Answers
The y-intercept represents the base price of $200 for airfare from NYC.
The slope represent a cost of $0.30 cents per mile traveled.
According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.
According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.
If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this trip, a linear equation that models the situation is given by;
y = mx + c
y = 0.30x + 200
when x = 2000, we have;
y = 0.30(2000) + 200 = $800.
when y = 500, we have;
500 = 0.30x + 200
300 = 0.30x
x = 1000 miles.
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Related Questions
What is the area of the polygon in square units?
Answers
The area of the polygon is 92 units²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The polygon can be divided into two; A trapezoid and a triangle.
Area of a trapezoid = 1/2(a+b) h
= 1/2 ( 8+12) 2
= 8+12
= 20 units²
Area of the triangle = 1/2 bh
= 1/2 × 12 × 12
= 6×12
= 72units²
therefore area of the polygon
= area of trapezoid+ area of triangle
= 20+72 = 92 units²
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Graph the solution to the inequality on the number line.
q<69.5
Answers
The graph of the solution to the given inequality on the number line plotted is attached.
Inequalities are the mathematical expressions in which both sides are not equal.
In inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is q < 69.5.
The result can be shown in multiple forms.
Inequality Form:q<69.5
Interval Notation:(−∞,69.5)
Therefore, the graph the solution to the given inequality on the number line plotted below.
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PLEASE HELP I HAVE IT MARKED 100 POINTS FOR YOU WILL BRAINLIEST
Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.
π,√6,2√6,√7
(a) Without using your calculator, approximate the decimal equivalent of each number to the nearest tenth.
(B) Order the ribbon sizes from least to greatest.
Answers
pat a
π is approximately 3.1 to the nearest tenth.
√6 is approximately 2.4 to the nearest tenth.
2√6 is approximately 4.8 to the nearest tenth.
√7 is approximately 2.6 to the nearest tenth.
(b)
Ordering from least to greatest:
√6 π √7 2√6What is number approximation?An approximation is described as anything that is similar, but not exactly equal, to something else.
A number can be approximated by rounding off and a calculation can be approximated by rounding the values within it before performing the operations .
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Will mark brainliest.
Answers
Applying the secant-tangent theorem, the length of the diameter is approximately 13.9.
How to Apply the Secant-Tangent Theorem?Given the image above that shows a circle containing the diameter, assuming the length of the diameter is x, we can create the following equation based on the secant-tangent theorem:
25² = 19(x + 19)
625 = 19x + 361
625 - 361 = 19x + 361 - 361 [subtraction property]
264 = 19x
Divide both sides by 19:
x ≈ 13.9
The diameter is approximately 13.9.
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Arrange the numbers in order from least to greatest
Answers
Answer:
[tex]\sqrt{75}[/tex], 4.3, 20/13, [tex]\frac{\pi }{4}[/tex]
If a bipartite graph has 14 vertices in one part, 10 vertices in the other part, and 70 edges, what is its chromatic number?
Answers
The graph has 14 vertices and 10 vertices and 70 edges, but this does not affect the chromatic number, which is 2.
A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets. In such a graph, it is always possible to color the vertices with two colors such that no two adjacent vertices have the same color. Therefore, the chromatic number of a bipartite graph is always 2.
In this problem, the bipartite graph has 14 vertices in one part and 10 vertices in the other part, which makes a total of 24 vertices. Since the graph has 70 edges, it means that each vertex in one part is connected to exactly 5 vertices in the other part (70/14=5). Similarly, each vertex in the other part is connected to exactly 7 vertices in the first part (70/10=7).
To color this bipartite graph with two colors, we can assign one color to the first set of vertices and the other color to the second set of vertices. This coloring satisfies the condition that no two adjacent vertices have the same color, and therefore, the chromatic number of the graph is 2.
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Robert’s soccer team needs to be off the soccer field by 12:15pm. Each game is at most 1 3/4 hours long. What time should the game begin to be sure that the team finishes on time?
Answers
The requried game should start no later than 10:30 am to ensure that the team finishes on time.
If the game is at most 1 3/4 hours long, then the latest it can end is 1:45 pm (which is 1 hour and 45 minutes after the start time).
If the team needs to be off the field by 12:15 pm, then the latest the game can start is:
12:15 pm - 1 hour and 45 minutes = 10:30 am
Therefore, the game should start no later than 10:30 am to ensure that the team finishes on time.
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Correct answer gets brainliest!!!!
Answers
A square pyramid has a square base with four vertices, and an additional vertex at the apex of the pyramid, for a total of five vertices or zero-dimensional objects.
