The range for this situation represents all possible values of the cost of filling the gas tank in dollars.
Explanation:The range for this situation represents the set of all possible outputs of the function, which in this case is the cost of filling the gas tank.
Since the equation given is p(g) = 3.5g, the range would be all possible values of p, the cost of filling the gas tank.
The range would depend on the values of g, the amount of gas in gallons, that you input into the equation.
For example, if you fill the tank with 1 gallon of gas, the cost would be p(1) = 3.5 * 1 = $3.50.
If you fill the tank with 3 gallons of gas, the cost would be p(3) = 3.5 * 3 = $10.50.
Therefore, the range for this situation would be all values of p, the cost, that can be obtained by inputting different values of g, the amount of gas in gallons, into the equation p(g) = 3.5g.
The range for this situation is from $0 (empty tank) to $42 (full tank). The cost can be any value in this range depending on the number of gallons pumped into the tank.
In this context, the function [tex]\( p(g) = 3.5g \)[/tex] represents the cost p of filling the gas tank with g gallons of gas. The range of the function is the set of all possible values for the cost.
Since the cost is directly proportional to the number of gallons, we can evaluate the function for the minimum and maximum values of g . The minimum value of g is 0 gallons (empty tank), and the maximum value is 12 gallons (full tank).
1. For g = 0 , [tex]\( p(0) = 3.5 \times 0 = 0 \)[/tex]. So, the minimum cost is $0.
2. For g = 12 , [tex]\( p(12) = 3.5 \times 12 = 42 \)[/tex]. So, the maximum cost is $42.
Therefore, the range for this situation is from $0 (empty tank) to $42 (full tank). The cost can be any value in this range depending on the number of gallons pumped into the tank.
Express the polynomial x2 − x4 + 2x2 in standard form and then classify it.
Answer:
-x⁴ + 3x² is the standard form, and this is a quartic binomial.
Step-by-step explanation:
We look to see if there are any like terms first. x² and 2x² are like terms; they combine to make 3x². So this polynomial really only has two terms when simplified.
The standard form of a polynomial has all of its terms in decreasing order of degree.
-x⁴ ⇒ degree 4
3x² ⇒ degree 2
Therefore, standard form is
-x⁴ + 3x²
The degree of this polynomial is the degree of the highest degree term, which is 4. A degree 4 polynomial is called a quartic polynomial.There are two terms, so we can further classify this as a binomial.
Therefore, the answer is quartic binomial
Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary.
To round the sum of a sequence properly, consider the precision of the terms given. For example, an answer of 921.996 from a calculator should be rounded to 922.00, aligning with the hundredth place of the term 13.77 as the most precise figure. Apply appropriate rounding rules such as rounding up if the next digit is greater than 5.
Explanation:When calculating the sum of a sequence and needing to round the answer to a specific decimal place, we must pay close attention to the significant figures and rounding rules.
For instance, if a calculator gives an answer of 921.996, we should round to the nearest hundredth.
This is because the last significant figure in the given sequence's general term (for example, 13.77) is in the hundredth place.
Following the rule of rounding, if the first digit to be dropped is greater than 5, we round up.
Therefore, the answer would be rounded to 922.00.
Let's consider other examples:
For the calculation resulting in 119.902, since we're limiting it to the tenths place, we round down to 119.9.
For 201.867, rounding to the hundredth place gives us 201.87.
When rounding 2,085.5688 to five significant figures, we get 2,085.6.
For a quick intuitive check, recall that one eighth of 1,000 is 125, a simple multiplication by a reciprocal number without doing long division.
In summary, always align your rounding method to the precision indicated by the sequence terms or the specific requirements of the question.
Research scientists need a certain type of bacteria to conduct an experiment. There are 2,500 bacteria in a certain culture. The culture grows at a rate of 25% daily. The scientists needs at least 10,000 bacteria to conduct an experiment. What is the least number of days they need to wait for the bacteria culture to reach a quantity of 10,000? (Hint: use a guess-and-check method to determine the lowest number of days that satisfy the requirement.)
Answer:
7 days
Step-by-step explanation:
At 25% per day, it will take approximately 3 days to double the population, so approximately 6 days for the population to quadruple. Checking that number, we find it is not quite enough for the experiment, so another day is required.
"Guess and check" as a method of solution works especially well if you have an automated checker to evaluate your guess. A graphing calculator or spreadsheet can work well for this.
_____
We guess 3 days as the doubling time using the "rule of 72" that says the product of percentage and doubling time is about 72. That is, 72/25 ≈ 3. (This is only a very rough approximation of doubling time, best for rates near 8%.)
