A store is offering a clearance sale on soda it costs 3.20 for a packk of 8 cans or a single can can be bought for 0.50
The question revolves around determining whether it's more economical to purchase soda in a pack or individually at a clearance sale. The provided example further illustrates the price elasticity of demand using the sale of diet cola as an illustration.
Explanation:The question concerns the cost comparison between buying individual cans of soda versus buying them in a pack during a clearance sale. With a pack of 8 cans costing $3.20, the price per can in a pack is $0.40. On the other hand, a single can costs $0.50. Looking at these prices and comparing them to the provided reference information, buying soda by the pack falls into the '50-99 cents per pack' range, indicating that it's more cost-effective compared to buying soda cans individually for $0.50 each.
Additionally, the example involving diet cola and its price changes introduces the concept of price elasticity of demand, which measures how the quantity demanded of a good responds to a change in price. The given statistics demonstrate a direct relationship between the price of diet cola and the number of cans sold: a rise in price reduces sales, leading to less total revenue, indicating that the demand for diet cola is price elastic.
Please show work; i will give brainliest for quickest and corect answer
Solve the equation x^{2}+4x-16=0
Answer:
x=2
Step-by-step explanation:
x^2 + 4x - 16 = 0
I'm using the quadratic formula to solve this equation.
A = 1
B = 4
C = -16
x = -b +- [tex]\sqrt{b^2 - 4ac}[/tex]
over 2a
Plug it in:
x= -4 +- [tex]\sqrt{4^2 -4(-16)}[/tex] over 2
x= -4 +- [tex]\sqrt{16+64[/tex] over 2
x = -4 +-[tex]\sqrt{80}[/tex] over 2
x = -4 +- 4[tex]\sqrt{5[/tex]
Divide by 2.
x = -2 +- 2[tex]\sqrt{5[/tex]
Therefore, x would be -2 + 2[tex]\sqrt{5}[/tex], -2 - 2[tex]\sqrt{5}[/tex]
Convert to decimal form: 2.47213595, -6.47213595
Round it: 2.4714595 = 2.5 and -6.47213595 = -6.5
Please help me I don’t know how
Answer:
6 5/6
Step-by-step explanation:
8
- 1 1/6
We need to borrow from the 8
We will borrow 1 from the 8 and make it a 7. The 1 will be written in the form 6/6
7 6/6
- 1 1/6
-----------------
6 5/6
If the volume of the prism is 240 cubic inches, what is the base length?
A)
10 inches
12 inches
13 inches
D)15 inches
Without additional information about the height or area of the base of the prism, it is impossible to determine the base length from the volume alone.
Explanation:To determine the base length of a prism when the volume is known, one must have additional information about the prism, such as the area of the base or other dimensions. Since the question does not provide any information about the height or the area of the base, we cannot calculate the base length solely from the volume. Typically, the volume of a prism is calculated using the formula V = base area × height. Without knowing either the base area or the height of the prism in this question, we cannot find the base length. Thus, we cannot choose from the provided options (10 inches, 12 inches, 13 inches, 15 inches) without additional information about the prism.
2(x - 5) + 7 = x + 8 what is x represents
Answer: [tex]x=11[/tex]
Reorder the terms in parentheses
[tex]+(+2x-10)+7=x+8[/tex]
Remove unnecessary parentheses
[tex]+2x-10+7=+x+8[/tex]
Move all terms containing x to the left and all other terms to the right
[tex]+2x-1x=+8+10-7[/tex]
Simplify left and right side of the equation
[tex]+1x=+11[/tex]
divide both sides of the equation by 1 to get x
[tex]x=11[/tex]
What does statement that is not correct to use probability to describe an event.
A) the probability of seeing the Stars night is 0.70
B) the probability of going back to time is 0
C) The probability of having leftovers for dinner tonight is 35 percent
D) The probability of finding my keys is - 1/5
The incorrect statement is option D) The probability of finding my keys is - 1/5, as probabilities cannot be negative. Probabilities range between 0 and 1, and the calculation for combined probability of independent events involves multiplication, not addition.
The statement that is not correct to use probability to describe is option D) The probability of finding my keys is - 1/5. Probabilities range from 0 to 1 (or 0% to 100%), where 0 indicates impossibility and 1 indicates certainty. A negative probability does not make sense within this framework, so option D reflects a misunderstanding of how probabilities are represented.