Answer:
A.) 5
Points are 0 dimensional objects.
A random sample of 10 subjects have weights with a standard deviation of 12.5602 kg. What is the variance of their weights? Be sure to include the appropriate units with the result
Answers
The requried, variance of their weights is 157.789 kg².
To calculate the variance, we need to square the standard deviation since variance is the square of the standard deviation. Thus, the variance of the weights of the 10 subjects is:
Variance = (Standard Deviation)² = (12.5602 kg)² = 157.789 kg²
Therefore, the variance of their weights is 157.789 kg².
Note that the units of the variance are the square of the units of the standard deviation.
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In the first month of operations, Company made three purchases of merchandise in the following sequence: 300 units at $7, 410 units at $8 and 210 units at $9.
Assuming there are 390 units on hand, compute the cost of the ending inventory under the FIFO method and LIFO method.
Answers
The cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.
To calculate the cost of the ending inventory under FIFO method, we need to first determine the cost of goods sold (COGS) for the month.
The cost of goods sold for the month would be:
300 units x $7 = $2,100
90 units x $8 = $720
20 units x $8 = $160
210 units x $9 = $1,890
Total COGS = $4,870
To calculate the cost of the ending inventory, we need to determine the cost of the remaining 390 units on hand.
Under FIFO, the cost of the ending inventory is based on the cost of the most recent purchases.
Therefore, the cost of the ending inventory would be:
20 units x $8 = $160 (from the 410 units purchased at $8)
370 units x $9 = $3,330 (from the 210 units purchased at $9 and the remaining 160 units of the 410 units purchased at $8)
Total cost of ending inventory = $3,490
Therefore, the cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The solution of the logarithm equation, log₁₄ 144 = 2 is 14² = 144.
How to solve logarithm equation?The logarithm equation can be solved using the law of logarithm. Therefore,
log₁₄ 144 = 2
If you have a single logarithm on one side of the equation, you can express it as an exponential equation and solve it.
Hence,
logₐ b = x can be represented as follows:
aˣ = b
Therefore,
log₁₄ 144 = 2
14² = 144
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SELECT THE EQUATION THAT RELATES COST WITH GROUP SIZE! HELP ASAP
Answers
The point-slope linear function that relates cost with group size is given as follows:
D. y - 115 = 5(x - 17).
How to obtain the equation of the line?The point-slope equation of a line is given as follows:
y - y* = m(x - x*).
In which:
m is the slope.(x*, y*) are the coordinates of a point.When the group size increases by 3, the cost increases by $15, hence the slope m is given as follows:
m = 15/3
m = 5.
One point is x = 17 and y = 115, hence the equation can be given as follows:
y - 115 = 5(x - 17).
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arrange 16 coins in 10 rows with 4 in each row
Answers
Answer:
1.3
Step-by-step explanation:
if you subtract 16 and 10 gives u six then turn it into a mix number and divide that into 4s in each ten groups then you would get your answer that way hope it helps
James Bennett also allocates wealth between youth and old age. He has no cash currently (in his youth), but will inherit $3000 in his old age. He can lend and borrow at the bank at 18% (that is, lending $1 in youth will give him $1.18 in old age). He has an investment opportunity that costs $12,000 now in his youth and has a payoff of $15,000 in his old age. This is the only investment opportunity available to him. What is the most he can consume in his youth?
Answers
Answer:
To determine the most James Bennett can consume in his youth, we need to find the maximum amount he can borrow from the bank to invest in the opportunity, while still being able to pay back the loan with interest in his old age.
Let x be the amount that James borrows from the bank in his youth. He invests this amount in the opportunity and receives a payoff of $15,000 in his old age. With this payoff, he can pay back the loan plus interest, which is:
Loan + interest = x + 0.18x = 1.18x
So, he needs to have at least $1.18x in his old age to be able to pay back the loan. He will also receive an inheritance of $3000 in his old age, so his total wealth in his old age will be:
Total wealth in old age = $1.18x + $3000
To determine the maximum amount he can consume in his youth, we need to subtract the cost of the investment opportunity and the amount borrowed from the bank from his initial wealth:
Initial wealth = $0 (no cash currently)
Maximum consumption in youth = Initial wealth - Cost of investment - Amount borrowed
Maximum consumption in youth = -$12,000 - x
Since James wants to maximize his consumption in his youth, we need to find the value of x that maximizes the expression -$12,000 - x, subject to the constraint that his total wealth in his old age is at least $1.18x + $3000.
To find this value of x, we can set up the following optimization problem:
Maximize -$12,000 - x
Subject to: $1.18x + $3000 >= $1.18x (i.e., his total wealth in old age is at least $1.18x + $3000)
Simplifying the constraint, we get:
$3000 >= 0
This constraint is always satisfied, so it does not affect the solution. Therefore, we can simply maximize the objective function -$12,000 - x:
d/dx (-$12,000 - x) = -1
Setting the derivative equal to 0 to find the maximum, we get:
-1 = 0
This is never true, so there is no maximum value of -$12,000 - x. This means that James cannot afford to invest in the opportunity and still have a positive wealth in his old age. Therefore, he cannot consume anything in his youth, since he has no cash currently and cannot invest in the opportunity.
Step-by-step explanation:
Help much needed pls and thank you
Answers
The coordinates in polar form are equal to (r, θ) = (8, 11π / 6).
How to transform coordinates in rectangular form into polar form
In this problem we find the definition of a set of coordinates in rectangular form into polar form, that is:
(x, y) → (r, θ)
Where:
x, y - Coordinates in rectangular form.r - Normθ - Direction, in radians.Where the norm and the direction of the point are determined by these equations:
r = √(x² + y²)
θ = tan⁻¹ (y / x)
Finally, we determine the coordinates in polar form:
Norm
r = √[(4√3)² + (- 4)²]
r = √(48 + 16)
r = √64
r = 8
Direction
θ = tan⁻¹ (- 4 / 4√3)
θ = tan⁻¹ (- √3 / 3)
θ = 11π / 6
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6. Thurston and Kim continue downloading songs in this manner for 8 weeks. What ordered pair would represent the total number of songs they have each downloaded?
Answers
The ordered pair which represents the total number of songs they have each downloaded in 8 weeks is given by (40, 120).
Thurston downloaded 5 songs each week.
He continued downloading songs for 8 weeks in same rate.
So the total number of songs he downloaded for total of 8 weeks = 8*5 = 40 songs.
Kim downloaded 15 songs each week.
She continued downloading songs for 8 weeks in same rate.
So total number of songs she downloaded for total of 8 week = 8*15 = 120 songs.
The required ordered pair = (total number of songs Thurston downloaded for total of 8 weeks, total number of songs Kim downloaded for total of 8 week) = (40, 120).
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The question is incomplete. The complete question will be -
"Thurston downloaded 5 songs each week and Kim downloaded 15 songs each week. Thurston and Kim continue downloading songs in this manner for 8 weeks. What ordered pair would represent the total number of songs they have each downloaded?"
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
The equation for the total cost of all adult tickets (a) and student tickets (s).
4a + 2.5s = 2,820
a + s = 900
The number of adults ticket and student tickets is 380 and 520.
We have,
Adults ticket cost = $4
Student ticket cost = $2.5
Now,
Total amount earned = $2,820
The equation for the total cost of all adult tickets (a) and student tickets (s).
4a + 2.5s = 2,820 ______(1)
And,
The number of tickets sold = 900.
We can write as equation as:
a + s = 900 ______(2)
Now,
We have two equations.
4a + 2.5s = 2820
a + s = 900
Solving for s.
s = 900 - a
Substituting in (1)
4a + 2.5(900 - a) = 2820
Simplifying and solving for a.
4a + 2250 - 2.5a = 2820
1.5a = 570
a = 380
Now,
a + s = 900
380 + s = 900
s = 520
Therefore,
The number of adults ticket and student tickets is 380 and 520.
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15. What integer is missing from the number line below?
Answers
The missing integer on the number line below is given as follows:
-7.
How to obtain the missing integer?The missing integer on the number line is obtained applying the proportions in the context of the problem.
The vertical trace is the mean of -10 and -5, hence it is given as follows:
(-10 - 5)/2 = -7.5.
(we obtain the mean of the two numbers as the middle trace is exactly halfway between these two values).
The missing integer on the number line is the integer number exactly to the right(greater) of -7.5, hence it is of:
-7.
(nearest integer that is greater than -7.5).
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The McGee family is looking to rent a large truck for their upcoming move. With Luther's Moving, they would pay $38 for the first day plus $7 per additional day. With Springdale Rent-a-Truck, in comparison, the family would pay $44 for the first day plus $4 per additional day. Before deciding on which company to use, Mrs. McGee wants to find out what number of additional days would make the two choices equivalent with regards to cost. What would the total cost be? How many additional days would that be?
The McGee family would pay _______$ either way if they rented the truck for ____ additional days.
HELPPPP
Answers
Answer: The McGee family would pay $52 either way if they rented the truck for 2 additional days.