The rabbit population in a small zoo starts with 150 rabbits. The rabbit population is decreasing at a rate of 15% each week. Which of the following represents the total number of fish, F(x), after x number of weeks. (4.2)
a. F(x) = 150( .15)^x
b. F(x) = 150 (1.15)^x
c. F(x) = .85 (150)^x
d. F(x) = 150 (.85)^x
e. None of the above.
Answer:
e. none of the above
Step-by-step explanation:
I had this question as well and if you look closely, the question describes the function in terms of rabbits, when the actual question describes fish. I believe that because the question is asking for fish when only information on rabbits has been given, the only logical answer would be e. none of the above...
Final answer:
The correct formula representing the total number of rabbits after x weeks, with a starting population of 150 and a decrease of 15% per week, is F(x) = 150 (0.85)ˣ. The correct option is d.
Explanation:
The rabbit population in a small zoo starts with 150 rabbits and decreases at a rate of 15% each week. To represent the total number of rabbits, F(x), after x number of weeks, we need to find the correct formula. A decrease of 15% per week is the same as the population being at 85% of the previous week's population (100% - 15% = 85%). So, the correct formula would be the initial population multiplied by the weekly percentage to the power of the number of weeks. Therefore, the correct formula is F(x) = 150 (0.85)ˣ, which corresponds to option d.
what is the area of a triangle with vertices at (-3 3) (-3,2) and (1,2)?
How many combinations of 7 candidates can fill 3 vacancies on a city council?
Answer:
35 combinations
Step-by-step explanation:
You have to use the formula for finding combinations in probability. It looks like this:
₇C₃ = [tex]\frac{7!}{3!(7-3)!}[/tex]
so that gives you
₇C₃ = [tex]\frac{7*6*5*4!}{3*2*1*4!}[/tex]
The 4 factorials cancel each other out, and when you do the math, you get 210/6. That divides evenly into 35. So there are 35 combinations.
Adelia drove from her house to Townsville one evening. Her distance was 180 miles. She left home at 6:27 and was at townsville at 6:42 what was her speed
Answer: 720 mph or 12 miles a minute
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
(I actually have the problem in front of me, and I think you switched the minute and hour hands on the clock)
Adel
left at 5:30 and arrived at 8:30. That’s 3 hours, which is 180 minutes. 180/180 = 1 mile per minute
60 minutes in an hour
60*1 = 60 mph
suppose f(x)=x^2-2 find the graph of f(1/2x)
Answer:
graph g(x)=1/4 x^2 - 2
Step-by-step explanation:
You are to replace x with (1/2x) in the expression x^2-2
So you have (1/2x)^2-2
1/4 x^2-2
Graph some points for g(x)=1/4 x^2-2
The vertex is (0,-2) and the parabola is open up.
I would graph 2 more points besides the vertex
x | g(x) ordered pairs to graph
----------- (-1,-1.75) and (0,-2) and (1,-1.75)
-1 -1.75
0 -2
1 -1.75
Comment has been deleted
A man is walking along a straight road. He notices the top of a tower. Between the ground where he is standing and the top of the tower, there is a 25 degree angle. If the height of the tower is h = 8m, then what is the distance of the man from the tower
Answer:
17.2 m
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you the relationship between the adjacent side of a right triangle and the opposite side is given by ...
Tan = Opposite/Adjacent
Filling in the given information, we have ...
tan(25°) = (8 m)/distance
distance = (8 m)/tan(25°) ≈ 17.156 m
The man is about 17.2 meters from the tower.
Final answer:
The distance of the man from the tower can be found by dividing the height of the tower (8m) by the tangent of the 25-degree angle, using trigonometry.
Explanation:
The distance of the man from the tower is determined using trigonometry, where we have a right-angled triangle with the tower's height as the opposite side and the distance of the man from the tower as the adjacent side to the 25-degree angle.
To find the adjacent side (the distance from the man to the tower), we can use the trigonometric function tangent, which relates the opposite side to the adjacent side in a right-angled triangle.
The formula is:
tangent(25 degrees) = opposite / adjacent
Plugging in the value of the tower's height:
tangent(25 degrees) = 8m / distance
Solving for the distance:
distance = 8m / tangent(25 degrees)
When probability is not found by considering all possible outcomes, but by testing and experimentation, it is called _____ probability.