The correct way to calculate the combined probability of two independent events is to multiply their individual probabilities. For example, to find P(A AND B) when dealing with independent events, you would calculate P(A) * P(B). Therefore, if P(A) = .2 and P(B) = .3, the correct answer for P(A AND B) would be .06, which corresponds to option D in the exercise provided.
It is also important to clarify misconceptions such as adding probabilities of non-mutually exclusive events. For instance, the fallacy that if there is a 60 percent chance of rain on one day and a 70 percent chance on another, then there is a 130 percent chance of rain over the weekend.
This is incorrect because probabilities cannot exceed 100%. Instead, you would evaluate the chances of rain differently depending on the independence or interdependence of the weather on those days.
choose 1 answer:
a. 11/27
b. 16/27
c. 1
d. 27/16
1A research firm finds that the average number of customers that are in Somerset Mall on a
Saturday varies sinusoidally with time. The mall is open from 9:00 am to 9:00 pm; the minimum
number of customers is at 9:00 am and 9:00 pm when there are zero customers. The maximum
number of customers is at 3:00 pm when there are 875 customers in the mall,
Answer: C(t) = -475.5*cos(t*pi/6) + 475.5
Step-by-step explanation:
We know that we have a sinusoidal relation, with a minimum at 9:00 am and at 9:00 pm.
If we define the 9:00 am as our t = 0, we have that the maximum, at 3:00pm, is at t = 6 hours.
and the other minimum, at 9:00pm, is at t = 12 hours.
Then we need to find a trigonometric function that has the minimum at t = 0, we can do this as:
-Cos(c*t)
when t = 0
-cos(0) = - 1
then we have a function:
C(t) = -A*cos(c*t) + B
where A, c and B are constants.
We know that at t = 0 we have 0 customers, and that at t = 6h we have 875 customers, that is the maximum.
then:
C(0) = 0 = -A + B
this means that A = B, then our function is:
C(0) = -A*cos(c*t) + A.
now, at t = 6h we have a maximum, this means that -A*cos(c*6h) = A
then:
C(6h) = A + A = 875
2A = 875
A = 875/2 = 437.5
and we also have that, if -cos(c*6) = 1
then cos(c*6) = -1
and we know that cos(pi) = -1
then c*6 = pi
c = pi/6
Then our function is
C(t) = -475.5*cos(t*pi/6) + 475.5
Final answer:
On average, one customer arrives every two minutes at Somerset Mall on a Saturday, which means it takes six minutes on average for three customers to arrive. This question applies trigonometry, algebra, and statistical concepts.
Explanation:
A research firm finds that the average number of customers in Somerset Mall on a Saturday varies sinusoidally with time. The question involves understanding sinusoidal functions, their applications, and basic statistical concepts related to customer arrival rates. The sinusoidal nature of customer arrivals is a practical application of trigonometry and algebra in solving real-world problems.
Part a: Average Minutes Between Arrivals
Given that 30 customers arrive per hour, to find the average time between successive arrivals, we divide the number of minutes in an hour by the number of arrivals: 60 minutes / 30 customers = 2 minutes. Therefore, on average, one customer arrives every two minutes.
Part b: Time for Three Customers to Arrive
Since one customer arrives every two minutes on average, for three customers to arrive, it would take 3 * 2 minutes = 6 minutes on average.
The model's assumption that customers arrive one at a time and at a constant rate throughout the day simplifies the real-life complexity of customer behavior and peak shopping times. This is a critical consideration in the practical application of mathematical models in business.
Sarah’s essential (fixed) expenses are $750 per month, her essential (flexible) expenses are $500 per month, and her non-essential expenses are $250 per month. Her 401-K retirement account has $6,000, her education savings account has $3,000, and her emergency fund savings account has $2,300. Sarah wants an emergency fund of 5 times monthly living expenses. How much more does Sarah need to save to have an adequate emergency fund?
a.
$1,450
b.
$5,200
c.
$0
d.
$950
Answer:
B. 5,200
Step-by-step explanation:
Sarah's essential (fixed) expenses = $750 per month
Her essential (flexible) expenses = $500 per month
Her non-essential expenses = $250 per month
Her total monthly living expenses = 750 + 500 + 250 = $1,500
Sarah wants an emergency fund of 5 times monthly living expenses.