Step-by-step explanation:
Luther's Moving Company:
38 is how much they'll pay on the first day plus 7 per every additional day
This is represented by 7x+38
Springdale Rent-a-Truck
44 is how much they'll pay on the first day plus 4 per every additional day
This is represented by 4x+44
Set the equations equal to each other
7x+38=4x+44
Move the 38 to the other side by subtracting
7x=4x+44-38
7x=4x+6
Move 4x to the other side by subtracting
7x-4x=6
3x=6
Divide 3 to get x alone
3x/3=6/3
x=2
They'll be equal after 2 additional days
Plug in 2 to each equation
Luther: 7(2)+38
14+38=52
Springdale: 44+4(2)
44+8=52
I NEED HELP WITH 5,6,7,8
( 20 ) points
Answers
The number of bacteria this morning is 119000 and the surface area of the solid is 25344 square meters
Number of bacteria this morningGiven that
Yesterday = 35000Percentage increase = 240%So, we have
This morning = 35000 * (1 + 240%)
Evaluate
This morning = 119000
The fractional partHere, we have
Fractional part = 28/70
Simplify
Fractional part = 2/5
So, the 28 is 2/5 of 70 as the fractional part
The volume of the solidStart by calculating the base area using
base area = 1/2 * (6 + 10) * 10
base area = 80
So, we have
Volume = base area * height
Volume = 80 * 13
Volume = 1040 cubic cm
The surface area of the solidThis is calculated as
Surface area = bh * (b1 + b2 + b3)l
So, we have
Surface area = 12 * 6 * (10 + 10 + 12) * 11
Evaluate
Surface area = 25344
So, the surface area of the solid is 25344 square meters
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Find the value of x to the nearest tenth
Answers
Answer:
Step-by-step explanation:
Answer:
my answer is 23.49
Step-by-step explanation:
you will use sin rule
you can also find the angle for Z because angles in a triangle add up to 180
then use sin rule
25/sin 70=x/sin 62
then substitute for x
✓
For the statement, find the constant of variation and the variation equation.
y varies inversely as the square of x; y = 0.045 when x = 4
The constant of variation k is.
(Type an integer or a decimal.)
Answers
Answer:
k = 0.72
Step-by-step explanation:
If y varies inversely as the square of x, then we know that the variation equation is:
[tex]y=k/x^2[/tex], where k is the constant of variation.
We can find the constant variation by plugging in 0.045 for y, 4 for x, and solving for k;
[tex]0.045=k/4^2\\0.045=k/16\\0.72=k[/tex]
Janelle and Dante find the surface area of a cylinder. Janelle Find the area of the curved surface A = bh= (8) (18) = 144 ft² Then find the area of each base A = πr² = π(9)² = 254.4 ft² Total surface area = 144 + 2(254.4) 652.8 ft² Dante 8 ft 9 ft Find the area of the curved surface A = Ph= (18T) (8) = 452.4 ft² Then find the area of each base A = πr² = π(9)² = 254.4 ft² Total surface area = 452.4 + 2(254.4) 961.2 ft² A. Is either student correct? Explain. B. Use Appropriate Tools Which method would you use to find the surface area of the cylinder? Is it more efficient than the method used by Janelle and Dante?
Answers
B. The most appropriate tool to use to find the surface area of a cylinder is a formula that combines the area of the curved surface and the area of the two bases. The formula is:
Total surface area = 2πr² + 2πrh
where r is the radius of the cylinder and h is the height.
Janelle found the area of the curved surface and the area of each base separately, and then added them together. This is a valid method, but it requires more steps than the formula.
Dante used the formula, but he made a mistake by using the diameter instead of the radius to find the height. The correct height is 9 feet, not 8 feet. However, his final answer is still correct because he used the correct area for the curved surface.
Using the formula is more efficient than Janelle's method because it requires fewer steps and calculations.
HURRY
Find the unit vector that has the same direction as the vector v.
v = 3i - 5j
Answers
The unit vector in the direction of v = 3i - 5j is (3√(34)i - 5√(34)j) / 34.
To find the unit vector in the direction of the given vector, we first need to find the magnitude of the vector v. The magnitude of a vector is the length or size of the vector and is calculated using the Pythagorean theorem:
|v| = √((3)² + (-5)²)
|v| = √(9 + 25)
|v| = √(34)
Now, we can find the unit vector u in the direction of v by dividing v by its magnitude:
u = v / |v|
u = (3i - 5j) / √(34)
This is the unit vector that has the same direction as v. To simplify the answer, we can rationalize the denominator by multiplying the numerator and denominator by √(34):
u = (3i - 5j) / √(34) * √(34) / √(34)
u = (3√(34)i - 5√(34)j) / 34
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Find PN and QP.
