It is better to buy 1 liter of soda for $1 compare to 1 gallon of soda for $4 .
As given in the question,
1 liter of soda for $1 ____(1)
1 gallon of soda for $4
Relation between gallons and liters is given by:
1 gallon is equal to 3.785 liters
1 gallon of soda = $4
⇒ 3.785 liter = $4
⇒ 1 liter = $ ( 4 / 3.785 )
⇒ 1 liter = $ 1.056 _____(2)
From (1) and (2)
$1.056 > $1
It shows $1.056 is little bit higher than $1.
Therefore, it is better to buy 1 liter of soda for $1 compare to 1 gallon of soda for $4 .
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is it a compound interest problem, a saving annuity problem, a payout annuity problem, or a loan problem ?
a. Marcy received an inheritance of 20000, and invested it at 6% interest. She is going to use it for college, withdrawing money for tuition and expenses each quarter. How much can she take out each quarter if she has 3 years of school ?
1. The scenario represents a payout annuity.
2. Marcy can withdraw $1,833.60 per quarter until after 3 years when the inheritance will be exhausted.
What is a periodic withdrawal of a sum lump?A periodic withdrawal is the opposite of a periodic payment.
In a periodic withdrawal, the investor withdraws a constant amount from the investment that earns interest until it is exhausted.
A periodic withdrawal is the same as a payout annuity, which involves periodic receipts from the invested capital.
Using an online finance calculator, we can compute the quarterly withdrawals as follows:
N (# of periods) = 12 quarters (3 x 4)
I/Y (Interest per year) = 6%
PV (Present Value) = $20,000
FV (Future Value) = $0
Results:
Withdrawals = $-1,833.60
Sum of all periodic payments = $-22,003.20
Total Interest $2,003.20
Thus, in this payout annuity, Marcy can withdraw $1,833.60 quarterly for 3 years.
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The point (-13, 24) is on the graph of y = f(x). Find the corresponding point on the graph of y= g(x), where g(x) = 1/4f(x)
Answer:
(−12,2)
Step-by-step explanation:
1:
Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value
(4) and divide it by 2 to get 2
.
Therefore, the new point is
(−12,2)
2:
Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value
(−12) to get −10
.
Therefore, the new point is
(-10,4)
3:
Making the input of the function negative will multiply every x-value by
−
1
. To get the new point, we will take the x-value
(−12) and multiply it by −1 to get 12.
Therefore, the new point is
(12,4)
4:
Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value
(−12) by 4 to get −3
.
Therefore, the new point is
(−3,4)
5:
Multiplying the whole function by
4
increases all y-values by a factor of
4
, so the new y-value will be
4
times the original value
(4), or 16.
Therefore, the new point is
(−12,16)
6:
Multiplying the whole function by
−1
also multiplies every y-value by
−1
, so the new y-value will be
−1
times the original value
(4), or −4.
Therefore, the new point is
(−12,−4)
IS this a function or no (ALGEBRA
We can see that the same input is mapped into two different outputs, so this is not a function.
Is this a function?A relation maps elements called inputs into another elements called outputs.
Such that a relation is a function if each input is mapped into only one output.
The notation used is (input, output).
So, here we can see the points:
(4, 12) and (4, 15).
The input 4 is being mapped into two different outputs, thus, this is not a function.
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Please help, it's due today!
Answer:
Output= -31
Step-by-step explanation:
f(x)= -3x²+8x-3
Therefore, f(-2)= -3(-2)²+8(-2)-3
= -3×4 -16 -3
= -12-16-3
= -31
please I need to know number 2 :)
Answer: [tex]-4 < m \le -3[/tex]
=========================================================
Reason:
If m = -4, then f(x) = m becomes f(x) = -4. This yields the single solution x = -4
How do we get this solution? Start at -4 on the y axis. Move horizontally until reaching the curve. You should arrive at (-4,-4) which is the lowest point of this curve. Then move upward until reaching the x axis to arrive at x = -4
All of this says that the input x = -4 leads to the output y = f(x) = -4
---------------
We've gone over m = -4 leading to one solution, so that's out of the question since we want two solutions.