1500 × 5 = $7,500
Currently she is having her emergency fund savings account is = $2,300
She needs to save more = 7,500 - 2,300 = $5,200
Sarah need to save more $5,200.
Sarah need to save $5,200 to have an adequate emergency fund.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Sarah's essential (fixed) expenses = $750 per month
Her essential (flexible) expenses = $500 per month
Her non-essential expenses = $250 per month
⇒ total monthly living expenses = 750 + 500 + 250 = $1,500
∵ Sarah wants an emergency fund of 5 times monthly living expenses.
∴ emergency fund = 1500 × 5 = $7,500
Currently she is having her emergency fund savings account = $2,300
Thus, Amount needs to be save = 7,500 - 2,300 = $5,200
Thus, Sarah need to save $5,200 to have an adequate emergency fund.
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Cards in a deck are numbered 1-4. You pick one card and keeps it. You pick a second card. The tree diagram shows you possible outcomes. What is the probability you picked a 1 and then a 2
A transformation named T maps XYZ to X'Y'Z'. The transformation shown is a reflection translation dilation
Answer:
Step-by-step explanation:
Where is the image
Which expression is equivalent to |a|≤3 ?
1. a ≤ –3 or a ≥ 3
2. a ≥ –3 and a ≤ 3
3. a ≥ –3 or a ≤ 3
4. a ≤ –3 and a ≥ 3
=====================================================
Explanation:
The rule is that if [tex]|a| \le k[/tex] for some positive number k, then it can be written as the compound inequality [tex]-k \le a \le k[/tex]. This is a shorthand way of writing the two inequalities [tex]a \ge -k \ \text{ and } \ a \le k[/tex] combined together.
note: [tex]-k \le a[/tex] is the same as [tex]a \ge -k[/tex]
From here, we replace k with 3
Therefore, [tex]|a| \le 3[/tex] turns into [tex]-3 \le a \le 3[/tex] which breaks down further to [tex]a \ge -3 \ \text{ and } \ a \le 3[/tex]
The keyword "and" is important as we can't pick one or the other. We must pick both [tex]a \ge -3[/tex] and also [tex]a \le 3[/tex]
Answer:
Choice 2.
Step-by-step explanation:
Given: △ABC with a2 + b2 = c2 and right △DEF constructed with legs a and b and hypotenuse n
Prove: △ABC is a right triangle.
Complete the missing parts of the paragraph proof.
Proof:
We are given a2 + b2 = c2 for △ABC and right
△DEF constructed with legs a and b and hypotenuse n. Since △DEF is a right triangle, we know that a2 + b2 = n2 because of the . By substitution, c2 = n2 Using the square root property and the principle root, we can take the square root of both sides to get
c = n. By , triangles ABC and DEF are congruent. Since it is given that
∠F is a right angle, then ∠ is also a right angle by CPCTC. Therefore, △ABC is a right triangle by
Answer:
Pythagorean Theorem
SSS
C
the definition of right triangle
Step-by-step explanation:
Filip decides to buy a muffin.
There is 1 chocolate, 2 blueberry and 3 lemon muffins.
If he picks one at random, what are the chances of him picking a blueberry muffin?
Answer in the form of a fraction in its simplest form.
Answer:
1/2
Step-by-step explanation:
Do I get brainliest?
Answer:
1/2
Step-by-step explanation:
A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4)
Which is the best approximate solution of the system of linear equations y = 1.5x – 1 and y = 1?
(0.33, 1)
(1.33, 1)
(1.83, 1)
(2.33, 1)
Answer:
Question 1. (2.2, -1.4)
Question 2. (1.33, 1)
Step-by-step explanation:
Equations for the given lines are
-----(1)
It is given that this line passes through two points (0, 2.5) and (2.2, 1.4).
------(2)
This equation passes through (0, -3) and (2.2, -1.4).
Now we have to find a common point through which these lines pass or solution of these equations.
From equations (1) and (2),
x =
x = 2.2
From equation (2),
y = -1.4
Therefore, solution of these equations is (2.2, -1.4).
Question 2.
The given equations are y = 1.5x - 1 and y = 1
From these equations,
1 = 1.5x - 1
1.5x = 2
x =
Therefore, the solution of the system of linear equations is (1.33, 1).