Answer:
Step-by-step explanation:
Observational probability
A missile is launched from the ground. Its height,h(x) can be represented by a qyadratic function in terms of time, x, in seconds after 1 second the missile is 103 feet in the air; after 2 seconds it is 192 feet in the air. Find the height in feet of the missile after 5 seconds in the air
Answer:
375 ft
Step-by-step explanation:
The increase in height in the 1st second is 103 ft. In the 2nd second, it is 192-103 = 89 ft, a decrease of 14 ft. In the next three seconds, the increases in height can be expected to be ...
89 -14 = 75 ft
75 -14 = 61 ft
61 -14 = 47 ft
for a total increase in height over those 3 seconds of ...
75 + 61 + 47 = 183 ft
Then the height after 5 seconds in the air is ...
192 ft + 183 ft = 375 ft
_____
You can model the height function with the quadratic equation ...
h(t) = at^2 +bt
We need to find the values of "a" and "b", which we can do by substituting the given data point values. The given data is ...
h(1) = a + b = 103
h(2) = 4a + 2b = 192
Subtracting twice the first equation from the second, we get
(4a +2b) -2(a +b) = (192) -2(103)
2a = -14 . . . . . simplify
a = -7 . . . . . . . divide by 2
b = 103 -a = 110 . . . . find b using the first equation
Then the quadratic model of height is ...
h(t) = -7t^2 +110t
and the height at 5 seconds is ...
h(5) = -7·25 +110·5 = 375 . . . feet
The perimeter of a rectangular garden is 64 centimeters. The length of the garden is three times the width. Find the length
and the width
Answer:
width 8 centimeters
length 24 centimeters
Step-by-step explanation:
L=3W : equation a .
W=64/xW : equation b .
x=2L+2W .
=2(3W)+2W .
x=8W .
Answer:
Length = 24 cm
and, Width = 8 cm
Step-by-step explanation:
It is given that,
Length = 3 × (width)
⇒ L = 3W → (1)
Also, since perimeter = 64 cm
And perimeter of rectangular garden = 2(L + W) = 64
From equation (1)
2(3W + W) = 64
2 × 4W = 64
⇒ 8W = 64
⇒ W = 8 cm
Putting value in equation (1)
L = 3 × 8 = 24 cm
thus, Length = 24 cm
and, Width = 8 cm
Help! the file is attached
Answer:
924/5 ft/s369.6 ftStep-by-step explanation:
126 mi/h = (126 mi)/(1 h)·(5280 ft)/(1 mi)·(1 h)/(3600 s) = (126·5280/3600) ft/s
126 mi/h = 184.8 ft/s = 924/5 ft/s
__
In 2 seconds, the parachutist falls ...
(184.8 ft/s)·(2 s) = 369.6 ft
What value of z should we use when making a 98% confidence interval for p? 1) 2.33 2)1.75 3)It's impossible to make a 98% CI 4) 2.88
Answer: Option 1) 2.33
Step-by-step explanation:
For the 98% confidence interval we have that the area between 0 and the z score is equal to:
98% corresponds to 0.98
then the area between 0 and z is half of that:
a = 0.98/2 = 0.490
Now you can search in a table, and you will find that the z-score for this is z = 2.326
So the correct answer is 1) 2.33
where the result is rounded up.
The value of z we should use when making a 98% confidence interval for p is mathematically given as
x= 2.33
Option A
The value of z we should use when making a 98% confidence interval
Generally, we solve for
1/2* 0.98 = 0.49
Using the Normal curve table we determine that the nearest value 0.4901 and its z value is 2.33
Option A
For more information on Arithmetic
https://brainly.com/question/22568180
Solve using elimination PLEASE I NEED HELP!!! IT WOULD REALLY MEAN A LOT IF ANYONE CAN ANSWER THIS! 16 POINTS!!!
2x+4y=1
x-4y=5
Answer:
(x, y) = (2, -3/4)
Step-by-step explanation:
The point of the "elimination" technique is to combine the equations in a way that eliminates one of the variables. Sometimes this involves multiplying one or both of the equations by constants before you add those results together. In any event, the first step is to look at the coefficients of the variable terms to see if there is a simple combination of them that will result in zero.
The y terms have coefficients that are opposites of each other (4, -4), so you can simply add the two equations to eliminate y as a variable.
(2x +4y) +(x -4y) = (1) +(5)
3x = 6 . . . . . simplify
x = 2 . . . . . . divide by 3
Now, you find y by substituting this value into one of the equations. I would choose the equation with the positive y-coefficient:
2(2) +4y = 1
4y = -3 . . . . . . subtract 4
y = -3/4
Then the solution is ...