But if m = -3 for instance, then notice how tracing a horizontal line to the curve arrives at two locations instead of one. We arrive at x = -2 and x = -5 as the solutions to f(x) = -3
All of these solutions mentioned are negative which fits the criteria we're after. If m is in the interval from -4 to -3, excluding -4 but including -3, then we'll have f(x) = m with two negative solutions for x.
In which quadrant of the coordinate graph does point F
ie?
• Quadrant I
o Quadrant II
• Quadrant III
O Quadrant IV
Answer:
Quadrant IV .
Step-by-step explanation:
I hope it will be helpful for you.
If 3x. (6x) ≤ 9, which of the following inequalities must be true?
Answer:
if x=0than 3×0×(6×0)_< 9
Evaluate the integral.
[tex]\pi\int\limits^{\frac{3\pi}{4}}_{\frac{\pi}{6}} {sin^4x+4sin^2x} \, dx[/tex]
By using trigonometric formulas and integration rules, we conclude that the integral is approximately equal to - 7.764 units.
How to determine the value of a definite integral
In this problem we must determine the solution to a definite integral of trigonometric equations, which requires the use of trigonometric formula and integration rules to be found. The integral can be simplified by using the following formulas:
sin⁴ x = (1 / 8) · (3 - 4 · cos 2x + cos 4x)
sin² x = (1 /2) · (1 - cos 2x)
Then, the integral is simplified into this form:
[tex]I = \pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{4} x \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{2} x \,dx[/tex]
[tex]I = \frac{\pi}{8} \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (3 - 4\cdot \cos 2x + \cos 4x) \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (1 - \cos 2x) \,dx[/tex]
[tex]I = \frac{3\pi}{8}\cdot x - \frac{\pi}{4} \cdot \sin 2x + \frac {\pi}{32}\cdot \sin 4x - 4\pi \cdot x - 2\pi\cdot \sin 2x[/tex], for x ∈ [π / 6, 3π / 4]
And the definite integral is:
I = 2.159 + 1.466 - 0.085 - 23.028 + 11.724
I = - 7.764
The definite integral of f(x) = sin⁴ x + 4 · sin² x for x ∈ [π / 6, 3π / 4] is approximately equal to - 7.764.
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which of thr following options is an equivalent function too f(x)=2(5)2x
Although part of your question is missing, you might be referring to this full question: Which of the following options is an equivalent function to f(x) = 2(5)^2x? choices:
f(x) = 50^x
f(x) = 100^x
f(x) = 2(25)^x
f(x) = 4(25)^x
The equivalent function too expression is f(x)= 2(25)ˣ. Thus option c is correct.
The expression of function f(x) given, f(x)=2(5)²ˣ.
Functions are said to be equal if they have same domain or codomain such that f(x) = g(x). Thus, the two functions are equal functions.
∴ The function after solving expression is,
f(x)= 2×(5²)ˣ
f(x)= 2×(25)ˣ
Hence, the correct equivalent function is f(x)= 2(25)ˣ.
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There are 12 F/A-18 aircraft, where: 3 are F/A-18A's 4 are F/A-18E's 5 are F/A-18F's If three of these twelve aircraft are selected at random, so that every possible selection is equally likely, what is the probability that all three of them will be F/A-18E's, rounded to two decimal places?
When three of these twelve aircraft are selected at random, the probability that all three of them will be F/A-18E's is 0.018.
How to calculate the probability?Based on the information given, there are are 12 F/A-18 aircraft, where: 3 are F/A-18A's 4 are F/A-18E's 5 are F/A-18F's. The total number of aircraft will be 12.
When three of these twelve aircraft are selected at random, so that every possible selection is equally likely, the probability that all three of them will be F/A-18E's will be:
= 4/12 × 3/11 × 2/10
It should be noted that this is without replacement that's why we have 10, 11 and 12 as the denominator.