The correct approximate solution of the system of linear equations[tex]\( y = 1.5x - 1 \) and \( y = 1 \) is \( (1.33, 1) \).[/tex]
To find the solution, we need to set the two equations equal to each other since they both equal \( y \). This gives us the equation:
[tex]\[ 1.5x - 1 = 1 \][/tex]
Now, we solve for [tex]\( x \)[/tex]:
[tex]\[ 1.5x = 1 + 1 \][/tex]
[tex]\[ 1.5x = 2 \][/tex]
[tex]\[ x = \frac{2}{1.5} \][/tex]
[tex]\[ x = 1.\overline{3} \][/tex]
[tex]\[ x \approx 1.33 \][/tex]
Having found [tex]\( x \)[/tex], we can now find the corresponding [tex]\( y \)[/tex] value by substituting [tex]\( x \)[/tex] into either of the original equations. Since [tex]\( y = 1 \)[/tex] is given, we already know that [tex]\( y \)[/tex] is exactly 1. Therefore, the solution to the system is approximately [tex]\( (1.33, 1) \)[/tex].
to help local charity, Sam decides to run an advertisment where he gives away 10% of the days sales to the charity. If the store sells $8,564 on that day, Then how much will Sam give away ?
Answer:
856.4
Step-by-step explanation:
10% of 8564 =856.4
2x + 3y = 1200
3x + 2y = 1300
Based on the system of equations above, what is the
value of 5x+ 5y?
To find the value of 5x + 5y, you can solve the system of equations using the elimination method, and substitute the values of x and y into the expression.
Explanation:To find the value of 5x + 5y based on the system of equations:
2x + 3y = 1200
3x + 2y = 1300
we can solve the system by either substitution or elimination method. Let's use the elimination method:
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations the same. Subtract the second equation from the first equation to eliminate x. Solve for y. Substitute the value of y back into one of the original equations to solve for x. Once you have the values of x and y, substitute them into 5x + 5y and calculate the final value.
The value of 5x + 5y in this system of equations is 12500.
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The equation y= ax describes the graph of a line. If the value of a is positive,
What direction does the line go?
Answer:
Step-by-step explanation:
If the value a is positive in the linear equation y = a x ( for example: y = 2 x ) then the line ( from the left to the right ) must go up and to the right. It also passes through the origin ( 0, 0 ). For x = 1: y = 2 * 1 = 2, so that point is ( 1, 2 ), x2 > x1, and y2 > y1.Answer:A. goes up and to the right.
Final answer:
The line described by the equation y = ax slopes upward to the right when the value of a is positive, illustrating a positive relationship between x and y.
Explanation:
The equation y = ax describes a linear relationship between x and y. When the value of a is positive, the line slopes upward to the right on a graph. This behavior is because a positive slope indicates that as the x-value increases, the y-value also increases, leading to an upward trajectory on the graph.
The direction in which the line moves across the graph depends solely on the sign of a, where a positive a signifies an upward slope and a negative a results in a downward slope. Specifically, for a positive a, for every unit increase in x, there is a proportional increase in y, making the graph rise from left to right.
write a faction where is the numerator and denominator are both greater than 9. 10 write the fraction in simplest form
Answer:
10/20=1/2
Step-by-step explanation:
Which function graph has axis of symmetry x=2
Answer: The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. The vertex of the parabola is (2,1) . So, the axis of symmetry is the line x=2.
Step-by-step explanation:
Solve the system of equations 3x + y = 3 and 7x + 2y = 1.
1. Solve for the variable y in the first equation: y = 3 − 3x
2. Substitute the value for y into the second equation: 7x + 2(3 − 3x) = 1
3. Solve for x: x =
Answer:
(-5, 18)
Step-by-step explanation:
7x + 2(3 − 3x) = 1 simplifies to
7x + 6 - 6x = 1, which, in turn, simplifies to:
x = -5
Using y = 3 - 3x (see Step 1), we find that y = 3 - 3(-5) = 3 + 15 = 18.
Thus, the solution is (-5, 18).
Answer:
Step-by-step explanation:
here is the answer
Josh spent $42 on snacks.Maia spend $48 on hotdogs and hamburgers.Max spent 35 on rolls,condiments,lettuce,and tomatoes,and Mark and Victoria each spent $40 on drinks. How much did they spend in total?