(x, y) = (2, -3/4)
_____
A graphing calculator confirms this solution.
You watch a roulette wheel spin 8 consecutive times and the ball lands on a red slot each time. what is the probability that the ball will land on a red slot on the next spin?
Answer:
0.5
Step-by-step explanation:
A roulette wheel is half red and half black. Each spin is independent: past spins don't change the probability of future spins. So even if you got 8 reds in a row, the probability of the next spin being red is still 50/50.
Arlo invested $4000 in an account that earns 5.5% interest, compounded annually. The formula for compound interest is A(t)=P(1+i)^t. How much did Arlo have in the account after 4 years?
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.055}{1}\right)^{1\cdot 4}\implies A=4000(1.055)^4\implies A\approx 4955.2986[/tex]
Answer:
$ 4955.30 ( approx )
Step-by-step explanation:
The formula for compound interest is,
[tex] A(t)=P(1+i)^t[/tex]
Where, P is the principal amount,
i is the rate per period,
t is the number of periods,
Here, P = $ 4000,
i = 5.5% = 0.055
t = 4 years,
By substituting the values,
The amount in the account after 4 years would be,
[tex]A=4000(1+0.055)^4=4000(1.055)^4=4955.2986025\approx \$4955.30[/tex]
Use the figure to answer the questions
a. Explain why the triangles are similar
Geometry - Shaping Sheet
Triangle ______ and Triangle ______ are similar by the __________ postulate. This postulate works because __ (explain your reasoning here) ________.
*Use this format to appropriately write your answer below this box.
b. Find the value of x
Answer:
A. EAB and EDC by AAA because congruent corresponding angles lead to similar triangles regardless of side length. This postulate works because the parallel lines cause angle a and angle d to be congruent as well as angle b being congruent to angle c, and vertical angle e is congruent.
Step-by-step explanation:
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer: The slope of the line is: [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The slope can be calculated with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
You need to choose two points of the line. You can pick the point (6,2) and the point (-6,-6)
You can identify that:
[tex]y_2=-6\\y_1=2\\x_2=-6\\x_1=6[/tex]
Now, you must substitute these values into the formula:
[tex]m=\frac{-6-2}{-6-6}[/tex]
With this procedure you get that the the slope of the line on the graph is:
[tex]m=\frac{-8}{-12}[/tex]
[tex]m=\frac{2}{3}[/tex]
4. Divide –50m3n5 by –5m2n2.
A. 10mn3
B. –45m5n7
C. –10mn3
D. 45m5n7
Answer:
A. 10mn³
Step-by-step explanation:
To divide numbers in power form but to the same base, we simply subtract the powers and then divide the coefficients of the the bases.
-50m³n⁵ /-5m²n²
=10m⁽³⁻²⁾ n⁽⁵⁻²⁾
=10mn³
A negative number divided by a negative number = a positive number.
Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution? v +4 = 8 – v v +4 = 8 4 + v = 8 – v 2v + 4 = 8
v + 4 + v = 8
The first thing I'd do is add up those two vs:
2v + 4 = 8
Answer: last choice, 2v + 4 = 8
Answer:
d. 2v + 4 = 8
Step-by-step explanation: just took the test
Is it true that since sin^2x + cos^2x = 1, then sin(x) + cos(x) = 1? Explain your answer.
Answer:
No it is not true because plugging in something like x = pi/4 radians (equivalent to 45 degrees) leads to the left side not being equal to 1. The left side will simplify to sqrt(2). So the equation is not true when x = pi/4 radians. There are infinitely other counter examples to use
Need help with a math question
Answer:
There are 10 possible ways the student can schedule the three classes
Step-by-step explanation:
The college student is choosing 3 classes to take during the first, second, and third semester from 5 electives.
Therefore, the student is choosing 3 items from a total of 5 and the order is not of key concern here. This is thus a combination problem;
5C3 = 10
read as 5 choose 3
The above mathematical operation can be performed using any modern calculator.
Find four solutions of the given function. Write the solutions as ordered pairs.
4x – y = 4
The four solutions to the function 4x - y = 4 are determined by selecting different x values and calculating the corresponding y values, resulting in the ordered pairs (0, -4), (1, 0), (2, 4), and (3, 8).
Explanation:To find four solutions to the function 4x – y = 4, we need to choose four different values for x and compute the corresponding y values.