= 4/12 × 3/11 × 2/10
= 1/3 × 3/11 × 1/5
= 3 /165
= 0.018
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Line 1: m = 4/5
Line 2: m = -5/4
Are the lines parallel, perpendicular, or neither?
neither
perpendicular
parallel
Prove the second property one pair of congruent legs is true (prove segment DA is congruent to CB)
Answer
he trapeziunm is an isosceles trapezoid since there are pairs of congruent base angles ADC and BCD
Lines AB and DC are the bases'
To proof that
[tex]\bar{AD}\cong\bar{BC}[/tex]WDraw perpendicular line segments from A to P and from B to Q which are perpendicular to line DC
∠APD =∠BQC (Right angle)
That is ∠D ≅ ∠C
Now the perpendiculars AP and BQ are congruent
By AAS Property, triangles APD and BQC are congruent and this implies that the hypotenuses AD and BC are congruent.
Therefore the legs AD and BC are congruent.
The following is the prime factorization of which composite number?
22.3².5
120
60
20
180
The prime factorization given as 2².3².5 is for the number D. 180.
What are prime numbers?It should be noted that prime numbers are numbers that can only be divided by itself and one. This include 2, 3, 5, 7, etc
A composite number is one that can be generated by multiplying two smaller positive numbers. It is a positive integer with at least one divisor other than 1 and itself. Prime factorization is defined as the process of determining a number's prime factors so that the original number is evenly divisible by these factors.
In this case, it should be noted that we are given the expression as 2². 3². 5. It simply means that we have to multiply them to get the original number.
This will be:
= 2² × 3² × 5
= 4 × 9 × 5
= 180
Therefore, the number is 180.
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Ela enjoys scuba diving. On one particular trip she was diving at a rate of 5 ½ ft per
minute. If Ela started at the surface, how far below the surface was she after 6 minutes?
(Hint: below sea level is a negative value)
Answer:
30 1/2
Step-by-step explanation:
_______ angles are used to relate the values returned by inverse trigonometric functions to angles larger than 90°.
A. Obtuse
B. Acute
C. Right
D. Complementary
Answer:
Acute
Step-by-step explanation:
Obtuse angles are angles that are larger than 90 but less than 180
Acute angles are angles that are less than 90 degrees
Right angles are angles that is exactly 90 degrees
Complementary angles are two angles whose sum is 90 degrees
Using this info, it seems the answer to this question is B. Acute because it says "the values returned by inverse to angles larger than 90" and since acute is the opposite of obtuse imma say B but im not too sure
An airport in a country that has an elevated occurance of terrorism profiles airline passengers and semi-randomly selects who will undergo additional screening. If one person is stoped, everyone they are traveling with is also stopped. Over the course of several months, the airport security stops 15% of passengers for this extra screening. On a certain day, 519 passengers go through security at this airport. Let the variable be the number of those people who are chosen for additional screening.
Is the number of passengers who are chosen for additional screening a binomial random variable? Select all that apply.
Yes. All four conditions are met.
No. There is not a fixed number of trials.
No. The trials cannot reasonably be assumed to be independent.
No. The outcomes cannot be described as only "success" and "failure."
No. The probability of success is not the same for each trial.
No. there is not a fixed number of trials. The correct option is B.
What is a binomial random variable?A variable with only two outcomes is said to be binary. Examples of binary categorical variables are sex (male/female) and having a tattoo (yes/no).
Each trial must be independent, meaning that it must have a defined number of trials and a constant success rate. Its probability needs to range from 0 to 1.
There are only two conceivable outcomes for each individual. They are either filtered or they are not. We are not interested in learning how many people were screened, though.
It is an inverse binomial, we want to know how many persons will be screened before 10, which is a binomial. Therefore, since there are an arbitrary number of trials, this is not a binomial equation, and option B provides the solution.
Therefore, there is not a fixed number of trials. The correct option is B.
