek needs to pay 3 more pounds
the side of a square is 9in. what is the perimeter?
Answer:
36in
Step-by-step explanation:
A square has four sides. If the length of one is 9 inches, then we multiply it by four to get 9*4 = 36in as our perimeter.
FINAL ANSWER: 36in
A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 6 feet in length. How many 18-inch pieces can the dressmaker cut from 5 of these rolls of ribbon?
Before you try that problem, answer the question below.
How many inches of ribbon does the dressmaker have, in total?
(on delta math)
Answer: 20 pieces, 72 inches of ribbon
Step-by-step explanation: 6/1.5=4 4x5=20 6x12= 72 inches
c. A parallelogram
has an area of 7 square units. If the height that corresponds to
a base is unit, what is the base?
If a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units, then the base is 28 units.
As per the question statement, a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units.
We are required to find out the base of the parallelogram.
To solve this question, we need to know the formula to calculate the area of a parallelogram, which goes as
Area of Parallelogram = (Base * Height)
Putting our data obtain from the question statement, in the above-mentioned formula, we can calculate the value of the base of our concerned parallelogram, i.e.,
[tex]7=(base*\frac{1}{4})\\or, base=(7*4)\\or, base = 28[/tex]
Therefore, base of our concerned parallelogram is 28 units.
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Which ordered pair is a solution to every linear equation of the form y = mx, where m is a real
number?
The ordered pair which is a solution to every linear equation of the form given is; (0, 0).
Which ordered pair is a solution to the linear equation?It follows from the task content that the ordered pair which satisfies the equation of the form y =Mx be determined.
On this note, since the product of any real number, slope in this scenario and 0 is; 0.
Ultimately, it follows that the required ordered pair is; (0, 0) for any real number value of the slope, m.
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The ratio of two numbers is 8:7. The product of these numbers is 896. What is the smaller of these two
numbers?
Answer:
28
Step-by-step explanation:
You want the smaller of the two factors of 896 that have the ratio 8:7.
SetupLet x represent the smaller of the two factors (the one we want to find). Then the larger factor is (8/7)x, and their product is ...
x(8/7)x = 896
(8/7)x² = 896
SolutionMultiplying by the inverse of the coefficient of x², we have ...
x² = (7/8)(896) = 784
x = √784 = 28 . . . . . . . . take square root
The smaller of the two numbers is 28.
__
Additional comment
The larger is (8/7)(28) = 32.
I dont understand the problem i think it's 4.5 but i dont know
Answer:
probably 4.5
"Step-by-step explanation:
To break even, we need the total profit to be equal to 0. If we make x dollars in 2012, then we need to solve
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
This gives us x = 0.45 in thousands.
Since the question asks us to give the answer in hundreds, we multiply by 10 and get 4.5. Thus the profit in 2012 must be 4.5 (in hundreds) to break even."
when two items are thrown from the same height how does it affect the two in different ways if so
The height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.
What is time of motion?
The time of motion of an object is the time taken for an object to travel from point of projection to the projection plane or it can be said as the time a projected object spent in air.
The time taken for an object dropped from a certain height is calculated as follows;
h = vt + ¹/₂gt²
where;
h is the height from the which the object is droppedv is the initial vertical velocity of the objectt is the time of motion of the objectg is acceleration due to gravitywhen the object is dropped from rest, v = 0
h = ¹/₂gt²
t = √(2h/g)
Thus, the height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.
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what is the length of the conjugate axis? (y-2)^2/16 -(x+1)^2/144=1
Answer: 24
A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant, which is always greater than unity.
the fixed point is called the focus and the fixed line is directrix and the ratio is the eccentricity.
The general equation for the vertical hyperbola is
[ (y-k)^2 / a^2 ] – [ (x-h)^2 / b^2 ] = 1
The conjugate axis of the vertical hyperbola is y = k
Length of the conjugate axis = 2b
According to the question k = 2, h = -1, a = 4, b = 12
Length of the conjugate axis = 2b = 2 * 12 = 24
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Find the midpoint of the segment with endpoints (9,3) and (6,-7)
Answer:
(7.5, -2)
Step-by-step explanation:
Label the coordinates(x₁,y₁) and (x₂,y₂)
Input the values into the formula (x₁ + x₂)/2, (y₁ + y₂)/2
Add the values in the parentheses and divide each result by 2
Perform the indicated operation.
4
0 -4 -8
0
1
0
0
0
1
-1
3
4R3+R1 R1
0
0
0
1
0
0
1
-1
3
Answer:
Can someone help me please
Answer: 4 0 4
Step-by-step explanation:
Help!!
Find the after-tax return to a corporation that buys a share of preferred stock at $49, sells it at year-end at $49, and receives a $4 year-end dividend. The firm is in the 21% tax bracket.
This is what I got so far:
Before-tax:
(49-49)+4 = 4,
4/49 = 0.0816,
After-tax:
0.0816 (1-021) = 0.06448 or 6.45%
Based on the calculation below, the after-tax return to the corporation is $3.16 per share or 6.44% if expressed in percentage.
How do we calculate the after-tax return?The after-tax return can be calculated using the following formula:
After-tax return = Total return * ( 100% - tax rate) .............. (1)
Where:
Total return Received = Dividend received + Change in price = $4 + ($49 - $49 ) = $4 + $0 = $4
Tax rate = 21%
Substituting the values into equation (1), we have:
After tax return = $4 * ( 100% - 21%)
After-tax return = $3.16 per share
The after-tax return can also be expressed in percentages as follows:
After-tax return in percentage = After-tax return / Share price = $3.16 / $49 = 0.06444897 = 6.44%
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A school playground is in the shape of a rectangle 800 feet long and 100 feet wideIf fencing costs $15 per yard, what will it cost to place fencing around the playground?
Tina spent $182 on 13 pamphlet sets for her beauty shop. How much does each pamphlet set cost?
Answer:
14 dollars
Step-by-step explanation:
182 divided by 13 is 14 dollars
may starclan light ur path
A car rental agency advertised renting a car for $26.95 per day and $0.33 per mile. If Greg rents this car for 3 days, how many whole miles can he drive on a $200 budget?
Answer: 361 miles
Step-by-step explanation: 26.95x3=80.85
200-80.85=119.15
119.15/0.33
=361.06
create and equivalent expression for 12^-7 x 12^5
The required equivalent expression to 12⁻⁷ x 12⁵ is 12⁻².
Given that,
To determine the equivalent expression for 12⁻⁷ x 12⁵.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
= 12⁻⁷ x 12⁵
Simplifying
= 12⁻⁷ x 12⁵
Since, when the same value has a difference in the exponent in the product then it retains the base value and the addition of the exponent takes place.
= 12⁻⁷⁺⁵
=12⁻²
Thus, the required equivalent expression to 12⁻⁷ x 12⁵ is 12⁻².
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write an equation that is parallel to y=-5/2x-5
A parallel equation (when graphed) will have the same slope, but a different y-intercept.
As long as you keep y = -[tex]\frac{5}{2}[/tex]x + b, you can input anything for b to solve this question.
Given:
y = -[tex]\frac{5}{2}[/tex]x - 5
Equation of a parallel line:
y = -[tex]\frac{5}{2}[/tex]x + 6, y = -[tex]\frac{5}{2}[/tex]x + 1,356, y = -[tex]\frac{5}{2}[/tex]x - 8, etc
Example answer you can use:
y = -[tex]\frac{5}{2}[/tex]x - 8
You want to buy a $193,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan for the rest.
Answer:
Down Payment = 5% of 168,000. You finance 95% of 168,000 which is the PV of your payments.
Use the same annuity formula as in your student loan question with monthly rate = 7%/12 and t=12*30 =360 months. That will give you your payment amount.
you will make 360 payments so total Payments = 360*pmt. Total Payments less principal = total interest paid.
Distributive Property and Combining Like Terms WS2
Objective
To simplify algebraic expressions using the distributive property.
Simplify
1. 4(3x+1) 12x+4
2. −5(5x−4)
3. -(2x-1)
I need to know the answer
The equivalent expressions of the given expressions are
4(3x + 1) = 12x + 4-5(5x − 4) = -25x + 20-(2x - 1) = -2x + 1How to simplify the algebraic expressions using the distributive property?The expressions are given as
4(3x + 1)-5(5x − 4)-(2x - 1)The distributive property stated that
a(b + c)= ab + ac
Using the above as a guide, the equivalent expressions are
4(3x + 1) = 12x + 4-5(5x − 4) = -25x + 20-(2x - 1) = -2x + 1Read more about distributive property at
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As indicated below, write the equations of the line passing through the point (2, 4) and parallel to the line whose equation is y = x. Complete your work in the space provided. Part 1: Point-Slope form of the linear equation Part 2: Slope-intercept form of the linear equation Part 3: The general form of the linear equation
Part 1
[tex]y-4=x-2[/tex]
Part 2
[tex]y=x+2[/tex]
Part 3
[tex]x-y+2=0[/tex]
What is the answer to -5 - 7.
Answer:
it is negative 12
Step-by-step explanation:
-12
Answer:
-12
Step-by-step explanation:
All whole numbers can also be classified as
integers and rational numbers.