Answer:
$165
Step-by-step explanation:
Money spent:
Josh=42
Maia=48
Max=35
Mark and Victoria = 40
35 + 40 + 42 + 48 = $165
Answer:
$205 as it was said $40 each for Mark and Victoria
Step-by-step explanation:
Josh =42 sn
Maia = 48 hd/hb
42+48 = 90
Max = 35 rolls,cd,lt+tm
Mark =40 drinks
Victoria = 40 drinks
35 +80 = 115
115+90 = $205
If Angle 2 is congruent to angle 4 and Angle 5 is congruent to angle 7, which describes all the lines that must be parallel?
Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16.
Only lines r and s must be parallel.
Only lines t and u must be parallel.
Lines r and s and lines t and u must be parallel.
Neither lines r and s nor lines t and u must be parallel.
Answer:
C.Lines r and s and lines t and u must be parallel.
Step-by-step explanation:
Line r s and t must be parallel and c is closest to that lol
The lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
If Angle 2 is congruent to angle 4 and Angle 5 is congruent to angle 7.
From the information given we can draw lines r, s, t, and u(please attached picture)
From the picture, we can clearly see: lines r and s and lines t and u must be parallel.
Thus, the lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.
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Which number is the greatest? 0.35, 0.2, 0.56, 0.8, 0.09
Answer:
0.8
Step-by-step explanation:
What is the factorization of the polynomial below?
3x^3- 12X^2-96x
Pythagorean theorem:
Is a triangle with the following side lengths a right triangle? Why?
a = 8
b = 15
c = 17
Example:
This does/does not make a right triangle because...
Answer:
This does make a right triangle
Step-by-step explanation:
Because when you square 8 you get 64 and when you square 15 you get 225. Then you add those together and you should get 289 so when you find the square root of 289 is 17 which makes those number true
Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle. This is because these side lengths satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have:
a² + b² = 8² + 15² = 64 + 225 = 289
c² = 17² = 289
Since a² + b² = c², these side lengths satisfy the Pythagorean theorem, and the triangle is a right triangle.
Thus,
Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.
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Anja simplified the expression
10x9 15
10 to 15. What mistake did Anja make?
Answer:
10 times 9 is 90 divide 90 bye 15 and there u go
Step-by-step explanation:
She subtracted the coefficients instead of dividing them
A senator wishes to estimate the proportion of United States voters who favor
abolishing the Electoral College. How large a sample is needed in order to be 90%
confident that the sample proportion will not differ from the true proportion by more
than 3%?
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
Step-by-step explanation:
The confidence level is 90% and the significance level would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2 =0.05[/tex] and the critical value for this case is:
[tex] z_{\alpha/2}= 1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we want a margin of error of [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
Since we don't hace any prior info for the population proportion we can use [tex]\hat p =0.5[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
Using the sample size formula, the required number of sample is 752.
Using the confidence interval relation :
[tex] n = \frac{pq}{(\frac{E}{Z_{crit}})^{2}} [/tex] p =sample proportion = 0.5 q = 1 - p = 1 - 0.5 = 0.5 Zcrit at 90% = 1.645 E = Error Margin = 3% = 0.03Substituting the values into the equation :
n = [tex] \frac{0.5 \times 0.5}{(\frac{0.03}{1.645})^{2} }[/tex]
[tex] n = \frac{0.25}{0.0003325}[/tex]
[tex] n = 751.67[/tex]
Therefore, the required number of sample is 752.
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What are the answers?
Answer:
あなたがこれを翻訳するなら私はあなたを愛しています
Step-by-step explanation:
私は英語がわかりませんが、答えは4倍になります
What is the third quartile of the box-and-whisker plot?
A)
10)
B)
20
C)
25
D)
30
Answer:
D) 30
Step-by-step explanation:
The third quartile is the last line of the box
Hope this helps!
A box and whisker plot is a graphical representation of variance. The third quartile of the box-and-whisker plot is 30.
What is a box-and-whisker plot?A box and whisker plot is a graphical representation of variance in a set of data.
The third quartile of the box-and-whisker plot is the rightmost line of the box, which means the third quartile of the box-and-whisker plot is 30.
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