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Which values are solutions to the inequality below? √x≤=7 check all that apply: A.48 B. 14 C. 51 D. -15 E. 2 F. NO SOLUTION
The correct options are (A) and (B).
Because
[tex]\begin{gathered} \sqrt[]{48}<7 \\ \text{and } \\ \sqrt[]{14}<7 \end{gathered}[/tex]Simplify the expression.
Answer:
Step-by-step explanation:
[tex]m^{a}[/tex] × [tex]m^{b}[/tex] = [tex]m^{a+b}[/tex]
[tex](m^{a}) ^{b}[/tex] = [tex]m^{ab}[/tex]
P(6 or 7 or diamond or club) =
Answer:
The answer is 17/52. Explanation: The number of diamond cards is 13, and the number of '6' cards is 4 Picking one diamond out of 13 is 13C1
Step-by-step explanation:
14) Solve. Which number will be an ordered pair for the solution of y = 6x + 1; (2,__) a) 13 b) 11 c) 8 d) 3
14) y = 6x + 1
( 2, y)
if x = 2 as stated in the coordinate, then y = 6(2) + 1 = 12 + 1 = 13
y =13
The ordered
Write your answer as a fraction or mixed number in simplest form. 4 6/7 ÷ 9
The value of the given expression in simplest form is 34/63.
Mixed fraction
It is a form of a fraction which is defined as the ones having a fraction and a whole number.
Example: 2(1/7), where 2 is a whole number and 1/7 is a fraction.
To convert 2(1/7) into improper fraction , we will multiply 7 and 2 and then add 1 to it to get the numerator part and 7 will be the denominator of the fraction that is 15/7.
Given expression:
4(6/7) ÷ 9
We have to find the value of the given expression in simplest form.
We can write the mixed fraction 4(6/7) as 34/7
(34/7) ÷ 9
(34/7)*(1/9) = (34*1)/(7*9) = 34/63
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Help PLEASE thats the question if you have the answer type below
The equation that represent the data in the table shown is y = -2x + 3.
How to know if the system is linear?Linear systems are sets of equations associated with each other and that have two or more variables. In linear systems, only linear equations are entered, that is, expressions where the greatest exponent of the unknowns is equal to 1.
A linear equation is in the form:
y = mx + b
Where:
m is the slope b is the y interceptFrom the table, using the point (0, 3) and (1, 1):
y - 3 = [(1 - 3)/(1 - 0)](x - 0)
y - 3 = -2xy = -2x + 3
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A school is arranging chairs in rows for an assembly. $11$ chairs make a complete row, and right now there are $110$ chairs total. The school wants to have as few empty seats as possible, but all rows of chairs must be complete. If $70$ students will attend the assembly, how many chairs should be removed?
Answer:
40
Step-by-step explanation:
Write the equation of the line in point-slope form that passes through the given point with the given slope. (,)open 1 comma 5 close; =−m equals negative 3
The equation of the line in point slope form that passes through (1,5) and slope = -3 , is y = -3x+6 .
The equation of line in point slope form passing through the points (x₁,y₁) and slope =m is given by the formula
(y-y₁)=m(x-x₁)
In the question ,
it is given that
the line passes through the point (1,5) and has a slope m = -3.
so the values become x₁=1 and y₁=5 and m = -3
Substituting the values in the formula for equation of line , we get
(y-5)=(-3)(x-1)
y-5= -3x + 1
y = -3x + 1 + 5
y = -3x+6
Therefore , the equation of the line in point slope form that passes through (1,5) and slope = -3 , is y = -3x+6 .
The given question is incomplete , the complete question is
Write the equation of the line in point-slope form that passes through the point (1,5) with slope = -3.
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3. Disney on Ice is traveling to Chicago to perform. The revenue from their ticketsales is a function of the ticket price, x, and can be modeled with (x - 8)(450 – 3x).What are the ticket prices at which Disney on Ice would make no money at all?Type Here: They would earn no money when the function is equal oExplain or show your reasoning.Type Here: (x-3)(450-3x) = 0
the price of the ticket which Disney on ice would make no money at all is:
[tex](x-8)(450-3x)=0[/tex]and here, are two posible solutions:
[tex]\begin{gathered} 1)x-8=0 \\ 2)450-3x=0 \end{gathered}[/tex]for the first one 1)
[tex]x=8[/tex]for the second one 2)
[tex]\begin{gathered} 450=3x \\ \frac{450}{3}=x \\ 150=x \end{gathered}[/tex]and in this problem the realistic answer is the first one, so the solution is $8 dollars
1. Select all the conditions for which it is possible to construct a triangle.
A 60°, 80°, and 80°
B) 4cm, 5cm, and 6CM
C)4 cm, 5 cm, and 15 cm
D)4cm, 5 cm, and 50°
E)30°, 60°, and 3 cm
The conditions for which it is possible to construct triangles are:
(D) 4cm, 5 cm, and 50°.(E) 30°, 60°, and 3 cm.What are triangles?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Three straight sides and three angles make up the two-dimensional shape of a triangle. Three sides, three vertices, and three angles make up a triangle. A triangle's three interior angles are always added up to 180 degrees. A triangle's two longest sides added together are always longer than its third side. The six different kinds of triangles are right, obtuse, acute, equilateral, scalene, and isosceles.So, the condition for which it is possible to construct a triangle:
(A) 60°, 80°, and 80°:
Not possible as the sum of angles is greater than 180°.(B) 4cm, 5cm, and 6cm:
Not possible as the square of the 2 shorter sides is greater than the square of the longest side.(C) 4 cm, 5 cm, and 15 cm:
Not possible as the square of the 2 shorter sides is greater than the square of the longest side.(D) 4cm, 5 cm, and 50°:
Yes, it is possible to construct a triangle.(E) 30°, 60°, and 3 cm:
Yes, it is possible to construct a triangle.
Therefore, the conditions for which it is possible to construct triangles are:
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What is the slope of the line perpendicular to the line represented by the equation 2x+2y=-12
The slope of the line perpendicular to the line given by equation 2x+2y=-12 is found as 1.
What is the definition of line slope?The slope of a line measures its steepness as well as direction.The slope of a line is defined as the change throughout y coordinate in relation to the transitions in x coordinate.The net change in y coordinates is Δy, while the net change in x coordinates is Δx.So m represents the change in y coordinate in relation to a shift in x coordinate.The slope can be calculated using the following formula:
m = Δy/Δx
Where, m is the slope.
The equation of the line is; 2x+2y=-12
Write the equation in slope-intercept form.
2x + 2y = -12
Divide by 2.
x + y = -6
y = -x - 6
Slope m₁ = -1 and y-intercept = -6.
As, both line are perpendicular.
Thus,
m₁ x m₂ = -1
m₂ = -1/m₁
Put the value.
m₂ = -1/(-1)
m₂ = 1
The slope of the perpendicular line is found as 1.
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There are ten options, but I cannot send all ten at once. Please draw out the correct graph!
To answer this question we need to remember that:
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]then:
[tex]\begin{gathered} \sec \theta=-\frac{13}{5} \\ \frac{1}{\cos \theta}=-\frac{13}{5} \\ \cos \theta=-\frac{5}{13} \\ \theta=\cos ^{-1}(-\frac{5}{13}) \\ \theta=112.62 \end{gathered}[/tex]There's only one angle that gives this result that it is real. Therefore the answer is 112.62
Which equation represents the proportional relationship displayed in the table?
x: 4, 9, 11, 14
y: 32, 72, 88, 112
A. y = 8x
B. y = 8x + 4
C. y = 1/8x
Answer:
A. y = 8x
Step-by-step explanation:
y = 8x
From first term
32 = 8(4)
32=32
Correct
The price of an item has been reduced by 60%. The original price was $65. What is the price of the item now?
Answer:
$26
Step-by-step explanation:
65 x 60% = 39
65 - 39 = 26