True
False
Answer:
True
Step-by-step explanation:
We use definitions to help us in this problem. The definition of an integer is a whole number that is not a fraction or has any fractional value. This definition includes all whole numbers, so we know that all whole numbers can be classified as integers. That's one condition done. The definition of a rational number is a number that can be written as a fraction. All whole numbers can be written as a fraction (i.e. 12/1, -3/1, 10000/1). This means that all whole numbers are also rational numbers, giving us our final answer of True.
FINAL ANSWER: True
The graph of y=x^3-2x^2-3x is shown in Figure 1. Based on the graph, what do you think are the solutions of the equation x^3-2x^2-3x=0? Confirm that your values are solutions by substituting them in place of x in the equation x^3-2x^2-3x=0 to see that you get a true statement.
The solutions to the given equation are x = -1, x = 0 and x = 3
Graph of Cubic EquationFrom the question, we are to determine the solution of the given equation.
The given equation is
x³ -2x² -3x = 0
The graph of the function y = x³ -2x² -3x is shown below
The solutions of the equation x³ -2x² -3x = 0 are the values where the graph cuts the x-axis
From the graph, we can observe that
The curve cuts the x-axis at x = -1, x = 0 and x = 3
Hence, the solutions to the given equation are x = -1, x = 0 and x = 3
Testing the solutions
For x = -1
x³ -2x² -3x = 0
(-1)³ -2(-1)² -3(-1) = 0
-1 -2(1) +3 = 0
-1 -2+3 = 0
-3+3 = 0
0 = 0
For x = 0
x³ -2x² -3x = 0
(0)³ -2(0)² -3(0) = 0
0 - 0 - 0 =0
0 = 0
For x = 3
x³ -2x² -3x = 0
(3)³ -2(3)² -3(3) = 0
27 -2(9) - 9 = 0
27 -18 - 9 = 0
0 = 0
Since, all the statements are true, then values are solutions of the equation.
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4 is subtracted from the square of a number.
Answer: x^2-4
Step-by-step explanation: I can only assume that is the answer given the limited prompt. Please comment and let me know if that is the desired answer or if you need more help. (X = a number ^2 = squared -4 = 4 is subtracted)
Solve x ^ 2 - 5x + 10 = 0 using the quadratic formula .
Answer:
2-5X + 10= 0 = 75
Using The Form Quadratic Is,
Step-by-step explanation:
The Step By Step Explanation Is Simple,
2-5= 3
+
3+10=13
But Were Missing The 5x's, So It's Time To Add It.
13+3=16 x 5= 75
As You See, Our Answer Came To 75, So Therefore,
Your Answer Is 75.
have data on the weights in grams of 5 baby pythons. Thè mèan weight is 3l.B and dre standard deviation of the r,veights is2.79. The correct units for the standard deviation are
We have data on the weights in grams of 5 baby pythons. Their mean weight is 31.8 and the standard deviation of the weights is 2.79 . The correct units for the standard deviation is Grams.
According to the question statement, We have data on the weights in grams of 5 baby pythons. Their mean weight is 31.8 and the standard deviation of the weights is 2.79.
The correct units for the standard deviation is Grams because the unit of standard deviation is the unit of simple data and the unit of variance is the square of the simple data unit.
And as we know the unit of weight is Grams only hence we conclude that Grams is the correct unit of standard deviation.
Standard Deviation: Abbreviated as SD and standard deviation is a measure of the amount of variation of a set of values. A low standard deviation indicates that the values tend to be close to the mean (expected value) of the set, while a more or high SD indicates that the values are spread out over a wider range.To learn more about standard deviation, click on the given link below
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Evaluate the expression:
2
3
+
6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming}[/tex]
[tex]\mathsf{\dfrac{2}{3} + 6}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathsf{\dfrac{2}{3} + 6}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{6}{1}}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{6\times3}{3\times1}}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{18}{3}}[/tex]
[tex]\mathsf{= \dfrac{2 + 18}{3 - 0}}[/tex]
[tex]\mathsf{= \dfrac{20}{3}}[/tex]
[tex]\mathsf{= 6 \dfrac{2}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{20}{3}\ or\ 6 \dfrac{2}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the first five terms of the recursive sequence. Show all your work. an = 3a n-1 - 6 where a1 = 7
======================================================
Work Shown:
First replace every copy of n with 2
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_2 = 3*(a_{2-1}) - 6\\\\a_2 = 3*(a_{1}) - 6\\\\a_2 = 3*(7) - 6\\\\a_2 = 21 - 6\\\\a_2 = 15\\\\[/tex]
Notice how the second term [tex]a_2[/tex] relies on the first term [tex]a_1[/tex]
Then repeat for n = 3
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_3 = 3*(a_{3-1}) - 6\\\\a_3 = 3*(a_{2}) - 6\\\\a_3 = 3*(15) - 6\\\\a_3 = 45 - 6\\\\a_3 = 39\\\\[/tex]
Same goes with n = 4
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_4 = 3*(a_{4-1}) - 6\\\\a_4 = 3*(a_{3}) - 6\\\\a_4 = 3*(39) - 6\\\\a_4 = 117 - 6\\\\a_4 = 111\\\\[/tex]
Finally plug in n = 5
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_5 = 3*(a_{5-1}) - 6\\\\a_5 = 3*(a_{4}) - 6\\\\a_5 = 3*(111) - 6\\\\a_5 = 333 - 6\\\\a_5 = 327\\\\[/tex]
-----------------------------------
We have this summary:
[tex]a_1 = 7\\\\a_2 = 15\\\\a_3 = 39\\\\a_4 = 111\\\\a_5 = 327\\\\[/tex]
The first five terms are: 7, 15, 39, 111, 327
Interns,
Mr. Howell, the prestigious founder and owner of our company Coal is Gold Electricity would like you to perform an
analysis on the company’s emission control. The government is providing subsidies to encourage reducing emissions.
Mr. Howell would like to know is it worth reducing emissions with the subsidy. The pertinent information can be found
in Mr. Howell’s email below.
“Mr. Kleppin,
As you know, my company has supplied the energy needs of the entire state since 1968! I can’t believe they are
demanding that we reduce our emissions! This will force us to pass on the increase in the cost to our customers!
Thankfully, the government will be providing a subsidy to offset these costs! The current subsidy is $500 per pound of
pollution reduction each day with a minimum reduction of 15 pounds per day. I have spoken to the engineering
department regarding the cost to reduce emissions. They informed me that the average daily cost to us is a fixed daily
cost of $100 in addition to $30 times the square of the quantity of pounds of pollution reduced each day. Currently, I
would like to reduce emissions by 15 pounds of pollutant per day. At this level, what is the marginal average daily cost of
reducing emissions to 16 pounds of pollutant per day? What is the average daily cost at this reduction level? Is the
average daily cost increasing or decreasing at this reduction level? With the government subsidy, what would be our
average daily cost for reducing emissions by 15 pounds of pollutant per day? The government would like us to reduce
emissions by 20 pounds of pollutants per day. Could we accomplish this with no cost to us? If not, at what reduction level
would we have no cost to us? What do you recommend? I would like you, Mr. Kleppin, to give the interns a chance to
earn one of the 10 available positions at the end of their internship by giving them the opportunity to do the analysis.”
As per the given information about that Mr. Howell the prestigious founder and owner of our company Coal is Gold Electricity:-
POUNDS FC SQ. OF POUNDS TVC TC AC SUBSIDY
1 100 1 30 130 130.0 500
2 100 4 120 220 110.0 1000
3 100 9 270 370 123.3 1500
4 100 16 480 580 145.0 2000
5 100 25 750 850 170.0 2500
6 100 36 1080 1180 196.7 3000
7 100 49 1470 1570 224.3 3500
8 100 64 1920 2020 252.5 4000
9 100 81 2430 2530 281.1 4500
10 100 100 3000 3100 310.0 5000
11 100 121 3630 3730 339.1 5500
12 100 144 4320 4420 368.3 6000
13 100 169 5070 5170 397.7 6500
14 100 196 5880 5980 427.1 7000
15 100 225 6750 6850 456.7 7500
16 100 256 7680 7780 486.3 8000
17 100 289 8670 8770 515.9 8500
18 100 324 9720 9820 545.6 9000
19 100 361 10830 10930 575.3 9500
20 100 400 12000 12100 605.0 10000
Here, FC = Fixed Cost
TVC = Total Variable Cost
TC = Total Cost
AC = Average Cost
(i) Marginal Cost of a 16-pound reduction in emissions = 7680 - 6750
= $930
(ii) Average Price at a decline of 15-pound = 6850 / 15 = $456.67
( Every additional unit results in an increase in Variable Cost per unit. The Average Cost will thus rise as the amount increases. )
(iii) Since our expenses are less than the subsidies in pounds (15), there will be no net cost.
(iv) It will cost us $12,000 to maintain the decrease level at 20 pounds, of which the corporation may recoup $10,000. Thus, the final price will be $2100.
(v) Break Even can be calculated between 16-17 pounds (You can refer to the table for the clarifications)
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