IMAGE ATTACHED PLS HELP
Answers
Answer:
PN: 15
QP: 15
Step-by-step explanation:
if QN is 30 and P is in the middle of N and Q then the distance from P must be 15
Suppose that in 1990, a coffee cost $2, and the CPI at the time is 99. Suppose that in 2022, a coffee cost $6, and the CPI at the time is 260.
Compute the percentage change in the real price of a coffee from 1990 to 2022. (Hint: convert the 1990 price of a coffee into 2022 dollars, and then calculate the percentage change in the prices, using the 2022 price as the new value, and 1990 as the previous value.) Round your answer to two places after the decimal point (0.01).
Answers
After accounting for inflation, the true price of coffee climbed by 14.22% between 1990 and 2022.
To compute the percentage change in the real price of a coffee from 1990 to 2022, we need to adjust the 1990 price for inflation using the CPI for both years.
The inflation rate from 1990 to 2022 is given by:
Inflation rate = ((CPI in 2022 - CPI in 1990) / CPI in 1990) * 100%
= ((260 - 99) / 99) * 100%
= 162.63%
This means that prices increased by 162.63% from 1990 to 2022.
To adjust the 1990 price of $2 for inflation, we multiply it by the inflation factor:
Inflation factor = CPI in 2022 / CPI in 1990
= 260 / 99
= 2.6262
Adjusted price in 2022 dollars = 2 * 2.6262 = 5.2524
Now we can calculate the percentage change in the real price of a coffee from 1990 to 2022:
Percentage change = ((2022 price - 1990 price) / 1990 price) * 100%
= ((6 - 5.2524) / 5.2524) * 100%
= 14.22%
Therefore, the real price of a coffee increased by 14.22% from 1990 to 2022 after adjusting for inflation.
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(b) How long will it take the investment to reach one–quarter million dollars? Round to the nearest tenth of a year. Round values in intermediate steps to three decimal places.
Answers
13) The linear equation in two variables y = 0.10x +175 models the total weekly cost, y, in
dollars, for renting and driving it x miles. The equation indicates that the rental
company charges a fixed amount of $175 for the week plus a cost of $0.10 for each mile
the car is driven. Find the solution of y = 0.10x +175 using 185 for x.
Answers
y = 0.10(185) + 175
y = 18.5 + 175
y = 193.5
Therefore, if you rent and drive the car for 185 miles in a week, the total weekly cost will be $193.50.
50 points
Barbara Young owes $39,600 on a 6%, 110-day note. On day 75, she pays $11,880 on the note. On day 80, she pays an additional $15,840.
Based on the U.S. Rule, calculate the following. (Use a 360-day year, and round all answers to the nearest cent.)
1. Adjusted balance after the first payment: $
2. Adjusted balance after the second payment: $
3. Balance at maturity: $
Answers
Answer:
$13,080.50 + $13,080.50 x 0.06 x 30/360 = $13,393.03
Step-by-step explanation:
Adjusted balance after the first payment: $39,600 + $39,600 x 0.06 x 75/360 - $11,880 = $28,770
Adjusted balance after the second payment: $28,770 + $28,770 x 0.06 x 5/360 - $15,840 = $13,080.50 tell me if it's not clear
College level Trigonometry any help will do!!
Answers
The magnitude of the resultant force is approximately 9.07 lb.
We have,
To use the parallelogram rule to find the magnitude of the resultant force for the two forces, we first draw a diagram:
B (11 lb)
/|
/ |
/ |
/ |
/ |
/ |
/θ |
/ |
A (7 lb) |
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\|
C
where A and B are the magnitudes of the given forces, and θ is the angle between them.
Using the parallelogram rule, we draw a parallelogram with sides AB and BC:
B (11 lb)
/|
/ |
/ |
/ |
/ |
/ |
/θ |
/ |
A (7 lb) D
\ |
\ |
\ |
\ |
\ |
\ |
\ |
\|
C
The diagonal BD represents the magnitude and direction of the resultant force.
To find its magnitude, we use the Law of Cosines:
BD^2 = AB^2 + BC^2 - 2(AB)(BC)cos(θ)
BD^2 = (7 lb)^2 + (11 lb)^2 - 2(7 lb)(11 lb)cos(133 degrees)
BD^2 = 49 + 121 - 2(77)cos(133 degrees)
BD^2 = 170 - 154cos(133 degrees)
BD ≈ 9.07 lb (rounded to two decimal places)
Therefore,
The magnitude of the resultant force is approximately 9.07 lb.
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