For example, let's choose x = 0, x = 1, x = 2, and x = 3. Substituting these values into the equation:
For x = 0: 4 * 0 - y = 4, so y = -4 For x = 1: 4 * 1 - y = 4, so y = 0 For x = 2: 4 * 2 - y = 4, so y = 4 For x = 3: 4 * 3 - y = 4, so y = 8
So the four solutions (order pairs) are (0, -4), (1, 0), (2, 4), and (3, 8).
Learn more about Finding solutions here:https://brainly.com/question/33750042
#SPJ2
To find solutions for the given equation 4x - y = 4, pick x values and plug them into the equation to solve for y, resulting in ordered pairs like (0, -4) and (1, 0).
Given equation: 4x - y = 4
Choose x values and plug them into the equation to solve for y.
Write the solutions as ordered pairs (x, y).
Four solutions are (0, -4), (1, 0), (2, 4), and (3, 8).
I need help
You find 20 books that you checked out from the library as you are cleaning your room. You need to take 4 books back to the library, and you want to set them aside in a pile on your desk. Â
How many ways can 4Â of the 20Â books be arranged in a pile?
Answer:
the answer is 20P4 = 4845
Step-by-step explanation:
Answer:
There are 20 ways to pick the first book, 19 ways for the second
Step-by-step explanation:
If order of the 4 books does not matter then
₂₀C₄ = 20! / (20-4)!4! = 20!/(16!*4!) = 4845 ways
Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv 6 \pmod{7}. \end{align*}
4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.
We construct a number [tex]x[/tex] such that taking it mod 4, 5, and 7 leaves the desired remainders:
[tex]x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6[/tex]
Taken mod 4, the last two terms vanish and we have[tex]x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4[/tex]
so we multiply the first term by 3.
Taken mod 5, the first and last terms vanish and we have[tex]x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5[/tex]
so we multiply the second term by 2.
Taken mod 7, the first two terms vanish and we have[tex]x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7[/tex]
so we multiply the last term by 7.
Now,
[tex]x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147[/tex]
By the CRT, the system of congruences has a general solution
[tex]n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}[/tex]
or all integers [tex]27+140k[/tex], [tex]k\in\mathbb Z[/tex], the least (and positive) of which is 27.
The parabola x = y² - 9 opens:
a.)up
b.)down
c.) right
d.)left
Answer:
Right side towards positive x axis
Step-by-step explanation:
Let us see the basic rule to find the orientation of parabolas.
1. If power if x is 2 and y is 1 , the parabola opens up or down.
2. If the power of y is 2 and that of x is 1 , the parabola opens right or left.
3. If the coefficient of [tex]x^{2}[/tex] in case 1 is negative it opens downward
4. If the coefficient of [tex]y^{2}[/tex] in case 2 is negative , it opens left towards negative x axis.
Hence our equation is
[tex]x=y^2-9[/tex]
here is satisfies the case 2. hence it opens right or left . Also the coefficient of
[tex]y^{2}[/tex] is positive so it opens up to the right side , that is towards positive x axis.
the correct answer is c.) right.
The student's question pertains to the orientation of a parabola described by the equation x = y² - 9. In order to determine the direction in which the parabola opens, we observe the equation. The parabola relates y² to x, indicating that for every value of y, we have a corresponding value of x. Since y² is the variable being squared and x is by itself, the parabola is a sideways parabola. Furthermore, because there is no negative sign in front of the y² term, the parabola opens to the right of the coordinate system. Therefore, the correct answer is c.) right.
Which equation is equivalent to
log5x^3 - logx^2 = 2?
Answer:
the second option and x=20
Answer:
the second one and then x=20
Step-by-step explanation:
What he said. It's correct.
Find all solutions of the equation. leave answers in trigonometric form x^3-8=0 2cis
[tex]x^3-8=0[/tex]
[tex]x^3=8=8\mathrm{cis}\,0^\circ[/tex]
By DeMoivre's theorem, we have
[tex]x=8^{1/3}\mathrm{cis}\left(\dfrac{0^\circ+360^\circ k}3\right)[/tex]
with [tex]k=0,1,2[/tex]. Then we have three solutions,
[tex]x=2\mathrm{cis}\,0^\circ=2[/tex]
[tex]x=2\mathrm{cis}\,120^\circ[/tex]
[tex]x=2\mathrm{cis}\,240^\circ[/tex]
Solve log (7x + 7) = 1. Round to the nearest thousandth if necessary. 0.429 2.333 1.143 0.875
Step-by-step explanation:
log(7·x + 7) = 1
7·x + 7 = 10^1
7·x = 10 - 7
x = 3/7 = 0.4285714285
Answer:
0.429
Step-by-step explanation: